Dask¶
Dask is a flexible library for parallel computing in Python.
Dask is composed of two parts:
 Dynamic task scheduling optimized for computation. This is similar to Airflow, Luigi, Celery, or Make, but optimized for interactive computational workloads.
 “Big Data” collections like parallel arrays, dataframes, and lists that extend common interfaces like NumPy, Pandas, or Python iterators to largerthanmemory or distributed environments. These parallel collections run on top of dynamic task schedulers.
Dask emphasizes the following virtues:
 Familiar: Provides parallelized NumPy array and Pandas DataFrame objects
 Flexible: Provides a task scheduling interface for more custom workloads and integration with other projects.
 Native: Enables distributed computing in pure Python with access to the PyData stack.
 Fast: Operates with low overhead, low latency, and minimal serialization necessary for fast numerical algorithms
 Scales up: Runs resiliently on clusters with 1000s of cores
 Scales down: Trivial to set up and run on a laptop in a single process
 Responsive: Designed with interactive computing in mind, it provides rapid feedback and diagnostics to aid humans
See the dask.distributed documentation (separate website) for more technical information on Dask’s distributed scheduler.
Familiar user interface¶
Dask DataFrame mimics Pandas  documentation
import pandas as pd import dask.dataframe as dd
df = pd.read_csv('20150101.csv') df = dd.read_csv('2015**.csv')
df.groupby(df.user_id).value.mean() df.groupby(df.user_id).value.mean().compute()
Dask Array mimics NumPy  documentation
import numpy as np import dask.array as da
f = h5py.File('myfile.hdf5') f = h5py.File('myfile.hdf5')
x = np.array(f['/smalldata']) x = da.from_array(f['/bigdata'],
chunks=(1000, 1000))
x  x.mean(axis=1) x  x.mean(axis=1).compute()
Dask Bag mimics iterators, Toolz, and PySpark  documentation
import dask.bag as db
b = db.read_text('2015**.json.gz').map(json.loads)
b.pluck('name').frequencies().topk(10, lambda pair: pair[1]).compute()
Dask Delayed mimics for loops and wraps custom code  documentation
from dask import delayed
L = []
for fn in filenames: # Use for loops to build up computation
data = delayed(load)(fn) # Delay execution of function
L.append(delayed(process)(data)) # Build connections between variables
result = delayed(summarize)(L)
result.compute()
The concurrent.futures interface provides general submission of custom tasks:  documentation
from dask.distributed import Client
client = Client('scheduler:port')
futures = []
for fn in filenames:
future = client.submit(load, fn)
futures.append(future)
summary = client.submit(summarize, futures)
summary.result()
Scales from laptops to clusters¶
Dask is convenient on a laptop. It installs trivially with
conda
or pip
and extends the size of convenient datasets from “fits in
memory” to “fits on disk”.
Dask can scale to a cluster of 100s of machines. It is resilient, elastic, data local, and low latency. For more information, see the documentation about the distributed scheduler.
This ease of transition between singlemachine to moderate cluster enables users to both start simple and grow when necessary.
Complex Algorithms¶
Dask represents parallel computations with task graphs. These
directed acyclic graphs may have arbitrary structure, which enables both
developers and users the freedom to build sophisticated algorithms and to
handle messy situations not easily managed by the map/filter/groupby
paradigm common in most data engineering frameworks.
We originally needed this complexity to build complex algorithms for ndimensional arrays but have found it to be equally valuable when dealing with messy situations in everyday problems.
Index¶
Getting Started
Install Dask¶
You can install dask with conda
, with pip
, or by installing from source.
Conda¶
Dask is installed by default in Anaconda.
You can update Dask using the conda command:
conda install dask
This installs Dask and all common dependencies, including Pandas and NumPy.
Dask packages are maintained both on the default channel and on condaforge.
Optionally, you can obtain a minimal Dask installation using the following command:
conda install daskcore
This will install a minimal set of dependencies required to run Dask similar to (but not exactly the same as) pip install dask
below.
Pip¶
You can install everything required for most common uses of Dask (arrays, dataframes, …) This installs both Dask and dependencies like NumPy, Pandas, and so on that are necessary for different workloads. This is often the right choice for Dask users:
pip install "dask[complete]" # Install everything
You can also install only the Dask library. Modules like dask.array
,
dask.dataframe
, dask.delayed
, or dask.distributed
won’t work until you also install NumPy,
Pandas, Toolz, or Tornado, respectively. This is common for downstream library
maintainers:
pip install dask # Install only core parts of dask
We also maintain other dependency sets for different subsets of functionality:
pip install "dask[array]" # Install requirements for dask array
pip install "dask[bag]" # Install requirements for dask bag
pip install "dask[dataframe]" # Install requirements for dask dataframe
pip install "dask[delayed]" # Install requirements for dask delayed
pip install "dask[distributed]" # Install requirements for distributed dask
We have these options so that users of the lightweight core Dask scheduler aren’t required to download the more exotic dependencies of the collections (Numpy, Pandas, Tornado, etc.).
Install from Source¶
To install Dask from source, clone the repository from github:
git clone https://github.com/dask/dask.git
cd dask
python setup.py install
or use pip
locally if you want to install all dependencies as well:
pip install e ".[complete]"
You can view the list of all dependencies within the extras_require
field
of setup.py
.
Anaconda¶
Dask is included by default in the Anaconda distribution.
Test¶
Test Dask with py.test
:
cd dask
py.test dask
Please be aware that installing Dask naively may not install all
requirements by default. Please read the pip
section above which discusses
requirements. You may choose to install the dask[complete]
version which includes
all dependencies for all collections. Alternatively, you may choose to test
only certain submodules depending on the libraries within your environment.
For example, to test only Dask core and Dask array we would run tests as
follows:
py.test dask/tests dask/array/tests
Setup¶
This page describes various ways to set up Dask on different hardware, either locally on your own machine or on a distributed cluster. If you are just getting started, then this page is unnecessary. Dask does not require any setup if you only want to use it on a single computer.
Dask has two families of task schedulers:
 Single machine scheduler: This scheduler provides basic features on a local process or thread pool. This scheduler was made first and is the default. It is simple and cheap to use. It can only be used on a single machine and does not scale.
 Distributed scheduler: This scheduler is more sophisticated. It offers more features, but also requires a bit more effort to set up. It can run locally or distributed across a cluster.
If you import Dask, set up a computation, and then call compute
, then you
will use the singlemachine scheduler by default. To use the dask.distributed
scheduler you must set up a Client
import dask.dataframe as dd
df = dd.read_csv(...)
df.x.sum().compute() # This uses the singlemachine scheduler by default
from dask.distributed import Client
client = Client(...) # Connect to distributed cluster and override default
df.x.sum().compute() # This now runs on the distributed system
Note that the newer dask.distributed
scheduler is often preferable, even on
single workstations. It contains many diagnostics and features not found in
the older singlemachine scheduler. The following pages explain in more detail
how to set up Dask on a variety of local and distributed hardware.
 Single Machine:
 Default Scheduler: The nosetup default. Uses local threads or processes for largerthanmemory processing
 dask.distributed: The sophistication of the newer system on a single machine. This provides more advanced features while still requiring almost no setup.
 Distributed computing:
 Manual Setup: The command line interface to set up
daskscheduler
anddaskworker
processes. Useful for IT or anyone building a deployment solution.  SSH: Use SSH to set up Dask across an unmanaged cluster.
 High Performance Computers: How to run Dask on traditional HPC environments using tools like MPI, or job schedulers like SLURM, SGE, TORQUE, LSF, and so on.
 Kubernetes: Deploy Dask with the popular Kubernetes resource manager using either Helm or a native deployment.
 YARN / Hadoop: Deploy Dask on YARN clusters, such as are found in traditional Hadoop installations.
 Python API (advanced): Create
Scheduler
andWorker
objects from Python as part of a distributed Tornado TCP application. This page is useful for those building custom frameworks.  Docker containers are available and may be useful in some of the solutions above.
 Cloud for current recommendations on how to deploy Dask and Jupyter on common cloud providers like Amazon, Google, or Microsoft Azure.
 Manual Setup: The command line interface to set up
SingleMachine Scheduler¶
The default Dask scheduler provides parallelism on a single machine by using either threads or processes. It is the default choice used by Dask because it requires no setup. You don’t need to make any choices or set anything up to use this scheduler. However, you do have a choice between threads and processes:
Threads: Use multiple threads in the same process. This option is good for numeric code that releases the GIL (like NumPy, Pandas, ScikitLearn, Numba, …) because data is free to share. This is the default scheduler for
dask.array
,dask.dataframe
, anddask.delayed
Processes: Send data to separate processes for processing. This option is good when operating on pure Python objects like strings or JSONlike dictionary data that holds onto the GIL, but not very good when operating on numeric data like Pandas DataFrames or NumPy arrays. Using processes avoids GIL issues, but can also result in a lot of interprocess communication, which can be slow. This is the default scheduler for
dask.bag
, and it is sometimes useful withdask.dataframe
Note that the
dask.distributed
scheduler is often a better choice when working with GILbound code. See dask.distributed on a single machineSinglethreaded: Execute computations in a single thread. This option provides no parallelism, but is useful when debugging or profiling. Turning your parallel execution into a sequential one can be a convenient option in many situations where you want to better understand what is going on
Selecting Threads, Processes, or Single Threaded¶
You can select between these options by specifying one of the following three
values to the scheduler=
keyword:
"threads"
: Uses a ThreadPool in the local process"processes"
: Uses a ProcessPool to spread work between processes"singlethreaded"
: Uses a forloop in the current thread
You can specify these options in any of the following ways:
When calling
.compute()
x.compute(scheduler='threads')
With a context manager
with dask.config.set(scheduler='threads'): x.compute() y.compute()
As a global setting
dask.config.set(scheduler='threads')
Single Machine: dask.distributed¶
The dask.distributed
scheduler works well on a single machine. It is sometimes
preferred over the default scheduler for the following reasons:
 It provides access to asynchronous API, notably Futures
 It provides a diagnostic dashboard that can provide valuable insight on performance and progress
 It handles data locality with more sophistication, and so can be more efficient than the multiprocessing scheduler on workloads that require multiple processes
You can create a dask.distributed
scheduler by importing and creating a
Client
with no arguments. This overrides whatever default was previously
set.
from dask.distributed import Client
client = Client()
You can navigate to http://localhost:8787/status to see the diagnostic dashboard if you have Bokeh installed.
Client¶
You can trivially set up a local cluster on your machine by instantiating a Dask Client with no arguments
from dask.distributed import Client
client = Client()
This sets up a scheduler in your local process and several processes running singlethreaded Workers.
If you want to run workers in your same process, you can pass the
processes=False
keyword argument.
client = Client(processes=False)
This is sometimes preferable if you want to avoid interworker communication and your computations release the GIL. This is common when primarily using NumPy or Dask Array.
LocalCluster¶
The Client()
call described above is shorthand for creating a LocalCluster
and then passing that to your client.
from dask.distributed import Client, LocalCluster
cluster = LocalCluster()
client = Client(cluster)
This is equivalent, but somewhat more explicit. You may want to look at the
keyword arguments available on LocalCluster
to understand the options available
to you on handling the mixture of threads and processes, like specifying explicit
ports, and so on.

class
distributed.deploy.local.
LocalCluster
(n_workers=None, threads_per_worker=None, processes=True, loop=None, start=None, ip=None, scheduler_port=0, silence_logs=30, dashboard_address=':8787', diagnostics_port=None, services=None, worker_services=None, service_kwargs=None, asynchronous=False, security=None, protocol=None, blocked_handlers=None, **worker_kwargs)¶ Create local Scheduler and Workers
This creates a “cluster” of a scheduler and workers running on the local machine.
Parameters:  n_workers: int
Number of workers to start
 processes: bool
Whether to use processes (True) or threads (False). Defaults to True
 threads_per_worker: int
Number of threads per each worker
 scheduler_port: int
Port of the scheduler. 8786 by default, use 0 to choose a random port
 silence_logs: logging level
Level of logs to print out to stdout.
logging.WARN
by default. Use a falsey value like False or None for no change. ip: string
IP address on which the scheduler will listen, defaults to only localhost
 dashboard_address: str
Address on which to listen for the Bokeh diagnostics server like ‘localhost:8787’ or ‘0.0.0.0:8787’. Defaults to ‘:8787’. Set to
None
to disable the dashboard. Use port 0 for a random port. diagnostics_port: int
Deprecated. See dashboard_address.
 asynchronous: bool (False by default)
Set to True if using this cluster within async/await functions or within Tornado gen.coroutines. This should remain False for normal use.
 kwargs: dict
Extra worker arguments, will be passed to the Worker constructor.
 blocked_handlers: List[str]
A list of strings specifying a blacklist of handlers to disallow on the Scheduler, like
['feed', 'run_function']
 service_kwargs: Dict[str, Dict]
Extra keywords to hand to the running services
 security : Security
 protocol: str (optional)
Protocol to use like
tcp://
,tls://
,inproc://
This defaults to sensible choice given other keyword arguments likeprocesses
andsecurity
Examples
>>> c = LocalCluster() # Create a local cluster with as many workers as cores # doctest: +SKIP >>> c # doctest: +SKIP LocalCluster("127.0.0.1:8786", workers=8, ncores=8)
>>> c = Client(c) # connect to local cluster # doctest: +SKIP
Add a new worker to the cluster
>>> w = c.start_worker(ncores=2) # doctest: +SKIP
Shut down the extra worker
>>> c.stop_worker(w) # doctest: +SKIP
Pass extra keyword arguments to Bokeh
>>> LocalCluster(service_kwargs={'bokeh': {'prefix': '/foo'}}) # doctest: +SKIP

close
(timeout=20)¶ Close the cluster

scale_down
(workers)¶ Remove
workers
from the clusterGiven a list of worker addresses this function should remove those workers from the cluster. This may require tracking which jobs are associated to which worker address.
This can be implemented either as a function or as a Tornado coroutine.

scale_up
(n, **kwargs)¶ Bring the total count of workers up to
n
This function/coroutine should bring the total number of workers up to the number
n
.This can be implemented either as a function or as a Tornado coroutine.

start_worker
(**kwargs)¶ Add a new worker to the running cluster
Parameters:  port: int (optional)
Port on which to serve the worker, defaults to 0 or random
 ncores: int (optional)
Number of threads to use. Defaults to number of logical cores
Returns:  The created Worker or Nanny object. Can be discarded.
Examples
>>> c = LocalCluster() # doctest: +SKIP >>> c.start_worker(ncores=2) # doctest: +SKIP

stop_worker
(w)¶ Stop a running worker
Examples
>>> c = LocalCluster() # doctest: +SKIP >>> w = c.start_worker(ncores=2) # doctest: +SKIP >>> c.stop_worker(w) # doctest: +SKIP
Command Line¶
This is the most fundamental way to deploy Dask on multiple machines. In production environments, this process is often automated by some other resource manager. Hence, it is rare that people need to follow these instructions explicitly. Instead, these instructions are useful for IT professionals who may want to set up automated services to deploy Dask within their institution.
A dask.distributed
network consists of one daskscheduler
process and
several daskworker
processes that connect to that scheduler. These are
normal Python processes that can be executed from the command line. We launch
the daskscheduler
executable in one process and the daskworker
executable in several processes, possibly on different machines.
To accomplish this, launch daskscheduler
on one node:
$ daskscheduler
Scheduler at: tcp://192.0.0.100:8786
Then, launch daskworker
on the rest of the nodes, providing the address to
the node that hosts daskscheduler
:
$ daskworker tcp://192.0.0.100:8786
Start worker at: tcp://192.0.0.1:12345
Registered to: tcp://192.0.0.100:8786
$ daskworker tcp://192.0.0.100:8786
Start worker at: tcp://192.0.0.2:40483
Registered to: tcp://192.0.0.100:8786
$ daskworker tcp://192.0.0.100:8786
Start worker at: tcp://192.0.0.3:27372
Registered to: tcp://192.0.0.100:8786
The workers connect to the scheduler, which then sets up a longrunning network connection back to the worker. The workers will learn the location of other workers from the scheduler.
Handling Ports¶
The scheduler and workers both need to accept TCP connections on an open port.
By default, the scheduler binds to port 8786
and the worker binds to a
random open port. If you are behind a firewall then you may have to open
particular ports or tell Dask to listen on particular ports with the port
and workerport
keywords.:
daskscheduler port 8000
daskworker bokehport 8000 nannyport 8001
Nanny Processes¶
Dask workers are run within a nanny process that monitors the worker process and restarts it if necessary.
Diagnostic Web Servers¶
Additionally, Dask schedulers and workers host interactive diagnostic web
servers using Bokeh. These are optional, but
generally useful to users. The diagnostic server on the scheduler is
particularly valuable, and is served on port 8787
by default (configurable
with the bokehport
keyword).
Note
For more information about relevant ports, please take a look at the help
pages with daskscheduler help
and daskworker help
Automated Tools¶
There are various mechanisms to deploy these executables on a cluster, ranging from manually SSHing into all of the machines to more automated systems like SGE/SLURM/Torque or Yarn/Mesos. Additionally, cluster SSH tools exist to send the same commands to many machines. We recommend searching online for “cluster ssh” or “cssh”.
API¶
Warning
These may be outdated. We recommend referring to the help
text of your
installed version.
daskscheduler¶
$ daskscheduler help
Usage: daskscheduler [OPTIONS]
Options:
host TEXT URI, IP or hostname of this server
port INTEGER Serving port
interface TEXT Preferred network interface like 'eth0' or 'ib0'
tlscafile PATH CA cert(s) file for TLS (in PEM format)
tlscert PATH certificate file for TLS (in PEM format)
tlskey PATH private key file for TLS (in PEM format)
bokehport INTEGER Bokeh port for visual diagnostics
bokeh / nobokeh Launch Bokeh Web UI [default: True]
show / noshow Show web UI
bokehwhitelist TEXT IP addresses to whitelist for bokeh
bokehprefix TEXT Prefix for the bokeh app
usexheaders BOOLEAN User xheaders in bokeh app for ssl termination in
header [default: False]
pidfile TEXT File to write the process PID
schedulerfile TEXT File to write connection information. This may be a
good way to share connection information if your
cluster is on a shared network file system
localdirectory TEXT Directory to place scheduler files
preload TEXT Module that should be loaded by each worker process
like "foo.bar" or "/path/to/foo.py"
help Show this message and exit
daskworker¶
$ daskworker help
Usage: daskworker [OPTIONS] [SCHEDULER]
Options:
tlscafile PATH CA cert(s) file for TLS (in PEM format)
tlscert PATH certificate file for TLS (in PEM format)
tlskey PATH private key file for TLS (in PEM format)
workerport INTEGER Serving computation port, defaults to random
nannyport INTEGER Serving nanny port, defaults to random
bokehport INTEGER Bokeh port, defaults to 8789
bokeh / nobokeh Launch Bokeh Web UI [default: True]
listenaddress TEXT The address to which the worker binds.
Example: tcp://0.0.0.0:9000
contactaddress TEXT The address the worker advertises to the
scheduler for communication with it and other
workers. Example: tcp://127.0.0.1:9000
host TEXT Serving host. Should be an ip address that is
visible to the scheduler and other workers.
See listenaddress and contactaddress if
you need different listen and contact
addresses. See interface
interface TEXT Network interface like 'eth0' or 'ib0'
nthreads INTEGER Number of threads per process
nprocs INTEGER Number of worker processes. Defaults to one
name TEXT A unique name for this worker like 'worker1'
memorylimit TEXT Bytes of memory that the worker can use. This
can be an integer (bytes), float (fraction of
total system memory), string (like 5GB or
5000M), 'auto', or zero for no memory
management
reconnect / noreconnect Reconnect to scheduler if disconnected
nanny / nonanny Start workers in nanny process for management
pidfile TEXT File to write the process PID
localdirectory TEXT Directory to place worker files
resources TEXT Resources for task constraints like "GPU=2
MEM=10e9"
schedulerfile TEXT Filename to JSON encoded scheduler information.
Use with daskscheduler schedulerfile
deathtimeout FLOAT Seconds to wait for a scheduler before closing
bokehprefix TEXT Prefix for the bokeh app
preload TEXT Module that should be loaded by each worker
process like "foo.bar" or "/path/to/foo.py"
help Show this message and exit
SSH¶
The convenience script daskssh
opens several SSH connections to your
target computers and initializes the network accordingly. You can
give it a list of hostnames or IP addresses:
$ daskssh 192.168.0.1 192.168.0.2 192.168.0.3 192.168.0.4
Or you can use normal UNIX grouping:
$ daskssh 192.168.0.{1,2,3,4}
Or you can specify a hostfile that includes a list of hosts:
$ cat hostfile.txt
192.168.0.1
192.168.0.2
192.168.0.3
192.168.0.4
$ daskssh hostfile hostfile.txt
The daskssh
utility depends on the paramiko
:
pip install paramiko
CLI Options¶
Launch a distributed cluster over SSH. A daskscheduler
process will run
on the first host specified in [HOSTNAMES] or in the hostfile (unless
scheduler
is specified explicitly). One or more daskworker
processes
will be run on each host in [HOSTNAMES] or in the hostfile. Use command line
flags to adjust how many daskworker process are run on each host
(nprocs
) and how many cpus are used by each daskworker process
(nthreads
).
Options:
Note
This table may grow out of date, you should check daskssh help
to get an uptodate listing of all options.
Option  TYPE  Description 

–scheduler  TEXT  Specify scheduler node. Defaults to first address 
–schedulerport  INTEGER  Specify scheduler port number. Defaults to port 8786 
–nthreads  INTEGER  Number of threads per worker process. Defaults to number of cores divided by the number of processes per host 
–nprocs  INTEGER  Number of worker processes per host. Defaults to one 
–hostfile  PATH  Textfile with hostnames/IP addresses 
–sshusername  TEXT  Username to use when establishing SSH connections 
–sshport  INTEGER  Port to use for SSH connections 
–sshprivatekey  TEXT  Private key file to use for SSH connections 
–logdirectory  PATH  Directory to use on all cluster nodes for the output of daskscheduler and daskworker commands 
–remotepython  TEXT  Path to Python on remote nodes 
–memorylimit  TEXT  Bytes of memory that the worker can use. This can be an integer (bytes), float(fraction of total system memory) string (like 5GB or 5000M), ‘auto’, or zero for no memory management 
–workerport  INTEGER  Serving computation port, defaults to random 
–nannyport  INTEGER  Serving nanny port, defaults to random 
–nohost  Do not pass the hostname to the worker 
High Performance Computers¶
Relevant Machines¶
This page includes instructions and guidelines when deploying Dask on high performance supercomputers commonly found in scientific and industry research labs. These systems commonly have the following attributes:
 Some mechanism to launch MPI applications or use job schedulers like SLURM, SGE, TORQUE, LSF, DRMAA, PBS, or others
 A shared network file system visible to all machines in the cluster
 A high performance network interconnect, such as Infiniband
 Little or no nodelocal storage
Where to start¶
Most of this page documents various ways and best practices to use Dask on an HPC cluster. This is technical and aimed both at users with some experience deploying Dask and also system administrators.
The preferred and simplest way to run Dask on HPC systems today both for new, experienced users or administrator is to use daskjobqueue.
However, daskjobqueue is slightly oriented toward interactive analysis usage, and it might be better to use tools like daskmpi in some routine batch production workloads.
Daskjobqueue and Daskdrmaa¶
The following projects provide easy highlevel access to Dask using resource managers that are commonly deployed on HPC systems:
 daskjobqueue for use with PBS, SLURM, LSF, SGE and other resource managers
 daskdrmaa for use with any DRMAA compliant resource manager
They provide interfaces that look like the following:
from dask_jobqueue import PBSCluster
cluster = PBSCluster(cores=36,
memory="100GB",
project='P48500028',
queue='premium',
interface='ib0',
walltime='02:00:00')
cluster.scale(100) # Start 100 workers in 100 jobs that match the description above
from dask.distributed import Client
client = Client(cluster) # Connect to that cluster
Daskjobqueue provides a lot of possibilities like adaptive dynamic scaling of workers, we recommend reading the daskjobqueue documentation first to get a basic system running and then returning to this documentation for finetuning if necessary.
Using MPI¶
Note
This section may not be necessary if you use a tool like daskjobqueue.
You can launch a Dask network using mpirun
or mpiexec
and the
daskmpi
command line executable.
mpirun np 4 daskmpi schedulerfile /home/$USER/scheduler.json
from dask.distributed import Client
client = Client(scheduler_file='/path/to/scheduler.json')
This depends on the mpi4py library. It only
uses MPI to start the Dask cluster and not for internode communication. MPI
implementations differ: the use of mpirun np 4
is specific to the
mpich
or openmpi
MPI implementation installed through conda and linked
to mpi4py.
conda install mpi4py
It is not necessary to use exactly this implementation, but you may want to
verify that your mpi4py
Python library is linked against the proper
mpirun/mpiexec
executable and that the flags used (like np 4
) are
correct for your system. The system administrator of your cluster should be
very familiar with these concerns and able to help.
In some setups, MPI processes are not allowed to fork other processes. In this
case, we recommend using nonanny
option in order to prevent dask from
using an additional nanny process to manage workers.
Run daskmpi help
to see more options for the daskmpi
command.
High Performance Network¶
Many HPC systems have both standard Ethernet networks as well as
highperformance networks capable of increased bandwidth. You can instruct
Dask to use the highperformance network interface by using the interface
keyword with the daskworker
, daskscheduler
, or daskmpi
commands or
the interface=
keyword with the daskjobqueue Cluster
objects:
mpirun np 4 daskmpi schedulerfile /home/$USER/scheduler.json interface ib0
In the code example above, we have assumed that your cluster has an Infiniband
network interface called ib0
. You can check this by asking your system
administrator or by inspecting the output of ifconfig
$ ifconfig
lo Link encap:Local Loopback # Localhost
inet addr:127.0.0.1 Mask:255.0.0.0
inet6 addr: ::1/128 Scope:Host
eth0 Link encap:Ethernet HWaddr XX:XX:XX:XX:XX:XX # Ethernet
inet addr:192.168.0.101
...
ib0 Link encap:Infiniband # Fast InfiniBand
inet addr:172.42.0.101
https://stackoverflow.com/questions/43881157/howdoiuseaninfinibandnetworkwithdask
No Local Storage¶
Users often exceed memory limits available to a specific Dask deployment. In normal operation, Dask spills excess data to disk. However, in HPC systems, the individual compute nodes often lack locally attached storage, preferring instead to store data in a robust high performance network storage solution. As a result, when a Dask cluster starts to exceed memory limits, its workers can start making many small writes to the remote network file system. This is both inefficient (small writes to a network file system are much slower than local storage for this use case) and potentially dangerous to the file system itself.
See this page
for more information on Dask’s memory policies. Consider changing the
following values in your ~/.config/dask/distributed.yaml
file:
distributed:
worker:
memory:
target: false # don't spill to disk
spill: false # don't spill to disk
pause: 0.80 # pause execution at 80% memory use
terminate: 0.95 # restart the worker at 95% use
This stops Dask workers from spilling to disk, and instead relies entirely on mechanisms to stop them from processing when they reach memory limits.
As a reminder, you can set the memory limit for a worker using the
memorylimit
keyword:
daskmpi ... memorylimit 10GB
Alternatively, if you do have local storage mounted on your compute nodes, you
can point Dask workers to use a particular location in your filesystem using
the localdirectory
keyword:
daskmpi ... localdirectory /scratch
Launch Many Small Jobs¶
Note
This section is not necessary if you use a tool like daskjobqueue.
HPC job schedulers are optimized for large monolithic jobs with many nodes that all need to run as a group at the same time. Dask jobs can be quite a bit more flexible: workers can come and go without strongly affecting the job. If we split our job into many smaller jobs, we can often get through the job scheduling queue much more quickly than a typical job. This is particularly valuable when we want to get started right away and interact with a Jupyter notebook session rather than waiting for hours for a suitable allocation block to become free.
So, to get a large cluster quickly, we recommend allocating a daskscheduler process on one node with a modest wall time (the intended time of your session) and then allocating many small singlenode daskworker jobs with shorter wall times (perhaps 30 minutes) that can easily squeeze into extra space in the job scheduler. As you need more computation, you can add more of these singlenode jobs or let them expire.
Use Dask to colaunch a Jupyter server¶
Dask can help you by launching other services alongside it. For example, you
can run a Jupyter notebook server on the machine running the daskscheduler
process with the following commands
from dask.distributed import Client
client = Client(scheduler_file='scheduler.json')
import socket
host = client.run_on_scheduler(socket.gethostname)
def start_jlab(dask_scheduler):
import subprocess
proc = subprocess.Popen(['/path/to/jupyter', 'lab', 'ip', host, 'nobrowser'])
dask_scheduler.jlab_proc = proc
client.run_on_scheduler(start_jlab)
Kubernetes¶
Kubernetes and Helm¶
It is easy to launch a Dask cluster and a Jupyter notebook server on cloud resources using Kubernetes and Helm.
This is particularly useful when you want to deploy a fresh Python environment on Cloud services like Amazon Web Services, Google Compute Engine, or Microsoft Azure.
If you already have Python environments running in a preexisting Kubernetes cluster, then you may prefer the Kubernetes native documentation, which is a bit lighter weight.
Launch Kubernetes Cluster¶
This document assumes that you have a Kubernetes cluster and Helm installed.
If this is not the case, then you might consider setting up a Kubernetes cluster on one of the common cloud providers like Google, Amazon, or Microsoft. We recommend the first part of the documentation in the guide Zero to JupyterHub that focuses on Kubernetes and Helm (you do not need to follow all of these instructions). Also, JupyterHub is not necessary to deploy Dask:
Alternatively, you may want to experiment with Kubernetes locally using Minikube.
Helm Install Dask¶
Dask maintains a Helm chart in the default stable channel at https://kubernetescharts.storage.googleapis.com . This should be added to your helm installation by default. You can update the known channels to make sure you have uptodate charts as follows:
helm repo update
Now, you can launch Dask on your Kubernetes cluster using the Dask Helm chart:
helm install stable/dask
This deploys a daskscheduler
, several daskworker
processes, and
also an optional Jupyter server.
Verify Deployment¶
This might take a minute to deploy. You can check its status with
kubectl
:
kubectl get pods
kubectl get services
$ kubectl get pods
NAME READY STATUS RESTARTS AGE
baldeeljupyter924045334twtxd 0/1 ContainerCreating 0 1m
baldeelscheduler3074430035cn1dt 1/1 Running 0 1m
baldeelworker3032746726202jt 1/1 Running 0 1m
baldeelworker3032746726b8nqq 1/1 Running 0 1m
baldeelworker3032746726d0chx 0/1 ContainerCreating 0 1m
$ kubectl get services
NAME TYPE CLUSTERIP EXTERNALIP PORT(S) AGE
baldeeljupyter LoadBalancer 10.11.247.201 35.226.183.149 80:30173/TCP 2m
baldeelscheduler LoadBalancer 10.11.245.241 35.202.201.129 8786:31166/TCP,80:31626/TCP 2m
kubernetes ClusterIP 10.11.240.1 <none> 443/TCP
48m
You can use the addresses under EXTERNALIP
to connect to your nowrunning
Jupyter and Dask systems.
Notice the name baldeel
. This is the name that Helm has given to your
particular deployment of Dask. You could, for example, have multiple
DaskandJupyter clusters running at once, and each would be given a different
name. Note that you will need to use this name to refer to your deployment in the future.
Additionally, you can list all active helm deployments with:
helm list
NAME REVISION UPDATED STATUS CHART NAMESPACE
baldeel 1 Wed Dec 6 11:19:54 2017 DEPLOYED dask0.1.0 default
Connect to Dask and Jupyter¶
When we ran kubectl get services
, we saw some externally visible IPs:
mrocklin@pangeo181919:~$ kubectl get services
NAME TYPE CLUSTERIP EXTERNALIP PORT(S) AGE
baldeeljupyter LoadBalancer 10.11.247.201 35.226.183.149 80:30173/TCP 2m
baldeelscheduler LoadBalancer 10.11.245.241 35.202.201.129 8786:31166/TCP,80:31626/TCP 2m
kubernetes ClusterIP 10.11.240.1 <none> 443/TCP 48m
We can navigate to these services from any web browser. Here, one is the Dask diagnostic
dashboard, and the other is the Jupyter server. You can log into the Jupyter
notebook server with the password, dask
.
You can create a notebook and create a Dask client from there. The
DASK_SCHEDULER_ADDRESS
environment variable has been populated with the
address of the Dask scheduler. This is available in Python in the config
dictionary.
>>> from dask.distributed import Client, config
>>> config['scheduleraddress']
'baldeelscheduler:8786'
Although you don’t need to use this address, the Dask client will find this variable automatically.
from dask.distributed import Client, config
client = Client()
Configure Environment¶
By default, the Helm deployment launches three workers using two cores each and a standard conda environment. We can customize this environment by creating a small yaml file that implements a subset of the values in the dask helm chart values.yaml file.
For example, we can increase the number of workers, and include extra conda and pip packages to install on the both the workers and Jupyter server (these two environments should be matched).
# config.yaml
worker:
replicas: 8
resources:
limits:
cpu: 2
memory: 7.5G
requests:
cpu: 2
memory: 7.5G
env:
 name: EXTRA_CONDA_PACKAGES
value: numba xarray c condaforge
 name: EXTRA_PIP_PACKAGES
value: s3fs daskml upgrade
# We want to keep the same packages on the worker and jupyter environments
jupyter:
enabled: true
env:
 name: EXTRA_CONDA_PACKAGES
value: numba xarray matplotlib c condaforge
 name: EXTRA_PIP_PACKAGES
value: s3fs daskml upgrade
This config file overrides the configuration for the number and size of workers and the conda and pip packages installed on the worker and Jupyter containers. In general, we will want to make sure that these two software environments match.
Update your deployment to use this configuration file. Note that you will not use helm install for this stage: that would create a new deployment on the same Kubernetes cluster. Instead, you will upgrade your existing deployment by using the current name:
helm upgrade baldeel stable/dask f config.yaml
This will update those containers that need to be updated. It may take a minute or so.
As a reminder, you can list the names of deployments you have using helm
list
Check status and logs¶
For standard issues, you should be able to see the worker status and logs using the
Dask dashboard (in particular, you can see the worker links from the info/
page).
However, if your workers aren’t starting, you can check the status of pods and
their logs with the following commands:
kubectl get pods
kubectl logs <PODNAME>
mrocklin@pangeo181919:~$ kubectl get pods
NAME READY STATUS RESTARTS AGE
baldeeljupyter3805078281n1qk2 1/1 Running 0 18m
baldeelscheduler3074430035cn1dt 1/1 Running 0 58m
baldeelworker19318819141q09p 1/1 Running 0 18m
baldeelworker1931881914856mm 1/1 Running 0 18m
baldeelworker19318819149lgzb 1/1 Running 0 18m
baldeelworker1931881914bdn2c 1/1 Running 0 16m
baldeelworker1931881914jq70m 1/1 Running 0 17m
baldeelworker1931881914qsgj7 1/1 Running 0 18m
baldeelworker1931881914s2phd 1/1 Running 0 17m
baldeelworker1931881914srmmg 1/1 Running 0 17m
mrocklin@pangeo181919:~$ kubectl logs baldeelworker1931881914856mm
EXTRA_CONDA_PACKAGES environment variable found. Installing.
Fetching package metadata ...........
Solving package specifications: .
Package plan for installation in environment /opt/conda/envs/dask:
The following NEW packages will be INSTALLED:
fasteners: 0.14.1py36_2 condaforge
monotonic: 1.3py36_0 condaforge
zarr: 2.1.4py36_0 condaforge
Proceed ([y]/n)?
monotonic1.3 100% ############################### Time: 0:00:00 11.16 MB/s
fasteners0.14 100% ############################### Time: 0:00:00 576.56 kB/s
...
Delete a Helm deployment¶
You can always delete a helm deployment using its name:
helm delete baldeel purge
Note that this does not destroy any clusters that you may have allocated on a Cloud service (you will need to delete those explicitly).
Avoid the Jupyter Server¶
Sometimes you do not need to run a Jupyter server alongside your Dask cluster.
jupyter:
enabled: false
Kubernetes Native¶
See external documentation on DaskKubernetes for more information.
Kubernetes is a popular system for deploying distributed applications on clusters, particularly in the cloud. You can use Kubernetes to launch Dask workers in the following two ways:
Helm: You can launch a Dask scheduler, several workers, and an optional Jupyter Notebook server on a Kubernetes easily using Helm
helm repo update # get latest helm charts helm install stable/dask # deploy standard dask chart
This is a good choice if you want to do the following:
 Run a managed Dask cluster for a long period of time
 Also deploy a Jupyter server from which to run code
 Share the same Dask cluster between many automated services
 Try out Dask for the first time on a cloudbased system like Amazon, Google, or Microsoft Azure (see also our Cloud documentation)
Note
For more information, see Dask and Helm documentation.
Native: You can quickly deploy Dask workers on Kubernetes from within a Python script or interactive session using DaskKubernetes
from dask_kubernetes import KubeCluster cluster = KubeCluster.from_yaml('workertemplate.yaml') cluster.scale(20) # add 20 workers cluster.adapt() # or create and destroy workers dynamically based on workload from dask.distributed import Client client = Client(cluster)
This is a good choice if you want to do the following:
 Dynamically create a personal and ephemeral deployment for interactive use
 Allow many individuals the ability to launch their own custom dask deployments, rather than depend on a centralized system
 Quickly adapt Dask cluster size to the current workload
Note
For more information, see DaskKubernetes documentation.
You may also want to see the documentation on using Dask with Docker containers to help you manage your software environments on Kubernetes.
Python API (advanced)¶
In some rare cases, experts may want to create Scheduler
and Worker
objects explicitly in Python manually. This is often necessary when making
tools to automatically deploy Dask in custom settings.
However, often it is sufficient to rely on the Dask command line interface.
Scheduler¶
To start the Scheduler, provide the listening port (defaults to 8786) and Tornado
IOLoop (defaults to IOLoop.current()
)
from distributed import Scheduler
from tornado.ioloop import IOLoop
from threading import Thread
s = Scheduler()
s.start('tcp://:8786') # Listen on TCP port 8786
loop = IOLoop.current()
loop.start()
Alternatively, you may want the IOLoop and scheduler to run in a separate
thread. In this case, you would replace the loop.start()
call with the
following:
t = Thread(target=loop.start, daemon=True)
t.start()
Worker¶
On other nodes, start worker processes that point to the URL of the scheduler.
from distributed import Worker
from tornado.ioloop import IOLoop
from threading import Thread
w = Worker('tcp://127.0.0.1:8786')
w.start() # choose randomly assigned port
loop = IOLoop.current()
loop.start()
Alternatively, replace Worker
with Nanny
if you want your workers to be
managed in a separate process by a local nanny process. This allows workers to
restart themselves in case of failure. Also, it provides some additional monitoring,
and is useful when coordinating many workers that should live in different
processes in order to avoid the GIL.
Cloud Deployments¶
To get started running Dask on common Cloud providers like Amazon, Google, or Microsoft, we currently recommend deploying Dask with Kubernetes and Helm.
All three major cloud vendors now provide managed Kubernetes services. This allows us to reliably provide the same experience across all clouds, and ensures that solutions for any one provider remain uptodate.
Alternatively, if you are deploying on a cloudhosted Hadoop cluster like Amazon EMR or Google Cloud DataProc, you will want to use DaskYarn. Documentation on deploying on Amazon EMR specifically can be found here, the process is similar for Google Cloud DataProc.
Data Access¶
You may want to install additional libraries in your Jupyter and worker images to access the object stores of each cloud:
Historical Libraries¶
Dask previously maintained libraries for deploying Dask on Amazon’s EC2. Due to sporadic interest, and churn both within the Dask library and EC2 itself, these were not well maintained. They have since been deprecated in favor of the Kubernetes and Helm solution.
Adaptive Deployments¶
Motivation¶
Most Dask deployments are static with a single scheduler and a fixed number of workers. This results in predictable behavior, but is wasteful of resources in two situations:
 The user may not be using the cluster, or perhaps they are busy interpreting a recent result or plot, and so the workers sit idly, taking up valuable shared resources from other potential users
 The user may be very active, and is limited by their original allocation.
Particularly efficient users may learn to manually add and remove workers during their session, but this is rare. Instead, we would like the size of a Dask cluster to match the computational needs at any given time. This is the goal of the adaptive deployments discussed in this document. These are particularly helpful for interactive workloads, which are characterized by long periods of inactivity interrupted with short bursts of heavy activity. Adaptive deployments can result in both faster analyses that give users much more power, but with much less pressure on computational resources.
Adaptive¶
To make setting up adaptive deployments easy, some Dask deployment solutions
offer an .adapt()
method. Here is an example with
dask_kubernetes.KubeCluster.
from dask_kubernetes import KubeCluster
cluster = KubeCluster()
cluster.adapt(minimum=0, maximum=100) # scale between 0 and 100 workers
For more keyword options, see the Adaptive class below:
Adaptive (scheduler[, cluster, interval, …]) 
Adaptively allocate workers based on scheduler load. 
Dependence on a Resource Manager¶
The Dask scheduler does not know how to launch workers on its own. Instead, it relies on an external resource scheduler like Kubernetes above, or Yarn, SGE, SLURM, Mesos, or some other inhouse system (see setup documentation for options). In order to use adaptive deployments, you must provide some mechanism for the scheduler to launch new workers. Typically, this is done by using one of the solutions listed in the setup documentation, or by subclassing from the Cluster superclass and implementing that API.
Cluster 
Superclass for cluster objects 
Scaling Heuristics¶
The Dask scheduler tracks a variety of information that is useful to correctly allocate the number of workers:
 The historical runtime of every function and task that it has seen, and all of the functions that it is currently able to run for users
 The amount of memory used and available on each worker
 Which workers are idle or saturated for various reasons, like the presence of specialized hardware
From these, it is able to determine a target number of workers by dividing the
cumulative expected runtime of all pending tasks by the target_duration
parameter (defaults to five seconds). This number of workers serves as a
baseline request for the resource manager. This number can be altered for a
variety of reasons:
 If the cluster needs more memory, then it will choose either the target number of workers or twice the current number of workers (whichever is larger)
 If the target is outside of the range of the minimum and maximum values, then it is clipped to fit within that range
Additionally, when scaling down, Dask preferentially chooses those workers that
are idle and have the least data in memory. It moves that data to other
machines before retiring the worker. To avoid rapid cycling of the cluster up
and down in size, we only retire a worker after a few cycles have gone by where
it has consistently been a good idea to retire it (controlled by the
wait_count
and interval
parameters).
API¶

class
distributed.deploy.
Adaptive
(scheduler, cluster=None, interval='1s', startup_cost='1s', scale_factor=2, minimum=0, maximum=None, wait_count=3, target_duration='5s', worker_key=<function Adaptive.<lambda>>, **kwargs)¶ Adaptively allocate workers based on scheduler load. A superclass.
Contains logic to dynamically resize a Dask cluster based on current use. This class needs to be paired with a system that can create and destroy Dask workers using a cluster resource manager. Typically it is built into already existing solutions, rather than used directly by users. It is most commonly used from the
.adapt(...)
method of various Dask cluster classes.Parameters:  scheduler: distributed.Scheduler
 cluster: object
Must have scale_up and scale_down methods/coroutines
 startup_cost : timedelta or str, default “1s”
Estimate of the number of seconds for nnFactor representing how costly it is to start an additional worker. Affects quickly to adapt to high tasks per worker loads
 interval : timedelta or str, default “1000 ms”
Milliseconds between checks
 wait_count: int, default 3
Number of consecutive times that a worker should be suggested for removal before we remove it.
 scale_factor : int, default 2
Factor to scale by when it’s determined additional workers are needed
 target_duration: timedelta or str, default “5s”
Amount of time we want a computation to take. This affects how aggressively we scale up.
 worker_key: Callable[WorkerState]
Function to group workers together when scaling down See Scheduler.workers_to_close for more information
 minimum: int
Minimum number of workers to keep around
 maximum: int
Maximum number of workers to keep around
 **kwargs:
Extra parameters to pass to Scheduler.workers_to_close
Notes
Subclasses can override
Adaptive.should_scale_up()
andAdaptive.workers_to_close()
to control when the cluster should be resized. The default implementation checks if there are too many tasks per worker or too little memory available (seeAdaptive.needs_cpu()
andAdaptive.needs_memory()
).Adaptive.get_scale_up_kwargs()
method controls the arguments passed to the cluster’sscale_up
method.Examples
This is commonly used from existing Dask classes, like KubeCluster
>>> from dask_kubernetes import KubeCluster >>> cluster = KubeCluster() >>> cluster.adapt(minimum=10, maximum=100)
Alternatively you can use it from your own Cluster class by subclassing from Dask’s Cluster superclass
>>> from distributed.deploy import Cluster >>> class MyCluster(Cluster): ... def scale_up(self, n): ... """ Bring worker count up to n """ ... def scale_down(self, workers): ... """ Remove worker addresses from cluster """
>>> cluster = MyCluster() >>> cluster.adapt(minimum=10, maximum=100)

class
distributed.deploy.
Cluster
¶ Superclass for cluster objects
This expects a local Scheduler defined on the object. It provides common methods and an IPython widget display.
Clusters inheriting from this class should provide the following:
A local
Scheduler
object at.scheduler
scale_up and scale_down methods as defined below:
 def scale_up(self, n: int):
‘’’ Brings total worker count up to
n
‘’‘ def scale_down(self, workers: List[str]):
‘’’ Close the workers with the given addresses ‘’‘
This will provide a general
scale
method as well as an IPython widget for display.See also
LocalCluster
 a simple implementation with local workers
Examples
>>> from distributed.deploy import Cluster >>> class MyCluster(cluster): ... def scale_up(self, n): ... ''' Bring the total worker count up to n ''' ... pass ... def scale_down(self, workers): ... ''' Close the workers with the given addresses ''' ... pass
>>> cluster = MyCluster() >>> cluster.scale(5) # scale manually >>> cluster.adapt(minimum=1, maximum=100) # scale automatically
Docker Images¶
Example docker images are maintained at https://github.com/dask/daskdocker and https://hub.docker.com/r/daskdev/ .
Each image installs the full Dask conda package (including the distributed scheduler), Numpy, and Pandas on top of a Miniconda installation on top of a Debian image.
These images are large, around 1GB.
daskdev/dask
: This a normal debian + miniconda image with the full Dask conda package (including the distributed scheduler), Numpy, and Pandas. This image is about 1GB in size.daskdev/dasknotebook
: This is based on the Jupyter basenotebook image and so it is suitable for use both normally as a Jupyter server, and also as part of a JupyterHub deployment. It also includes a matching Dask software environment described above. This image is about 2GB in size.
Example¶
Here is a simple example on the local host network
docker run it network host daskdev/dask daskscheduler # start scheduler
docker run it network host daskdev/dask daskworker localhost:8786 # start worker
docker run it network host daskdev/dask daskworker localhost:8786 # start worker
docker run it network host daskdev/dask daskworker localhost:8786 # start worker
docker run it network host daskdev/dasknotebook # start Jupyter server
Extensibility¶
Users can mildly customize the software environment by populating the
environment variables EXTRA_APT_PACKAGES
, EXTRA_CONDA_PACKAGES
, and
EXTRA_PIP_PACKAGES
. If these environment variables are set, they will
trigger calls to the following respectively:
aptget install $EXTRA_APT_PACKAGES
conda install $EXTRA_CONDA_PACKAGES
pip install $EXTRA_PIP_PACKAGES
Note that using these can significantly delay the container from starting,
especially when using apt
, or conda
(pip
is relatively fast).
Remember that it is important for software versions to match between Dask workers and Dask clients. As a result, it is often useful to include the same extra packages in both Jupyter and Worker images.
Source¶
Docker files are maintained at https://github.com/dask/daskdocker. This repository also includes a dockercompose configuration.
Use Cases¶
Dask is a versatile tool that supports a variety of workloads. This page contains brief and illustrative examples of how people use Dask in practice. This page emphasizes breadth and hopefully inspires readers to find new ways that Dask can serve them beyond their original intent.
Overview¶
Dask use cases can be roughly divided in the following two categories:
 Large NumPy/Pandas/Lists with dask.array, dask.dataframe, dask.bag to analyze large datasets with familiar techniques. This is similar to Databases, Spark, or big array libraries
 Custom task scheduling. You submit a graph of functions that depend on each other for custom workloads. This is similar to Luigi, Airflow, Celery, or Makefiles
Most people today approach Dask assuming it is a framework like Spark, designed for the first use case around large collections of uniformly shaped data. However, many of the more productive and novel use cases fall into the second category where Dask is used to parallelize custom workflows.
Dask compute environments can be divided into the following two categories:
 Single machine parallelism with threads or processes: the Dask singlemachine scheduler leverages the full CPU power of a laptop or a large workstation and changes the space limitation from “fits in memory” to “fits on disk”. This scheduler is simple to use and doesn’t have the computational or conceptual overhead of most “big data” systems
 Distributed cluster parallelism on multiple nodes: the Dask distributed scheduler coordinates the actions of multiple machines on a cluster. It scales anywhere from a single machine to a thousand machines, but not significantly beyond
The single machine scheduler is more useful to individuals (more people have personal laptops than have access to clusters) and probably accounts for 80+% of the use of Dask today. On the other hand, the distributed machine scheduler is more useful to larger organizations like universities, research labs, or private companies.
Below we give specific examples of how people use Dask. We start with large NumPy/Pandas/List examples because they’re somewhat more familiar to people looking at “big data” frameworks. We then follow with custom scheduling examples, which tend to be applicable more often and are, arguably, a bit more interesting.
Collection Examples¶
Dask contains large parallel collections for ndimensional arrays (similar to NumPy), DataFrames (similar to Pandas), and lists (similar to PyToolz or PySpark).
On disk arrays¶
Scientists studying the earth have 10GB to 100GB of regularly gridded weather data on their laptop’s hard drive stored as many individual HDF5 or NetCDF files. They use dask.array to treat this stack of HDF5 or NetCDF files as a single NumPy array (or a collection of NumPy arrays with the XArray project). They slice, perform reductions, compute seasonal averaging, etc., all with straight Numpy syntax. These computations take a few minutes to execute (reading 100GB from disk is somewhat slow), but previously infeasible computations become convenient from the comfort of a personal laptop.
It’s not so much parallel computing that is valuable here, but rather the ability to comfortably compute on largerthanmemory data without special hardware.
import h5py
dataset = h5py.File('myfile.hdf5')['/x']
import dask.array as da
x = da.from_array(dataset, chunks=dataset.chunks)
y = x[::10]  x.mean(axis=0)
y.compute()
Directory of CSV or tabular HDF files¶
Analysts studying time series data have a large directory of CSV, HDF, or other formatted tabular files. They usually use Pandas for this kind of data but, either the volume is too large, or dealing with a large number of files is confusing, it can be a slow process. So, they can use dask.dataframe to logically wrap all of these different files into one logical DataFrame that is built on demand to save space. Since most of their Pandas workflow is the same (Dask’s DataFrame is a subset of Pandas), they can switch from Pandas to Dask and back easily without significantly changing their code.
import dask.dataframe as dd
df = dd.read_csv('data/2016*.*.csv', parse_dates=['timestamp'])
df.groupby(df.timestamp.dt.hour).value.mean().compute()
Directory of CSV files on HDFS¶
The same analysts as above use dask.dataframe with the dask.distributed scheduler to analyze terabytes of data on their institution’s Hadoop cluster straight from Python. This uses either the hdfs3 or pyarrow Python libraries for HDFS management.
This solution is particularly attractive because it stays within the Python ecosystem, and uses the speed and algorithm set of Pandas, a tool which the analyst is already very comfortable with.
from dask.distributed import Client
client = Client('clusteraddress:8786')
import dask.dataframe as dd
df = dd.read_csv('hdfs://data/2016*.*.csv', parse_dates=['timestamp'])
df.groupby(df.timestamp.dt.hour).value.mean().compute()
Directories of custom format files¶
The same analysts also have a bunch of files of a custom format not supported by dask.dataframe, or perhaps these files are in a directory structure that encodes important information about their data (such as the date or other metadata). To work around this, they use dask.delayed to teach dask.dataframe how to load the data and then pass it into dask.dataframe for tabular algorithms.
 Example Notebook: https://gist.github.com/mrocklin/e7b7b3a65f2835cda813096332ec73ca
JSON data¶
Data Engineers with click stream data from a website, or mechanical engineers with telemetry data from mechanical instruments, have large volumes of data in JSON or some other semistructured format. They use dask.bag to manipulate many Python objects in parallel, either on their personal machine where they stream the data through memory, or across a cluster.
import dask.bag as db
import json
records = db.read_text('data/2015**.json').map(json.loads)
records.filter(lambda d: d['name'] == 'Alice').pluck('id').frequencies()
Custom Examples¶
The large collections (array, dataframe, bag) are wonderful when they fit the application, for example, if you want to perform a groupby on a directory of CSV data. However, several parallel computing applications don’t fit neatly into one of these higher level abstractions. Fortunately, Dask provides a wide variety of ways to parallelize more custom applications. These use the same machinery as the arrays and DataFrames, but allow the user to develop custom algorithms specific to their problem.
Embarrassingly parallel computation¶
Some programmers have a function that they want to run many times on different inputs. Their function and inputs might use arrays or DataFrames internally, but conceptually their problem isn’t a single large array or DataFrame.
They want to run these functions in parallel on their laptop while they prototype, but they also intend to eventually use an inhouse cluster. To accomplish this, they wrap their function in dask.delayed and then let the appropriate dask scheduler parallelize and load balance the work.
def process(data):
...
return ...
Normal Sequential Processing:
results = [process(x) for x in inputs]
Build Dask Computation:
from dask import compute, delayed
values = [delayed(process)(x) for x in inputs]
Multiple Threads:
import dask.threaded
results = compute(*values, scheduler='threads')
Multiple Processes:
import dask.multiprocessing
results = compute(*values, scheduler='processes')
Distributed Cluster:
from dask.distributed import Client
client = Client("clusteraddress:8786")
results = compute(*values, scheduler='distributed')
Complex dependencies¶
A financial analyst has many models that depend on each other in a complex web of computations.
data = [load(fn) for fn in filenames]
reference = load_from_database(query)
A = [model_a(x, reference) for x in data]
B = [model_b(x, reference) for x in data]
roll_A = [roll(A[i], A[i + 1]) for i in range(len(A)  1)]
roll_B = [roll(B[i], B[i + 1]) for i in range(len(B)  1)]
compare = [compare_ab(a, b) for a, b in zip(A, B)]
results = summarize(compare, roll_A, roll_B)
These models are time consuming and need to be run on a variety of inputs and situations. Now, the analyst has his code as a collection of Python functions, and is trying to figure out how to parallelize such a codebase. To solve this, he uses dask.delayed to wrap his function calls and capture the implicit parallelism.
from dask import compute, delayed
data = [delayed(load)(fn) for fn in filenames]
reference = delayed(load_from_database)(query)
A = [delayed(model_a)(x, reference) for x in data]
B = [delayed(model_b)(x, reference) for x in data]
roll_A = [delayed(roll)(A[i], A[i + 1]) for i in range(len(A)  1)]
roll_B = [delayed(roll)(B[i], B[i + 1]) for i in range(len(B)  1)]
compare = [delayed(compare_ab)(a, b) for a, b in zip(A, B)]
lazy_results = delayed(summarize)(compare, roll_A, roll_B)
The analyst then depends on the dask schedulers to run this complex web of computations in parallel.
results = compute(lazy_results)
He sees how easy it was to transition from experimental code to a scalable parallel version. This code is also easy enough for his teammates to easily understand and extend it in the future.
Algorithm developer¶
A couple of graduate students in machine learning are prototyping novel parallel algorithms. They are in a situation much like the financial analyst above, except that they need to benchmark and profile their computation heavily under a variety of situations and scales. The dask profiling tools provide the feedback they need to understand their parallel performance, including how long each task takes, how intense communication is, and their scheduling overhead. They scale their algorithm between 1 and 50 cores on single workstations and then scale out to a cluster running their computation at thousands of cores. They don’t have access to an institutional cluster, so instead they use dask on the cloud to easily provision clusters of varying sizes.
Their algorithm is written in the same way in all cases. This drastically reduces the cognitive load, and lets the readers of their work experiment with their system on their own machines, aiding reproducibility.
ScikitLearn or Joblib User¶
A data scientist wants to scale her machine learning pipeline to run on a
cluster to accelerate parameter searches. She already uses the sklearn
njobs=
parameter to accelerate computations on her local computer
with Joblib. Now, she wraps her sklearn
code with a context manager to
parallelize the exact same code across a cluster (also available with
IPyParallel)
import distributed.joblib
with joblib.parallel_backend('distributed',
scheduler_host=('192.168.1.100', 8786)):
result = GridSearchCV( ... ) # normal sklearn code
Academic Cluster Administrator¶
A system administrator for a university compute cluster wants to enable many researchers to use the available cluster resources, which are currently lying idle. The research faculty and graduate students lack experience with job schedulers and MPI, but are comfortable interacting with Python code through a Jupyter notebook.
Teaching the faculty and graduate students to parallelize software has proven to be time consuming. Instead, the administrator sets up dask.distributed on a sandbox allocation of the cluster and broadly publishes the address of the scheduler, pointing researchers to the dask.distributed quickstart. Utilization of the cluster climbs steadily over the next week as researchers are more easily able to parallelize their computations without having to learn foreign interfaces. The administrator is happy because resources are being used without significant handholding.
As utilization increases, the administrator has a new problem: the shared dask.distributed cluster is being overused. The administrator tracks use through Dask diagnostics to identify which users are taking most of the resources. He contacts these users and teaches them how to launch their own dask.distributed clusters using the traditional job scheduler on their cluster, making space for more new users in the sandbox allocation.
Financial Modeling Team¶
Similar to the case above, a team of modelers working at a financial institution run a complex network of computational models on top of each other. They started using dask.delayed individually, as suggested above, but realized that they often perform highly overlapping computations, such as always reading the same data.
Now, they decide to use the same Dask cluster collaboratively to save on these costs. Because Dask intelligently hashes computations in a way similar to how Git works, they find that, when two people submit similar computations, the overlapping part of the computation runs only once.
Ever since working collaboratively on the same cluster, they find that their frequently running jobs run much faster because most of the work is already done by previous users. When they share scripts with colleagues, they find that those repeated scripts complete immediately rather than taking several hours.
They are now able to iterate and share data as a team more effectively, decreasing their time to result and increasing their competitive edge.
As this becomes more heavily used on the company cluster, they decide to set up
an autoscaling system. They use their dynamic job scheduler (perhaps SGE,
LSF, Mesos, or Marathon) to run a single daskscheduler
24/7 and then scale
up and down the number of daskworkers
running on the cluster based on
computational load. This solution ends up being more responsive (and thus more
heavily used) than their previous attempts to provide institutionwide access
to parallel computing. But because it responds to load, it still acts as a good
citizen in the cluster.
Streaming data engineering¶
A data engineer responsible for watching a data feed needs to scale out a continuous process. She combines dask.distributed with normal Python Queues to produce a rudimentary but effective stream processing system.
Because dask.distributed is elastic, she can scale up or scale down her cluster resources in response to demand.
Community¶
Dask is used and developed by individuals at a variety of institutions. It sits within the broader Python numeric ecosystem commonly referred to as PyData or SciPy.
Discussion¶
Conversation happens in the following places:
 Usage questions are directed to Stack Overflow with the #dask tag. Dask developers monitor this tag and get emails whenever a question is asked
 Bug reports and feature requests are managed on the GitHub issue tracker
 Chat occurs on at gitter.im/dask/dask for general conversation and gitter.im/dask/dev for developer conversation. Note that because gitter chat is not searchable by future users we discourage usage questions and bug reports on gitter and instead ask people to use Stack Overflow or GitHub.
 Monthly developer meeting happens the first Thursday of the month at 4pm UTC (11am in New York, 8am in Los Angeles, 12am in Beijing) at https://appear.in/daskdev
Asking for help¶
We welcome usage questions and bug reports from all users, even those who are new to using the project. There are a few things you can do to improve the likelihood of quickly getting a good answer.
Ask questions in the right place: We strongly prefer the use of StackOverflow or Github issues over Gitter chat. Github and StackOverflow are more easily searchable by future users, and therefore is more efficient for everyone’s time. Gitter chat is strictly reserved for developer and community discussion.
If you have a general question about how something should work or want best practices then use Stack Overflow. If you think you have found a bug then use GitHub
Ask only in one place: Please restrict yourself to posting your question in only one place (likely Stack Overflow or Github) and don’t post in both
Create a minimal example: It is ideal to create minimal, complete, verifiable examples. This significantly reduces the time that answerers spend understanding your situation, resulting in higher quality answers more quickly.
See also this blogpost about crafting minimal bug reports. These have a much higher likelihood of being answered
Paid support¶
Dask is an open source project that originated at Anaconda Inc. In addition to the previous options, Anaconda offers paid training and support: https://www.anaconda.com/support.
Why Dask?¶
This document gives highlevel motivation on why people choose to adopt Dask.
Python’s role in Data Science¶
Python has grown to become the dominant language both in data analytics and general programming:
This is fueled both by computational libraries like Numpy, Pandas, and ScikitLearn and by a wealth of libraries for visualization, interactive notebooks, collaboration, and so forth.
However, these packages were not designed to scale beyond a single machine. Dask was developed to scale these packages and the surrounding ecosystem. It works with the existing Python ecosystem to scale it to multicore machines and distributed clusters.
Familiar API¶
Analysts often use tools like Pandas, ScikitLearn, Numpy, and the rest of the Python ecosystem to analyze data on their personal computer. They like these tools because they are efficient, intuitive, and widely trusted. However, when they choose to apply their analyses to larger datasets, they find that these tools were not designed to scale beyond a single machine. Therefore, the analyst is forced to rewrite their computation using a more scalable tool, often in another language altogether. This rewrite process slows down discovery and causes frustration.
Dask provides ways to scale Pandas, ScikitLearn, and Numpy workflows with minimal rewriting. It integrates well with these tools so that it copies most of their API and uses their data structures internally. Moreover, Dask is codeveloped with these libraries to ensure that they evolve consistently, minimizing friction caused from transitioning from workloads on a local laptop, to a multicore workstation, and to a distributed cluster. Analysts familiar with Pandas/ScikitLearn/Numpy will be immediately familiar with their Dask equivalents, and have much of their intuition carry over to a scalable context.
Scales out to clusters¶
As datasets and computations scale faster than CPUs and RAM, we need to find ways to scale our computations across multiple machines. This introduces many new concerns:
 How to have computers talk to each other over the network?
 How and when to move data between machines?
 How to recover from machine failures?
 How to deploy on an inhouse cluster?
 How to deploy on the cloud?
 How to deploy on an HPC supercomputer?
 How to provide an API to this system that users find intuitive?
 …
While it is possible to build these systems inhouse (and indeed, many exist), many organizations are increasingly depending on solutions developed within the open source community. These tend to be more robust, secure, and fully featured without being tended by inhouse staff.
Dask solves these problems. It is routinely run on thousandmachine clusters to process hundreds of terabytes of data efficiently. It has utilities and documentation on how to deploy inhouse, on the cloud, or on HPC supercomputers. It supports encryption and authentication using TLS/SSL certificates. It is resilient and can handle the failure of worker nodes gracefully and is elastic, and so can take advantage of new nodes added onthefly. Dask includes several user APIs that are used and smoothed over by thousands of researchers across the globe working in different domains.
Scales down to single computers¶
But a massive cluster is not always the right choice
Today’s laptops and workstations are surprisingly powerful and, if used correctly, can often handle datasets and computations for which we previously depended on clusters. A modern laptop has a multicore CPU, 32GB of RAM, and flashbased hard drives that can stream through data several times faster than HDDs or SSDs of even a year or two ago.
As a result, analysts can often manipulate 100GB+ datasets on their laptop or 1TB+ datasets on a workstation without bothering with the cluster at all. They sometimes prefer this for the following reasons:
 They can use their local software environment, rather than being constrained by what is available on the cluster
 They can more easily work while in transit, at a coffee shop, or at home away from the VPN
 Debugging errors and analyzing performance are generally much easier on a single machine without having to pore through logs
 Generally their iteration cycles are faster
 Their computations may be more efficient because all of the data is local and doesn’t need to flow through the network or between separate processes
Dask can enable efficient parallel computations on single machines by leveraging their multicore CPUs and streaming data efficiently from disk. It can run on a distributed cluster, but it doesn’t have to. Dask allows you to swap out the cluster for singlemachine schedulers which are surprisingly lightweight, require no setup, and can run entirely within the same process as the user’s session.
To avoid excess memory use, Dask is good at finding ways to evaluate computations in a lowmemory footprint when possible by pulling in chunks of data from disk, doing the necessary processing, and throwing away intermediate values as quickly as possible. This lets analysts perform computations on moderately large datasets (100GB+) even on relatively lowpower laptops. This requires no configuration and no setup, meaning that adding Dask to a singlemachine computation adds very little cognitive overhead.
Integrates with the Python ecosystem¶
Python includes computational libraries like Numpy, Pandas, and ScikitLearn, along with thousands of others in data access, plotting, statistics, image and signal processing, and more. These libraries work together seamlessly to produce a cohesive ecosystem of packages that coevolve to meet the needs of analysts in many domains.
This ecosystem is tied together by common standards and protocols to which everyone adheres, which allows these packages to benefit each other in surprising and delightful ways.
Dask evolved from within this ecosystem. It abides by these standards and protocols and actively engages in community efforts to push forward new ones. This enables the rest of the ecosystem to benefit from parallel and distributed computing with minimal coordination. Dask does not seek to disrupt or displace the existing ecosystem, but rather to complement and benefit it from within.
As a result, Dask development is pushed forward by developer communities from Pandas, Numpy, ScikitLearn, ScikitImage, Jupyter, and others. This engagement from the broader community growth helps users to trust the project and helps to ensure that the Python ecosystem will continue to evolve in a smooth and sustainable manner.
Supports complex applications¶
Some parallel computations are simple and just apply the same routine onto many inputs without any kind of coordination. These are simple to parallelize with any system.
Somewhat more complex computations can be expressed with the mapshufflereduce pattern popularized by Hadoop and Spark. This is often sufficient to do most data cleaning tasks, databasestyle queries, and some lightweight machine learning algorithms.
However, more complex parallel computations exist which do not fit into these paradigms, and so are difficult to perform with traditional bigdata technologies. These include more advanced algorithms for statistics or machine learning, time series or local operations, or bespoke parallelism often found within the systems of large enterprises.
Many companies and institutions today have problems which are clearly parallelizable, but not clearly transformable into a big DataFrame computation. Today these companies tend to solve their problems either by writing custom code with lowlevel systems like MPI, ZeroMQ, or sockets and complex queuing systems, or by shoving their problem into a standard bigdata technology like MapReduce or Spark, and hoping for the best.
Dask helps to resolve these situations by exposing lowlevel APIs to its internal task scheduler which is capable of executing very advanced computations. This gives engineers within the institution the ability to build their own parallel computing system using the same engine that powers Dask’s arrays, DataFrames, and machine learning algorithms, but now with the institution’s own custom logic. This allows engineers to keep complex business logic inhouse while still relying on Dask to handle network communication, load balancing, resilience, diagnostics, etc..
Responsive feedback¶
Because everything happens remotely, interactive parallel computing can be frustrating for users. They don’t have a good sense of how computations are progressing, what might be going wrong, or what parts of their code should they focus on for performance. The added distance between a user and their computation can drastically affect how quickly they are able to identify and resolve bugs and performance problems, which can drastically increase their time to solution.
Dask keeps users informed and content with a suite of helpful diagnostic and investigative tools including the following:
 A realtime and responsive dashboard that shows current progress, communication costs, memory use, and more, updated every 100ms
 A statistical profiler installed on every worker that polls each thread every 10ms to determine which lines in your code are taking up the most time across your entire computation
 An embedded IPython kernel in every worker and the scheduler, allowing users to directly investigate the state of their computation with a popup terminal
 The ability to reraise errors locally, so that they can use the traditional debugging tools to which they are accustomed, even when the error happens remotely
Collections
Dask collections are the main interaction point for users. They look like NumPy and Pandas but generate dask graphs internally. If you are a dask user then you should start here.
User Interfaces¶
Dask supports several user interfaces:
 HighLevel
 Arrays: Parallel NumPy
 Bags: Parallel lists
 DataFrames: Parallel Pandas
 Machine Learning : Parallel ScikitLearn
 Others from external projects, like XArray
Each of these user interfaces employs the same underlying parallel computing machinery, and so has the same scaling, diagnostics, resilience, and so on, but each provides a different set of parallel algorithms and programming style.
This document helps you to decide which user interface best suits your needs, and gives some general information that applies to all interfaces. The pages linked above give more information about each interface in greater depth.
HighLevel Collections¶
Many people who start using Dask are explicitly looking for a scalable version of NumPy, Pandas, or ScikitLearn. For these situations, the starting point within Dask is usually fairly clear. If you want scalable NumPy arrays, then start with Dask array; if you want scalable Pandas DataFrames, then start with Dask DataFrame, and so on.
These highlevel interfaces copy the standard interface with slight variations. These interfaces automatically parallelize over larger datasets for you for a large subset of the API from the original project.
# Arrays
import dask.array as da
x = da.random.uniform(low=0, high=10, size=(10000, 10000), # normal numpy code
chunks=(1000, 1000)) # break into chunks of size 1000x1000
y = x + x.T  x.mean(axis=0) # Use normal syntax for high level algorithms
# DataFrames
import dask.dataframe as dd
df = dd.read_csv('2018**.csv', parse_dates='timestamp', # normal Pandas code
blocksize=64000000) # break text into 64MB chunks
s = df.groupby('name').balance.mean() # Use normal syntax for high level algorithms
# Bags / lists
import dask.bag as db
b = db.read_text('*.json').map(json.loads)
total = (b.filter(lambda d: d['name'] == 'Alice')
.map(lambda d: d['balance'])
.sum())
It is important to remember that, while APIs may be similar, some differences do exist. Additionally, the performance of some algorithms may differ from their inmemory counterparts due to the advantages and disadvantages of parallel programming. Some thought and attention is still required when using Dask.
LowLevel Interfaces¶
Often when parallelizing existing code bases or building custom algorithms, you run into code that is parallelizable, but isn’t just a big DataFrame or array. Consider the forloopy code below:
results = []
for a in A:
for b in B:
if a < b:
c = f(a, b)
else:
c = g(a, b)
results.append(c)
There is potential parallelism in this code (the many calls to f
and g
can be done in parallel), but it’s not clear how to rewrite it into a big
array or DataFrame so that it can use a higherlevel API. Even if you could
rewrite it into one of these paradigms, it’s not clear that this would be a
good idea. Much of the meaning would likely be lost in translation, and this
process would become much more difficult for more complex systems.
Instead, Dask’s lowerlevel APIs let you write parallel code one function call at a time within the context of your existing for loops. A common solution here is to use Dask delayed to wrap individual function calls into a lazily constructed task graph:
import dask
lazy_results = []
for a in A:
for b in B:
if a < b:
c = dask.delayed(f)(a, b) # add lazy task
else:
c = dask.delayed(g)(a, b) # add lazy task
lazy_results.append(c)
results = dask.compute(*lazy_results) # compute all in parallel
Combining High and LowLevel Interfaces¶
It is common to combine high and lowlevel interfaces. For example, you might use Dask array/bag/dataframe to load in data and do initial preprocessing, then switch to Dask delayed for a custom algorithm that is specific to your domain, then switch back to Dask array/dataframe to clean up and store results. Understanding both sets of user interfaces, and how to switch between them, can be a productive combination.
# Convert to a list of delayed Pandas dataframes
delayed_values = df.to_delayed()
# Manipulate delayed values arbitrarily as you like
# Convert many delayed Pandas DataFrames back to a single Dask DataFrame
df = dd.from_delayed(delayed_values)
Laziness and Computing¶
Most Dask user interfaces are lazy, meaning that they do not evaluate until
you explicitly ask for a result using the compute
method:
# This array syntax doesn't cause computation
y = x + x.T  x.mean(axis=0)
# Trigger computation by explicitly calling the compute method
y = y.compute()
If you have multiple results that you want to compute at the same time, use the
dask.compute
function. This can share intermediate results and so be more
efficient:
# compute multiple results at the same time with the compute function
min, max = dask.compute(y.min(), y.max())
Note that the compute()
function returns inmemory results. It converts
Dask DataFrames to Pandas DataFrames, Dask arrays to NumPy arrays, and Dask
bags to lists. You should only call compute on results that will fit
comfortably in memory. If your result does not fit in memory, then you might
consider writing it to disk instead.
# Write larger results out to disk rather than store them in memory
my_dask_dataframe.to_parquet('myfile.parquet')
my_dask_array.to_hdf5('myfile.hdf5')
my_dask_bag.to_textfiles('myfile.*.txt')
Persist into Distributed Memory¶
Alternatively, if you are on a cluster, then you may want to trigger a
computation and store the results in distributed memory. In this case you do
not want to call compute
, which would create a single Pandas, NumPy, or
list result. Instead, you want to call persist
, which returns a new Dask
object that points to actively computing, or already computed results spread
around your cluster’s memory.
# Compute returns an inmemory nonDask object
y = y.compute()
# Persist returns an inmemory Dask object that uses distributed storage if available
y = y.persist()
This is common to see after data loading an preprocessing steps, but before rapid iteration, exploration, or complex algorithms. For example, we might read in a lot of data, filter down to a more manageable subset, and then persist data into memory so that we can iterate quickly.
import dask.dataframe as dd
df = dd.read_parquet('...')
df = df[df.name == 'Alice'] # select important subset of data
df = df.persist() # trigger computation in the background
# These are all relatively fast now that the relevant data is in memory
df.groupby(df.id).balance.sum().compute() # explore data quickly
df.groupby(df.id).balance.mean().compute() # explore data quickly
df.id.nunique() # explore data quickly
Lazy vs Immediate¶
As mentioned above, most Dask workloads are lazy, that is, they don’t start any
work until you explicitly trigger them with a call to compute()
.
However, sometimes you do want to submit work as quickly as possible, track it
over time, submit new work or cancel work depending on partial results, and so
on. This can be useful when tracking or responding to realtime events,
handling streaming data, or when building complex and adaptive algorithms.
For these situations, people typically turn to the futures interface which is a lowlevel interface like Dask delayed, but operates immediately rather than lazily.
Here is the same example with Dask delayed and Dask futures to illustrate the difference.
Delayed: Lazy¶
@dask.delayed
def inc(x):
return x + 1
@dask.delayed
def add(x, y):
return x + y
a = inc(1) # no work has happened yet
b = inc(2) # no work has happened yet
c = add(a, b) # no work has happened yet
c = c.compute() # This triggers all of the above computations
Futures: Immediate¶
from dask.distributed import Client
client = Client()
def inc(x):
return x + 1
def add(x, y):
return x + y
a = client.submit(inc, 1) # work starts immediately
b = client.submit(inc, 2) # work starts immediately
c = client.submit(add, a, b) # work starts immediately
c = c.result() # block until work finishes, then gather result
You can also trigger work with the highlevel collections using the
persist
function. This will cause work to happen in the background when
using the distributed scheduler.
Combining Interfaces¶
There are established ways to combine the interfaces above:
The highlevel interfaces (array, bag, dataframe) have a
to_delayed
method that can convert to a sequence (or grid) of Dask delayed objectsdelayeds = df.to_delayed()
The highlevel interfaces (array, bag, dataframe) have a
from_delayed
method that can convert from either Delayed or Future objectsdf = dd.from_delayed(delayeds) df = dd.from_delayed(futures)
The
Client.compute
method converts Delayed objects into Futuresfutures = client.compute(delayeds)
The
dask.distributed.futures_of
function gathers futures from persisted collectionsfrom dask.distributed import futures_of df = df.persist() # start computation in the background futures = futures_of(df)
The Dask.delayed object converts Futures into delayed objects
delayed_value = dask.delayed(future)
The approaches above should suffice to convert any interface into any other. We often see some antipatterns that do not work as well:
 Calling lowlevel APIs (delayed or futures) on highlevel objects (like
Dask arrays or DataFrames). This downgrades those objects to their NumPy or
Pandas equivalents, which may not be desired.
Often people are looking for APIs like
dask.array.map_blocks
ordask.dataframe.map_partitions
instead.  Calling
compute()
on Future objects. Often people want the.result()
method instead.  Calling NumPy/Pandas functions on highlevel Dask objects or highlevel Dask functions on NumPy/Pandas objects
Conclusion¶
Most people who use Dask start with only one of the interfaces above but eventually learn how to use a few interfaces together. This helps them leverage the sophisticated algorithms in the highlevel interfaces while also working around tricky problems with the lowlevel interfaces.
For more information, see the documentation for the particular user interfaces below:
 High Level
 Arrays: Parallel NumPy
 Bags: Parallel lists
 DataFrames: Parallel Pandas
 Machine Learning : Parallel ScikitLearn
 Others from external projects, like XArray
Array¶
API¶
Top level user functions:
all (a[, axis, out, keepdims]) 
Test whether all array elements along a given axis evaluate to True. 
allclose (a, b[, rtol, atol, equal_nan]) 
Returns True if two arrays are elementwise equal within a tolerance. 
angle (x[, deg]) 
Return the angle of the complex argument. 
any (a[, axis, out, keepdims]) 
Test whether any array element along a given axis evaluates to True. 
apply_along_axis (func1d, axis, arr, *args, …) 
Apply a function to 1D slices along the given axis. 
apply_over_axes (func, a, axes) 
Apply a function repeatedly over multiple axes. 
arange (*args, **kwargs) 
Return evenly spaced values from start to stop with step size step. 
arccos (x, /[, out, where, casting, order, …]) 
Trigonometric inverse cosine, elementwise. 
arccosh (x, /[, out, where, casting, order, …]) 
Inverse hyperbolic cosine, elementwise. 
arcsin (x, /[, out, where, casting, order, …]) 
Inverse sine, elementwise. 
arcsinh (x, /[, out, where, casting, order, …]) 
Inverse hyperbolic sine elementwise. 
arctan (x, /[, out, where, casting, order, …]) 
Trigonometric inverse tangent, elementwise. 
arctan2 (x1, x2, /[, out, where, casting, …]) 
Elementwise arc tangent of x1/x2 choosing the quadrant correctly. 
arctanh (x, /[, out, where, casting, order, …]) 
Inverse hyperbolic tangent elementwise. 
argmax (a[, axis, out]) 
Returns the indices of the maximum values along an axis. 
argmin (a[, axis, out]) 
Returns the indices of the minimum values along an axis. 
argtopk (a, k[, axis, split_every]) 
Extract the indices of the k largest elements from a on the given axis, and return them sorted from largest to smallest. 
argwhere (a) 
Find the indices of array elements that are nonzero, grouped by element. 
around (a[, decimals, out]) 
Evenly round to the given number of decimals. 
array (object[, dtype, copy, order, subok, ndmin]) 
Create an array. 
asanyarray (a) 
Convert the input to a dask array. 
asarray (a, **kwargs) 
Convert the input to a dask array. 
atleast_1d (*arys) 
Convert inputs to arrays with at least one dimension. 
atleast_2d (*arys) 
View inputs as arrays with at least two dimensions. 
atleast_3d (*arys) 
View inputs as arrays with at least three dimensions. 
average (a[, axis, weights, returned]) 
Compute the weighted average along the specified axis. 
bincount (x[, weights, minlength]) 
Count number of occurrences of each value in array of nonnegative ints. 
bitwise_and (x1, x2, /[, out, where, …]) 
Compute the bitwise AND of two arrays elementwise. 
bitwise_not (x, /[, out, where, casting, …]) 
Compute bitwise inversion, or bitwise NOT, elementwise. 
bitwise_or (x1, x2, /[, out, where, casting, …]) 
Compute the bitwise OR of two arrays elementwise. 
bitwise_xor (x1, x2, /[, out, where, …]) 
Compute the bitwise XOR of two arrays elementwise. 
block (arrays[, allow_unknown_chunksizes]) 
Assemble an ndarray from nested lists of blocks. 
broadcast_arrays (*args, **kwargs) 
Broadcast any number of arrays against each other. 
broadcast_to (x, shape[, chunks]) 
Broadcast an array to a new shape. 
coarsen (reduction, x, axes[, trim_excess]) 
Coarsen array by applying reduction to fixed size neighborhoods 
ceil (x, /[, out, where, casting, order, …]) 
Return the ceiling of the input, elementwise. 
choose (a, choices[, out, mode]) 
Construct an array from an index array and a set of arrays to choose from. 
clip (*args, **kwargs) 
Clip (limit) the values in an array. 
compress (condition, a[, axis, out]) 
Return selected slices of an array along given axis. 
concatenate (seq[, axis, …]) 
Concatenate arrays along an existing axis 
conj (x, /[, out, where, casting, order, …]) 
Return the complex conjugate, elementwise. 
copysign (x1, x2, /[, out, where, casting, …]) 
Change the sign of x1 to that of x2, elementwise. 
corrcoef (x[, y, rowvar, bias, ddof]) 
Return Pearson productmoment correlation coefficients. 
cos (x, /[, out, where, casting, order, …]) 
Cosine elementwise. 
cosh (x, /[, out, where, casting, order, …]) 
Hyperbolic cosine, elementwise. 
count_nonzero (a[, axis]) 
Counts the number of nonzero values in the array a . 
cov (m[, y, rowvar, bias, ddof, fweights, …]) 
Estimate a covariance matrix, given data and weights. 
cumprod (a[, axis, dtype, out]) 
Return the cumulative product of elements along a given axis. 
cumsum (a[, axis, dtype, out]) 
Return the cumulative sum of the elements along a given axis. 
deg2rad (x, /[, out, where, casting, order, …]) 
Convert angles from degrees to radians. 
degrees (x, /[, out, where, casting, order, …]) 
Convert angles from radians to degrees. 
diag (v[, k]) 
Extract a diagonal or construct a diagonal array. 
diagonal (a[, offset, axis1, axis2]) 
Return specified diagonals. 
diff (a[, n, axis, prepend, append]) 
Calculate the nth discrete difference along the given axis. 
digitize (x, bins[, right]) 
Return the indices of the bins to which each value in input array belongs. 
dot (a, b[, out]) 
Dot product of two arrays. 
dstack (tup) 
Stack arrays in sequence depth wise (along third axis). 
ediff1d (ary[, to_end, to_begin]) 
The differences between consecutive elements of an array. 
einsum (subscripts, *operands[, out, dtype, …]) 
Evaluates the Einstein summation convention on the operands. 
empty (*args, **kwargs) 
Blocked variant of empty 
empty_like (a[, dtype, chunks]) 
Return a new array with the same shape and type as a given array. 
exp (x, /[, out, where, casting, order, …]) 
Calculate the exponential of all elements in the input array. 
expm1 (x, /[, out, where, casting, order, …]) 
Calculate exp(x)  1 for all elements in the array. 
eye (N, chunks[, M, k, dtype]) 
Return a 2D Array with ones on the diagonal and zeros elsewhere. 
fabs (x, /[, out, where, casting, order, …]) 
Compute the absolute values elementwise. 
fix (*args, **kwargs) 
Round to nearest integer towards zero. 
flatnonzero (a) 
Return indices that are nonzero in the flattened version of a. 
flip (m, axis) 
Reverse element order along axis. 
flipud (m) 
Flip array in the up/down direction. 
fliplr (m) 
Flip array in the left/right direction. 
floor (x, /[, out, where, casting, order, …]) 
Return the floor of the input, elementwise. 
fmax (x1, x2, /[, out, where, casting, …]) 
Elementwise maximum of array elements. 
fmin (x1, x2, /[, out, where, casting, …]) 
Elementwise minimum of array elements. 
fmod (x1, x2, /[, out, where, casting, …]) 
Return the elementwise remainder of division. 
frexp (x[, out1, out2], / [[, out, where, …]) 
Decompose the elements of x into mantissa and twos exponent. 
fromfunction (function, shape, **kwargs) 
Construct an array by executing a function over each coordinate. 
frompyfunc (func, nin, nout) 
Takes an arbitrary Python function and returns a NumPy ufunc. 
full (*args, **kwargs) 
Blocked variant of full 
full_like (a, fill_value[, dtype, chunks]) 
Return a full array with the same shape and type as a given array. 
gradient (f, *varargs, **kwargs) 
Return the gradient of an Ndimensional array. 
histogram (a[, bins, range, normed, weights, …]) 
Blocked variant of numpy.histogram() . 
hstack (tup) 
Stack arrays in sequence horizontally (column wise). 
hypot (x1, x2, /[, out, where, casting, …]) 
Given the “legs” of a right triangle, return its hypotenuse. 
imag (*args, **kwargs) 
Return the imaginary part of the complex argument. 
indices (dimensions[, dtype, chunks]) 
Implements NumPy’s indices for Dask Arrays. 
insert (arr, obj, values[, axis]) 
Insert values along the given axis before the given indices. 
invert (x, /[, out, where, casting, order, …]) 
Compute bitwise inversion, or bitwise NOT, elementwise. 
isclose (a, b[, rtol, atol, equal_nan]) 
Returns a boolean array where two arrays are elementwise equal within a tolerance. 
iscomplex (*args, **kwargs) 
Returns a bool array, where True if input element is complex. 
isfinite (x, /[, out, where, casting, order, …]) 
Test elementwise for finiteness (not infinity or not Not a Number). 
isin (element, test_elements[, …]) 
Calculates element in test_elements, broadcasting over element only. 
isinf (x, /[, out, where, casting, order, …]) 
Test elementwise for positive or negative infinity. 
isneginf (*args, **kwargs) 
Test elementwise for negative infinity, return result as bool array. 
isnan (x, /[, out, where, casting, order, …]) 
Test elementwise for NaN and return result as a boolean array. 
isnull (values) 
pandas.isnull for dask arrays 
isposinf (*args, **kwargs) 
Test elementwise for positive infinity, return result as bool array. 
isreal (*args, **kwargs) 
Returns a bool array, where True if input element is real. 
ldexp (x1, x2, /[, out, where, casting, …]) 
Returns x1 * 2**x2, elementwise. 
linspace (start, stop[, num, endpoint, …]) 
Return num evenly spaced values over the closed interval [start, stop]. 
log (x, /[, out, where, casting, order, …]) 
Natural logarithm, elementwise. 
log10 (x, /[, out, where, casting, order, …]) 
Return the base 10 logarithm of the input array, elementwise. 
log1p (x, /[, out, where, casting, order, …]) 
Return the natural logarithm of one plus the input array, elementwise. 
log2 (x, /[, out, where, casting, order, …]) 
Base2 logarithm of x. 
logaddexp (x1, x2, /[, out, where, casting, …]) 
Logarithm of the sum of exponentiations of the inputs. 
logaddexp2 (x1, x2, /[, out, where, casting, …]) 
Logarithm of the sum of exponentiations of the inputs in base2. 
logical_and (x1, x2, /[, out, where, …]) 
Compute the truth value of x1 AND x2 elementwise. 
logical_not (x, /[, out, where, casting, …]) 
Compute the truth value of NOT x elementwise. 
logical_or (x1, x2, /[, out, where, casting, …]) 
Compute the truth value of x1 OR x2 elementwise. 
logical_xor (x1, x2, /[, out, where, …]) 
Compute the truth value of x1 XOR x2, elementwise. 
map_blocks (func, *args, **kwargs) 
Map a function across all blocks of a dask array. 
map_overlap (x, func, depth[, boundary, trim]) 
Map a function over blocks of the array with some overlap 
matmul (a, b) 

max (a[, axis, out, keepdims, initial]) 
Return the maximum of an array or maximum along an axis. 
maximum (x1, x2, /[, out, where, casting, …]) 
Elementwise maximum of array elements. 
mean (a[, axis, dtype, out, keepdims]) 
Compute the arithmetic mean along the specified axis. 
meshgrid (*xi, **kwargs) 
Return coordinate matrices from coordinate vectors. 
min (a[, axis, out, keepdims, initial]) 
Return the minimum of an array or minimum along an axis. 
minimum (x1, x2, /[, out, where, casting, …]) 
Elementwise minimum of array elements. 
modf (x[, out1, out2], / [[, out, where, …]) 
Return the fractional and integral parts of an array, elementwise. 
moment (a, order[, axis, dtype, keepdims, …]) 

nanargmax (x, axis, **kwargs) 

nanargmin (x, axis, **kwargs) 

nancumprod (a[, axis, dtype, out]) 
Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one. 
nancumsum (a[, axis, dtype, out]) 
Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. 
nanmax (a[, axis, out, keepdims]) 
Return the maximum of an array or maximum along an axis, ignoring any NaNs. 
nanmean (a[, axis, dtype, out, keepdims]) 
Compute the arithmetic mean along the specified axis, ignoring NaNs. 
nanmin (a[, axis, out, keepdims]) 
Return minimum of an array or minimum along an axis, ignoring any NaNs. 
nanprod (a[, axis, dtype, out, keepdims]) 
Return the product of array elements over a given axis treating Not a Numbers (NaNs) as ones. 
nanstd (a[, axis, dtype, out, ddof, keepdims]) 
Compute the standard deviation along the specified axis, while ignoring NaNs. 
nansum (a[, axis, dtype, out, keepdims]) 
Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. 
nanvar (a[, axis, dtype, out, ddof, keepdims]) 
Compute the variance along the specified axis, while ignoring NaNs. 
nan_to_num (*args, **kwargs) 
Replace NaN with zero and infinity with large finite numbers. 
nextafter (x1, x2, /[, out, where, casting, …]) 
Return the next floatingpoint value after x1 towards x2, elementwise. 
nonzero (a) 
Return the indices of the elements that are nonzero. 
notnull (values) 
pandas.notnull for dask arrays 
ones (*args, **kwargs) 
Blocked variant of ones 
ones_like (a[, dtype, chunks]) 
Return an array of ones with the same shape and type as a given array. 
outer (a, b[, out]) 
Compute the outer product of two vectors. 
pad (array, pad_width, mode, **kwargs) 
Pads an array. 
percentile (a, q[, interpolation]) 
Approximate percentile of 1D array 
PerformanceWarning 
A warning given when bad chunking may cause poor performance 
piecewise (x, condlist, funclist, *args, **kw) 
Evaluate a piecewisedefined function. 
prod (a[, axis, dtype, out, keepdims, initial]) 
Return the product of array elements over a given axis. 
ptp (a[, axis, out, keepdims]) 
Range of values (maximum  minimum) along an axis. 
rad2deg (x, /[, out, where, casting, order, …]) 
Convert angles from radians to degrees. 
radians (x, /[, out, where, casting, order, …]) 
Convert angles from degrees to radians. 
ravel (a[, order]) 
Return a contiguous flattened array. 
real (*args, **kwargs) 
Return the real part of the complex argument. 
rechunk (x, chunks[, threshold, block_size_limit]) 
Convert blocks in dask array x for new chunks. 
repeat (a, repeats[, axis]) 
Repeat elements of an array. 
reshape (x, shape) 
Reshape array to new shape 
result_type (*arrays_and_dtypes) 
Returns the type that results from applying the NumPy type promotion rules to the arguments. 
rint (x, /[, out, where, casting, order, …]) 
Round elements of the array to the nearest integer. 
roll (a, shift[, axis]) 
Roll array elements along a given axis. 
round (a[, decimals, out]) 
Round an array to the given number of decimals. 
sign (x, /[, out, where, casting, order, …]) 
Returns an elementwise indication of the sign of a number. 
signbit (x, /[, out, where, casting, order, …]) 
Returns elementwise True where signbit is set (less than zero). 
sin (x, /[, out, where, casting, order, …]) 
Trigonometric sine, elementwise. 
sinh (x, /[, out, where, casting, order, …]) 
Hyperbolic sine, elementwise. 
sqrt (x, /[, out, where, casting, order, …]) 
Return the nonnegative squareroot of an array, elementwise. 
square (x, /[, out, where, casting, order, …]) 
Return the elementwise square of the input. 
squeeze (a[, axis]) 
Remove singledimensional entries from the shape of an array. 
stack (seq[, axis]) 
Stack arrays along a new axis 
std (a[, axis, dtype, out, ddof, keepdims]) 
Compute the standard deviation along the specified axis. 
sum (a[, axis, dtype, out, keepdims, initial]) 
Sum of array elements over a given axis. 
take (a, indices[, axis, out, mode]) 
Take elements from an array along an axis. 
tan (x, /[, out, where, casting, order, …]) 
Compute tangent elementwise. 
tanh (x, /[, out, where, casting, order, …]) 
Compute hyperbolic tangent elementwise. 
tensordot (a, b[, axes]) 
Compute tensor dot product along specified axes for arrays >= 1D. 
tile (A, reps) 
Construct an array by repeating A the number of times given by reps. 
topk (a, k[, axis, split_every]) 
Extract the k largest elements from a on the given axis, and return them sorted from largest to smallest. 
transpose (a[, axes]) 
Permute the dimensions of an array. 
tril (m[, k]) 
Lower triangle of an array with elements above the kth diagonal zeroed. 
triu (m[, k]) 
Upper triangle of an array with elements above the kth diagonal zeroed. 
trunc (x, /[, out, where, casting, order, …]) 
Return the truncated value of the input, elementwise. 
unique (ar[, return_index, return_inverse, …]) 
Find the unique elements of an array. 
unravel_index (indices, shape[, order]) 
Converts a flat index or array of flat indices into a tuple of coordinate arrays. 
var (a[, axis, dtype, out, ddof, keepdims]) 
Compute the variance along the specified axis. 
vdot (a, b) 
Return the dot product of two vectors. 
vstack (tup) 
Stack arrays in sequence vertically (row wise). 
where (condition, [x, y]) 
Return elements chosen from x or y depending on condition. 
zeros (*args, **kwargs) 
Blocked variant of zeros 
zeros_like (a[, dtype, chunks]) 
Return an array of zeros with the same shape and type as a given array. 
Fast Fourier Transforms¶
fft.fft_wrap (fft_func[, kind, dtype]) 
Wrap 1D, 2D, and ND real and complex FFT functions 
fft.fft (a[, n, axis]) 
Wrapping of numpy.fft.fft 
fft.fft2 (a[, s, axes]) 
Wrapping of numpy.fft.fft2 
fft.fftn (a[, s, axes]) 
Wrapping of numpy.fft.fftn 
fft.ifft (a[, n, axis]) 
Wrapping of numpy.fft.ifft 
fft.ifft2 (a[, s, axes]) 
Wrapping of numpy.fft.ifft2 
fft.ifftn (a[, s, axes]) 
Wrapping of numpy.fft.ifftn 
fft.rfft (a[, n, axis]) 
Wrapping of numpy.fft.rfft 
fft.rfft2 (a[, s, axes]) 
Wrapping of numpy.fft.rfft2 
fft.rfftn (a[, s, axes]) 
Wrapping of numpy.fft.rfftn 
fft.irfft (a[, n, axis]) 
Wrapping of numpy.fft.irfft 
fft.irfft2 (a[, s, axes]) 
Wrapping of numpy.fft.irfft2 
fft.irfftn (a[, s, axes]) 
Wrapping of numpy.fft.irfftn 
fft.hfft (a[, n, axis]) 
Wrapping of numpy.fft.hfft 
fft.ihfft (a[, n, axis]) 
Wrapping of numpy.fft.ihfft 
fft.fftfreq (n[, d]) 
Return the Discrete Fourier Transform sample frequencies. 
fft.rfftfreq (n[, d]) 
Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). 
fft.fftshift (x[, axes]) 
Shift the zerofrequency component to the center of the spectrum. 
fft.ifftshift (x[, axes]) 
The inverse of fftshift. 
Linear Algebra¶
linalg.cholesky (a[, lower]) 
Returns the Cholesky decomposition, \(A = L L^*\) or \(A = U^* U\) of a Hermitian positivedefinite matrix A. 
linalg.inv (a) 
Compute the inverse of a matrix with LU decomposition and forward / backward substitutions. 
linalg.lstsq (a, b) 
Return the leastsquares solution to a linear matrix equation using QR decomposition. 
linalg.lu (a) 
Compute the lu decomposition of a matrix. 
linalg.norm (x[, ord, axis, keepdims]) 
Matrix or vector norm. 
linalg.qr (a) 
Compute the qr factorization of a matrix. 
linalg.solve (a, b[, sym_pos]) 
Solve the equation a x = b for x . 
linalg.solve_triangular (a, b[, lower]) 
Solve the equation a x = b for x, assuming a is a triangular matrix. 
linalg.svd (a) 
Compute the singular value decomposition of a matrix. 
linalg.svd_compressed (a, k[, n_power_iter, seed]) 
Randomly compressed rankk thin Singular Value Decomposition. 
linalg.sfqr (data[, name]) 
Direct ShortandFat QR 
linalg.tsqr (data[, compute_svd, …]) 
Direct TallandSkinny QR algorithm 
Masked Arrays¶
ma.filled (a[, fill_value]) 
Return input as an array with masked data replaced by a fill value. 
ma.fix_invalid (a[, mask, copy, fill_value]) 
Return input with invalid data masked and replaced by a fill value. 
ma.getdata (a[, subok]) 
Return the data of a masked array as an ndarray. 
ma.getmaskarray (arr) 
Return the mask of a masked array, or full boolean array of False. 
ma.masked_array ([data, mask, dtype, copy, …]) 
An array class with possibly masked values. 
ma.masked_equal (x, value[, copy]) 
Mask an array where equal to a given value. 
ma.masked_greater (x, value[, copy]) 
Mask an array where greater than a given value. 
ma.masked_greater_equal (x, value[, copy]) 
Mask an array where greater than or equal to a given value. 
ma.masked_inside (x, v1, v2[, copy]) 
Mask an array inside a given interval. 
ma.masked_invalid (a[, copy]) 
Mask an array where invalid values occur (NaNs or infs). 
ma.masked_less (x, value[, copy]) 
Mask an array where less than a given value. 
ma.masked_less_equal (x, value[, copy]) 
Mask an array where less than or equal to a given value. 
ma.masked_not_equal (x, value[, copy]) 
Mask an array where not equal to a given value. 
ma.masked_outside (x, v1, v2[, copy]) 
Mask an array outside a given interval. 
ma.masked_values (x, value[, rtol, atol, …]) 
Mask using floating point equality. 
ma.masked_where (condition, a[, copy]) 
Mask an array where a condition is met. 
ma.set_fill_value (a, fill_value) 
Set the filling value of a, if a is a masked array. 
Random¶
random.beta (a, b[, size]) 
Draw samples from a Beta distribution. 
random.binomial (n, p[, size]) 
Draw samples from a binomial distribution. 
random.chisquare (df[, size]) 
Draw samples from a chisquare distribution. 
random.choice (a[, size, replace, p]) 
Generates a random sample from a given 1D array 
random.exponential ([scale, size]) 
Draw samples from an exponential distribution. 
random.f (dfnum, dfden[, size]) 
Draw samples from an F distribution. 
random.gamma (shape[, scale, size]) 
Draw samples from a Gamma distribution. 
random.geometric (p[, size]) 
Draw samples from the geometric distribution. 
random.gumbel ([loc, scale, size]) 
Draw samples from a Gumbel distribution. 
random.hypergeometric (ngood, nbad, nsample) 
Draw samples from a Hypergeometric distribution. 
random.laplace ([loc, scale, size]) 
Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). 
random.logistic ([loc, scale, size]) 
Draw samples from a logistic distribution. 
random.lognormal ([mean, sigma, size]) 
Draw samples from a lognormal distribution. 
random.logseries (p[, size]) 
Draw samples from a logarithmic series distribution. 
random.negative_binomial (n, p[, size]) 
Draw samples from a negative binomial distribution. 
random.noncentral_chisquare (df, nonc[, size]) 
Draw samples from a noncentral chisquare distribution. 
random.noncentral_f (dfnum, dfden, nonc[, size]) 
Draw samples from the noncentral F distribution. 
random.normal ([loc, scale, size]) 
Draw random samples from a normal (Gaussian) distribution. 
random.pareto (a[, size]) 
Draw samples from a Pareto II or Lomax distribution with specified shape. 
random.poisson ([lam, size]) 
Draw samples from a Poisson distribution. 
random.power (a[, size]) 
Draws samples in [0, 1] from a power distribution with positive exponent a  1. 
random.randint (low[, high, size, dtype]) 
Return random integers from low (inclusive) to high (exclusive). 
random.random ([size]) 
Return random floats in the halfopen interval [0.0, 1.0). 
random.random_sample ([size]) 
Return random floats in the halfopen interval [0.0, 1.0). 
random.rayleigh ([scale, size]) 
Draw samples from a Rayleigh distribution. 
random.standard_cauchy ([size]) 
Draw samples from a standard Cauchy distribution with mode = 0. 
random.standard_exponential ([size]) 
Draw samples from the standard exponential distribution. 
random.standard_gamma (shape[, size]) 
Draw samples from a standard Gamma distribution. 
random.standard_normal ([size]) 
Draw samples from a standard Normal distribution (mean=0, stdev=1). 
random.standard_t (df[, size]) 
Draw samples from a standard Student’s t distribution with df degrees of freedom. 
random.triangular (left, mode, right[, size]) 
Draw samples from the triangular distribution over the interval [left, right] . 
random.uniform ([low, high, size]) 
Draw samples from a uniform distribution. 
random.vonmises (mu, kappa[, size]) 
Draw samples from a von Mises distribution. 
random.wald (mean, scale[, size]) 
Draw samples from a Wald, or inverse Gaussian, distribution. 
random.weibull (a[, size]) 
Draw samples from a Weibull distribution. 
random.zipf (a[, size]) 
Standard distributions 
Stats¶
stats.ttest_ind (a, b[, axis, equal_var]) 
Calculate the Ttest for the means of two independent samples of scores. 
stats.ttest_1samp (a, popmean[, axis, nan_policy]) 
Calculate the Ttest for the mean of ONE group of scores. 
stats.ttest_rel (a, b[, axis, nan_policy]) 
Calculate the Ttest on TWO RELATED samples of scores, a and b. 
stats.chisquare (f_obs[, f_exp, ddof, axis]) 
Calculate a oneway chi square test. 
stats.power_divergence (f_obs[, f_exp, ddof, …]) 
CressieRead power divergence statistic and goodness of fit test. 
stats.skew (a[, axis, bias, nan_policy]) 
Compute the skewness of a data set. 
stats.skewtest (a[, axis, nan_policy]) 
Test whether the skew is different from the normal distribution. 
stats.kurtosis (a[, axis, fisher, bias, …]) 
Compute the kurtosis (Fisher or Pearson) of a dataset. 
stats.kurtosistest (a[, axis, nan_policy]) 
Test whether a dataset has normal kurtosis. 
stats.normaltest (a[, axis, nan_policy]) 
Test whether a sample differs from a normal distribution. 
stats.f_oneway (*args) 
Performs a 1way ANOVA. 
stats.moment (a[, moment, axis, nan_policy]) 
Calculate the nth moment about the mean for a sample. 
Image Support¶
image.imread (filename[, imread, preprocess]) 
Read a stack of images into a dask array 
Slightly Overlapping Computations¶
overlap.overlap (x, depth, boundary) 
Share boundaries between neighboring blocks 
overlap.map_overlap (x, func, depth[, …]) 
Map a function over blocks of the array with some overlap 
overlap.trim_internal (x, axes[, boundary]) 
Trim sides from each block 
overlap.trim_overlap (x, depth[, boundary]) 
Trim sides from each block. 
Create and Store Arrays¶
from_array (x, chunks[, name, lock, asarray, …]) 
Create dask array from something that looks like an array 
from_delayed (value, shape, dtype[, name]) 
Create a dask array from a dask delayed value 
from_npy_stack (dirname[, mmap_mode]) 
Load dask array from stack of npy files 
from_zarr (url[, component, storage_options, …]) 
Load array from the zarr storage format 
from_tiledb 

store (sources, targets[, lock, regions, …]) 
Store dask arrays in arraylike objects, overwrite data in target 
to_hdf5 (filename, *args, **kwargs) 
Store arrays in HDF5 file 
to_zarr (arr, url[, component, …]) 
Save array to the zarr storage format 
to_npy_stack (dirname, x[, axis]) 
Write dask array to a stack of .npy files 
to_tiledb 
Generalized Ufuncs¶
apply_gufunc (func, signature, *args, **kwargs) 
Apply a generalized ufunc or similar python function to arrays. 
as_gufunc ([signature]) 
Decorator for dask.array.gufunc . 
gufunc (pyfunc, **kwargs) 
Binds pyfunc into dask.array.apply_gufunc when called. 
Internal functions¶
blockwise (func, out_ind, *args, **kwargs) 
Tensor operation: Generalized inner and outer products 
normalize_chunks (chunks[, shape, limit, …]) 
Normalize chunks to tuple of tuples 
Other functions¶

dask.array.
from_array
(x, chunks, name=None, lock=False, asarray=True, fancy=True, getitem=None)¶ Create dask array from something that looks like an array
Input must have a
.shape
and support numpystyle slicing.Parameters:  x : array_like
 chunks : int, tuple
How to chunk the array. Must be one of the following forms:  A blocksize like 1000.  A blockshape like (1000, 1000).  Explicit sizes of all blocks along all dimensions like
((1000, 1000, 500), (400, 400)).
1 or None as a blocksize indicate the size of the corresponding dimension.
 name : str, optional
The key name to use for the array. Defaults to a hash of
x
. By default, hash uses python’s standard sha1. This behaviour can be changed by installing cityhash, xxhash or murmurhash. If installed, a largefactor speedup can be obtained in the tokenisation step. Usename=False
to generate a random name instead of hashing (fast) lock : bool or Lock, optional
If
x
doesn’t support concurrent reads then provide a lock here, or pass in True to have dask.array create one for you. asarray : bool, optional
If True (default), then chunks will be converted to instances of
ndarray
. Set to False to pass passed chunks through unchanged. fancy : bool, optional
If
x
doesn’t support fancy indexing (e.g. indexing with lists or arrays) then set to False. Default is True.
Examples
>>> x = h5py.File('...')['/data/path'] # doctest: +SKIP >>> a = da.from_array(x, chunks=(1000, 1000)) # doctest: +SKIP
If your underlying datastore does not support concurrent reads then include the
lock=True
keyword argument orlock=mylock
if you want multiple arrays to coordinate around the same lock.>>> a = da.from_array(x, chunks=(1000, 1000), lock=True) # doctest: +SKIP

dask.array.
from_delayed
(value, shape, dtype, name=None)¶ Create a dask array from a dask delayed value
This routine is useful for constructing dask arrays in an adhoc fashion using dask delayed, particularly when combined with stack and concatenate.
The dask array will consist of a single chunk.
Examples
>>> from dask import delayed >>> value = delayed(np.ones)(5) >>> array = from_delayed(value, (5,), float) >>> array dask.array<fromvalue, shape=(5,), dtype=float64, chunksize=(5,)> >>> array.compute() array([1., 1., 1., 1., 1.])

dask.array.
store
(sources, targets, lock=True, regions=None, compute=True, return_stored=False, **kwargs)¶ Store dask arrays in arraylike objects, overwrite data in target
This stores dask arrays into object that supports numpystyle setitem indexing. It stores values chunk by chunk so that it does not have to fill up memory. For best performance you can align the block size of the storage target with the block size of your array.
If your data fits in memory then you may prefer calling
np.array(myarray)
instead.Parameters:  sources: Array or iterable of Arrays
 targets: arraylike or Delayed or iterable of arraylikes and/or Delayeds
These should support setitem syntax
target[10:20] = ...
 lock: boolean or threading.Lock, optional
Whether or not to lock the data stores while storing. Pass True (lock each file individually), False (don’t lock) or a particular
threading.Lock
object to be shared among all writes. regions: tuple of slices or iterable of tuple of slices
Each
region
tuple inregions
should be such thattarget[region].shape = source.shape
for the corresponding source and target in sources and targets, respectively. compute: boolean, optional
If true compute immediately, return
dask.delayed.Delayed
otherwise return_stored: boolean, optional
Optionally return the stored result (default False).
Examples
>>> x = ... # doctest: +SKIP
>>> import h5py # doctest: +SKIP >>> f = h5py.File('myfile.hdf5') # doctest: +SKIP >>> dset = f.create_dataset('/data', shape=x.shape, ... chunks=x.chunks, ... dtype='f8') # doctest: +SKIP
>>> store(x, dset) # doctest: +SKIP
Alternatively store many arrays at the same time
>>> store([x, y, z], [dset1, dset2, dset3]) # doctest: +SKIP

dask.array.
coarsen
(reduction, x, axes, trim_excess=False)¶ Coarsen array by applying reduction to fixed size neighborhoods
Parameters:  reduction: function
Function like np.sum, np.mean, etc…
 x: np.ndarray
Array to be coarsened
 axes: dict
Mapping of axis to coarsening factor
Examples
>>> x = np.array([1, 2, 3, 4, 5, 6]) >>> coarsen(np.sum, x, {0: 2}) array([ 3, 7, 11]) >>> coarsen(np.max, x, {0: 3}) array([3, 6])
Provide dictionary of scale per dimension
>>> x = np.arange(24).reshape((4, 6)) >>> x array([[ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23]])
>>> coarsen(np.min, x, {0: 2, 1: 3}) array([[ 0, 3], [12, 15]])
You must avoid excess elements explicitly
>>> x = np.array([1, 2, 3, 4, 5, 6, 7, 8]) >>> coarsen(np.min, x, {0: 3}, trim_excess=True) array([1, 4])

dask.array.
stack
(seq, axis=0)¶ Stack arrays along a new axis
Given a sequence of dask arrays, form a new dask array by stacking them along a new dimension (axis=0 by default)
See also
Examples
Create slices
>>> import dask.array as da >>> import numpy as np
>>> data = [from_array(np.ones((4, 4)), chunks=(2, 2)) ... for i in range(3)]
>>> x = da.stack(data, axis=0) >>> x.shape (3, 4, 4)
>>> da.stack(data, axis=1).shape (4, 3, 4)
>>> da.stack(data, axis=1).shape (4, 4, 3)
Result is a new dask Array

dask.array.
concatenate
(seq, axis=0, allow_unknown_chunksizes=False)¶ Concatenate arrays along an existing axis
Given a sequence of dask Arrays form a new dask Array by stacking them along an existing dimension (axis=0 by default)
Parameters:  seq: list of dask.arrays
 axis: int
Dimension along which to align all of the arrays
 allow_unknown_chunksizes: bool
Allow unknown chunksizes, such as come from converting from dask dataframes. Dask.array is unable to verify that chunks line up. If data comes from differently aligned sources then this can cause unexpected results.
See also
Examples
Create slices
>>> import dask.array as da >>> import numpy as np
>>> data = [from_array(np.ones((4, 4)), chunks=(2, 2)) ... for i in range(3)]
>>> x = da.concatenate(data, axis=0) >>> x.shape (12, 4)
>>> da.concatenate(data, axis=1).shape (4, 12)
Result is a new dask Array

dask.array.
all
(a, axis=None, out=None, keepdims=<no value>)¶ Test whether all array elements along a given axis evaluate to True.
Parameters:  a : array_like
Input array or object that can be converted to an array.
 axis : None or int or tuple of ints, optional
Axis or axes along which a logical AND reduction is performed. The default (axis = None) is to perform a logical AND over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis.
New in version 1.7.0.
If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before.
 out : ndarray, optional
Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if
dtype(out)
is float, the result will consist of 0.0’s and 1.0’s). See doc.ufuncs (Section “Output arguments”) for more details. keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.
If the default value is passed, then keepdims will not be passed through to the all method of subclasses of ndarray, however any nondefault value will be. If the subclass’ method does not implement keepdims any exceptions will be raised.
Returns:  all : ndarray, bool
A new boolean or array is returned unless out is specified, in which case a reference to out is returned.
See also
ndarray.all
 equivalent method
any
 Test whether any element along a given axis evaluates to True.
Notes
Not a Number (NaN), positive infinity and negative infinity evaluate to True because these are not equal to zero.
Examples
>>> np.all([[True,False],[True,True]]) False
>>> np.all([[True,False],[True,True]], axis=0) array([ True, False])
>>> np.all([1, 4, 5]) True
>>> np.all([1.0, np.nan]) True
>>> o=np.array([False]) >>> z=np.all([1, 4, 5], out=o) >>> id(z), id(o), z # doctest: +SKIP (28293632, 28293632, array([ True]))

dask.array.
allclose
(a, b, rtol=1e05, atol=1e08, equal_nan=False)¶ Returns True if two arrays are elementwise equal within a tolerance.
The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.
If either array contains one or more NaNs, False is returned. Infs are treated as equal if they are in the same place and of the same sign in both arrays.
Parameters:  a, b : array_like
Input arrays to compare.
 rtol : float
The relative tolerance parameter (see Notes).
 atol : float
The absolute tolerance parameter (see Notes).
 equal_nan : bool
Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.
New in version 1.10.0.
Returns:  allclose : bool
Returns True if the two arrays are equal within the given tolerance; False otherwise.
Notes
If the following equation is elementwise True, then allclose returns True.
absolute(a  b) <= (atol + rtol * absolute(b))The above equation is not symmetric in a and b, so that
allclose(a, b)
might be different fromallclose(b, a)
in some rare cases.The comparison of a and b uses standard broadcasting, which means that a and b need not have the same shape in order for
allclose(a, b)
to evaluate to True. The same is true for equal but not array_equal.Examples
>>> np.allclose([1e10,1e7], [1.00001e10,1e8]) False >>> np.allclose([1e10,1e8], [1.00001e10,1e9]) True >>> np.allclose([1e10,1e8], [1.0001e10,1e9]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) True

dask.array.
angle
(x, deg=0)¶ Return the angle of the complex argument.
Parameters:  z : array_like
A complex number or sequence of complex numbers.
 deg : bool, optional
Return angle in degrees if True, radians if False (default).
Returns:  angle : ndarray or scalar
The counterclockwise angle from the positive real axis on the complex plane, with dtype as numpy.float64.
 ..versionchanged:: 1.16.0
This function works on subclasses of ndarray like ma.array.
See also
arctan2
,absolute
Examples
>>> np.angle([1.0, 1.0j, 1+1j]) # in radians # doctest: +SKIP array([ 0. , 1.57079633, 0.78539816]) >>> np.angle(1+1j, deg=True) # in degrees # doctest: +SKIP 45.0

dask.array.
any
(a, axis=None, out=None, keepdims=<no value>)¶ Test whether any array element along a given axis evaluates to True.
Returns single boolean unless axis is not
None
Parameters:  a : array_like
Input array or object that can be converted to an array.
 axis : None or int or tuple of ints, optional
Axis or axes along which a logical OR reduction is performed. The default (axis = None) is to perform a logical OR over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis.
New in version 1.7.0.
If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before.
 out : ndarray, optional
Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if it is of type float, then it will remain so, returning 1.0 for True and 0.0 for False, regardless of the type of a). See doc.ufuncs (Section “Output arguments”) for details.
 keepdims : bool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.
If the default value is passed, then keepdims will not be passed through to the any method of subclasses of ndarray, however any nondefault value will be. If the subclass’ method does not implement keepdims any exceptions will be raised.
Returns:  any : bool or ndarray
A new boolean or ndarray is returned unless out is specified, in which case a reference to out is returned.
See also
ndarray.any
 equivalent method
all
 Test whether all elements along a given axis evaluate to True.
Notes
Not a Number (NaN), positive infinity and negative infinity evaluate to True because these are not equal to zero.
Examples
>>> np.any([[True, False], [True, True]]) True
>>> np.any([[True, False], [False, False]], axis=0) array([ True, False])
>>> np.any([1, 0, 5]) True
>>> np.any(np.nan) True
>>> o=np.array([False]) >>> z=np.any([1, 4, 5], out=o) >>> z, o (array([ True]), array([ True])) >>> # Check now that z is a reference to o >>> z is o True >>> id(z), id(o) # identity of z and o # doctest: +SKIP (191614240, 191614240)

dask.array.
apply_along_axis
(func1d, axis, arr, *args, **kwargs)¶ Apply a function to 1D slices along the given axis.
Execute func1d(a, *args) where func1d operates on 1D arrays and a is a 1D slice of arr along axis.
This is equivalent to (but faster than) the following use of ndindex and s_, which sets each of
ii
,jj
, andkk
to a tuple of indices:Ni, Nk = a.shape[:axis], a.shape[axis+1:] for ii in ndindex(Ni): for kk in ndindex(Nk): f = func1d(arr[ii + s_[:,] + kk]) Nj = f.shape for jj in ndindex(Nj): out[ii + jj + kk] = f[jj]
Equivalently, eliminating the inner loop, this can be expressed as:
Ni, Nk = a.shape[:axis], a.shape[axis+1:] for ii in ndindex(Ni): for kk in ndindex(Nk): out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])
Parameters:  func1d : function (M,) > (Nj…)
This function should accept 1D arrays. It is applied to 1D slices of arr along the specified axis.
 axis : integer
Axis along which arr is sliced.
 arr : ndarray (Ni…, M, Nk…)
Input array.
 args : any
Additional arguments to func1d.
 kwargs : any
Additional named arguments to func1d.
New in version 1.9.0.
Returns:  out : ndarray (Ni…, Nj…, Nk…)
The output array. The shape of out is identical to the shape of arr, except along the axis dimension. This axis is removed, and replaced with new dimensions equal to the shape of the return value of func1d. So if func1d returns a scalar out will have one fewer dimensions than arr.
See also
apply_over_axes
 Apply a function repeatedly over multiple axes.
Examples
>>> def my_func(a): ... """Average first and last element of a 1D array""" ... return (a[0] + a[1]) * 0.5 >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) >>> np.apply_along_axis(my_func, 0, b) array([ 4., 5., 6.]) >>> np.apply_along_axis(my_func, 1, b) array([ 2., 5., 8.])
For a function that returns a 1D array, the number of dimensions in outarr is the same as arr.
>>> b = np.array([[8,1,7], [4,3,9], [5,2,6]]) >>> np.apply_along_axis(sorted, 1, b) array([[1, 7, 8], [3, 4, 9], [2, 5, 6]])
For a function that returns a higher dimensional array, those dimensions are inserted in place of the axis dimension.
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) >>> np.apply_along_axis(np.diag, 1, b) array([[[1, 0, 0], [0, 2, 0], [0, 0, 3]], [[4, 0, 0], [0, 5, 0], [0, 0, 6]], [[7, 0, 0], [0, 8, 0], [0, 0, 9]]])

dask.array.
apply_over_axes
(func, a, axes)¶ Apply a function repeatedly over multiple axes.
func is called as res = func(a, axis), where axis is the first element of axes. The result res of the function call must have either the same dimensions as a or one less dimension. If res has one less dimension than a, a dimension is inserted before axis. The call to func is then repeated for each axis in axes, with res as the first argument.
Parameters:  func : function
This function must take two arguments, func(a, axis).
 a : array_like
Input array.
 axes : array_like
Axes over which func is applied; the elements must be integers.
Returns:  apply_over_axis : ndarray
The output array. The number of dimensions is the same as a, but the shape can be different. This depends on whether func changes the shape of its output with respect to its input.
See also
apply_along_axis
 Apply a function to 1D slices of an array along the given axis.
Notes
This function is equivalent to tuple axis arguments to reorderable ufuncs with keepdims=True. Tuple axis arguments to ufuncs have been available since version 1.7.0.
Examples
>>> a = np.arange(24).reshape(2,3,4) >>> a array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]])
Sum over axes 0 and 2. The result has same number of dimensions as the original array:
>>> np.apply_over_axes(np.sum, a, [0,2]) array([[[ 60], [ 92], [124]]])
Tuple axis arguments to ufuncs are equivalent:
>>> np.sum(a, axis=(0,2), keepdims=True) array([[[ 60], [ 92], [124]]])

dask.array.
arange
(*args, **kwargs)¶ Return evenly spaced values from start to stop with step size step.
The values are halfopen [start, stop), so including start and excluding stop. This is basically the same as python’s range function but for dask arrays.
When using a noninteger step, such as 0.1, the results will often not be consistent. It is better to use linspace for these cases.
Parameters:  start : int, optional
The starting value of the sequence. The default is 0.
 stop : int
The end of the interval, this value is excluded from the interval.
 step : int, optional
The spacing between the values. The default is 1 when not specified. The last value of the sequence.
 chunks : int
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
. dtype : numpy.dtype
Output dtype. Omit to infer it from start, stop, step
Returns:  samples : dask array
See also

dask.array.
arccos
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Trigonometric inverse cosine, elementwise.
The inverse of cos so that, if
y = cos(x)
, thenx = arccos(y)
.Parameters:  x : array_like
xcoordinate on the unit circle. For real arguments, the domain is [1, 1].
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  angle : ndarray
The angle of the ray intersecting the unit circle at the given xcoordinate in radians [0, pi]. This is a scalar if x is a scalar.
Notes
arccos is a multivalued function: for each x there are infinitely many numbers z such that cos(z) = x. The convention is to return the angle z whose real part lies in [0, pi].
For realvalued input data types, arccos always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arccos is a complex analytic function that has branch cuts [inf, 1] and [1, inf] and is continuous from above on the former and from below on the latter.
The inverse cos is also known as acos or cos^1.
References
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/
Examples
We expect the arccos of 1 to be 0, and of 1 to be pi:
>>> np.arccos([1, 1]) # doctest: +SKIP array([ 0. , 3.14159265])
Plot arccos:
>>> import matplotlib.pyplot as plt # doctest: +SKIP >>> x = np.linspace(1, 1, num=100) # doctest: +SKIP >>> plt.plot(x, np.arccos(x)) # doctest: +SKIP >>> plt.axis('tight') # doctest: +SKIP >>> plt.show() # doctest: +SKIP

dask.array.
arccosh
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Inverse hyperbolic cosine, elementwise.
Parameters:  x : array_like
Input array.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  arccosh : ndarray
Array of the same shape as x. This is a scalar if x is a scalar.
Notes
arccosh is a multivalued function: for each x there are infinitely many numbers z such that cosh(z) = x. The convention is to return the z whose imaginary part lies in [pi, pi] and the real part in
[0, inf]
.For realvalued input data types, arccosh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arccosh is a complex analytical function that has a branch cut [inf, 1] and is continuous from above on it.
References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arccosh Examples
>>> np.arccosh([np.e, 10.0]) # doctest: +SKIP array([ 1.65745445, 2.99322285]) >>> np.arccosh(1) # doctest: +SKIP 0.0

dask.array.
arcsin
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Inverse sine, elementwise.
Parameters:  x : array_like
ycoordinate on the unit circle.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  angle : ndarray
The inverse sine of each element in x, in radians and in the closed interval
[pi/2, pi/2]
. This is a scalar if x is a scalar.
Notes
arcsin is a multivalued function: for each x there are infinitely many numbers z such that \(sin(z) = x\). The convention is to return the angle z whose real part lies in [pi/2, pi/2].
For realvalued input data types, arcsin always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arcsin is a complex analytic function that has, by convention, the branch cuts [inf, 1] and [1, inf] and is continuous from above on the former and from below on the latter.
The inverse sine is also known as asin or sin^{1}.
References
Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79ff. http://www.math.sfu.ca/~cbm/aands/
Examples
>>> np.arcsin(1) # pi/2 # doctest: +SKIP 1.5707963267948966 >>> np.arcsin(1) # pi/2 # doctest: +SKIP 1.5707963267948966 >>> np.arcsin(0) # doctest: +SKIP 0.0

dask.array.
arcsinh
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Inverse hyperbolic sine elementwise.
Parameters:  x : array_like
Input array.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Array of the same shape as x. This is a scalar if x is a scalar.
Notes
arcsinh is a multivalued function: for each x there are infinitely many numbers z such that sinh(z) = x. The convention is to return the z whose imaginary part lies in [pi/2, pi/2].
For realvalued input data types, arcsinh always returns real output. For each value that cannot be expressed as a real number or infinity, it returns
nan
and sets the invalid floating point error flag.For complexvalued input, arccos is a complex analytical function that has branch cuts [1j, infj] and [1j, infj] and is continuous from the right on the former and from the left on the latter.
The inverse hyperbolic sine is also known as asinh or
sinh^1
.References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arcsinh Examples
>>> np.arcsinh(np.array([np.e, 10.0])) # doctest: +SKIP array([ 1.72538256, 2.99822295])

dask.array.
arctan
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Trigonometric inverse tangent, elementwise.
The inverse of tan, so that if
y = tan(x)
thenx = arctan(y)
.Parameters:  x : array_like
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Out has the same shape as x. Its real part is in
[pi/2, pi/2]
(arctan(+/inf)
returns+/pi/2
). This is a scalar if x is a scalar.
See also
Notes
arctan is a multivalued function: for each x there are infinitely many numbers z such that tan(z) = x. The convention is to return the angle z whose real part lies in [pi/2, pi/2].
For realvalued input data types, arctan always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arctan is a complex analytic function that has [1j, infj] and [1j, infj] as branch cuts, and is continuous from the left on the former and from the right on the latter.
The inverse tangent is also known as atan or tan^{1}.
References
Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/
Examples
We expect the arctan of 0 to be 0, and of 1 to be pi/4:
>>> np.arctan([0, 1]) # doctest: +SKIP array([ 0. , 0.78539816])
>>> np.pi/4 # doctest: +SKIP 0.78539816339744828
Plot arctan:
>>> import matplotlib.pyplot as plt # doctest: +SKIP >>> x = np.linspace(10, 10) # doctest: +SKIP >>> plt.plot(x, np.arctan(x)) # doctest: +SKIP >>> plt.axis('tight') # doctest: +SKIP >>> plt.show() # doctest: +SKIP

dask.array.
arctan2
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Elementwise arc tangent of
x1/x2
choosing the quadrant correctly.The quadrant (i.e., branch) is chosen so that
arctan2(x1, x2)
is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (x2, x1). (Note the role reversal: the “ycoordinate” is the first function parameter, the “xcoordinate” is the second.) By IEEE convention, this function is defined for x2 = +/0 and for either or both of x1 and x2 = +/inf (see Notes for specific values).This function is not defined for complexvalued arguments; for the socalled argument of complex values, use angle.
Parameters:  x1 : array_like, realvalued
ycoordinates.
 x2 : array_like, realvalued
xcoordinates. x2 must be broadcastable to match the shape of x1 or vice versa.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  angle : ndarray
Array of angles in radians, in the range
[pi, pi]
. This is a scalar if both x1 and x2 are scalars.
Notes
arctan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard: [1]
x1 x2 arctan2(x1,x2) +/ 0 +0 +/ 0 +/ 0 0 +/ pi > 0 +/inf +0 / +pi < 0 +/inf 0 / pi +/inf +inf +/ (pi/4) +/inf inf +/ (3*pi/4) Note that +0 and 0 are distinct floating point numbers, as are +inf and inf.
References
[1] (1, 2) ISO/IEC standard 9899:1999, “Programming language C.” Examples
Consider four points in different quadrants:
>>> x = np.array([1, +1, +1, 1]) # doctest: +SKIP >>> y = np.array([1, 1, +1, +1]) # doctest: +SKIP >>> np.arctan2(y, x) * 180 / np.pi # doctest: +SKIP array([135., 45., 45., 135.])
Note the order of the parameters. arctan2 is defined also when x2 = 0 and at several other special points, obtaining values in the range
[pi, pi]
:>>> np.arctan2([1., 1.], [0., 0.]) # doctest: +SKIP array([ 1.57079633, 1.57079633]) >>> np.arctan2([0., 0., np.inf], [+0., 0., np.inf]) # doctest: +SKIP array([ 0. , 3.14159265, 0.78539816])

dask.array.
arctanh
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Inverse hyperbolic tangent elementwise.
Parameters:  x : array_like
Input array.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Array of the same shape as x. This is a scalar if x is a scalar.
See also
emath.arctanh
Notes
arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [pi/2, pi/2].
For realvalued input data types, arctanh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, arctanh is a complex analytical function that has branch cuts [1, inf] and [1, inf] and is continuous from above on the former and from below on the latter.
The inverse hyperbolic tangent is also known as atanh or
tanh^1
.References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arctanh Examples
>>> np.arctanh([0, 0.5]) # doctest: +SKIP array([ 0. , 0.54930614])

dask.array.
argmax
(a, axis=None, out=None)¶ Returns the indices of the maximum values along an axis.
Parameters:  a : array_like
Input array.
 axis : int, optional
By default, the index is into the flattened array, otherwise along the specified axis.
 out : array, optional
If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.
Returns:  index_array : ndarray of ints
Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed.
See also
ndarray.argmax
,argmin
amax
 The maximum value along a given axis.
unravel_index
 Convert a flat index into an index tuple.
Notes
In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned.
Examples
>>> a = np.arange(6).reshape(2,3) + 10 >>> a array([[10, 11, 12], [13, 14, 15]]) >>> np.argmax(a) 5 >>> np.argmax(a, axis=0) array([1, 1, 1]) >>> np.argmax(a, axis=1) array([2, 2])
Indexes of the maximal elements of a Ndimensional array:
>>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape) >>> ind (1, 2) >>> a[ind] 15
>>> b = np.arange(6) >>> b[1] = 5 >>> b array([0, 5, 2, 3, 4, 5]) >>> np.argmax(b) # Only the first occurrence is returned. 1

dask.array.
argmin
(a, axis=None, out=None)¶ Returns the indices of the minimum values along an axis.
Parameters:  a : array_like
Input array.
 axis : int, optional
By default, the index is into the flattened array, otherwise along the specified axis.
 out : array, optional
If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.
Returns:  index_array : ndarray of ints
Array of indices into the array. It has the same shape as a.shape with the dimension along axis removed.
See also
ndarray.argmin
,argmax
amin
 The minimum value along a given axis.
unravel_index
 Convert a flat index into an index tuple.
Notes
In case of multiple occurrences of the minimum values, the indices corresponding to the first occurrence are returned.
Examples
>>> a = np.arange(6).reshape(2,3) + 10 >>> a array([[10, 11, 12], [13, 14, 15]]) >>> np.argmin(a) 0 >>> np.argmin(a, axis=0) array([0, 0, 0]) >>> np.argmin(a, axis=1) array([0, 0])
Indices of the minimum elements of a Ndimensional array:
>>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape) >>> ind (0, 0) >>> a[ind] 10
>>> b = np.arange(6) + 10 >>> b[4] = 10 >>> b array([10, 11, 12, 13, 10, 15]) >>> np.argmin(b) # Only the first occurrence is returned. 0

dask.array.
argtopk
(a, k, axis=1, split_every=None)¶ Extract the indices of the k largest elements from a on the given axis, and return them sorted from largest to smallest. If k is negative, extract the indices of the k smallest elements instead, and return them sorted from smallest to largest.
This performs best when
k
is much smaller than the chunk size. All results will be returned in a single chunk along the given axis.Parameters:  x: Array
Data being sorted
 k: int
 axis: int, optional
 split_every: int >=2, optional
See
topk()
. The performance considerations for topk also apply here.
Returns:  Selection of np.intp indices of x with size abs(k) along the given axis.
Examples
>>> import dask.array as da >>> x = np.array([5, 1, 3, 6]) >>> d = da.from_array(x, chunks=2) >>> d.argtopk(2).compute() array([3, 0]) >>> d.argtopk(2).compute() array([1, 2])

dask.array.
argwhere
(a)¶ Find the indices of array elements that are nonzero, grouped by element.
Parameters:  a : array_like
Input data.
Returns:  index_array : ndarray
Indices of elements that are nonzero. Indices are grouped by element.
Notes
np.argwhere(a)
is the same asnp.transpose(np.nonzero(a))
.The output of
argwhere
is not suitable for indexing arrays. For this purpose usenonzero(a)
instead.Examples
>>> x = np.arange(6).reshape(2,3) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.argwhere(x>1) array([[0, 2], [1, 0], [1, 1], [1, 2]])

dask.array.
around
(a, decimals=0, out=None)¶ Evenly round to the given number of decimals.
Parameters:  a : array_like
Input data.
 decimals : int, optional
Number of decimal places to round to (default: 0). If decimals is negative, it specifies the number of positions to the left of the decimal point.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. See doc.ufuncs (Section “Output arguments”) for details.
Returns:  rounded_array : ndarray
An array of the same type as a, containing the rounded values. Unless out was specified, a new array is created. A reference to the result is returned.
The real and imaginary parts of complex numbers are rounded separately. The result of rounding a float is a float.
Notes
For values exactly halfway between rounded decimal values, NumPy rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, 0.5 and 0.5 round to 0.0, etc. Results may also be surprising due to the inexact representation of decimal fractions in the IEEE floating point standard [1] and errors introduced when scaling by powers of ten.
References
[1] (1, 2) “Lecture Notes on the Status of IEEE 754”, William Kahan, https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF [2] “How Futile are Mindless Assessments of Roundoff in FloatingPoint Computation?”, William Kahan, https://people.eecs.berkeley.edu/~wkahan/Mindless.pdf Examples
>>> np.around([0.37, 1.64]) array([ 0., 2.]) >>> np.around([0.37, 1.64], decimals=1) array([ 0.4, 1.6]) >>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value array([ 0., 2., 2., 4., 4.]) >>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned array([ 1, 2, 3, 11]) >>> np.around([1,2,3,11], decimals=1) array([ 0, 0, 0, 10])

dask.array.
array
(object, dtype=None, copy=True, order='K', subok=False, ndmin=0)¶ Create an array.
Parameters:  object : array_like
An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence.
 dtype : datatype, optional
The desired datatype for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence. This argument can only be used to ‘upcast’ the array. For downcasting, use the .astype(t) method.
 copy : bool, optional
If true (default), then the object is copied. Otherwise, a copy will only be made if __array__ returns a copy, if obj is a nested sequence, or if a copy is needed to satisfy any of the other requirements (dtype, order, etc.).
 order : {‘K’, ‘A’, ‘C’, ‘F’}, optional
Specify the memory layout of the array. If object is not an array, the newly created array will be in C order (row major) unless ‘F’ is specified, in which case it will be in Fortran order (column major). If object is an array the following holds.
order no copy copy=True ‘K’ unchanged F & C order preserved, otherwise most similar order ‘A’ unchanged F order if input is F and not C, otherwise C order ‘C’ C order C order ‘F’ F order F order When
copy=False
and a copy is made for other reasons, the result is the same as ifcopy=True
, with some exceptions for A, see the Notes section. The default order is ‘K’. subok : bool, optional
If True, then subclasses will be passedthrough, otherwise the returned array will be forced to be a baseclass array (default).
 ndmin : int, optional
Specifies the minimum number of dimensions that the resulting array should have. Ones will be prepended to the shape as needed to meet this requirement.
Returns:  out : ndarray
An array object satisfying the specified requirements.
See also
empty_like
 Return an empty array with shape and type of input.
ones_like
 Return an array of ones with shape and type of input.
zeros_like
 Return an array of zeros with shape and type of input.
full_like
 Return a new array with shape of input filled with value.
empty
 Return a new uninitialized array.
ones
 Return a new array setting values to one.
zeros
 Return a new array setting values to zero.
full
 Return a new array of given shape filled with value.
Notes
When order is ‘A’ and object is an array in neither ‘C’ nor ‘F’ order, and a copy is forced by a change in dtype, then the order of the result is not necessarily ‘C’ as expected. This is likely a bug.
Examples
>>> np.array([1, 2, 3]) array([1, 2, 3])
Upcasting:
>>> np.array([1, 2, 3.0]) array([ 1., 2., 3.])
More than one dimension:
>>> np.array([[1, 2], [3, 4]]) array([[1, 2], [3, 4]])
Minimum dimensions 2:
>>> np.array([1, 2, 3], ndmin=2) array([[1, 2, 3]])
Type provided:
>>> np.array([1, 2, 3], dtype=complex) array([ 1.+0.j, 2.+0.j, 3.+0.j])
Datatype consisting of more than one element:
>>> x = np.array([(1,2),(3,4)],dtype=[('a','<i4'),('b','<i4')]) >>> x['a'] array([1, 3])
Creating an array from subclasses:
>>> np.array(np.mat('1 2; 3 4')) array([[1, 2], [3, 4]])
>>> np.array(np.mat('1 2; 3 4'), subok=True) matrix([[1, 2], [3, 4]])

dask.array.
asanyarray
(a)¶ Convert the input to a dask array.
Subclasses of
np.ndarray
will be passed through as chunks unchanged.Parameters:  a : arraylike
Input data, in any form that can be converted to a dask array.
Returns:  out : dask array
Dask array interpretation of a.
Examples
>>> import dask.array as da >>> import numpy as np >>> x = np.arange(3) >>> da.asanyarray(x) dask.array<array, shape=(3,), dtype=int64, chunksize=(3,)>
>>> y = [[1, 2, 3], [4, 5, 6]] >>> da.asanyarray(y) dask.array<array, shape=(2, 3), dtype=int64, chunksize=(2, 3)>

dask.array.
asarray
(a, **kwargs)¶ Convert the input to a dask array.
Parameters:  a : arraylike
Input data, in any form that can be converted to a dask array.
Returns:  out : dask array
Dask array interpretation of a.
Examples
>>> import dask.array as da >>> import numpy as np >>> x = np.arange(3) >>> da.asarray(x) dask.array<array, shape=(3,), dtype=int64, chunksize=(3,)>
>>> y = [[1, 2, 3], [4, 5, 6]] >>> da.asarray(y) dask.array<array, shape=(2, 3), dtype=int64, chunksize=(2, 3)>

dask.array.
atleast_1d
(*arys)¶ Convert inputs to arrays with at least one dimension.
Scalar inputs are converted to 1dimensional arrays, whilst higherdimensional inputs are preserved.
Parameters:  arys1, arys2, … : array_like
One or more input arrays.
Returns:  ret : ndarray
An array, or list of arrays, each with
a.ndim >= 1
. Copies are made only if necessary.
See also
Examples
>>> np.atleast_1d(1.0) array([ 1.])
>>> x = np.arange(9.0).reshape(3,3) >>> np.atleast_1d(x) array([[ 0., 1., 2.], [ 3., 4., 5.], [ 6., 7., 8.]]) >>> np.atleast_1d(x) is x True
>>> np.atleast_1d(1, [3, 4]) [array([1]), array([3, 4])]

dask.array.
atleast_2d
(*arys)¶ View inputs as arrays with at least two dimensions.
Parameters:  arys1, arys2, … : array_like
One or more arraylike sequences. Nonarray inputs are converted to arrays. Arrays that already have two or more dimensions are preserved.
Returns:  res, res2, … : ndarray
An array, or list of arrays, each with
a.ndim >= 2
. Copies are avoided where possible, and views with two or more dimensions are returned.
See also
Examples
>>> np.atleast_2d(3.0) array([[ 3.]])
>>> x = np.arange(3.0) >>> np.atleast_2d(x) array([[ 0., 1., 2.]]) >>> np.atleast_2d(x).base is x True
>>> np.atleast_2d(1, [1, 2], [[1, 2]]) [array([[1]]), array([[1, 2]]), array([[1, 2]])]

dask.array.
atleast_3d
(*arys)¶ View inputs as arrays with at least three dimensions.
Parameters:  arys1, arys2, … : array_like
One or more arraylike sequences. Nonarray inputs are converted to arrays. Arrays that already have three or more dimensions are preserved.
Returns:  res1, res2, … : ndarray
An array, or list of arrays, each with
a.ndim >= 3
. Copies are avoided where possible, and views with three or more dimensions are returned. For example, a 1D array of shape(N,)
becomes a view of shape(1, N, 1)
, and a 2D array of shape(M, N)
becomes a view of shape(M, N, 1)
.
See also
Examples
>>> np.atleast_3d(3.0) array([[[ 3.]]])
>>> x = np.arange(3.0) >>> np.atleast_3d(x).shape (1, 3, 1)
>>> x = np.arange(12.0).reshape(4,3) >>> np.atleast_3d(x).shape (4, 3, 1) >>> np.atleast_3d(x).base is x.base # x is a reshape, so not base itself True
>>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]): ... print(arr, arr.shape) ... [[[1] [2]]] (1, 2, 1) [[[1] [2]]] (1, 2, 1) [[[1 2]]] (1, 1, 2)

dask.array.
average
(a, axis=None, weights=None, returned=False)¶ Compute the weighted average along the specified axis.
Parameters:  a : array_like
Array containing data to be averaged. If a is not an array, a conversion is attempted.
 axis : None or int or tuple of ints, optional
Axis or axes along which to average a. The default, axis=None, will average over all of the elements of the input array. If axis is negative it counts from the last to the first axis.
New in version 1.7.0.
If axis is a tuple of ints, averaging is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before.
 weights : array_like, optional
An array of weights associated with the values in a. Each value in a contributes to the average according to its associated weight. The weights array can either be 1D (in which case its length must be the size of a along the given axis) or of the same shape as a. If weights=None, then all data in a are assumed to have a weight equal to one.
 returned : bool, optional
Default is False. If True, the tuple (average, sum_of_weights) is returned, otherwise only the average is returned. If weights=None, sum_of_weights is equivalent to the number of elements over which the average is taken.
Returns:  retval, [sum_of_weights] : array_type or double
Return the average along the specified axis. When returned is True, return a tuple with the average as the first element and the sum of the weights as the second element. sum_of_weights is of the same type as retval. The result dtype follows a genereal pattern. If weights is None, the result dtype will be that of a , or
float64
if a is integral. Otherwise, if weights is not None and a is non integral, the result type will be the type of lowest precision capable of representing values of both a and weights. If a happens to be integral, the previous rules still applies but the result dtype will at least befloat64
.
Raises:  ZeroDivisionError
When all weights along axis are zero. See numpy.ma.average for a version robust to this type of error.
 TypeError
When the length of 1D weights is not the same as the shape of a along axis.
See also
ma.average
 average for masked arrays – useful if your data contains “missing” values
numpy.result_type
 Returns the type that results from applying the numpy type promotion rules to the arguments.
Examples
>>> data = range(1,5) >>> data [1, 2, 3, 4] >>> np.average(data) 2.5 >>> np.average(range(1,11), weights=range(10,0,1)) 4.0
>>> data = np.arange(6).reshape((3,2)) >>> data array([[0, 1], [2, 3], [4, 5]]) >>> np.average(data, axis=1, weights=[1./4, 3./4]) array([ 0.75, 2.75, 4.75]) >>> np.average(data, weights=[1./4, 3./4])
Traceback (most recent call last): … TypeError: Axis must be specified when shapes of a and weights differ.
>>> a = np.ones(5, dtype=np.float128) >>> w = np.ones(5, dtype=np.complex64) >>> avg = np.average(a, weights=w) >>> print(avg.dtype) complex256

dask.array.
bincount
(x, weights=None, minlength=0)¶ Count number of occurrences of each value in array of nonnegative ints.
The number of bins (of size 1) is one larger than the largest value in x. If minlength is specified, there will be at least this number of bins in the output array (though it will be longer if necessary, depending on the contents of x). Each bin gives the number of occurrences of its index value in x. If weights is specified the input array is weighted by it, i.e. if a value
n
is found at positioni
,out[n] += weight[i]
instead ofout[n] += 1
.Parameters:  x : array_like, 1 dimension, nonnegative ints
Input array.
 weights : array_like, optional
Weights, array of the same shape as x.
 minlength : int, optional
A minimum number of bins for the output array.
New in version 1.6.0.
Returns:  out : ndarray of ints
The result of binning the input array. The length of out is equal to
np.amax(x)+1
.
Raises:  ValueError
If the input is not 1dimensional, or contains elements with negative values, or if minlength is negative.
 TypeError
If the type of the input is float or complex.
Examples
>>> np.bincount(np.arange(5)) array([1, 1, 1, 1, 1]) >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7])) array([1, 3, 1, 1, 0, 0, 0, 1])
>>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23]) >>> np.bincount(x).size == np.amax(x)+1 True
The input array needs to be of integer dtype, otherwise a TypeError is raised:
>>> np.bincount(np.arange(5, dtype=float)) Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: array cannot be safely cast to required type
A possible use of
bincount
is to perform sums over variablesize chunks of an array, using theweights
keyword.>>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., 0.6]) # weights >>> x = np.array([0, 1, 1, 2, 2, 2]) >>> np.bincount(x, weights=w) array([ 0.3, 0.7, 1.1])

dask.array.
bitwise_and
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute the bitwise AND of two arrays elementwise.
Computes the bitwise AND of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator
&
.Parameters:  x1, x2 : array_like
Only integer and boolean types are handled.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Result. This is a scalar if both x1 and x2 are scalars.
See also
logical_and
,bitwise_or
,bitwise_xor
binary_repr
 Return the binary representation of the input number as a string.
Examples
The number 13 is represented by
00001101
. Likewise, 17 is represented by00010001
. The bitwise AND of 13 and 17 is therefore000000001
, or 1:>>> np.bitwise_and(13, 17) # doctest: +SKIP 1
>>> np.bitwise_and(14, 13) # doctest: +SKIP 12 >>> np.binary_repr(12) # doctest: +SKIP '1100' >>> np.bitwise_and([14,3], 13) # doctest: +SKIP array([12, 1])
>>> np.bitwise_and([11,7], [4,25]) # doctest: +SKIP array([0, 1]) >>> np.bitwise_and(np.array([2,5,255]), np.array([3,14,16])) # doctest: +SKIP array([ 2, 4, 16]) >>> np.bitwise_and([True, True], [False, True]) # doctest: +SKIP array([False, True])

dask.array.
bitwise_not
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute bitwise inversion, or bitwise NOT, elementwise.
Computes the bitwise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator
~
.For signed integer inputs, the two’s complement is returned. In a two’scomplement system negative numbers are represented by the two’s complement of the absolute value. This is the most common method of representing signed integers on computers [1]. A Nbit two’scomplement system can represent every integer in the range \(2^{N1}\) to \(+2^{N1}1\).
Parameters:  x : array_like
Only integer and boolean types are handled.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Result. This is a scalar if x is a scalar.
See also
bitwise_and
,bitwise_or
,bitwise_xor
,logical_not
binary_repr
 Return the binary representation of the input number as a string.
Notes
bitwise_not is an alias for invert:
>>> np.bitwise_not is np.invert # doctest: +SKIP True
References
[1] (1, 2) Wikipedia, “Two’s complement”, https://en.wikipedia.org/wiki/Two’s_complement Examples
We’ve seen that 13 is represented by
00001101
. The invert or bitwise NOT of 13 is then:>>> np.invert(np.array([13], dtype=uint8)) # doctest: +SKIP array([242], dtype=uint8) >>> np.binary_repr(x, width=8) # doctest: +SKIP '00001101' >>> np.binary_repr(242, width=8) # doctest: +SKIP '11110010'
The result depends on the bitwidth:
>>> np.invert(np.array([13], dtype=uint16)) # doctest: +SKIP array([65522], dtype=uint16) >>> np.binary_repr(x, width=16) # doctest: +SKIP '0000000000001101' >>> np.binary_repr(65522, width=16) # doctest: +SKIP '1111111111110010'
When using signed integer types the result is the two’s complement of the result for the unsigned type:
>>> np.invert(np.array([13], dtype=int8)) # doctest: +SKIP array([14], dtype=int8) >>> np.binary_repr(14, width=8) # doctest: +SKIP '11110010'
Booleans are accepted as well:
>>> np.invert(array([True, False])) # doctest: +SKIP array([False, True])

dask.array.
bitwise_or
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute the bitwise OR of two arrays elementwise.
Computes the bitwise OR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator

.Parameters:  x1, x2 : array_like
Only integer and boolean types are handled.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Result. This is a scalar if both x1 and x2 are scalars.
See also
logical_or
,bitwise_and
,bitwise_xor
binary_repr
 Return the binary representation of the input number as a string.
Examples
The number 13 has the binaray representation
00001101
. Likewise, 16 is represented by00010000
. The bitwise OR of 13 and 16 is then000111011
, or 29:>>> np.bitwise_or(13, 16) # doctest: +SKIP 29 >>> np.binary_repr(29) # doctest: +SKIP '11101'
>>> np.bitwise_or(32, 2) # doctest: +SKIP 34 >>> np.bitwise_or([33, 4], 1) # doctest: +SKIP array([33, 5]) >>> np.bitwise_or([33, 4], [1, 2]) # doctest: +SKIP array([33, 6])
>>> np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4])) # doctest: +SKIP array([ 6, 5, 255]) >>> np.array([2, 5, 255])  np.array([4, 4, 4]) # doctest: +SKIP array([ 6, 5, 255]) >>> np.bitwise_or(np.array([2, 5, 255, 2147483647L], dtype=np.int32), # doctest: +SKIP ... np.array([4, 4, 4, 2147483647L], dtype=np.int32)) array([ 6, 5, 255, 2147483647]) >>> np.bitwise_or([True, True], [False, True]) # doctest: +SKIP array([ True, True])

dask.array.
bitwise_xor
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute the bitwise XOR of two arrays elementwise.
Computes the bitwise XOR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator
^
.Parameters:  x1, x2 : array_like
Only integer and boolean types are handled.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Result. This is a scalar if both x1 and x2 are scalars.
See also
logical_xor
,bitwise_and
,bitwise_or
binary_repr
 Return the binary representation of the input number as a string.
Examples
The number 13 is represented by
00001101
. Likewise, 17 is represented by00010001
. The bitwise XOR of 13 and 17 is therefore00011100
, or 28:>>> np.bitwise_xor(13, 17) # doctest: +SKIP 28 >>> np.binary_repr(28) # doctest: +SKIP '11100'
>>> np.bitwise_xor(31, 5) # doctest: +SKIP 26 >>> np.bitwise_xor([31,3], 5) # doctest: +SKIP array([26, 6])
>>> np.bitwise_xor([31,3], [5,6]) # doctest: +SKIP array([26, 5]) >>> np.bitwise_xor([True, True], [False, True]) # doctest: +SKIP array([ True, False])

dask.array.
block
(arrays, allow_unknown_chunksizes=False)¶ Assemble an ndarray from nested lists of blocks.
Blocks in the innermost lists are concatenated along the last dimension (1), then these are concatenated along the secondlast dimension (2), and so on until the outermost list is reached
Blocks can be of any dimension, but will not be broadcasted using the normal rules. Instead, leading axes of size 1 are inserted, to make
block.ndim
the same for all blocks. This is primarily useful for working with scalars, and means that code likeblock([v, 1])
is valid, wherev.ndim == 1
.When the nested list is two levels deep, this allows block matrices to be constructed from their components.
Parameters:  arrays : nested list of array_like or scalars (but not tuples)
If passed a single ndarray or scalar (a nested list of depth 0), this is returned unmodified (and not copied).
Elements shapes must match along the appropriate axes (without broadcasting), but leading 1s will be prepended to the shape as necessary to make the dimensions match.
 allow_unknown_chunksizes: bool
Allow unknown chunksizes, such as come from converting from dask dataframes. Dask.array is unable to verify that chunks line up. If data comes from differently aligned sources then this can cause unexpected results.
Returns:  block_array : ndarray
The array assembled from the given blocks.
The dimensionality of the output is equal to the greatest of: * the dimensionality of all the inputs * the depth to which the input list is nested
Raises:  ValueError
 If list depths are mismatched  for instance,
[[a, b], c]
is illegal, and should be spelt[[a, b], [c]]
 If lists are empty  for instance,
[[a, b], []]
 If list depths are mismatched  for instance,
See also
concatenate
 Join a sequence of arrays together.
stack
 Stack arrays in sequence along a new dimension.
hstack
 Stack arrays in sequence horizontally (column wise).
vstack
 Stack arrays in sequence vertically (row wise).
dstack
 Stack arrays in sequence depth wise (along third dimension).
vsplit
 Split array into a list of multiple subarrays vertically.
Notes
When called with only scalars,
block
is equivalent to an ndarray call. Soblock([[1, 2], [3, 4]])
is equivalent toarray([[1, 2], [3, 4]])
.This function does not enforce that the blocks lie on a fixed grid.
block([[a, b], [c, d]])
is not restricted to arrays of the form:AAAbb AAAbb cccDD
But is also allowed to produce, for some
a, b, c, d
:AAAbb AAAbb cDDDD
Since concatenation happens along the last axis first, block is _not_ capable of producing the following directly:
AAAbb cccbb cccDD
Matlab’s “square bracket stacking”,
[A, B, ...; p, q, ...]
, is equivalent toblock([[A, B, ...], [p, q, ...]])
.

dask.array.
broadcast_arrays
(*args, **kwargs)¶ Broadcast any number of arrays against each other.
Parameters:  `*args` : array_likes
The arrays to broadcast.
 subok : bool, optional
If True, then subclasses will be passedthrough, otherwise the returned arrays will be forced to be a baseclass array (default).
Returns:  broadcasted : list of arrays
These arrays are views on the original arrays. They are typically not contiguous. Furthermore, more than one element of a broadcasted array may refer to a single memory location. If you need to write to the arrays, make copies first.
Examples
>>> x = np.array([[1,2,3]]) >>> y = np.array([[4],[5]]) >>> np.broadcast_arrays(x, y) [array([[1, 2, 3], [1, 2, 3]]), array([[4, 4, 4], [5, 5, 5]])]
Here is a useful idiom for getting contiguous copies instead of noncontiguous views.
>>> [np.array(a) for a in np.broadcast_arrays(x, y)] [array([[1, 2, 3], [1, 2, 3]]), array([[4, 4, 4], [5, 5, 5]])]

dask.array.
broadcast_to
(x, shape, chunks=None)¶ Broadcast an array to a new shape.
Parameters:  x : array_like
The array to broadcast.
 shape : tuple
The shape of the desired array.
 chunks : tuple, optional
If provided, then the result will use these chunks instead of the same chunks as the source array. Setting chunks explicitly as part of broadcast_to is more efficient than rechunking afterwards. Chunks are only allowed to differ from the original shape along dimensions that are new on the result or have size 1 the input array.
Returns:  broadcast : dask array
See also

dask.array.
coarsen
(reduction, x, axes, trim_excess=False) Coarsen array by applying reduction to fixed size neighborhoods
Parameters:  reduction: function
Function like np.sum, np.mean, etc…
 x: np.ndarray
Array to be coarsened
 axes: dict
Mapping of axis to coarsening factor
Examples
>>> x = np.array([1, 2, 3, 4, 5, 6]) >>> coarsen(np.sum, x, {0: 2}) array([ 3, 7, 11]) >>> coarsen(np.max, x, {0: 3}) array([3, 6])
Provide dictionary of scale per dimension
>>> x = np.arange(24).reshape((4, 6)) >>> x array([[ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23]])
>>> coarsen(np.min, x, {0: 2, 1: 3}) array([[ 0, 3], [12, 15]])
You must avoid excess elements explicitly
>>> x = np.array([1, 2, 3, 4, 5, 6, 7, 8]) >>> coarsen(np.min, x, {0: 3}, trim_excess=True) array([1, 4])

dask.array.
ceil
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Return the ceiling of the input, elementwise.
The ceil of the scalar x is the smallest integer i, such that i >= x. It is often denoted as \(\lceil x \rceil\).
Parameters:  x : array_like
Input data.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or scalar
The ceiling of each element in x, with float dtype. This is a scalar if x is a scalar.
Examples
>>> a = np.array([1.7, 1.5, 0.2, 0.2, 1.5, 1.7, 2.0]) # doctest: +SKIP >>> np.ceil(a) # doctest: +SKIP array([1., 1., 0., 1., 2., 2., 2.])

dask.array.
choose
(a, choices, out=None, mode='raise')¶ Construct an array from an index array and a set of arrays to choose from.
First of all, if confused or uncertain, definitely look at the Examples  in its full generality, this function is less simple than it might seem from the following code description (below ndi = numpy.lib.index_tricks):
np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)])
.But this omits some subtleties. Here is a fully general summary:
Given an “index” array (a) of integers and a sequence of n arrays (choices), a and each choice array are first broadcast, as necessary, to arrays of a common shape; calling these Ba and Bchoices[i], i = 0,…,n1 we have that, necessarily,
Ba.shape == Bchoices[i].shape
for each i. Then, a new array with shapeBa.shape
is created as follows: if
mode=raise
(the default), then, first of all, each element of a (and thus Ba) must be in the range [0, n1]; now, suppose that i (in that range) is the value at the (j0, j1, …, jm) position in Ba  then the value at the same position in the new array is the value in Bchoices[i] at that same position;  if
mode=wrap
, values in a (and thus Ba) may be any (signed) integer; modular arithmetic is used to map integers outside the range [0, n1] back into that range; and then the new array is constructed as above;  if
mode=clip
, values in a (and thus Ba) may be any (signed) integer; negative integers are mapped to 0; values greater than n1 are mapped to n1; and then the new array is constructed as above.
Parameters:  a : int array
This array must contain integers in [0, n1], where n is the number of choices, unless
mode=wrap
ormode=clip
, in which cases any integers are permissible. choices : sequence of arrays
Choice arrays. a and all of the choices must be broadcastable to the same shape. If choices is itself an array (not recommended), then its outermost dimension (i.e., the one corresponding to
choices.shape[0]
) is taken as defining the “sequence”. out : array, optional
If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype.
 mode : {‘raise’ (default), ‘wrap’, ‘clip’}, optional
Specifies how indices outside [0, n1] will be treated:
 ‘raise’ : an exception is raised
 ‘wrap’ : value becomes value mod n
 ‘clip’ : values < 0 are mapped to 0, values > n1 are mapped to n1
Returns:  merged_array : array
The merged result.
Raises:  ValueError: shape mismatch
If a and each choice array are not all broadcastable to the same shape.
See also
ndarray.choose
 equivalent method
Notes
To reduce the chance of misinterpretation, even though the following “abuse” is nominally supported, choices should neither be, nor be thought of as, a single array, i.e., the outermost sequencelike container should be either a list or a tuple.
Examples
>>> choices = [[0, 1, 2, 3], [10, 11, 12, 13], ... [20, 21, 22, 23], [30, 31, 32, 33]] >>> np.choose([2, 3, 1, 0], choices ... # the first element of the result will be the first element of the ... # third (2+1) "array" in choices, namely, 20; the second element ... # will be the second element of the fourth (3+1) choice array, i.e., ... # 31, etc. ... ) array([20, 31, 12, 3]) >>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (41) array([20, 31, 12, 3]) >>> # because there are 4 choice arrays >>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4) array([20, 1, 12, 3]) >>> # i.e., 0
A couple examples illustrating how choose broadcasts:
>>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]] >>> choices = [10, 10] >>> np.choose(a, choices) array([[ 10, 10, 10], [10, 10, 10], [ 10, 10, 10]])
>>> # With thanks to Anne Archibald >>> a = np.array([0, 1]).reshape((2,1,1)) >>> c1 = np.array([1, 2, 3]).reshape((1,3,1)) >>> c2 = np.array([1, 2, 3, 4, 5]).reshape((1,1,5)) >>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2 array([[[ 1, 1, 1, 1, 1], [ 2, 2, 2, 2, 2], [ 3, 3, 3, 3, 3]], [[1, 2, 3, 4, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5]]])
 if

dask.array.
clip
(*args, **kwargs)¶ Clip (limit) the values in an array.
Given an interval, values outside the interval are clipped to the interval edges. For example, if an interval of
[0, 1]
is specified, values smaller than 0 become 0, and values larger than 1 become 1.Parameters:  a : array_like
Array containing elements to clip.
 a_min : scalar or array_like or None
Minimum value. If None, clipping is not performed on lower interval edge. Not more than one of a_min and a_max may be None.
 a_max : scalar or array_like or None
Maximum value. If None, clipping is not performed on upper interval edge. Not more than one of a_min and a_max may be None. If a_min or a_max are array_like, then the three arrays will be broadcasted to match their shapes.
 out : ndarray, optional
The results will be placed in this array. It may be the input array for inplace clipping. out must be of the right shape to hold the output. Its type is preserved.
Returns:  clipped_array : ndarray
An array with the elements of a, but where values < a_min are replaced with a_min, and those > a_max with a_max.
See also
numpy.doc.ufuncs
 Section “Output arguments”
Examples
>>> a = np.arange(10) # doctest: +SKIP >>> np.clip(a, 1, 8) # doctest: +SKIP array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8]) >>> a # doctest: +SKIP array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.clip(a, 3, 6, out=a) # doctest: +SKIP array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6]) >>> a = np.arange(10) # doctest: +SKIP >>> a # doctest: +SKIP array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8) # doctest: +SKIP array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])

dask.array.
compress
(condition, a, axis=None, out=None)¶ Return selected slices of an array along given axis.
When working along a given axis, a slice along that axis is returned in output for each index where condition evaluates to True. When working on a 1D array, compress is equivalent to extract.
Parameters:  condition : 1D array of bools
Array that selects which entries to return. If len(condition) is less than the size of a along the given axis, then output is truncated to the length of the condition array.
 a : array_like
Array from which to extract a part.
 axis : int, optional
Axis along which to take slices. If None (default), work on the flattened array.
 out : ndarray, optional
Output array. Its type is preserved and it must be of the right shape to hold the output.
Returns:  compressed_array : ndarray
A copy of a without the slices along axis for which condition is false.
See also
take
,choose
,diag
,diagonal
,select
ndarray.compress
 Equivalent method in ndarray
np.extract
 Equivalent method when working on 1D arrays
numpy.doc.ufuncs
 Section “Output arguments”
Examples
>>> a = np.array([[1, 2], [3, 4], [5, 6]]) >>> a array([[1, 2], [3, 4], [5, 6]]) >>> np.compress([0, 1], a, axis=0) array([[3, 4]]) >>> np.compress([False, True, True], a, axis=0) array([[3, 4], [5, 6]]) >>> np.compress([False, True], a, axis=1) array([[2], [4], [6]])
Working on the flattened array does not return slices along an axis but selects elements.
>>> np.compress([False, True], a) array([2])

dask.array.
concatenate
(seq, axis=0, allow_unknown_chunksizes=False) Concatenate arrays along an existing axis
Given a sequence of dask Arrays form a new dask Array by stacking them along an existing dimension (axis=0 by default)
Parameters:  seq: list of dask.arrays
 axis: int
Dimension along which to align all of the arrays
 allow_unknown_chunksizes: bool
Allow unknown chunksizes, such as come from converting from dask dataframes. Dask.array is unable to verify that chunks line up. If data comes from differently aligned sources then this can cause unexpected results.
See also
Examples
Create slices
>>> import dask.array as da >>> import numpy as np
>>> data = [from_array(np.ones((4, 4)), chunks=(2, 2)) ... for i in range(3)]
>>> x = da.concatenate(data, axis=0) >>> x.shape (12, 4)
>>> da.concatenate(data, axis=1).shape (4, 12)
Result is a new dask Array

dask.array.
conj
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Return the complex conjugate, elementwise.
The complex conjugate of a complex number is obtained by changing the sign of its imaginary part.
Parameters:  x : array_like
Input value.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray
The complex conjugate of x, with same dtype as y. This is a scalar if x is a scalar.
Examples
>>> np.conjugate(1+2j) # doctest: +SKIP (12j)
>>> x = np.eye(2) + 1j * np.eye(2) # doctest: +SKIP >>> np.conjugate(x) # doctest: +SKIP array([[ 1.1.j, 0.0.j], [ 0.0.j, 1.1.j]])

dask.array.
copysign
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Change the sign of x1 to that of x2, elementwise.
If both arguments are arrays or sequences, they have to be of the same length. If x2 is a scalar, its sign will be copied to all elements of x1.
Parameters:  x1 : array_like
Values to change the sign of.
 x2 : array_like
The sign of x2 is copied to x1.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
The values of x1 with the sign of x2. This is a scalar if both x1 and x2 are scalars.
Examples
>>> np.copysign(1.3, 1) # doctest: +SKIP 1.3 >>> 1/np.copysign(0, 1) # doctest: +SKIP inf >>> 1/np.copysign(0, 1) # doctest: +SKIP inf
>>> np.copysign([1, 0, 1], 1.1) # doctest: +SKIP array([1., 0., 1.]) >>> np.copysign([1, 0, 1], np.arange(3)1) # doctest: +SKIP array([1., 0., 1.])

dask.array.
corrcoef
(x, y=None, rowvar=True, bias=<no value>, ddof=<no value>)¶ Return Pearson productmoment correlation coefficients.
Please refer to the documentation for cov for more detail. The relationship between the correlation coefficient matrix, R, and the covariance matrix, C, is
\[R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } }\]The values of R are between 1 and 1, inclusive.
Parameters:  x : array_like
A 1D or 2D array containing multiple variables and observations. Each row of x represents a variable, and each column a single observation of all those variables. Also see rowvar below.
 y : array_like, optional
An additional set of variables and observations. y has the same shape as x.
 rowvar : bool, optional
If rowvar is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations.
 bias : _NoValue, optional
Has no effect, do not use.
Deprecated since version 1.10.0.
 ddof : _NoValue, optional
Has no effect, do not use.
Deprecated since version 1.10.0.
Returns:  R : ndarray
The correlation coefficient matrix of the variables.
See also
cov
 Covariance matrix
Notes
Due to floating point rounding the resulting array may not be Hermitian, the diagonal elements may not be 1, and the elements may not satisfy the inequality abs(a) <= 1. The real and imaginary parts are clipped to the interval [1, 1] in an attempt to improve on that situation but is not much help in the complex case.
This function accepts but discards arguments bias and ddof. This is for backwards compatibility with previous versions of this function. These arguments had no effect on the return values of the function and can be safely ignored in this and previous versions of numpy.

dask.array.
cos
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Cosine elementwise.
Parameters:  x : array_like
Input array in radians.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray
The corresponding cosine values. This is a scalar if x is a scalar.
Notes
If out is provided, the function writes the result into it, and returns a reference to out. (See Examples)
References
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972.
Examples
>>> np.cos(np.array([0, np.pi/2, np.pi])) # doctest: +SKIP array([ 1.00000000e+00, 6.12303177e17, 1.00000000e+00]) >>> >>> # Example of providing the optional output parameter >>> out2 = np.cos([0.1], out1) # doctest: +SKIP >>> out2 is out1 # doctest: +SKIP True >>> >>> # Example of ValueError due to provision of shape mismatched `out` >>> np.cos(np.zeros((3,3)),np.zeros((2,2))) # doctest: +SKIP Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: invalid return array shape

dask.array.
cosh
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Hyperbolic cosine, elementwise.
Equivalent to
1/2 * (np.exp(x) + np.exp(x))
andnp.cos(1j*x)
.Parameters:  x : array_like
Input array.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Output array of same shape as x. This is a scalar if x is a scalar.
Examples
>>> np.cosh(0) # doctest: +SKIP 1.0
The hyperbolic cosine describes the shape of a hanging cable:
>>> import matplotlib.pyplot as plt # doctest: +SKIP >>> x = np.linspace(4, 4, 1000) # doctest: +SKIP >>> plt.plot(x, np.cosh(x)) # doctest: +SKIP >>> plt.show() # doctest: +SKIP

dask.array.
count_nonzero
(a, axis=None)¶ Counts the number of nonzero values in the array
a
.The word “nonzero” is in reference to the Python 2.x builtin method
__nonzero__()
(renamed__bool__()
in Python 3.x) of Python objects that tests an object’s “truthfulness”. For example, any number is considered truthful if it is nonzero, whereas any string is considered truthful if it is not the empty string. Thus, this function (recursively) counts how many elements ina
(and in subarrays thereof) have their__nonzero__()
or__bool__()
method evaluated toTrue
.Parameters:  a : array_like
The array for which to count nonzeros.
 axis : int or tuple, optional
Axis or tuple of axes along which to count nonzeros. Default is None, meaning that nonzeros will be counted along a flattened version of
a
.New in version 1.12.0.
Returns:  count : int or array of int
Number of nonzero values in the array along a given axis. Otherwise, the total number of nonzero values in the array is returned.
See also
nonzero
 Return the coordinates of all the nonzero values.
Examples
>>> np.count_nonzero(np.eye(4)) 4 >>> np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]]) 5 >>> np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]], axis=0) array([1, 1, 1, 1, 1]) >>> np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]], axis=1) array([2, 3])

dask.array.
cov
(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None, aweights=None)¶ Estimate a covariance matrix, given data and weights.
Covariance indicates the level to which two variables vary together. If we examine Ndimensional samples, \(X = [x_1, x_2, ... x_N]^T\), then the covariance matrix element \(C_{ij}\) is the covariance of \(x_i\) and \(x_j\). The element \(C_{ii}\) is the variance of \(x_i\).
See the notes for an outline of the algorithm.
Parameters:  m : array_like
A 1D or 2D array containing multiple variables and observations. Each row of m represents a variable, and each column a single observation of all those variables. Also see rowvar below.
 y : array_like, optional
An additional set of variables and observations. y has the same form as that of m.
 rowvar : bool, optional
If rowvar is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations.
 bias : bool, optional
Default normalization (False) is by
(N  1)
, whereN
is the number of observations given (unbiased estimate). If bias is True, then normalization is byN
. These values can be overridden by using the keywordddof
in numpy versions >= 1.5. ddof : int, optional
If not
None
the default value implied by bias is overridden. Note thatddof=1
will return the unbiased estimate, even if both fweights and aweights are specified, andddof=0
will return the simple average. See the notes for the details. The default value isNone
.New in version 1.5.
 fweights : array_like, int, optional
1D array of integer frequency weights; the number of times each observation vector should be repeated.
New in version 1.10.
 aweights : array_like, optional
1D array of observation vector weights. These relative weights are typically large for observations considered “important” and smaller for observations considered less “important”. If
ddof=0
the array of weights can be used to assign probabilities to observation vectors.New in version 1.10.
Returns:  out : ndarray
The covariance matrix of the variables.
See also
corrcoef
 Normalized covariance matrix
Notes
Assume that the observations are in the columns of the observation array m and let
f = fweights
anda = aweights
for brevity. The steps to compute the weighted covariance are as follows:>>> w = f * a >>> v1 = np.sum(w) >>> v2 = np.sum(w * a) >>> m = np.sum(m * w, axis=1, keepdims=True) / v1 >>> cov = np.dot(m * w, m.T) * v1 / (v1**2  ddof * v2)
Note that when
a == 1
, the normalization factorv1 / (v1**2  ddof * v2)
goes over to1 / (np.sum(f)  ddof)
as it should.Examples
Consider two variables, \(x_0\) and \(x_1\), which correlate perfectly, but in opposite directions:
>>> x = np.array([[0, 2], [1, 1], [2, 0]]).T >>> x array([[0, 1, 2], [2, 1, 0]])
Note how \(x_0\) increases while \(x_1\) decreases. The covariance matrix shows this clearly:
>>> np.cov(x) array([[ 1., 1.], [1., 1.]])
Note that element \(C_{0,1}\), which shows the correlation between \(x_0\) and \(x_1\), is negative.
Further, note how x and y are combined:
>>> x = [2.1, 1, 4.3] >>> y = [3, 1.1, 0.12] >>> X = np.stack((x, y), axis=0) >>> print(np.cov(X)) [[ 11.71 4.286 ] [ 4.286 2.14413333]] >>> print(np.cov(x, y)) [[ 11.71 4.286 ] [ 4.286 2.14413333]] >>> print(np.cov(x)) 11.71

dask.array.
cumprod
(a, axis=None, dtype=None, out=None)¶ Return the cumulative product of elements along a given axis.
Parameters:  a : array_like
Input array.
 axis : int, optional
Axis along which the cumulative product is computed. By default the input is flattened.
 dtype : dtype, optional
Type of the returned array, as well as of the accumulator in which the elements are multiplied. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type of the resulting values will be cast if necessary.
Returns:  cumprod : ndarray
A new array holding the result is returned unless out is specified, in which case a reference to out is returned.
See also
numpy.doc.ufuncs
 Section “Output arguments”
Notes
Arithmetic is modular when using integer types, and no error is raised on overflow.
Examples
>>> a = np.array([1,2,3]) >>> np.cumprod(a) # intermediate results 1, 1*2 ... # total product 1*2*3 = 6 array([1, 2, 6]) >>> a = np.array([[1, 2, 3], [4, 5, 6]]) >>> np.cumprod(a, dtype=float) # specify type of output array([ 1., 2., 6., 24., 120., 720.])
The cumulative product for each column (i.e., over the rows) of a:
>>> np.cumprod(a, axis=0) array([[ 1, 2, 3], [ 4, 10, 18]])
The cumulative product for each row (i.e. over the columns) of a:
>>> np.cumprod(a,axis=1) array([[ 1, 2, 6], [ 4, 20, 120]])

dask.array.
cumsum
(a, axis=None, dtype=None, out=None)¶ Return the cumulative sum of the elements along a given axis.
Parameters:  a : array_like
Input array.
 axis : int, optional
Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array.
 dtype : dtype, optional
Type of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used.
 out : ndarray, optional
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. See doc.ufuncs (Section “Output arguments”) for more details.
Returns:  cumsum_along_axis : ndarray.
A new array holding the result is returned unless out is specified, in which case a reference to out is returned. The result has the same size as a, and the same shape as a if axis is not None or a is a 1d array.
See also
Notes
Arithmetic is modular when using integer types, and no error is raised on overflow.
Examples
>>> a = np.array([[1,2,3], [4,5,6]]) >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.cumsum(a) array([ 1, 3, 6, 10, 15, 21]) >>> np.cumsum(a, dtype=float) # specifies type of output value(s) array([ 1., 3., 6., 10., 15., 21.])
>>> np.cumsum(a,axis=0) # sum over rows for each of the 3 columns array([[1, 2, 3], [5, 7, 9]]) >>> np.cumsum(a,axis=1) # sum over columns for each of the 2 rows array([[ 1, 3, 6], [ 4, 9, 15]])

dask.array.
deg2rad
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Convert angles from degrees to radians.
Parameters:  x : array_like
Angles in degrees.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray
The corresponding angle in radians. This is a scalar if x is a scalar.
See also
rad2deg
 Convert angles from radians to degrees.
unwrap
 Remove large jumps in angle by wrapping.
Notes
New in version 1.3.0.
deg2rad(x)
isx * pi / 180
.Examples
>>> np.deg2rad(180) # doctest: +SKIP 3.1415926535897931

dask.array.
degrees
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Convert angles from radians to degrees.
Parameters:  x : array_like
Input array in radians.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray of floats
The corresponding degree values; if out was supplied this is a reference to it. This is a scalar if x is a scalar.
See also
rad2deg
 equivalent function
Examples
Convert a radian array to degrees
>>> rad = np.arange(12.)*np.pi/6 # doctest: +SKIP >>> np.degrees(rad) # doctest: +SKIP array([ 0., 30., 60., 90., 120., 150., 180., 210., 240., 270., 300., 330.])
>>> out = np.zeros((rad.shape)) # doctest: +SKIP >>> r = degrees(rad, out) # doctest: +SKIP >>> np.all(r == out) # doctest: +SKIP True

dask.array.
diag
(v, k=0)¶ Extract a diagonal or construct a diagonal array.
See the more detailed documentation for
numpy.diagonal
if you use this function to extract a diagonal and wish to write to the resulting array; whether it returns a copy or a view depends on what version of numpy you are using.Parameters:  v : array_like
If v is a 2D array, return a copy of its kth diagonal. If v is a 1D array, return a 2D array with v on the kth diagonal.
 k : int, optional
Diagonal in question. The default is 0. Use k>0 for diagonals above the main diagonal, and k<0 for diagonals below the main diagonal.
Returns:  out : ndarray
The extracted diagonal or constructed diagonal array.
See also
Examples
>>> x = np.arange(9).reshape((3,3)) >>> x array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
>>> np.diag(x) array([0, 4, 8]) >>> np.diag(x, k=1) array([1, 5]) >>> np.diag(x, k=1) array([3, 7])
>>> np.diag(np.diag(x)) array([[0, 0, 0], [0, 4, 0], [0, 0, 8]])

dask.array.
diagonal
(a, offset=0, axis1=0, axis2=1)¶ Return specified diagonals.
If a is 2D, returns the diagonal of a with the given offset, i.e., the collection of elements of the form
a[i, i+offset]
. If a has more than two dimensions, then the axes specified by axis1 and axis2 are used to determine the 2D subarray whose diagonal is returned. The shape of the resulting array can be determined by removing axis1 and axis2 and appending an index to the right equal to the size of the resulting diagonals.In versions of NumPy prior to 1.7, this function always returned a new, independent array containing a copy of the values in the diagonal.
In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal, but depending on this fact is deprecated. Writing to the resulting array continues to work as it used to, but a FutureWarning is issued.
Starting in NumPy 1.9 it returns a readonly view on the original array. Attempting to write to the resulting array will produce an error.
In some future release, it will return a read/write view and writing to the returned array will alter your original array. The returned array will have the same type as the input array.
If you don’t write to the array returned by this function, then you can just ignore all of the above.
If you depend on the current behavior, then we suggest copying the returned array explicitly, i.e., use
np.diagonal(a).copy()
instead of justnp.diagonal(a)
. This will work with both past and future versions of NumPy.Parameters:  a : array_like
Array from which the diagonals are taken.
 offset : int, optional
Offset of the diagonal from the main diagonal. Can be positive or negative. Defaults to main diagonal (0).
 axis1 : int, optional
Axis to be used as the first axis of the 2D subarrays from which the diagonals should be taken. Defaults to first axis (0).
 axis2 : int, optional
Axis to be used as the second axis of the 2D subarrays from which the diagonals should be taken. Defaults to second axis (1).
Returns:  array_of_diagonals : ndarray
If a is 2D, then a 1D array containing the diagonal and of the same type as a is returned unless a is a matrix, in which case a 1D array rather than a (2D) matrix is returned in order to maintain backward compatibility.
If
a.ndim > 2
, then the dimensions specified by axis1 and axis2 are removed, and a new axis inserted at the end corresponding to the diagonal.
Raises:  ValueError
If the dimension of a is less than 2.
See also
diag
 MATLAB workalike for 1D and 2D arrays.
diagflat
 Create diagonal arrays.
trace
 Sum along diagonals.
Examples
>>> a = np.arange(4).reshape(2,2) >>> a array([[0, 1], [2, 3]]) >>> a.diagonal() array([0, 3]) >>> a.diagonal(1) array([1])
A 3D example:
>>> a = np.arange(8).reshape(2,2,2); a array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> a.diagonal(0, # Main diagonals of two arrays created by skipping ... 0, # across the outer(left)most axis last and ... 1) # the "middle" (row) axis first. array([[0, 6], [1, 7]])
The subarrays whose main diagonals we just obtained; note that each corresponds to fixing the rightmost (column) axis, and that the diagonals are “packed” in rows.
>>> a[:,:,0] # main diagonal is [0 6] array([[0, 2], [4, 6]]) >>> a[:,:,1] # main diagonal is [1 7] array([[1, 3], [5, 7]])

dask.array.
diff
(a, n=1, axis=1, prepend=<no value>, append=<no value>)¶ Calculate the nth discrete difference along the given axis.
The first difference is given by
out[n] = a[n+1]  a[n]
along the given axis, higher differences are calculated by using diff recursively.Parameters:  a : array_like
Input array
 n : int, optional
The number of times values are differenced. If zero, the input is returned asis.
 axis : int, optional
The axis along which the difference is taken, default is the last axis.
 prepend, append : array_like, optional
Values to prepend or append to “a” along axis prior to performing the difference. Scalar values are expanded to arrays with length 1 in the direction of axis and the shape of the input array in along all other axes. Otherwise the dimension and shape must match “a” except along axis.
Returns:  diff : ndarray
The nth differences. The shape of the output is the same as a except along axis where the dimension is smaller by n. The type of the output is the same as the type of the difference between any two elements of a. This is the same as the type of a in most cases. A notable exception is datetime64, which results in a timedelta64 output array.
Notes
Type is preserved for boolean arrays, so the result will contain False when consecutive elements are the same and True when they differ.
For unsigned integer arrays, the results will also be unsigned. This should not be surprising, as the result is consistent with calculating the difference directly:
>>> u8_arr = np.array([1, 0], dtype=np.uint8) >>> np.diff(u8_arr) array([255], dtype=uint8) >>> u8_arr[1,...]  u8_arr[0,...] array(255, np.uint8)
If this is not desirable, then the array should be cast to a larger integer type first:
>>> i16_arr = u8_arr.astype(np.int16) >>> np.diff(i16_arr) array([1], dtype=int16)
Examples
>>> x = np.array([1, 2, 4, 7, 0]) >>> np.diff(x) array([ 1, 2, 3, 7]) >>> np.diff(x, n=2) array([ 1, 1, 10])
>>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]]) >>> np.diff(x) array([[2, 3, 4], [5, 1, 2]]) >>> np.diff(x, axis=0) array([[1, 2, 0, 2]])
>>> x = np.arange('10661013', '10661016', dtype=np.datetime64) >>> np.diff(x) array([1, 1], dtype='timedelta64[D]')

dask.array.
digitize
(x, bins, right=False)¶ Return the indices of the bins to which each value in input array belongs.
right order of bins returned index i satisfies False
increasing bins[i1] <= x < bins[i]
True
increasing bins[i1] < x <= bins[i]
False
decreasing bins[i1] > x >= bins[i]
True
decreasing bins[i1] >= x > bins[i]
If values in x are beyond the bounds of bins, 0 or
len(bins)
is returned as appropriate.Parameters:  x : array_like
Input array to be binned. Prior to NumPy 1.10.0, this array had to be 1dimensional, but can now have any shape.
 bins : array_like
Array of bins. It has to be 1dimensional and monotonic.
 right : bool, optional
Indicating whether the intervals include the right or the left bin edge. Default behavior is (right==False) indicating that the interval does not include the right edge. The left bin end is open in this case, i.e., bins[i1] <= x < bins[i] is the default behavior for monotonically increasing bins.
Returns:  indices : ndarray of ints
Output array of indices, of same shape as x.
Raises:  ValueError
If bins is not monotonic.
 TypeError
If the type of the input is complex.
Notes
If values in x are such that they fall outside the bin range, attempting to index bins with the indices that digitize returns will result in an IndexError.
New in version 1.10.0.
np.digitize is implemented in terms of np.searchsorted. This means that a binary search is used to bin the values, which scales much better for larger number of bins than the previous linear search. It also removes the requirement for the input array to be 1dimensional.
For monotonically _increasing_ bins, the following are equivalent:
np.digitize(x, bins, right=True) np.searchsorted(bins, x, side='left')
Note that as the order of the arguments are reversed, the side must be too. The searchsorted call is marginally faster, as it does not do any monotonicity checks. Perhaps more importantly, it supports all dtypes.
Examples
>>> x = np.array([0.2, 6.4, 3.0, 1.6]) >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0]) >>> inds = np.digitize(x, bins) >>> inds array([1, 4, 3, 2]) >>> for n in range(x.size): ... print(bins[inds[n]1], "<=", x[n], "<", bins[inds[n]]) ... 0.0 <= 0.2 < 1.0 4.0 <= 6.4 < 10.0 2.5 <= 3.0 < 4.0 1.0 <= 1.6 < 2.5
>>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.]) >>> bins = np.array([0, 5, 10, 15, 20]) >>> np.digitize(x,bins,right=True) array([1, 2, 3, 4, 4]) >>> np.digitize(x,bins,right=False) array([1, 3, 3, 4, 5])

dask.array.
dot
(a, b, out=None)¶ Dot product of two arrays. Specifically,
If both a and b are 1D arrays, it is inner product of vectors (without complex conjugation).
If both a and b are 2D arrays, it is matrix multiplication, but using
matmul()
ora @ b
is preferred.If either a or b is 0D (scalar), it is equivalent to
multiply()
and usingnumpy.multiply(a, b)
ora * b
is preferred.If a is an ND array and b is a 1D array, it is a sum product over the last axis of a and b.
If a is an ND array and b is an MD array (where
M>=2
), it is a sum product over the last axis of a and the secondtolast axis of b:dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])
Parameters:  a : array_like
First argument.
 b : array_like
Second argument.
 out : ndarray, optional
Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be Ccontiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.
Returns:  output : ndarray
Returns the dot product of a and b. If a and b are both scalars or both 1D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.
Raises:  ValueError
If the last dimension of a is not the same size as the secondtolast dimension of b.
See also
Examples
>>> np.dot(3, 4) 12
Neither argument is complexconjugated:
>>> np.dot([2j, 3j], [2j, 3j]) (13+0j)
For 2D arrays it is the matrix product:
>>> a = [[1, 0], [0, 1]] >>> b = [[4, 1], [2, 2]] >>> np.dot(a, b) array([[4, 1], [2, 2]])
>>> a = np.arange(3*4*5*6).reshape((3,4,5,6)) >>> b = np.arange(3*4*5*6)[::1].reshape((5,4,6,3)) >>> np.dot(a, b)[2,3,2,1,2,2] 499128 >>> sum(a[2,3,2,:] * b[1,2,:,2]) 499128

dask.array.
dstack
(tup)¶ Stack arrays in sequence depth wise (along third axis).
This is equivalent to concatenation along the third axis after 2D arrays of shape (M,N) have been reshaped to (M,N,1) and 1D arrays of shape (N,) have been reshaped to (1,N,1). Rebuilds arrays divided by dsplit.
This function makes most sense for arrays with up to 3 dimensions. For instance, for pixeldata with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions concatenate, stack and block provide more general stacking and concatenation operations.
Parameters:  tup : sequence of arrays
The arrays must have the same shape along all but the third axis. 1D or 2D arrays must have the same shape.
Returns:  stacked : ndarray
The array formed by stacking the given arrays, will be at least 3D.
See also
stack
 Join a sequence of arrays along a new axis.
vstack
 Stack along first axis.
hstack
 Stack along second axis.
concatenate
 Join a sequence of arrays along an existing axis.
dsplit
 Split array along third axis.
Examples
>>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.dstack((a,b)) array([[[1, 2], [2, 3], [3, 4]]])
>>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.dstack((a,b)) array([[[1, 2]], [[2, 3]], [[3, 4]]])

dask.array.
ediff1d
(ary, to_end=None, to_begin=None)¶ The differences between consecutive elements of an array.
Parameters:  ary : array_like
If necessary, will be flattened before the differences are taken.
 to_end : array_like, optional
Number(s) to append at the end of the returned differences.
 to_begin : array_like, optional
Number(s) to prepend at the beginning of the returned differences.
Returns:  ediff1d : ndarray
The differences. Loosely, this is
ary.flat[1:]  ary.flat[:1]
.
Notes
When applied to masked arrays, this function drops the mask information if the to_begin and/or to_end parameters are used.
Examples
>>> x = np.array([1, 2, 4, 7, 0]) >>> np.ediff1d(x) array([ 1, 2, 3, 7])
>>> np.ediff1d(x, to_begin=99, to_end=np.array([88, 99])) array([99, 1, 2, 3, 7, 88, 99])
The returned array is always 1D.
>>> y = [[1, 2, 4], [1, 6, 24]] >>> np.ediff1d(y) array([ 1, 2, 3, 5, 18])

dask.array.
empty
(*args, **kwargs)¶ Blocked variant of empty
Follows the signature of empty exactly except that it also requires a keyword argument chunks=(…)
Original signature follows below. empty(shape, dtype=float, order=’C’)
Return a new array of given shape and type, without initializing entries.
Parameters:  shape : int or tuple of int
Shape of the empty array, e.g.,
(2, 3)
or2
. dtype : datatype, optional
Desired output datatype for the array, e.g, numpy.int8. Default is numpy.float64.
 order : {‘C’, ‘F’}, optional, default: ‘C’
Whether to store multidimensional data in rowmajor (Cstyle) or columnmajor (Fortranstyle) order in memory.
Returns:  out : ndarray
Array of uninitialized (arbitrary) data of the given shape, dtype, and order. Object arrays will be initialized to None.
See also
empty_like
 Return an empty array with shape and type of input.
ones
 Return a new array setting values to one.
zeros
 Return a new array setting values to zero.
full
 Return a new array of given shape filled with value.
Notes
empty, unlike zeros, does not set the array values to zero, and may therefore be marginally faster. On the other hand, it requires the user to manually set all the values in the array, and should be used with caution.
Examples
>>> np.empty([2, 2]) array([[ 9.74499359e+001, 6.69583040e309], [ 2.13182611e314, 3.06959433e309]]) #random
>>> np.empty([2, 2], dtype=int) array([[1073741821, 1067949133], [ 496041986, 19249760]]) #random

dask.array.
empty_like
(a, dtype=None, chunks=None)¶ Return a new array with the same shape and type as a given array.
Parameters:  a : array_like
The shape and datatype of a define these same attributes of the returned array.
 dtype : datatype, optional
Overrides the data type of the result.
 chunks : sequence of ints
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
.
Returns:  out : ndarray
Array of uninitialized (arbitrary) data with the same shape and type as a.
See also
ones_like
 Return an array of ones with shape and type of input.
zeros_like
 Return an array of zeros with shape and type of input.
empty
 Return a new uninitialized array.
ones
 Return a new array setting values to one.
zeros
 Return a new array setting values to zero.
Notes
This function does not initialize the returned array; to do that use zeros_like or ones_like instead. It may be marginally faster than the functions that do set the array values.

dask.array.
einsum
(subscripts, *operands, out=None, dtype=None, order='K', casting='safe', optimize=False)¶ Evaluates the Einstein summation convention on the operands.
Using the Einstein summation convention, many common multidimensional, linear algebraic array operations can be represented in a simple fashion. In implicit mode einsum computes these values.
In explicit mode, einsum provides further flexibility to compute other array operations that might not be considered classical Einstein summation operations, by disabling, or forcing summation over specified subscript labels.
See the notes and examples for clarification.
Parameters:  subscripts : str
Specifies the subscripts for summation as comma separated list of subscript labels. An implicit (classical Einstein summation) calculation is performed unless the explicit indicator ‘>’ is included as well as subscript labels of the precise output form.
 operands : list of array_like
These are the arrays for the operation.
 out : ndarray, optional
If provided, the calculation is done into this array.
 dtype : {datatype, None}, optional
If provided, forces the calculation to use the data type specified. Note that you may have to also give a more liberal casting parameter to allow the conversions. Default is None.
 order : {‘C’, ‘F’, ‘A’, ‘K’}, optional
Controls the memory layout of the output. ‘C’ means it should be C contiguous. ‘F’ means it should be Fortran contiguous, ‘A’ means it should be ‘F’ if the inputs are all ‘F’, ‘C’ otherwise. ‘K’ means it should be as close to the layout as the inputs as is possible, including arbitrarily permuted axes. Default is ‘K’.
 casting : {‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional
Controls what kind of data casting may occur. Setting this to ‘unsafe’ is not recommended, as it can adversely affect accumulations.
 ‘no’ means the data types should not be cast at all.
 ‘equiv’ means only byteorder changes are allowed.
 ‘safe’ means only casts which can preserve values are allowed.
 ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.
 ‘unsafe’ means any data conversions may be done.
Default is ‘safe’.
 optimize : {False, True, ‘greedy’, ‘optimal’}, optional
Controls if intermediate optimization should occur. No optimization will occur if False and True will default to the ‘greedy’ algorithm. Also accepts an explicit contraction list from the
np.einsum_path
function. Seenp.einsum_path
for more details. Defaults to False.
Returns:  output : ndarray
The calculation based on the Einstein summation convention.
Notes
New in version 1.6.0.
The Einstein summation convention can be used to compute many multidimensional, linear algebraic array operations. einsum provides a succinct way of representing these.
A nonexhaustive list of these operations, which can be computed by einsum, is shown below along with examples:
 Trace of an array,
numpy.trace()
.  Return a diagonal,
numpy.diag()
.  Array axis summations,
numpy.sum()
.  Transpositions and permutations,
numpy.transpose()
.  Matrix multiplication and dot product,
numpy.matmul()
numpy.dot()
.  Vector inner and outer products,
numpy.inner()
numpy.outer()
.  Broadcasting, elementwise and scalar multiplication,
numpy.multiply()
.  Tensor contractions,
numpy.tensordot()
.  Chained array operations, in efficient calculation order,
numpy.einsum_path()
.
The subscripts string is a commaseparated list of subscript labels, where each label refers to a dimension of the corresponding operand. Whenever a label is repeated it is summed, so
np.einsum('i,i', a, b)
is equivalent tonp.inner(a,b)
. If a label appears only once, it is not summed, sonp.einsum('i', a)
produces a view ofa
with no changes. A further examplenp.einsum('ij,jk', a, b)
describes traditional matrix multiplication and is equivalent tonp.matmul(a,b)
. Repeated subscript labels in one operand take the diagonal. For example,np.einsum('ii', a)
is equivalent tonp.trace(a)
.In implicit mode, the chosen subscripts are important since the axes of the output are reordered alphabetically. This means that
np.einsum('ij', a)
doesn’t affect a 2D array, whilenp.einsum('ji', a)
takes its transpose. Additionally,np.einsum('ij,jk', a, b)
returns a matrix multiplication, while,np.einsum('ij,jh', a, b)
returns the transpose of the multiplication since subscript ‘h’ precedes subscript ‘i’.In explicit mode the output can be directly controlled by specifying output subscript labels. This requires the identifier ‘>’ as well as the list of output subscript labels. This feature increases the flexibility of the function since summing can be disabled or forced when required. The call
np.einsum('i>', a)
is likenp.sum(a, axis=1)
, andnp.einsum('ii>i', a)
is likenp.diag(a)
. The difference is that einsum does not allow broadcasting by default. Additionallynp.einsum('ij,jh>ih', a, b)
directly specifies the order of the output subscript labels and therefore returns matrix multiplication, unlike the example above in implicit mode.To enable and control broadcasting, use an ellipsis. Default NumPystyle broadcasting is done by adding an ellipsis to the left of each term, like
np.einsum('...ii>...i', a)
. To take the trace along the first and last axes, you can donp.einsum('i...i', a)
, or to do a matrixmatrix product with the leftmost indices instead of rightmost, one can donp.einsum('ij...,jk...>ik...', a, b)
.When there is only one operand, no axes are summed, and no output parameter is provided, a view into the operand is returned instead of a new array. Thus, taking the diagonal as
np.einsum('ii>i', a)
produces a view (changed in version 1.10.0).einsum also provides an alternative way to provide the subscripts and operands as
einsum(op0, sublist0, op1, sublist1, ..., [sublistout])
. If the output shape is not provided in this format einsum will be calculated in implicit mode, otherwise it will be performed explicitly. The examples below have corresponding einsum calls with the two parameter methods.New in version 1.10.0.
Views returned from einsum are now writeable whenever the input array is writeable. For example,
np.einsum('ijk...>kji...', a)
will now have the same effect asnp.swapaxes(a, 0, 2)
andnp.einsum('ii>i', a)
will return a writeable view of the diagonal of a 2D array.New in version 1.12.0.
Added the
optimize
argument which will optimize the contraction order of an einsum expression. For a contraction with three or more operands this can greatly increase the computational efficiency at the cost of a larger memory footprint during computation.Typically a ‘greedy’ algorithm is applied which empirical tests have shown returns the optimal path in the majority of cases. In some cases ‘optimal’ will return the superlative path through a more expensive, exhaustive search. For iterative calculations it may be advisable to calculate the optimal path once and reuse that path by supplying it as an argument. An example is given below.
See
numpy.einsum_path()
for more details.Examples
>>> a = np.arange(25).reshape(5,5) >>> b = np.arange(5) >>> c = np.arange(6).reshape(2,3)
Trace of a matrix:
>>> np.einsum('ii', a) 60 >>> np.einsum(a, [0,0]) 60 >>> np.trace(a) 60
Extract the diagonal (requires explicit form):
>>> np.einsum('ii>i', a) array([ 0, 6, 12, 18, 24]) >>> np.einsum(a, [0,0], [0]) array([ 0, 6, 12, 18, 24]) >>> np.diag(a) array([ 0, 6, 12, 18, 24])
Sum over an axis (requires explicit form):
>>> np.einsum('ij>i', a) array([ 10, 35, 60, 85, 110]) >>> np.einsum(a, [0,1], [0]) array([ 10, 35, 60, 85, 110]) >>> np.sum(a, axis=1) array([ 10, 35, 60, 85, 110])
For higher dimensional arrays summing a single axis can be done with ellipsis:
>>> np.einsum('...j>...', a) array([ 10, 35, 60, 85, 110]) >>> np.einsum(a, [Ellipsis,1], [Ellipsis]) array([ 10, 35, 60, 85, 110])
Compute a matrix transpose, or reorder any number of axes:
>>> np.einsum('ji', c) array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum('ij>ji', c) array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum(c, [1,0]) array([[0, 3], [1, 4], [2, 5]]) >>> np.transpose(c) array([[0, 3], [1, 4], [2, 5]])
Vector inner products:
>>> np.einsum('i,i', b, b) 30 >>> np.einsum(b, [0], b, [0]) 30 >>> np.inner(b,b) 30
Matrix vector multiplication:
>>> np.einsum('ij,j', a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum(a, [0,1], b, [1]) array([ 30, 80, 130, 180, 230]) >>> np.dot(a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum('...j,j', a, b) array([ 30, 80, 130, 180, 230])
Broadcasting and scalar multiplication:
>>> np.einsum('..., ...', 3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum(',ij', 3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum(3, [Ellipsis], c, [Ellipsis]) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.multiply(3, c) array([[ 0, 3, 6], [ 9, 12, 15]])
Vector outer product:
>>> np.einsum('i,j', np.arange(2)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.einsum(np.arange(2)+1, [0], b, [1]) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.outer(np.arange(2)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]])
Tensor contraction:
>>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> np.einsum('ijk,jil>kl', a, b) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3]) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]]) >>> np.tensordot(a,b, axes=([1,0],[0,1])) array([[ 4400., 4730.], [ 4532., 4874.], [ 4664., 5018.], [ 4796., 5162.], [ 4928., 5306.]])
Writeable returned arrays (since version 1.10.0):
>>> a = np.zeros((3, 3)) >>> np.einsum('ii>i', a)[:] = 1 >>> a array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])
Example of ellipsis use:
>>> a = np.arange(6).reshape((3,2)) >>> b = np.arange(12).reshape((4,3)) >>> np.einsum('ki,jk>ij', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> np.einsum('ki,...k>i...', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> np.einsum('k...,jk', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]])
Chained array operations. For more complicated contractions, speed ups might be achieved by repeatedly computing a ‘greedy’ path or precomputing the ‘optimal’ path and repeatedly applying it, using an einsum_path insertion (since version 1.12.0). Performance improvements can be particularly significant with larger arrays:
>>> a = np.ones(64).reshape(2,4,8) # Basic `einsum`: ~1520ms (benchmarked on 3.1GHz Intel i5.) >>> for iteration in range(500): ... np.einsum('ijk,ilm,njm,nlk,abc>',a,a,a,a,a) # Suboptimal `einsum` (due to repeated path calculation time): ~330ms >>> for iteration in range(500): ... np.einsum('ijk,ilm,njm,nlk,abc>',a,a,a,a,a, optimize='optimal') # Greedy `einsum` (faster optimal path approximation): ~160ms >>> for iteration in range(500): ... np.einsum('ijk,ilm,njm,nlk,abc>',a,a,a,a,a, optimize='greedy') # Optimal `einsum` (best usage pattern in some use cases): ~110ms >>> path = np.einsum_path('ijk,ilm,njm,nlk,abc>',a,a,a,a,a, optimize='optimal')[0] >>> for iteration in range(500): ... np.einsum('ijk,ilm,njm,nlk,abc>',a,a,a,a,a, optimize=path)

dask.array.
exp
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Calculate the exponential of all elements in the input array.
Parameters:  x : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Output array, elementwise exponential of x. This is a scalar if x is a scalar.
See also
expm1
 Calculate
exp(x)  1
for all elements in the array. exp2
 Calculate
2**x
for all elements in the array.
Notes
The irrational number
e
is also known as Euler’s number. It is approximately 2.718281, and is the base of the natural logarithm,ln
(this means that, if \(x = \ln y = \log_e y\), then \(e^x = y\). For real input,exp(x)
is always positive.For complex arguments,
x = a + ib
, we can write \(e^x = e^a e^{ib}\). The first term, \(e^a\), is already known (it is the real argument, described above). The second term, \(e^{ib}\), is \(\cos b + i \sin b\), a function with magnitude 1 and a periodic phase.References
[1] Wikipedia, “Exponential function”, https://en.wikipedia.org/wiki/Exponential_function [2] M. Abramovitz and I. A. Stegun, “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” Dover, 1964, p. 69, http://www.math.sfu.ca/~cbm/aands/page_69.htm Examples
Plot the magnitude and phase of
exp(x)
in the complex plane:>>> import matplotlib.pyplot as plt # doctest: +SKIP
>>> x = np.linspace(2*np.pi, 2*np.pi, 100) # doctest: +SKIP >>> xx = x + 1j * x[:, np.newaxis] # a + ib over complex plane # doctest: +SKIP >>> out = np.exp(xx) # doctest: +SKIP
>>> plt.subplot(121) # doctest: +SKIP >>> plt.imshow(np.abs(out), # doctest: +SKIP ... extent=[2*np.pi, 2*np.pi, 2*np.pi, 2*np.pi], cmap='gray') >>> plt.title('Magnitude of exp(x)') # doctest: +SKIP
>>> plt.subplot(122) # doctest: +SKIP >>> plt.imshow(np.angle(out), # doctest: +SKIP ... extent=[2*np.pi, 2*np.pi, 2*np.pi, 2*np.pi], cmap='hsv') >>> plt.title('Phase (angle) of exp(x)') # doctest: +SKIP >>> plt.show() # doctest: +SKIP

dask.array.
expm1
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Calculate
exp(x)  1
for all elements in the array.Parameters:  x : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Elementwise exponential minus one:
out = exp(x)  1
. This is a scalar if x is a scalar.
See also
log1p
log(1 + x)
, the inverse of expm1.
Notes
This function provides greater precision than
exp(x)  1
for small values ofx
.Examples
The true value of
exp(1e10)  1
is1.00000000005e10
to about 32 significant digits. This example shows the superiority of expm1 in this case.>>> np.expm1(1e10) # doctest: +SKIP 1.00000000005e10 >>> np.exp(1e10)  1 # doctest: +SKIP 1.000000082740371e10

dask.array.
eye
(N, chunks, M=None, k=0, dtype=<class 'float'>)¶ Return a 2D Array with ones on the diagonal and zeros elsewhere.
Parameters:  N : int
Number of rows in the output.
 chunks: int
chunk size of resulting blocks
 M : int, optional
Number of columns in the output. If None, defaults to N.
 k : int, optional
Index of the diagonal: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal.
 dtype : datatype, optional
Datatype of the returned array.
Returns:  I : Array of shape (N,M)
An array where all elements are equal to zero, except for the kth diagonal, whose values are equal to one.

dask.array.
fabs
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute the absolute values elementwise.
This function returns the absolute values (positive magnitude) of the data in x. Complex values are not handled, use absolute to find the absolute values of complex data.
Parameters:  x : array_like
The array of numbers for which the absolute values are required. If x is a scalar, the result y will also be a scalar.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or scalar
The absolute values of x, the returned values are always floats. This is a scalar if x is a scalar.
See also
absolute
 Absolute values including complex types.
Examples
>>> np.fabs(1) # doctest: +SKIP 1.0 >>> np.fabs([1.2, 1.2]) # doctest: +SKIP array([ 1.2, 1.2])

dask.array.
fix
(*args, **kwargs)¶ Round to nearest integer towards zero.
Round an array of floats elementwise to nearest integer towards zero. The rounded values are returned as floats.
Parameters:  x : array_like
An array of floats to be rounded
 y : ndarray, optional
Output array
Returns:  out : ndarray of floats
The array of rounded numbers
Examples
>>> np.fix(3.14) # doctest: +SKIP 3.0 >>> np.fix(3) # doctest: +SKIP 3.0 >>> np.fix([2.1, 2.9, 2.1, 2.9]) # doctest: +SKIP array([ 2., 2., 2., 2.])

dask.array.
flatnonzero
(a)¶ Return indices that are nonzero in the flattened version of a.
This is equivalent to np.nonzero(np.ravel(a))[0].
Parameters:  a : array_like
Input data.
Returns:  res : ndarray
Output array, containing the indices of the elements of a.ravel() that are nonzero.
See also
Examples
>>> x = np.arange(2, 3) >>> x array([2, 1, 0, 1, 2]) >>> np.flatnonzero(x) array([0, 1, 3, 4])
Use the indices of the nonzero elements as an index array to extract these elements:
>>> x.ravel()[np.flatnonzero(x)] array([2, 1, 1, 2])

dask.array.
flip
(m, axis)¶ Reverse element order along axis.
Parameters:  axis : int
Axis to reverse element order of.
Returns:  reversed array : ndarray

dask.array.
flipud
(m)¶ Flip array in the up/down direction.
Flip the entries in each column in the up/down direction. Rows are preserved, but appear in a different order than before.
Parameters:  m : array_like
Input array.
Returns:  out : array_like
A view of m with the rows reversed. Since a view is returned, this operation is \(\mathcal O(1)\).
See also
fliplr
 Flip array in the left/right direction.
rot90
 Rotate array counterclockwise.
Notes
Equivalent to
m[::1,...]
. Does not require the array to be twodimensional.Examples
>>> A = np.diag([1.0, 2, 3]) >>> A array([[ 1., 0., 0.], [ 0., 2., 0.], [ 0., 0., 3.]]) >>> np.flipud(A) array([[ 0., 0., 3.], [ 0., 2., 0.], [ 1., 0., 0.]])
>>> A = np.random.randn(2,3,5) >>> np.all(np.flipud(A) == A[::1,...]) True
>>> np.flipud([1,2]) array([2, 1])

dask.array.
fliplr
(m)¶ Flip array in the left/right direction.
Flip the entries in each row in the left/right direction. Columns are preserved, but appear in a different order than before.
Parameters:  m : array_like
Input array, must be at least 2D.
Returns:  f : ndarray
A view of m with the columns reversed. Since a view is returned, this operation is \(\mathcal O(1)\).
See also
flipud
 Flip array in the up/down direction.
rot90
 Rotate array counterclockwise.
Notes
Equivalent to m[:,::1]. Requires the array to be at least 2D.
Examples
>>> A = np.diag([1.,2.,3.]) >>> A array([[ 1., 0., 0.], [ 0., 2., 0.], [ 0., 0., 3.]]) >>> np.fliplr(A) array([[ 0., 0., 1.], [ 0., 2., 0.], [ 3., 0., 0.]])
>>> A = np.random.randn(2,3,5) >>> np.all(np.fliplr(A) == A[:,::1,...]) True

dask.array.
floor
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Return the floor of the input, elementwise.
The floor of the scalar x is the largest integer i, such that i <= x. It is often denoted as \(\lfloor x \rfloor\).
Parameters:  x : array_like
Input data.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or scalar
The floor of each element in x. This is a scalar if x is a scalar.
Notes
Some spreadsheet programs calculate the “floortowardszero”, in other words
floor(2.5) == 2
. NumPy instead uses the definition of floor where floor(2.5) == 3.Examples
>>> a = np.array([1.7, 1.5, 0.2, 0.2, 1.5, 1.7, 2.0]) # doctest: +SKIP >>> np.floor(a) # doctest: +SKIP array([2., 2., 1., 0., 1., 1., 2.])

dask.array.
fmax
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Elementwise maximum of array elements.
Compare two arrays and returns a new array containing the elementwise maxima. If one of the elements being compared is a NaN, then the nonnan element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are ignored when possible.
Parameters:  x1, x2 : array_like
The arrays holding the elements to be compared. They must have the same shape.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or scalar
The maximum of x1 and x2, elementwise. This is a scalar if both x1 and x2 are scalars.
See also
Notes
New in version 1.3.0.
The fmax is equivalent to
np.where(x1 >= x2, x1, x2)
when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting.Examples
>>> np.fmax([2, 3, 4], [1, 5, 2]) # doctest: +SKIP array([ 2., 5., 4.])
>>> np.fmax(np.eye(2), [0.5, 2]) # doctest: +SKIP array([[ 1. , 2. ], [ 0.5, 2. ]])
>>> np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan]) # doctest: +SKIP array([ 0., 0., NaN])

dask.array.
fmin
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Elementwise minimum of array elements.
Compare two arrays and returns a new array containing the elementwise minima. If one of the elements being compared is a NaN, then the nonnan element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are ignored when possible.
Parameters:  x1, x2 : array_like
The arrays holding the elements to be compared. They must have the same shape.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or scalar
The minimum of x1 and x2, elementwise. This is a scalar if both x1 and x2 are scalars.
See also
Notes
New in version 1.3.0.
The fmin is equivalent to
np.where(x1 <= x2, x1, x2)
when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting.Examples
>>> np.fmin([2, 3, 4], [1, 5, 2]) # doctest: +SKIP array([1, 3, 2])
>>> np.fmin(np.eye(2), [0.5, 2]) # doctest: +SKIP array([[ 0.5, 0. ], [ 0. , 1. ]])
>>> np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan]) # doctest: +SKIP array([ 0., 0., NaN])

dask.array.
fmod
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Return the elementwise remainder of division.
This is the NumPy implementation of the C library function fmod, the remainder has the same sign as the dividend x1. It is equivalent to the Matlab(TM)
rem
function and should not be confused with the Python modulus operatorx1 % x2
.Parameters:  x1 : array_like
Dividend.
 x2 : array_like
Divisor.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : array_like
The remainder of the division of x1 by x2. This is a scalar if both x1 and x2 are scalars.
See also
remainder
 Equivalent to the Python
%
operator.
divide
Notes
The result of the modulo operation for negative dividend and divisors is bound by conventions. For fmod, the sign of result is the sign of the dividend, while for remainder the sign of the result is the sign of the divisor. The fmod function is equivalent to the Matlab(TM)
rem
function.Examples
>>> np.fmod([3, 2, 1, 1, 2, 3], 2) # doctest: +SKIP array([1, 0, 1, 1, 0, 1]) >>> np.remainder([3, 2, 1, 1, 2, 3], 2) # doctest: +SKIP array([1, 0, 1, 1, 0, 1])
>>> np.fmod([5, 3], [2, 2.]) # doctest: +SKIP array([ 1., 1.]) >>> a = np.arange(3, 3).reshape(3, 2) # doctest: +SKIP >>> a # doctest: +SKIP array([[3, 2], [1, 0], [ 1, 2]]) >>> np.fmod(a, [2,2]) # doctest: +SKIP array([[1, 0], [1, 0], [ 1, 0]])

dask.array.
frexp
(x, [out1, out2, ]/, [out=(None, None), ]*, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Decompose the elements of x into mantissa and twos exponent.
Returns (mantissa, exponent), where x = mantissa * 2**exponent`. The mantissa is lies in the open interval(1, 1), while the twos exponent is a signed integer.
Parameters:  x : array_like
Array of numbers to be decomposed.
 out1 : ndarray, optional
Output array for the mantissa. Must have the same shape as x.
 out2 : ndarray, optional
Output array for the exponent. Must have the same shape as x.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  mantissa : ndarray
Floating values between 1 and 1. This is a scalar if x is a scalar.
 exponent : ndarray
Integer exponents of 2. This is a scalar if x is a scalar.
See also
ldexp
 Compute
y = x1 * 2**x2
, the inverse of frexp.
Notes
Complex dtypes are not supported, they will raise a TypeError.
Examples
>>> x = np.arange(9) # doctest: +SKIP >>> y1, y2 = np.frexp(x) # doctest: +SKIP >>> y1 # doctest: +SKIP array([ 0. , 0.5 , 0.5 , 0.75 , 0.5 , 0.625, 0.75 , 0.875, 0.5 ]) >>> y2 # doctest: +SKIP array([0, 1, 2, 2, 3, 3, 3, 3, 4]) >>> y1 * 2**y2 # doctest: +SKIP array([ 0., 1., 2., 3., 4., 5., 6., 7., 8.])

dask.array.
fromfunction
(function, shape, **kwargs)¶ Construct an array by executing a function over each coordinate.
The resulting array therefore has a value
fn(x, y, z)
at coordinate(x, y, z)
.Parameters:  function : callable
The function is called with N parameters, where N is the rank of shape. Each parameter represents the coordinates of the array varying along a specific axis. For example, if shape were
(2, 2)
, then the parameters would bearray([[0, 0], [1, 1]])
andarray([[0, 1], [0, 1]])
 shape : (N,) tuple of ints
Shape of the output array, which also determines the shape of the coordinate arrays passed to function.
 dtype : datatype, optional
Datatype of the coordinate arrays passed to function. By default, dtype is float.
Returns:  fromfunction : any
The result of the call to function is passed back directly. Therefore the shape of fromfunction is completely determined by function. If function returns a scalar value, the shape of fromfunction would not match the shape parameter.
Notes
Keywords other than dtype are passed to function.
Examples
>>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int) array([[ True, False, False], [False, True, False], [False, False, True]])
>>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int) array([[0, 1, 2], [1, 2, 3], [2, 3, 4]])

dask.array.
frompyfunc
(func, nin, nout)¶ Takes an arbitrary Python function and returns a NumPy ufunc.
Can be used, for example, to add broadcasting to a builtin Python function (see Examples section).
Parameters:  func : Python function object
An arbitrary Python function.
 nin : int
The number of input arguments.
 nout : int
The number of objects returned by func.
Returns:  out : ufunc
Returns a NumPy universal function (
ufunc
) object.
See also
vectorize
 evaluates pyfunc over input arrays using broadcasting rules of numpy
Notes
The returned ufunc always returns PyObject arrays.
Examples
Use frompyfunc to add broadcasting to the Python function
oct
:>>> oct_array = np.frompyfunc(oct, 1, 1) >>> oct_array(np.array((10, 30, 100))) array([012, 036, 0144], dtype=object) >>> np.array((oct(10), oct(30), oct(100))) # for comparison array(['012', '036', '0144'], dtype='S4')

dask.array.
full
(*args, **kwargs)¶ Blocked variant of full
Follows the signature of full exactly except that it also requires a keyword argument chunks=(…)
Original signature follows below.
Return a new array of given shape and type, filled with fill_value.
Parameters:  shape : int or sequence of ints
Shape of the new array, e.g.,
(2, 3)
or2
. fill_value : scalar
Fill value.
 dtype : datatype, optional
 The desired datatype for the array The default, None, means
np.array(fill_value).dtype.
 order : {‘C’, ‘F’}, optional
Whether to store multidimensional data in C or Fortrancontiguous (row or columnwise) order in memory.
Returns:  out : ndarray
Array of fill_value with the given shape, dtype, and order.
See also
Examples
>>> np.full((2, 2), np.inf) array([[ inf, inf], [ inf, inf]]) >>> np.full((2, 2), 10) array([[10, 10], [10, 10]])

dask.array.
full_like
(a, fill_value, dtype=None, chunks=None)¶ Return a full array with the same shape and type as a given array.
Parameters:  a : array_like
The shape and datatype of a define these same attributes of the returned array.
 fill_value : scalar
Fill value.
 dtype : datatype, optional
Overrides the data type of the result.
 chunks : sequence of ints
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
.
Returns:  out : ndarray
Array of fill_value with the same shape and type as a.
See also
zeros_like
 Return an array of zeros with shape and type of input.
ones_like
 Return an array of ones with shape and type of input.
empty_like
 Return an empty array with shape and type of input.
zeros
 Return a new array setting values to zero.
ones
 Return a new array setting values to one.
empty
 Return a new uninitialized array.
full
 Fill a new array.

dask.array.
gradient
(f, *varargs, **kwargs)¶ Return the gradient of an Ndimensional array.
The gradient is computed using second order accurate central differences in the interior points and either first or second order accurate onesides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.
Parameters:  f : array_like
An Ndimensional array containing samples of a scalar function.
 varargs : list of scalar or array, optional
Spacing between f values. Default unitary spacing for all dimensions. Spacing can be specified using:
 single scalar to specify a sample distance for all dimensions.
 N scalars to specify a constant sample distance for each dimension. i.e. dx, dy, dz, …
 N arrays to specify the coordinates of the values along each dimension of F. The length of the array must match the size of the corresponding dimension
 Any combination of N scalars/arrays with the meaning of 2. and 3.
If axis is given, the number of varargs must equal the number of axes. Default: 1.
 edge_order : {1, 2}, optional
Gradient is calculated using Nth order accurate differences at the boundaries. Default: 1.
New in version 1.9.1.
 axis : None or int or tuple of ints, optional
Gradient is calculated only along the given axis or axes The default (axis = None) is to calculate the gradient for all the axes of the input array. axis may be negative, in which case it counts from the last to the first axis.
New in version 1.11.0.
Returns:  gradient : ndarray or list of ndarray
A set of ndarrays (or a single ndarray if there is only one dimension) corresponding to the derivatives of f with respect to each dimension. Each derivative has the same shape as f.
Notes
Assuming that \(f\in C^{3}\) (i.e., \(f\) has at least 3 continuous derivatives) and let \(h_{*}\) be a nonhomogeneous stepsize, we minimize the “consistency error” \(\eta_{i}\) between the true gradient and its estimate from a linear combination of the neighboring gridpoints:
\[\eta_{i} = f_{i}^{\left(1\right)}  \left[ \alpha f\left(x_{i}\right) + \beta f\left(x_{i} + h_{d}\right) + \gamma f\left(x_{i}h_{s}\right) \right]\]By substituting \(f(x_{i} + h_{d})\) and \(f(x_{i}  h_{s})\) with their Taylor series expansion, this translates into solving the following the linear system:
\[\begin{split}\left\{ \begin{array}{r} \alpha+\beta+\gamma=0 \\ \beta h_{d}\gamma h_{s}=1 \\ \beta h_{d}^{2}+\gamma h_{s}^{2}=0 \end{array} \right.\end{split}\]The resulting approximation of \(f_{i}^{(1)}\) is the following:
\[\hat f_{i}^{(1)} = \frac{ h_{s}^{2}f\left(x_{i} + h_{d}\right) + \left(h_{d}^{2}  h_{s}^{2}\right)f\left(x_{i}\right)  h_{d}^{2}f\left(x_{i}h_{s}\right)} { h_{s}h_{d}\left(h_{d} + h_{s}\right)} + \mathcal{O}\left(\frac{h_{d}h_{s}^{2} + h_{s}h_{d}^{2}}{h_{d} + h_{s}}\right)\]It is worth noting that if \(h_{s}=h_{d}\) (i.e., data are evenly spaced) we find the standard second order approximation:
\[\hat f_{i}^{(1)}= \frac{f\left(x_{i+1}\right)  f\left(x_{i1}\right)}{2h} + \mathcal{O}\left(h^{2}\right)\]With a similar procedure the forward/backward approximations used for boundaries can be derived.
References
[1] Quarteroni A., Sacco R., Saleri F. (2007) Numerical Mathematics (Texts in Applied Mathematics). New York: Springer. [2] Durran D. R. (1999) Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. New York: Springer. [3] Fornberg B. (1988) Generation of Finite Difference Formulas on Arbitrarily Spaced Grids, Mathematics of Computation 51, no. 184 : 699706. PDF. Examples
>>> f = np.array([1, 2, 4, 7, 11, 16], dtype=float) >>> np.gradient(f) array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ]) >>> np.gradient(f, 2) array([ 0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ])
Spacing can be also specified with an array that represents the coordinates of the values F along the dimensions. For instance a uniform spacing:
>>> x = np.arange(f.size) >>> np.gradient(f, x) array([ 1. , 1.5, 2.5, 3.5, 4.5, 5. ])
Or a non uniform one:
>>> x = np.array([0., 1., 1.5, 3.5, 4., 6.], dtype=float) >>> np.gradient(f, x) array([ 1. , 3. , 3.5, 6.7, 6.9, 2.5])
For two dimensional arrays, the return will be two arrays ordered by axis. In this example the first array stands for the gradient in rows and the second one in columns direction:
>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float)) [array([[ 2., 2., 1.], [ 2., 2., 1.]]), array([[ 1. , 2.5, 4. ], [ 1. , 1. , 1. ]])]
In this example the spacing is also specified: uniform for axis=0 and non uniform for axis=1
>>> dx = 2. >>> y = [1., 1.5, 3.5] >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), dx, y) [array([[ 1. , 1. , 0.5], [ 1. , 1. , 0.5]]), array([[ 2. , 2. , 2. ], [ 2. , 1.7, 0.5]])]
It is possible to specify how boundaries are treated using edge_order
>>> x = np.array([0, 1, 2, 3, 4]) >>> f = x**2 >>> np.gradient(f, edge_order=1) array([ 1., 2., 4., 6., 7.]) >>> np.gradient(f, edge_order=2) array([0., 2., 4., 6., 8.])
The axis keyword can be used to specify a subset of axes of which the gradient is calculated
>>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), axis=0) array([[ 2., 2., 1.], [ 2., 2., 1.]])

dask.array.
histogram
(a, bins=None, range=None, normed=False, weights=None, density=None)¶ Blocked variant of
numpy.histogram()
.Follows the signature of
numpy.histogram()
exactly with the following exceptions: Either an iterable specifying the
bins
or the number ofbins
and arange
argument is required as computingmin
andmax
over blocked arrays is an expensive operation that must be performed explicitly. weights
must be a dask.array.Array with the same block structure asa
.
Examples
Using number of bins and range:
>>> import dask.array as da >>> import numpy as np >>> x = da.from_array(np.arange(10000), chunks=10) >>> h, bins = da.histogram(x, bins=10, range=[0, 10000]) >>> bins array([ 0., 1000., 2000., 3000., 4000., 5000., 6000., 7000., 8000., 9000., 10000.]) >>> h.compute() array([1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000])
Explicitly specifying the bins:
>>> h, bins = da.histogram(x, bins=np.array([0, 5000, 10000])) >>> bins array([ 0, 5000, 10000]) >>> h.compute() array([5000, 5000])
 Either an iterable specifying the

dask.array.
hstack
(tup)¶ Stack arrays in sequence horizontally (column wise).
This is equivalent to concatenation along the second axis, except for 1D arrays where it concatenates along the first axis. Rebuilds arrays divided by hsplit.
This function makes most sense for arrays with up to 3 dimensions. For instance, for pixeldata with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions concatenate, stack and block provide more general stacking and concatenation operations.
Parameters:  tup : sequence of ndarrays
The arrays must have the same shape along all but the second axis, except 1D arrays which can be any length.
Returns:  stacked : ndarray
The array formed by stacking the given arrays.
See also
stack
 Join a sequence of arrays along a new axis.
vstack
 Stack arrays in sequence vertically (row wise).
dstack
 Stack arrays in sequence depth wise (along third axis).
concatenate
 Join a sequence of arrays along an existing axis.
hsplit
 Split array along second axis.
block
 Assemble arrays from blocks.
Examples
>>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.hstack((a,b)) array([1, 2, 3, 2, 3, 4]) >>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.hstack((a,b)) array([[1, 2], [2, 3], [3, 4]])

dask.array.
hypot
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Given the “legs” of a right triangle, return its hypotenuse.
Equivalent to
sqrt(x1**2 + x2**2)
, elementwise. If x1 or x2 is scalar_like (i.e., unambiguously castable to a scalar type), it is broadcast for use with each element of the other argument. (See Examples)Parameters:  x1, x2 : array_like
Leg of the triangle(s).
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  z : ndarray
The hypotenuse of the triangle(s). This is a scalar if both x1 and x2 are scalars.
Examples
>>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3))) # doctest: +SKIP array([[ 5., 5., 5.], [ 5., 5., 5.], [ 5., 5., 5.]])
Example showing broadcast of scalar_like argument:
>>> np.hypot(3*np.ones((3, 3)), [4]) # doctest: +SKIP array([[ 5., 5., 5.], [ 5., 5., 5.], [ 5., 5., 5.]])

dask.array.
imag
(*args, **kwargs)¶ Return the imaginary part of the complex argument.
Parameters:  val : array_like
Input array.
Returns:  out : ndarray or scalar
The imaginary component of the complex argument. If val is real, the type of val is used for the output. If val has complex elements, the returned type is float.
Examples
>>> a = np.array([1+2j, 3+4j, 5+6j]) # doctest: +SKIP >>> a.imag # doctest: +SKIP array([ 2., 4., 6.]) >>> a.imag = np.array([8, 10, 12]) # doctest: +SKIP >>> a # doctest: +SKIP array([ 1. +8.j, 3.+10.j, 5.+12.j]) >>> np.imag(1 + 1j) # doctest: +SKIP 1.0

dask.array.
indices
(dimensions, dtype=<class 'int'>, chunks='auto')¶ Implements NumPy’s
indices
for Dask Arrays.Generates a grid of indices covering the dimensions provided.
The final array has the shape
(len(dimensions), *dimensions)
. The chunks are used to specify the chunking for axis 1 up tolen(dimensions)
. The 0th axis always has chunks of length 1.Parameters:  dimensions : sequence of ints
The shape of the index grid.
 dtype : dtype, optional
Type to use for the array. Default is
int
. chunks : sequence of ints
The number of samples on each block. Note that the last block will have fewer samples if
len(array) % chunks != 0
.
Returns:  grid : dask array

dask.array.
insert
(arr, obj, values, axis=None)¶ Insert values along the given axis before the given indices.
Parameters:  arr : array_like
Input array.
 obj : int, slice or sequence of ints
Object that defines the index or indices before which values is inserted.
New in version 1.8.0.
Support for multiple insertions when obj is a single scalar or a sequence with one element (similar to calling insert multiple times).
 values : array_like
Values to insert into arr. If the type of values is different from that of arr, values is converted to the type of arr. values should be shaped so that
arr[...,obj,...] = values
is legal. axis : int, optional
Axis along which to insert values. If axis is None then arr is flattened first.
Returns:  out : ndarray
A copy of arr with values inserted. Note that insert does not occur inplace: a new array is returned. If axis is None, out is a flattened array.
See also
append
 Append elements at the end of an array.
concatenate
 Join a sequence of arrays along an existing axis.
delete
 Delete elements from an array.
Notes
Note that for higher dimensional inserts obj=0 behaves very different from obj=[0] just like arr[:,0,:] = values is different from arr[:,[0],:] = values.
Examples
>>> a = np.array([[1, 1], [2, 2], [3, 3]]) >>> a array([[1, 1], [2, 2], [3, 3]]) >>> np.insert(a, 1, 5) array([1, 5, 1, 2, 2, 3, 3]) >>> np.insert(a, 1, 5, axis=1) array([[1, 5, 1], [2, 5, 2], [3, 5, 3]])
Difference between sequence and scalars:
>>> np.insert(a, [1], [[1],[2],[3]], axis=1) array([[1, 1, 1], [2, 2, 2], [3, 3, 3]]) >>> np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1), ... np.insert(a, [1], [[1],[2],[3]], axis=1)) True
>>> b = a.flatten() >>> b array([1, 1, 2, 2, 3, 3]) >>> np.insert(b, [2, 2], [5, 6]) array([1, 1, 5, 6, 2, 2, 3, 3])
>>> np.insert(b, slice(2, 4), [5, 6]) array([1, 1, 5, 2, 6, 2, 3, 3])
>>> np.insert(b, [2, 2], [7.13, False]) # type casting array([1, 1, 7, 0, 2, 2, 3, 3])
>>> x = np.arange(8).reshape(2, 4) >>> idx = (1, 3) >>> np.insert(x, idx, 999, axis=1) array([[ 0, 999, 1, 2, 999, 3], [ 4, 999, 5, 6, 999, 7]])

dask.array.
invert
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute bitwise inversion, or bitwise NOT, elementwise.
Computes the bitwise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator
~
.For signed integer inputs, the two’s complement is returned. In a two’scomplement system negative numbers are represented by the two’s complement of the absolute value. This is the most common method of representing signed integers on computers [1]. A Nbit two’scomplement system can represent every integer in the range \(2^{N1}\) to \(+2^{N1}1\).
Parameters:  x : array_like
Only integer and boolean types are handled.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  out : ndarray or scalar
Result. This is a scalar if x is a scalar.
See also
bitwise_and
,bitwise_or
,bitwise_xor
,logical_not
binary_repr
 Return the binary representation of the input number as a string.
Notes
bitwise_not is an alias for invert:
>>> np.bitwise_not is np.invert # doctest: +SKIP True
References
[1] (1, 2) Wikipedia, “Two’s complement”, https://en.wikipedia.org/wiki/Two’s_complement Examples
We’ve seen that 13 is represented by
00001101
. The invert or bitwise NOT of 13 is then:>>> np.invert(np.array([13], dtype=uint8)) # doctest: +SKIP array([242], dtype=uint8) >>> np.binary_repr(x, width=8) # doctest: +SKIP '00001101' >>> np.binary_repr(242, width=8) # doctest: +SKIP '11110010'
The result depends on the bitwidth:
>>> np.invert(np.array([13], dtype=uint16)) # doctest: +SKIP array([65522], dtype=uint16) >>> np.binary_repr(x, width=16) # doctest: +SKIP '0000000000001101' >>> np.binary_repr(65522, width=16) # doctest: +SKIP '1111111111110010'
When using signed integer types the result is the two’s complement of the result for the unsigned type:
>>> np.invert(np.array([13], dtype=int8)) # doctest: +SKIP array([14], dtype=int8) >>> np.binary_repr(14, width=8) # doctest: +SKIP '11110010'
Booleans are accepted as well:
>>> np.invert(array([True, False])) # doctest: +SKIP array([False, True])

dask.array.
isclose
(a, b, rtol=1e05, atol=1e08, equal_nan=False)¶ Returns a boolean array where two arrays are elementwise equal within a tolerance.
The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference atol are added together to compare against the absolute difference between a and b.
Warning
The default atol is not appropriate for comparing numbers that are much smaller than one (see Notes).
Parameters:  a, b : array_like
Input arrays to compare.
 rtol : float
The relative tolerance parameter (see Notes).
 atol : float
The absolute tolerance parameter (see Notes).
 equal_nan : bool
Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.
Returns:  y : array_like
Returns a boolean array of where a and b are equal within the given tolerance. If both a and b are scalars, returns a single boolean value.
See also
Notes
New in version 1.7.0.
For finite values, isclose uses the following equation to test whether two floating point values are equivalent.
absolute(a  b) <= (atol + rtol * absolute(b))Unlike the builtin math.isclose, the above equation is not symmetric in a and b – it assumes b is the reference value – so that isclose(a, b) might be different from isclose(b, a). Furthermore, the default value of atol is not zero, and is used to determine what small values should be considered close to zero. The default value is appropriate for expected values of order unity: if the expected values are significantly smaller than one, it can result in false positives. atol should be carefully selected for the use case at hand. A zero value for atol will result in False if either a or b is zero.
Examples
>>> np.isclose([1e10,1e7], [1.00001e10,1e8]) array([True, False]) >>> np.isclose([1e10,1e8], [1.00001e10,1e9]) array([True, True]) >>> np.isclose([1e10,1e8], [1.0001e10,1e9]) array([False, True]) >>> np.isclose([1.0, np.nan], [1.0, np.nan]) array([True, False]) >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) array([True, True]) >>> np.isclose([1e8, 1e7], [0.0, 0.0]) array([ True, False], dtype=bool) >>> np.isclose([1e100, 1e7], [0.0, 0.0], atol=0.0) array([False, False], dtype=bool) >>> np.isclose([1e10, 1e10], [1e20, 0.0]) array([ True, True], dtype=bool) >>> np.isclose([1e10, 1e10], [1e20, 0.999999e10], atol=0.0) array([False, True], dtype=bool)

dask.array.
iscomplex
(*args, **kwargs)¶ Returns a bool array, where True if input element is complex.
What is tested is whether the input has a nonzero imaginary part, not if the input type is complex.
Parameters:  x : array_like
Input array.
Returns:  out : ndarray of bools
Output array.
Examples
>>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j]) # doctest: +SKIP array([ True, False, False, False, False, True])

dask.array.
isfinite
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Test elementwise for finiteness (not infinity or not Not a Number).
The result is returned as a boolean array.
Parameters:  x : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray, bool
True where
x
is not positive infinity, negative infinity, or NaN; false otherwise. This is a scalar if x is a scalar.
Notes
Not a Number, positive infinity and negative infinity are considered to be nonfinite.
NumPy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Also that positive infinity is not equivalent to negative infinity. But infinity is equivalent to positive infinity. Errors result if the second argument is also supplied when x is a scalar input, or if first and second arguments have different shapes.
Examples
>>> np.isfinite(1) # doctest: +SKIP True >>> np.isfinite(0) # doctest: +SKIP True >>> np.isfinite(np.nan) # doctest: +SKIP False >>> np.isfinite(np.inf) # doctest: +SKIP False >>> np.isfinite(np.NINF) # doctest: +SKIP False >>> np.isfinite([np.log(1.),1.,np.log(0)]) # doctest: +SKIP array([False, True, False])
>>> x = np.array([np.inf, 0., np.inf]) # doctest: +SKIP >>> y = np.array([2, 2, 2]) # doctest: +SKIP >>> np.isfinite(x, y) # doctest: +SKIP array([0, 1, 0]) >>> y # doctest: +SKIP array([0, 1, 0])

dask.array.
isin
(element, test_elements, assume_unique=False, invert=False)¶ Calculates element in test_elements, broadcasting over element only. Returns a boolean array of the same shape as element that is True where an element of element is in test_elements and False otherwise.
Parameters:  element : array_like
Input array.
 test_elements : array_like
The values against which to test each value of element. This argument is flattened if it is an array or array_like. See notes for behavior with nonarraylike parameters.
 assume_unique : bool, optional
If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False.
 invert : bool, optional
If True, the values in the returned array are inverted, as if calculating element not in test_elements. Default is False.
np.isin(a, b, invert=True)
is equivalent to (but faster than)np.invert(np.isin(a, b))
.
Returns:  isin : ndarray, bool
Has the same shape as element. The values element[isin] are in test_elements.
See also
in1d
 Flattened version of this function.
numpy.lib.arraysetops
 Module with a number of other functions for performing set operations on arrays.
Notes
isin is an elementwise function version of the python keyword in.
isin(a, b)
is roughly equivalent tonp.array([item in b for item in a])
if a and b are 1D sequences.element and test_elements are converted to arrays if they are not already. If test_elements is a set (or other nonsequence collection) it will be converted to an object array with one element, rather than an array of the values contained in test_elements. This is a consequence of the array constructor’s way of handling nonsequence collections. Converting the set to a list usually gives the desired behavior.
New in version 1.13.0.
Examples
>>> element = 2*np.arange(4).reshape((2, 2)) >>> element array([[0, 2], [4, 6]]) >>> test_elements = [1, 2, 4, 8] >>> mask = np.isin(element, test_elements) >>> mask array([[ False, True], [ True, False]]) >>> element[mask] array([2, 4])
The indices of the matched values can be obtained with nonzero:
>>> np.nonzero(mask) (array([0, 1]), array([1, 0]))
The test can also be inverted:
>>> mask = np.isin(element, test_elements, invert=True) >>> mask array([[ True, False], [ False, True]]) >>> element[mask] array([0, 6])
Because of how array handles sets, the following does not work as expected:
>>> test_set = {1, 2, 4, 8} >>> np.isin(element, test_set) array([[ False, False], [ False, False]])
Casting the set to a list gives the expected result:
>>> np.isin(element, list(test_set)) array([[ False, True], [ True, False]])

dask.array.
isinf
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Test elementwise for positive or negative infinity.
Returns a boolean array of the same shape as x, True where
x == +/inf
, otherwise False.Parameters:  x : array_like
Input values
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : bool (scalar) or boolean ndarray
True where
x
is positive or negative infinity, false otherwise. This is a scalar if x is a scalar.
Notes
NumPy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754).
Errors result if the second argument is supplied when the first argument is a scalar, or if the first and second arguments have different shapes.
Examples
>>> np.isinf(np.inf) # doctest: +SKIP True >>> np.isinf(np.nan) # doctest: +SKIP False >>> np.isinf(np.NINF) # doctest: +SKIP True >>> np.isinf([np.inf, np.inf, 1.0, np.nan]) # doctest: +SKIP array([ True, True, False, False])
>>> x = np.array([np.inf, 0., np.inf]) # doctest: +SKIP >>> y = np.array([2, 2, 2]) # doctest: +SKIP >>> np.isinf(x, y) # doctest: +SKIP array([1, 0, 1]) >>> y # doctest: +SKIP array([1, 0, 1])

dask.array.
isneginf
(*args, **kwargs)¶ Test elementwise for negative infinity, return result as bool array.
Parameters:  x : array_like
The input array.
 out : array_like, optional
A boolean array with the same shape and type as x to store the result.
Returns:  out : ndarray
A boolean array with the same dimensions as the input. If second argument is not supplied then a numpy boolean array is returned with values True where the corresponding element of the input is negative infinity and values False where the element of the input is not negative infinity.
If a second argument is supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True. The return value out is then a reference to that array.
Notes
NumPy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754).
Errors result if the second argument is also supplied when x is a scalar input, if first and second arguments have different shapes, or if the first argument has complex values.
Examples
>>> np.isneginf(np.NINF) # doctest: +SKIP array(True, dtype=bool) >>> np.isneginf(np.inf) # doctest: +SKIP array(False, dtype=bool) >>> np.isneginf(np.PINF) # doctest: +SKIP array(False, dtype=bool) >>> np.isneginf([np.inf, 0., np.inf]) # doctest: +SKIP array([ True, False, False])
>>> x = np.array([np.inf, 0., np.inf]) # doctest: +SKIP >>> y = np.array([2, 2, 2]) # doctest: +SKIP >>> np.isneginf(x, y) # doctest: +SKIP array([1, 0, 0]) >>> y # doctest: +SKIP array([1, 0, 0])

dask.array.
isnan
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Test elementwise for NaN and return result as a boolean array.
Parameters:  x : array_like
Input array.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or bool
True where
x
is NaN, false otherwise. This is a scalar if x is a scalar.
Notes
NumPy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity.
Examples
>>> np.isnan(np.nan) # doctest: +SKIP True >>> np.isnan(np.inf) # doctest: +SKIP False >>> np.isnan([np.log(1.),1.,np.log(0)]) # doctest: +SKIP array([ True, False, False])

dask.array.
isnull
(values)¶ pandas.isnull for dask arrays

dask.array.
isposinf
(*args, **kwargs)¶ Test elementwise for positive infinity, return result as bool array.
Parameters:  x : array_like
The input array.
 y : array_like, optional
A boolean array with the same shape as x to store the result.
Returns:  out : ndarray
A boolean array with the same dimensions as the input. If second argument is not supplied then a boolean array is returned with values True where the corresponding element of the input is positive infinity and values False where the element of the input is not positive infinity.
If a second argument is supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True. The return value out is then a reference to that array.
Notes
NumPy uses the IEEE Standard for Binary FloatingPoint for Arithmetic (IEEE 754).
Errors result if the second argument is also supplied when x is a scalar input, if first and second arguments have different shapes, or if the first argument has complex values
Examples
>>> np.isposinf(np.PINF) # doctest: +SKIP array(True, dtype=bool) >>> np.isposinf(np.inf) # doctest: +SKIP array(True, dtype=bool) >>> np.isposinf(np.NINF) # doctest: +SKIP array(False, dtype=bool) >>> np.isposinf([np.inf, 0., np.inf]) # doctest: +SKIP array([False, False, True])
>>> x = np.array([np.inf, 0., np.inf]) # doctest: +SKIP >>> y = np.array([2, 2, 2]) # doctest: +SKIP >>> np.isposinf(x, y) # doctest: +SKIP array([0, 0, 1]) >>> y # doctest: +SKIP array([0, 0, 1])

dask.array.
isreal
(*args, **kwargs)¶ Returns a bool array, where True if input element is real.
If element has complex type with zero complex part, the return value for that element is True.
Parameters:  x : array_like
Input array.
Returns:  out : ndarray, bool
Boolean array of same shape as x.
Examples
>>> np.isreal([1+1j, 1+0j, 4.5, 3, 2, 2j]) # doctest: +SKIP array([False, True, True, True, True, False])

dask.array.
ldexp
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Returns x1 * 2**x2, elementwise.
The mantissas x1 and twos exponents x2 are used to construct floating point numbers
x1 * 2**x2
.Parameters:  x1 : array_like
Array of multipliers.
 x2 : array_like, int
Array of twos exponents.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or scalar
The result of
x1 * 2**x2
. This is a scalar if both x1 and x2 are scalars.
See also
frexp
 Return (y1, y2) from
x = y1 * 2**y2
, inverse to ldexp.
Notes
Complex dtypes are not supported, they will raise a TypeError.
ldexp is useful as the inverse of frexp, if used by itself it is more clear to simply use the expression
x1 * 2**x2
.Examples
>>> np.ldexp(5, np.arange(4)) # doctest: +SKIP array([ 5., 10., 20., 40.], dtype=float32)
>>> x = np.arange(6) # doctest: +SKIP >>> np.ldexp(*np.frexp(x)) # doctest: +SKIP array([ 0., 1., 2., 3., 4., 5.])

dask.array.
linspace
(start, stop, num=50, endpoint=True, retstep=False, chunks='auto', dtype=None)¶ Return num evenly spaced values over the closed interval [start, stop].
Parameters:  start : scalar
The starting value of the sequence.
 stop : scalar
The last value of the sequence.
 num : int, optional
Number of samples to include in the returned dask array, including the endpoints. Default is 50.
 endpoint : bool, optional
If True,
stop
is the last sample. Otherwise, it is not included. Default is True. retstep : bool, optional
If True, return (samples, step), where step is the spacing between samples. Default is False.
 chunks : int
The number of samples on each block. Note that the last block will have fewer samples if num % blocksize != 0
 dtype : dtype, optional
The type of the output array.
Returns:  samples : dask array
 step : float, optional
Only returned if
retstep
is True. Size of spacing between samples.
See also

dask.array.
log
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Natural logarithm, elementwise.
The natural logarithm log is the inverse of the exponential function, so that log(exp(x)) = x. The natural logarithm is logarithm in base e.
Parameters:  x : array_like
Input value.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray
The natural logarithm of x, elementwise. This is a scalar if x is a scalar.
Notes
Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, log is a complex analytical function that has a branch cut [inf, 0] and is continuous from above on it. log handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm Examples
>>> np.log([1, np.e, np.e**2, 0]) # doctest: +SKIP array([ 0., 1., 2., Inf])

dask.array.
log10
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Return the base 10 logarithm of the input array, elementwise.
Parameters:  x : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray
The logarithm to the base 10 of x, elementwise. NaNs are returned where x is negative. This is a scalar if x is a scalar.
See also
emath.log10
Notes
Logarithm is a multivalued function: for each x there is an infinite number of z such that 10**z = x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log10 always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, log10 is a complex analytical function that has a branch cut [inf, 0] and is continuous from above on it. log10 handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm Examples
>>> np.log10([1e15, 3.]) # doctest: +SKIP array([15., NaN])

dask.array.
log1p
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Return the natural logarithm of one plus the input array, elementwise.
Calculates
log(1 + x)
.Parameters:  x : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray
Natural logarithm of 1 + x, elementwise. This is a scalar if x is a scalar.
See also
expm1
exp(x)  1
, the inverse of log1p.
Notes
For realvalued input, log1p is accurate also for x so small that 1 + x == 1 in floatingpoint accuracy.
Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = 1 + x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log1p always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, log1p is a complex analytical function that has a branch cut [inf, 1] and is continuous from above on it. log1p handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
References
[1] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ [2] Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm Examples
>>> np.log1p(1e99) # doctest: +SKIP 1e99 >>> np.log(1 + 1e99) # doctest: +SKIP 0.0

dask.array.
log2
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Base2 logarithm of x.
Parameters:  x : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray
Base2 logarithm of x. This is a scalar if x is a scalar.
Notes
New in version 1.3.0.
Logarithm is a multivalued function: for each x there is an infinite number of z such that 2**z = x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log2 always returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nan
and sets the invalid floating point error flag.For complexvalued input, log2 is a complex analytical function that has a branch cut [inf, 0] and is continuous from above on it. log2 handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
Examples
>>> x = np.array([0, 1, 2, 2**4]) # doctest: +SKIP >>> np.log2(x) # doctest: +SKIP array([Inf, 0., 1., 4.])
>>> xi = np.array([0+1.j, 1, 2+0.j, 4.j]) # doctest: +SKIP >>> np.log2(xi) # doctest: +SKIP array([ 0.+2.26618007j, 0.+0.j , 1.+0.j , 2.+2.26618007j])

dask.array.
logaddexp
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Logarithm of the sum of exponentiations of the inputs.
Calculates
log(exp(x1) + exp(x2))
. This function is useful in statistics where the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the logarithm of the calculated probability is stored. This function allows adding probabilities stored in such a fashion.Parameters:  x1, x2 : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  result : ndarray
Logarithm of
exp(x1) + exp(x2)
. This is a scalar if both x1 and x2 are scalars.
See also
logaddexp2
 Logarithm of the sum of exponentiations of inputs in base 2.
Notes
New in version 1.3.0.
Examples
>>> prob1 = np.log(1e50) # doctest: +SKIP >>> prob2 = np.log(2.5e50) # doctest: +SKIP >>> prob12 = np.logaddexp(prob1, prob2) # doctest: +SKIP >>> prob12 # doctest: +SKIP 113.87649168120691 >>> np.exp(prob12) # doctest: +SKIP 3.5000000000000057e50

dask.array.
logaddexp2
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Logarithm of the sum of exponentiations of the inputs in base2.
Calculates
log2(2**x1 + 2**x2)
. This function is useful in machine learning when the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the base2 logarithm of the calculated probability can be used instead. This function allows adding probabilities stored in such a fashion.Parameters:  x1, x2 : array_like
Input values.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  result : ndarray
Base2 logarithm of
2**x1 + 2**x2
. This is a scalar if both x1 and x2 are scalars.
See also
logaddexp
 Logarithm of the sum of exponentiations of the inputs.
Notes
New in version 1.3.0.
Examples
>>> prob1 = np.log2(1e50) # doctest: +SKIP >>> prob2 = np.log2(2.5e50) # doctest: +SKIP >>> prob12 = np.logaddexp2(prob1, prob2) # doctest: +SKIP >>> prob1, prob2, prob12 # doctest: +SKIP (166.09640474436813, 164.77447664948076, 164.28904982231052) >>> 2**prob12 # doctest: +SKIP 3.4999999999999914e50

dask.array.
logical_and
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute the truth value of x1 AND x2 elementwise.
Parameters:  x1, x2 : array_like
Input arrays. x1 and x2 must be of the same shape.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or bool
Boolean result with the same shape as x1 and x2 of the logical AND operation on corresponding elements of x1 and x2. This is a scalar if both x1 and x2 are scalars.
See also
Examples
>>> np.logical_and(True, False) # doctest: +SKIP False >>> np.logical_and([True, False], [False, False]) # doctest: +SKIP array([False, False])
>>> x = np.arange(5) # doctest: +SKIP >>> np.logical_and(x>1, x<4) # doctest: +SKIP array([False, False, True, True, False])

dask.array.
logical_not
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute the truth value of NOT x elementwise.
Parameters:  x : array_like
Logical NOT is applied to the elements of x.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : bool or ndarray of bool
Boolean result with the same shape as x of the NOT operation on elements of x. This is a scalar if x is a scalar.
See also
Examples
>>> np.logical_not(3) # doctest: +SKIP False >>> np.logical_not([True, False, 0, 1]) # doctest: +SKIP array([False, True, True, False])
>>> x = np.arange(5) # doctest: +SKIP >>> np.logical_not(x<3) # doctest: +SKIP array([False, False, False, True, True])

dask.array.
logical_or
(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Compute the truth value of x1 OR x2 elementwise.
Parameters:  x1, x2 : array_like
Logical OR is applied to the elements of x1 and x2. They have to be of the same shape.
 out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
 **kwargs
For other keywordonly arguments, see the ufunc docs.
Returns:  y : ndarray or bool
Boolean result with the same shape as x1 and x2 of the logical OR operation on elements of x1 and x2. This is a scalar if both x1 and x2 are scalars.
See also