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Array programming with Numpy

mustafa sarac
mustafa sarac

NumPy is the primary library for array programming in Python. It provides a multidimensional array object and array-aware functions that operate on the array. NumPy arrays store data and metadata like data type, shape, and strides to efficiently access and manipulate multidimensional data. Users interact with NumPy arrays using indexing to access elements and subarrays, operators for element-wise operations, and functions that perform vectorized calculations on entire arrays. NumPy handles looping over array elements to optimize performance while providing a simple and powerful programming interface for scientific computing in Python.

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Nature | Vol 585 | 17 September 2020 | 357 Review ArrayprogrammingwithNumPy Charles R. Harris1 , K. Jarrod Millman2,3,4 ✉, Stéfan J. van der Walt2,4,5 ✉, Ralf Gommers6 ✉, Pauli Virtanen7,8 , David Cournapeau9 , Eric Wieser10 , Julian Taylor11 , Sebastian Berg4 , Nathaniel J. Smith12 , Robert Kern13 , Matti Picus4 , Stephan Hoyer14 , Marten H. van Kerkwijk15 , Matthew Brett2,16 , Allan Haldane17 , Jaime Fernández del Río18 , Mark Wiebe19,20 , Pearu Peterson6,21,22 , Pierre Gérard-Marchant23,24 , Kevin Sheppard25 , Tyler Reddy26 , Warren Weckesser4 , Hameer Abbasi6 , Christoph Gohlke27 & Travis E. Oliphant6 Arrayprogrammingprovidesapowerful,compactandexpressivesyntaxfor accessing,manipulatingandoperatingondatainvectors,matricesand higher-dimensionalarrays.NumPyistheprimaryarrayprogramminglibraryforthe Pythonlanguage.Ithasanessentialroleinresearchanalysispipelinesinfieldsas diverseasphysics,chemistry,astronomy,geoscience,biology,psychology,materials science,engineering,financeandeconomics.Forexample,inastronomy,NumPywas animportantpartofthesoftwarestackusedinthediscoveryofgravitationalwaves1 andinthefirstimagingofablackhole2 .Herewereviewhowafewfundamentalarray conceptsleadtoasimpleandpowerfulprogrammingparadigmfororganizing, exploringandanalysingscientificdata.NumPyisthefoundationuponwhichthe scientificPythonecosystemisconstructed.Itissopervasivethatseveralprojects, targetingaudienceswithspecializedneeds,havedevelopedtheirownNumPy-like interfacesandarrayobjects.Owingtoitscentralpositionintheecosystem,NumPy increasinglyactsasaninteroperabilitylayerbetweensucharraycomputation librariesand,togetherwithitsapplicationprogramminginterface(API),providesa flexibleframeworktosupportthenextdecadeofscientificandindustrialanalysis. TwoPythonarraypackagesexistedbeforeNumPy.TheNumericpack- age was developed in the mid-1990s and provided array objects and array-awarefunctionsinPython.ItwaswritteninCandlinkedtostand- ardfastimplementationsoflinearalgebra3,4 .Oneofitsearliestuseswas to steer C++ applications for inertial confinement fusion research at LawrenceLivermoreNationalLaboratory5 .Tohandlelargeastronomi- calimagescomingfromtheHubbleSpaceTelescope,areimplementa- tionofNumeric,calledNumarray,addedsupportforstructuredarrays, flexibleindexing,memorymapping,byte-ordervariants,moreefficient memoryuse,flexibleIEEE754-standarderror-handlingcapabilities,and bettertype-castingrules6 .AlthoughNumarraywashighlycompatible withNumeric,thetwopackageshadenoughdifferencesthatitdivided the community; however, in 2005 NumPy emerged as a ‘best of both worlds’ unification7 —combining the features of Numarray with the small-array performance of Numeric and its rich C API. Now, 15 years later, NumPy underpins almost every Python library that does scientific or numerical computation8–11 , including SciPy12 , Matplotlib13 , pandas14 , scikit-learn15 and scikit-image16 . NumPy is a community-developed, open-source library, which provides a mul- tidimensional Python array object along with array-aware functions thatoperateonit.Becauseofitsinherentsimplicity,theNumPyarray is the de facto exchange format for array data in Python. NumPyoperatesonin-memoryarraysusingthecentralprocessing unit(CPU).Toutilizemodern,specializedstorageandhardware,there has been a recent proliferation of Python array packages. Unlike with the Numarray–Numeric divide, it is now much harder for these new libraries to fracture the user community—given how much work is alreadybuiltontopofNumPy.However,toprovidethecommunitywith access to new and exploratory technologies, NumPy is transitioning into a central coordinating mechanism that specifies a well defined array programming API and dispatches it, as appropriate, to special- ized array implementations. NumPyarrays TheNumPyarrayisadatastructurethatefficientlystoresandaccesses multidimensionalarrays17 (alsoknownastensors),andenablesawide variety of scientific computation. It consists of a pointer to memory, along with metadata used to interpret the data stored there, notably ‘data type’, ‘shape’ and ‘strides’ (Fig. 1a). https://doi.org/10.1038/s41586-020-2649-2 Received: 21 February 2020 Accepted: 17 June 2020 Published online: 16 September 2020 Open access Check for updates 1 Independent researcher, Logan, UT, USA. 2 Brain Imaging Center, University of California, Berkeley, Berkeley, CA, USA. 3 Division of Biostatistics, University of California, Berkeley, Berkeley, CA, USA. 4 Berkeley Institute for Data Science, University of California, Berkeley, Berkeley, CA, USA. 5 Applied Mathematics, Stellenbosch University, Stellenbosch, South Africa. 6 Quansight, Austin, TX, USA. 7 Department of Physics, University of Jyväskylä, Jyväskylä, Finland. 8 Nanoscience Center, University of Jyväskylä, Jyväskylä, Finland. 9 Mercari JP, Tokyo, Japan. 10 Department of Engineering, University of Cambridge, Cambridge, UK. 11 Independent researcher, Karlsruhe, Germany. 12 Independent researcher, Berkeley, CA, USA. 13 Enthought, Austin, TX, USA. 14 Google Research, Mountain View, CA, USA. 15 Department of Astronomy and Astrophysics, University of Toronto, Toronto, Ontario, Canada. 16 School of Psychology, University of Birmingham, Edgbaston, Birmingham, UK. 17 Department of Physics, Temple University, Philadelphia, PA, USA. 18 Google, Zurich, Switzerland. 19 Department of Physics and Astronomy, The University of British Columbia, Vancouver, British Columbia, Canada. 20 Amazon, Seattle, WA, USA. 21 Independent researcher, Saue, Estonia. 22 Department of Mechanics and Applied Mathematics, Institute of Cybernetics at Tallinn Technical University, Tallinn, Estonia. 23 Department of Biological and Agricultural Engineering, University of Georgia, Athens, GA, USA. 24 France-IX Services, Paris, France. 25 Department of Economics, University of Oxford, Oxford, UK. 26 CCS-7, Los Alamos National Laboratory, Los Alamos, NM, USA. 27 Laboratory for Fluorescence Dynamics, Biomedical Engineering Department, University of California, Irvine, Irvine, CA, USA. ✉e-mail: millman@berkeley.edu; stefanv@berkeley.edu; ralf.gommers@gmail.com
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358 | Nature | Vol 585 | 17 September 2020 Review The data type describes the nature of elements stored in an array. Anarrayhasasingledatatype,andeachelementofanarrayoccupies thesamenumberofbytesinmemory.Examplesofdatatypesinclude real and complex numbers (of lower and higher precision), strings, timestamps and pointers to Python objects. The shape of an array determines the number of elements along each axis, and the number of axes is the dimensionality of the array. For example, a vector of numbers can be stored as a one-dimensional array of shape N, whereas colour videos are four-dimensional arrays of shape (T, M, N, 3). Strides are necessary to interpret computer memory, which stores elementslinearly,asmultidimensionalarrays.Theydescribethenum- berofbytestomoveforwardinmemorytojumpfromrowtorow,col- umntocolumn,andsoforth.Consider,forexample,atwo-dimensional arrayoffloating-pointnumberswithshape(4, 3),whereeachelement occupies 8 bytes in memory. To move between consecutive columns, weneedtojumpforward8 bytesinmemory,andtoaccessthenextrow, 3 × 8 = 24 bytes. The strides of that array are therefore (24, 8). NumPy canstorearraysineitherCorFortranmemoryorder,iteratingfirstover either rows or columns. This allows external libraries written in those languages to access NumPy array data in memory directly. Users interact with NumPy arrays using ‘indexing’ (to access sub- arrays or individual elements), ‘operators’ (for example, +, − and × for vectorized operations and @ for matrix multiplication), as well as‘array-awarefunctions’;together,theseprovideaneasilyreadable, expressive, high-level API for array programming while NumPy deals with the underlying mechanics of making operations fast. Indexing an array returns single elements, subarrays or elements that satisfy a specific condition (Fig. 1b). Arrays can even be indexed usingotherarrays(Fig. 1c).Whereverpossible,indexingthatretrievesa subarrayreturnsa‘view’ontheoriginalarraysuchthatdataareshared between the two arrays. This provides a powerful way to operate on subsets of array data while limiting memory usage. To complement the array syntax, NumPy includes functions that perform vectorized calculations on arrays, including arithmetic, statistics and trigonometry (Fig. 1d). Vectorization—operating on entirearraysratherthantheirindividualelements—isessentialtoarray programming.Thismeansthatoperationsthatwouldtakemanytens oflinestoexpressinlanguagessuchasCcanoftenbeimplementedas asingle,clearPythonexpression.Thisresultsinconcisecodeandfrees users to focus on the details of their analysis, while NumPy handles looping over array elements near-optimally—for example, taking strides into consideration to best utilize the computer’s fast cache memory. Whenperformingavectorizedoperation(suchasaddition)ontwo arrays with the same shape, it is clear what should happen. Through ‘broadcasting’ NumPy allows the dimensions to differ, and produces results that appeal to intuition. A trivial example is the addition of a scalarvaluetoanarray,butbroadcastingalsogeneralizestomorecom- plex examples such as scaling each column of an array or generating agridofcoordinates.Inbroadcasting,oneorbotharraysarevirtually duplicated (that is, without copying any data in memory), so that the shapes of the operands match (Fig. 1d). Broadcasting is also applied when an array is indexed using arrays of indices (Fig. 1c). Other array-aware functions, such as sum, mean and maximum, performelement-by-element‘reductions’,aggregatingresultsacross one, multiple or all axes of a single array. For example, summing an n-dimensional array over d axes results in an array of dimension n − d (Fig. 1f). NumPyalsoincludesarray-awarefunctionsforcreating,reshaping, concatenating and padding arrays; searching, sorting and counting data; and reading and writing files. It provides extensive support for generatingpseudorandomnumbers,includesanassortmentofprob- ability distributions, and performs accelerated linear algebra, using oneofseveralbackendssuchasOpenBLAS18,19 orIntelMKLoptimized for the CPUs at hand (see Supplementary Methods for more details). Altogether, the combination of a simple in-memory array repre- sentation, a syntax that closely mimics mathematics, and a variety of array-aware utility functions forms a productive and powerfully expressive array programming language. In [1]: import numpy as np In [2]: x = np.arange(12) In [3]: x = x.reshape(4, 3) In [4]: x Out[4]: array([[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11]]) In [5]: np.mean(x, axis=0) Out[5]: array([4.5, 5.5, 6.5]) In [6]: x = x - np.mean(x, axis=0) In [7]: x Out[7]: array([[-4.5, -4.5, -4.5], [-1.5, -1.5, -1.5], [ 1.5, 1.5, 1.5], [ 4.5, 4.5, 4.5]]) a Data structure g Example x = 0 1 2 3 4 5 6 7 8 9 10 11 data data type shape strides 8-byte integer (4, 3) (24, 8) 1 2 3 4 5 6 70 8 9 10 11 8 bytes per element 3 × 8 = 24 bytes to jump one row down b Indexing (view) 10 1199 x[:,1:] → with slices 1 2 4 5 7 8 00 33 66 x[:,::2]→ with slices with steps 0 2 3 5 6 8 9 11 0 11 2 3 44 5 6 77 8 9 1010 11 Slices are start:end:step, any of which can be left blank d Vectorization + → 0 1 3 4 6 7 9 10 1 1 1 1 1 1 1 1 1 2 4 5 7 8 10 11 e Broadcasting × 3 6 0 9 1 2 → 0 0 3 6 6 12 9 18 f Reduction 0 1 3 4 6 7 9 10 2 5 8 11 3 12 21 30 sum axis 1 18 22 26 sum axis 0 66 sum axis (0,1) c Indexing (copy) 4 3 7 6 with arrays with broadcasting →x → ,2 1 1 0 x , 1 1 2 2 1 0 1 0 x with arraysx[0,1],x[1,2] 1 5→ →0 1 1 2 , x[x > 9] with masks10 11→→ 5 with scalarsx[1,2] Fig.1|TheNumPyarrayincorporatesseveralfundamentalarrayconcepts. a,TheNumPyarraydatastructureanditsassociatedmetadatafields. b,Indexinganarraywithslicesandsteps.Theseoperationsreturna‘view’of theoriginaldata.c,Indexinganarraywithmasks,scalarcoordinatesorother arrays,sothatitreturnsa‘copy’oftheoriginaldata.Inthebottomexample,an arrayisindexedwithotherarrays;thisbroadcaststheindexingarguments beforeperformingthelookup.d,Vectorizationefficientlyappliesoperations togroupsofelements.e,Broadcastinginthemultiplicationoftwo-dimensional arrays.f,Reductionoperationsactalongoneormoreaxes.Inthisexample, anarrayissummedalongselectaxestoproduceavector,oralongtwoaxes consecutivelytoproduceascalar.g,ExampleNumPycode,illustratingsomeof theseconcepts.
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Nature | Vol 585 | 17 September 2020 | 359 ScientificPythonecosystem Pythonisanopen-source,general-purposeinterpretedprogramming languagewellsuitedtostandardprogrammingtaskssuchascleaning data,interactingwithwebresourcesandparsingtext.Addingfastarray operations and linear algebra enables scientists to do all their work withinasingleprogramminglanguage—onethathastheadvantageof being famously easy to learn and teach, as witnessed by its adoption as a primary learning language in many universities. Even though NumPy is not part of Python’s standard library, it ben- efits from a good relationship with the Python developers. Over the years,thePythonlanguagehasaddednewfeaturesandspecialsyntax so that NumPy would have a more succinct and easier-to-read array notation.However,becauseitisnotpartofthestandardlibrary,NumPy is able to dictate its own release policies and development patterns. SciPyandMatplotlibaretightlycoupledwithNumPyintermsofhis- tory,developmentanduse.SciPyprovidesfundamentalalgorithmsfor scientificcomputing,includingmathematical,scientificandengineer- ingroutines.Matplotlibgeneratespublication-readyfiguresandvisu- alizations.ThecombinationofNumPy,SciPyandMatplotlib,together with an advanced interactive environment such as IPython20 or Jupy- ter21 ,providesasolidfoundationforarrayprogramminginPython.The scientificPythonecosystem(Fig. 2)buildsontopofthisfoundationto provide several, widely used technique-specific libraries15,16,22 , that in turn underlie numerous domain-specific projects23–28 . NumPy, at the base of the ecosystem of array-aware libraries, sets documentation standards, provides array testing infrastructure and adds build sup- port for Fortran and other compilers. Manyresearchgroupshavedesignedlarge,complexscientificlibrar- ies that add application-specific functionality to the ecosystem. For example, the eht-imaging library29 , developed by the Event Horizon Telescope collaboration for radio interferometry imaging, analysis andsimulation,reliesonmanylower-levelcomponentsofthescientific Pythonecosystem.Inparticular,theEHTcollaborationusedthislibrary forthefirstimagingofablackhole.Withineht-imaging,NumPyarrays are used to store and manipulate numerical data at every step in the processingchain:fromrawdatathroughcalibrationandimagerecon- struction.SciPysuppliestoolsforgeneralimage-processingtaskssuch asfilteringandimagealignment,andscikit-image,animage-processing library that extends SciPy, provides higher-level functionality such as edge filters and Hough transforms. The ‘scipy.optimize’ module performsmathematicaloptimization.NetworkX22 ,apackageforcom- plexnetworkanalysis,isusedtoverifyimagecomparisonconsistency. Astropy23,24 handlesstandardastronomicalfileformatsandcomputes time–coordinatetransformations.Matplotlibisusedtovisualizedata and to generate the final image of the black hole. Theinteractiveenvironmentcreatedbythearray programmingfoun- dation and the surrounding ecosystem of tools—inside of IPython or Jupyter—isideallysuitedtoexploratorydataanalysis.Userscanfluidly inspect,manipulateandvisualizetheirdata,andrapidlyiteratetorefine programmingstatements.Thesestatementsarethenstitchedtogether intoimperativeorfunctionalprograms,ornotebookscontainingboth computationandnarrative.Scientificcomputingbeyondexploratory workisoftendoneinatexteditororanintegrateddevelopmentenvi- ronment (IDE) such as Spyder. This rich and productive environment has made Python popular for scientific research. To complement this facility for exploratory work and rapid proto- typing,NumPyhasdevelopedacultureofusingtime-testedsoftware engineeringpracticestoimprovecollaborationandreduceerror30 .This culture is not only adopted by leaders in the project but also enthusi- astically taught to newcomers. The NumPy team was early to adopt distributedrevisioncontrolandcodereviewtoimprovecollaboration cantera Chemistry Biopython Biology Astropy Astronomy simpeg Geophysics NLTK Linguistics QuantEcon Economics SciPy Algorithms Matplotlib Plots scikit-learn Machine learning NetworkX Network analysis pandas, statsmodels Statistics scikit-image Image processing PsychoPykhmer Qiime2 FiPy deepchem librosaPyWavelets SunPy QuTiP yt nibabel yellowbrickmne-python scikit-HEP eht-imagingMDAnalysis iriscesium PyChrono Foundation Application-specific Domain-specific Technique-specific Array ProtocolsNumPy API Python Language IPython / Jupyter Interactive environments NumPy Arrays New array implementations Fig.2|NumPyisthebaseofthescientificPythonecosystem.EssentiallibrariesandprojectsthatdependonNumPy’sAPIgainaccesstonewarray implementationsthatsupportNumPy’sarrayprotocols(Fig. 3).
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360 | Nature | Vol 585 | 17 September 2020 Review oncode,andcontinuoustestingthatrunsanextensivebatteryofauto- mated tests for every proposed change to NumPy. The project also hascomprehensive,high-qualitydocumentation,integratedwiththe source code31–33 . Thiscultureofusingbestpracticesforproducingreliablescientific softwarehasbeenadoptedbytheecosystemoflibrariesthatbuildon NumPy.Forexample,inarecentawardgivenbytheRoyalAstronomi- cal Society to Astropy, they state: “The Astropy Project has provided hundredsofjuniorscientistswithexperienceinprofessional-standard softwaredevelopmentpracticesincludinguseofversioncontrol,unit testing, code review and issue tracking procedures. This is a vital skill setformodernresearchersthatisoftenmissingfromformaluniversity educationinphysicsorastronomy”34 .Communitymembersexplicitly work to address this lack of formal education through courses and workshops35–37 . Therecentrapidgrowthofdatascience,machinelearningandarti- ficial intelligence has further and dramatically boosted the scientific use of Python. Examples of its important applications, such as the eht-imaging library, now exist in almost every discipline in the natu- ralandsocialsciences.Thesetoolshavebecometheprimarysoftware environmentinmanyfields.NumPyanditsecosystemarecommonly taught in university courses, boot camps and summer schools, and are the focus of community conferences and workshops worldwide. NumPy and its API have become truly ubiquitous. Arrayproliferationandinteroperability NumPyprovidesin-memory,multidimensional,homogeneouslytyped (thatis,single-pointerandstrided)arraysonCPUs.Itrunsonmachines rangingfromembeddeddevicestotheworld’slargestsupercomputers, withperformanceapproachingthatofcompiledlanguages.Formost its existence, NumPy addressed the vast majority of array computa- tion use cases. However,scientificdatasetsnowroutinelyexceedthememorycapac- ity of a single machine and may be stored on multiple machines or in thecloud.Inaddition,therecentneedtoacceleratedeep-learningand artificialintelligenceapplicationshasledtotheemergenceofspecial- izedacceleratorhardware,includinggraphicsprocessingunits(GPUs), tensor processing units (TPUs) and field-programmable gate arrays (FPGAs).Owingtoitsin-memorydatamodel,NumPyiscurrentlyunable to directly utilize such storage and specialized hardware. However, both distributed data and also the parallel execution of GPUs, TPUs andFPGAsmapwelltotheparadigmofarrayprogramming:therefore leadingtoagapbetweenavailablemodernhardwarearchitecturesand the tools necessary to leverage their computational power. Thecommunity’seffortstofillthisgapledtoaproliferationofnew array implementations. For example, each deep-learning framework created its own arrays; the PyTorch38 , Tensorflow39 , Apache MXNet40 and JAX arrays all have the capability to run on CPUs and GPUs in a distributed fashion, using lazy evaluation to allow for additional per- formanceoptimizations.SciPyandPyData/Sparsebothprovidesparse arrays,whichtypicallycontainfewnon-zerovaluesandstoreonlythose in memory for efficiency. In addition, there are projects that build on NumPy arrays as data containers, and extend its capabilities. Distrib- uted arrays are made possible that way by Dask, and labelled arrays— referring to dimensions of an array by name rather than by index for clarity, compare x[:, 1] versus x.loc[:, 'time']—by xarray41 . Such libraries often mimic the NumPy API, because this lowers the barriertoentryfornewcomersandprovidesthewidercommunitywith astablearray programminginterface.This,inturn,preventsdisruptive schisms such as the divergence between Numeric and Numarray. But exploring new ways of working with arrays is experimental by nature and,infact,severalpromisinglibraries(suchasTheanoandCaffe)have alreadyceaseddevelopment.Andeachtimethatauserdecidestotrya newtechnology,theymustchangeimportstatementsandensurethatthe newlibraryimplementsallthepartsoftheNumPyAPItheycurrentlyuse. Ideally, operating on specialized arrays using NumPy functions or semantics would simply work, so that users could write code once, and would then benefit from switching between NumPy arrays, GPU arrays,distributedarraysandsoforthasappropriate.Tosupportarray operations between external array objects, NumPy therefore added the capability to act as a central coordination mechanism with a well specified API (Fig. 2). To facilitate this interoperability, NumPy provides ‘protocols’ (or contractsofoperation),thatallowforspecializedarraystobepassedto NumPyfunctions(Fig. 3).NumPy,inturn,dispatchesoperationstothe originatinglibrary,asrequired.Overfourhundredofthemostpopular NumPy functions are supported. The protocols are implemented by widely used libraries such as Dask, CuPy, xarray and PyData/Sparse. Thankstothesedevelopments,userscannow,forexample,scaletheir computationfromasinglemachinetodistributedsystemsusingDask. The protocols also compose well, allowing users to redeploy NumPy codeatscaleondistributed,multi-GPUsystemsvia,forinstance,CuPy arrays embedded in Dask arrays. Using NumPy’s high-level API, users can leverage highly parallel code execution on multiple systems with millions of cores, all with minimal code changes42 . These array protocols are now a key feature of NumPy, and are expected to only increase in importance. The NumPy developers— many of whom are authors of this Review—iteratively refine and add protocol designs to improve utility and simplify adoption. Output arrays Input arrays NumPy API np.stack np.reshape np.transpose np.argmin np.mean np.std np.max np.cos np.arctan np.log np.cumsum np.diff ... NumPy array protocols In [1]: import numpy as np In [2]: import dask.array as da In [3]: x = da.arange(12) In [4]: x = np.reshape(x, (4, 3)) In [5]: x Out[5]: dask.array<..., shape=(4, 3), ...> In [6]: np.mean(x, axis=0) Out[6]: dask.array<..., shape=(3,), ...> In [7]: x = x - np.mean(x, axis=0) In [8]: x Out[8]: dask.array<..., shape=(4, 3), ...> Array implementation NumPy Dask CuPy PyData/ Sparse ... ... Dask NumPy CuPy PyData Sparse ... Dask NumPy CuPy PyData Sparse Fig.3|NumPy’sAPIandarrayprotocolsexposenewarraystothe ecosystem.Inthisexample,NumPy’s‘mean’functioniscalledonaDaskarray. Thecallsucceedsbydispatchingtotheappropriatelibraryimplementation(in thiscase,Dask)andresultsinanewDaskarray.Comparethiscodetothe examplecodeinFig. 1g.
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Nature | Vol 585 | 17 September 2020 | 361 Discussion NumPy combines the expressive power of array programming, the performanceofC,andthereadability,usabilityandversatilityofPython inamature,welltested,welldocumentedandcommunity-developed library.LibrariesinthescientificPythonecosystemprovidefastimple- mentations of most important algorithms. Where extreme optimiza- tion is warranted, compiled languages can be used, such as Cython43 , Numba44 and Pythran45 ; these languages extend Python and trans- parently accelerate bottlenecks. Owing to NumPy’s simple memory model, it is easy to write low-level, hand-optimized code, usually in C orFortran,tomanipulateNumPyarraysandpassthembacktoPython. Furthermore, using array protocols, it is possible to utilize the full spectrumofspecializedhardwareaccelerationwithminimalchanges to existing code. NumPywasinitiallydevelopedbystudents,facultyandresearchers to provide an advanced, open-source array programming library for Python,whichwasfreetouseandunencumberedbylicenseserversand softwareprotectiondongles.Therewasasenseofbuildingsomething consequential together for the benefit of many others. Participating in such an endeavour, within a welcoming community of like-minded individuals, held a powerful attraction for many early contributors. These user–developers frequently had to write code from scratch to solve their own or their colleagues’ problems—often in low-level languages that preceded Python, such as Fortran46 and C. To them, theadvantagesofaninteractive,high-levelarraylibrarywereevident. Thedesignofthisnewtoolwasinformedbyotherpowerfulinteractive programming languages for scientific computing such as Basis47–50 , Yorick51 , R52 and APL53 , as well as commercial languages and environ- ments such as IDL (Interactive Data Language) and MATLAB. WhatbeganasanattempttoaddanarrayobjecttoPythonbecame thefoundationofavibrantecosystemoftools.Now,alargeamountof scientific work depends on NumPy being correct, fast and stable. It is nolongerasmallcommunityproject,butcorescientificinfrastructure. Thedeveloperculturehasmatured:althoughinitialdevelopmentwas highlyinformal,NumPynowhasaroadmapandaprocessforpropos- ing and discussing large changes. The project has formal governance structures and is fiscally sponsored by NumFOCUS, a nonprofit that promotes open practices in research, data and scientific computing. Overthepastfewyears,theprojectattracteditsfirstfundeddevelop- ment, sponsored by the Moore and Sloan Foundations, and received anawardaspartoftheChanZuckerbergInitiative’sEssentialsofOpen Source Software programme. With this funding, the project was (and is) able to have sustained focus over multiple months to implement substantial new features and improvements. That said, the develop- mentofNumPystilldependsheavilyoncontributionsmadebygradu- ate students and researchers in their free time (see Supplementary Methods for more details). NumPyisnolongermerelythefoundationalarraylibraryunderlying thescientificPythonecosystem,butithasbecomethestandardAPIfor tensor computation and a central coordinating mechanism between arraytypesandtechnologiesinPython.Workcontinuestoexpandon and improve these interoperability features. Overthenextdecade,NumPydeveloperswillfaceseveralchallenges. Newdeviceswillbedeveloped,andexistingspecializedhardwarewill evolvetomeetdiminishingreturnsonMoore’slaw.Therewillbemore, andawidervarietyof,datasciencepractitioners,alargeproportionof whom will use NumPy. The scale of scientific data gathering will con- tinue to increase, with the adoption of devices and instruments such as light-sheet microscopes and the Large Synoptic Survey Telescope (LSST)54 .Newgenerationlanguages,interpretersandcompilers,suchas Rust55 ,Julia56 andLLVM57 ,willcreatenewconceptsanddatastructures, and determine their viability. ThroughthemechanismsdescribedinthisReview,NumPyispoised to embrace such a changing landscape, and to continue playing a leading part in interactive scientific computation, although to do so willrequiresustainedfundingfromgovernment,academiaandindus- try.But,importantly,forNumPytomeettheneedsofthenextdecade ofdatascience,itwillalsoneedanewgenerationofgraduatestudents and community contributors to drive it forward. 1. Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016). 2. Chael, A. et al. High-resolution linear polarimetric imaging for the Event Horizon Telescope. Astrophys. J. 286, 11 (2016). 3. Dubois, P. F., Hinsen, K. & Hugunin, J. Numerical Python. Comput. Phys. 10, 262–267 (1996). 4. Ascher, D., Dubois, P. F., Hinsen, K., Hugunin, J. & Oliphant, T. E. An Open Source Project: Numerical Python (Lawrence Livermore National Laboratory, 2001). 5. Yang, T.-Y., Furnish, G. & Dubois, P. F. Steering object-oriented scientific computations. In Proc. TOOLS USA 97. Intl Conf. Technology of Object Oriented Systems and Languages (eds Ege, R., Singh, M. & Meyer, B.) 112–119 (IEEE, 1997). 6. Greenfield, P., Miller, J. T., Hsu, J. & White, R. L. numarray: a new scientific array package for Python. In PyCon DC 2003 http://citeseerx.ist.psu.edu/viewdoc/download?d oi=10.1.1.112.9899 (2003). 7. Oliphant, T. E. Guide to NumPy 1st edn (Trelgol Publishing, 2006). 8. Dubois, P. F. Python: batteries included. Comput. Sci. Eng. 9, 7–9 (2007). 9. Oliphant, T. E. Python for scientific computing. Comput. Sci. Eng. 9, 10–20 (2007). 10. Millman, K. J. & Aivazis, M. Python for scientists and engineers. Comput. Sci. Eng. 13, 9–12 (2011). 11. Pérez, F., Granger, B. E. & Hunter, J. D. Python: an ecosystem for scientific computing. Comput. Sci. Eng. 13, 13–21 (2011). Explains why the scientific Python ecosystem is a highly productive environment for research. 12. Virtanen, P. et al. SciPy 1.0—fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020); correction 17, 352 (2020). Introduces the SciPy library and includes a more detailed history of NumPy and SciPy. 13. Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007). 14. McKinney, W. Data structures for statistical computing in Python. In Proc. 9th Python in Science Conf. (eds van der Walt, S. & Millman, K. J.) 56–61 (2010). 15. Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011). 16. van der Walt, S. et al. scikit-image: image processing in Python. PeerJ 2, e453 (2014). 17. van der Walt, S., Colbert, S. C. & Varoquaux, G. The NumPy array: a structure for efficient numerical computation. Comput. Sci. Eng. 13, 22–30 (2011). Discusses the NumPy array data structure with a focus on how it enables efficient computation. 18. Wang, Q., Zhang, X., Zhang, Y. & Yi, Q. AUGEM: automatically generate high performance dense linear algebra kernels on x86 CPUs. In SC’13: Proc. Intl Conf. High Performance Computing, Networking, Storage and Analysis 25 (IEEE, 2013). 19. Xianyi, Z., Qian, W. & Yunquan, Z. Model-driven level 3 BLAS performance optimization on Loongson 3A processor. In 2012 IEEE 18th Intl Conf. Parallel and Distributed Systems 684–691 (IEEE, 2012). 20. Pérez, F. & Granger, B. E. IPython: a system for interactive scientific computing. Comput. Sci. Eng. 9, 21–29 (2007). 21. Kluyver, T. et al. Jupyter Notebooks—a publishing format for reproducible computational workflows. In Positioning and Power in Academic Publishing: Players, Agents and Agendas (eds Loizides, F. & Schmidt, B.) 87–90 (IOS Press, 2016). 22. Hagberg, A. A., Schult, D. A. & Swart, P. J. Exploring network structure, dynamics, and function using NetworkX. In Proc. 7th Python in Science Conf. (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 11–15 (2008). 23. Astropy Collaboration et al. Astropy: a community Python package for astronomy. Astron. Astrophys. 558, A33 (2013). 24. Price-Whelan, A. M. et al. The Astropy Project: building an open-science project and status of the v2.0 core package. Astron. J. 156, 123 (2018). 25. Cock, P. J. et al. Biopython: freely available Python tools for computational molecular biology and bioinformatics. Bioinformatics 25, 1422–1423 (2009). 26. Millman, K. J. & Brett, M. Analysis of functional magnetic resonance imaging in Python. Comput. Sci. Eng. 9, 52–55 (2007). 27. The SunPy Community et al. SunPy—Python for solar physics. Comput. Sci. Discov. 8, 014009 (2015). 28. Hamman, J., Rocklin, M. & Abernathy, R. Pangeo: a big-data ecosystem for scalable Earth system science. In EGU General Assembly Conf. Abstracts 12146 (2018). 29. Chael, A. A. et al. ehtim: imaging, analysis, and simulation software for radio interferometry. Astrophysics Source Code Library https://ascl.net/1904.004 (2019). 30. Millman, K. J. & Pérez, F. Developing open source scientific practice. In Implementing Reproducible Research (eds Stodden, V., Leisch, F. & Peng, R. D.) 149–183 (CRC Press, 2014). Describes the software engineering practices embraced by the NumPy and SciPy communities with a focus on how these practices improve research. 31. van der Walt, S. The SciPy Documentation Project (technical overview). In Proc. 7th Python in Science Conf. (SciPy 2008) (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 27–28 (2008). 32. Harrington, J. The SciPy Documentation Project. In Proc. 7th Python in Science Conference (SciPy 2008) (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 33–35 (2008). 33. Harrington, J. & Goldsmith, D. Progress report: NumPy and SciPy documentation in 2009. In Proc. 8th Python in Science Conf. (SciPy 2009) (eds Varoquaux, G., van der Walt, S. & Millman, K. J.) 84–87 (2009). 34. Royal Astronomical Society Report of the RAS ‘A’ Awards Committee 2020: Astropy Project: 2020 Group Achievement Award (A) https://ras.ac.uk/sites/default/files/2020-01/ Group%20Award%20-%20Astropy.pdf (2020). 35. Wilson, G. Software carpentry: getting scientists to write better code by making them more productive. Comput. Sci. Eng. 8, 66–69 (2006).
6
362 | Nature | Vol 585 | 17 September 2020 Review 36. Hannay, J. E. et al. How do scientists develop and use scientific software? In Proc. 2009 ICSE Workshop on Software Engineering for Computational Science and Engineering 1–8 (IEEE, 2009). 37. Millman, K. J., Brett, M., Barnowski, R. & Poline, J.-B. Teaching computational reproducibility for neuroimaging. Front. Neurosci. 12, 727 (2018). 38. Paszke, A. et al. Pytorch: an imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32 (eds Wallach, H. et al.) 8024–8035 (Neural Information Processing Systems, 2019). 39. Abadi, M. et al. TensorFlow: a system for large-scale machine learning. In OSDI’16: Proc. 12th USENIX Conf. Operating Systems Design and Implementation (chairs Keeton, K. & Roscoe, T.) 265–283 (USENIX Association, 2016). 40. Chen, T. et al. MXNet: a flexible and efficient machine learning library for heterogeneous distributed systems. Preprint at http://www.arxiv.org/abs/1512.01274 (2015). 41. Hoyer, S. & Hamman, J. xarray: N–D labeled arrays and datasets in Python. J. Open Res. Softw. 5, 10 (2017). 42. Entschev, P. Distributed multi-GPU computing with Dask, CuPy and RAPIDS. In EuroPython 2019 https://ep2019.europython.eu/media/conference/slides/ fX8dJsD-distributed-multi-gpu-computing-with-dask-cupy-and-rapids.pdf (2019). 43. Behnel, S. et al. Cython: the best of both worlds. Comput. Sci. Eng. 13, 31–39 (2011). 44. Lam, S. K., Pitrou, A. & Seibert, S. Numba: a LLVM-based Python JIT compiler. In Proc. Second Workshop on the LLVM Compiler Infrastructure in HPC, LLVM ’15 7:1–7:6 (ACM, 2015). 45. Guelton, S. et al. Pythran: enabling static optimization of scientific Python programs. Comput. Sci. Discov. 8, 014001 (2015). 46. Dongarra, J., Golub, G. H., Grosse, E., Moler, C. & Moore, K. Netlib and NA-Net: building a scientific computing community. IEEE Ann. Hist. Comput. 30, 30–41 (2008). 47. Barrett, K. A., Chiu, Y. H., Painter, J. F., Motteler, Z. C. & Dubois, P. F. Basis System, Part I: Running a Basis Program—A Tutorial for Beginners UCRL-MA-118543, Vol. 1 (Lawrence Livermore National Laboratory 1995). 48. Dubois, P. F. & Motteler, Z. Basis System, Part II: Basis Language Reference Manual UCRL-MA-118543, Vol. 2 (Lawrence Livermore National Laboratory, 1995). 49. Chiu, Y. H. & Dubois, P. F. Basis System, Part III: EZN User Manual UCRL-MA-118543, Vol. 3 (Lawrence Livermore National Laboratory, 1995). 50. Chiu, Y. H. & Dubois, P. F. Basis System, Part IV: EZD User Manual UCRL-MA-118543, Vol. 4 (Lawrence Livermore National Laboratory, 1995). 51. Munro, D. H. & Dubois, P. F. Using the Yorick interpreted language. Comput. Phys. 9, 609–615 (1995). 52. Ihaka, R. & Gentleman, R. R: a language for data analysis and graphics. J. Comput. Graph. Stat. 5, 299–314 (1996). 53. Iverson, K. E. A programming language. In Proc. 1962 Spring Joint Computer Conf. 345–351 (1962). 54. Jenness, T. et al. LSST data management software development practices and tools. In Proc. SPIE 10707, Software and Cyberinfrastructure for Astronomy V 1070709 (SPIE and International Society for Optics and Photonics, 2018). 55. Matsakis, N. D. & Klock, F. S. The Rust language. Ada Letters 34, 103–104 (2014). 56. Bezanson, J., Edelman, A., Karpinski, S. & Shah, V. B. Julia: a fresh approach to numerical computing. SIAM Rev. 59, 65–98 (2017). 57. Lattner, C. & Adve, V. LLVM: a compilation framework for lifelong program analysis and transformation. In Proc. 2004 Intl Symp. Code Generation and Optimization (CGO’04) 75–88 (IEEE, 2004). Acknowledgements We thank R. Barnowski, P. Dubois, M. Eickenberg, and P. Greenfield, who suggested text and provided helpful feedback on the manuscript. K.J.M. and S.J.v.d.W. were funded in part by the Gordon and Betty Moore Foundation through grant GBMF3834 and by the Alfred P. Sloan Foundation through grant 2013-10-27 to the University of California, Berkeley. S.J.v.d.W., S.B., M.P. and W.W. were funded in part by the Gordon and Betty Moore Foundation through grant GBMF5447 and by the Alfred P. Sloan Foundation through grant G-2017-9960 to the University of California, Berkeley. Author contributions K.J.M. and S.J.v.d.W. composed the manuscript with input from others. S.B., R.G., K.S., W.W., M.B. and T.R. contributed text. All authors contributed substantial code, documentation and/or expertise to the NumPy project. All authors reviewed the manuscript. Competing interests The authors declare no competing interests. Additional information Supplementary information is available for this paper at https://doi.org/10.1038/s41586-020- 2649-2. Correspondence and requests for materials should be addressed to K.J.M., S.J.v.W. or R.G. Peer review information Nature thanks Edouard Duchesnay, Alan Edelman and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Reprints and permissions information is available at http://www.nature.com/reprints. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 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Nature | Vol 585 | 17 September 2020 | 357 Review ArrayprogrammingwithNumPy Charles R. Harris1 , K. Jarrod Millman2,3,4 ✉, Stéfan J. van der Walt2,4,5 ✉, Ralf Gommers6 ✉, Pauli Virtanen7,8 , David Cournapeau9 , Eric Wieser10 , Julian Taylor11 , Sebastian Berg4 , Nathaniel J. Smith12 , Robert Kern13 , Matti Picus4 , Stephan Hoyer14 , Marten H. van Kerkwijk15 , Matthew Brett2,16 , Allan Haldane17 , Jaime Fernández del Río18 , Mark Wiebe19,20 , Pearu Peterson6,21,22 , Pierre Gérard-Marchant23,24 , Kevin Sheppard25 , Tyler Reddy26 , Warren Weckesser4 , Hameer Abbasi6 , Christoph Gohlke27 & Travis E. Oliphant6 Arrayprogrammingprovidesapowerful,compactandexpressivesyntaxfor accessing,manipulatingandoperatingondatainvectors,matricesand higher-dimensionalarrays.NumPyistheprimaryarrayprogramminglibraryforthe Pythonlanguage.Ithasanessentialroleinresearchanalysispipelinesinfieldsas diverseasphysics,chemistry,astronomy,geoscience,biology,psychology,materials science,engineering,financeandeconomics.Forexample,inastronomy,NumPywas animportantpartofthesoftwarestackusedinthediscoveryofgravitationalwaves1 andinthefirstimagingofablackhole2 .Herewereviewhowafewfundamentalarray conceptsleadtoasimpleandpowerfulprogrammingparadigmfororganizing, exploringandanalysingscientificdata.NumPyisthefoundationuponwhichthe scientificPythonecosystemisconstructed.Itissopervasivethatseveralprojects, targetingaudienceswithspecializedneeds,havedevelopedtheirownNumPy-like interfacesandarrayobjects.Owingtoitscentralpositionintheecosystem,NumPy increasinglyactsasaninteroperabilitylayerbetweensucharraycomputation librariesand,togetherwithitsapplicationprogramminginterface(API),providesa flexibleframeworktosupportthenextdecadeofscientificandindustrialanalysis. TwoPythonarraypackagesexistedbeforeNumPy.TheNumericpack- age was developed in the mid-1990s and provided array objects and array-awarefunctionsinPython.ItwaswritteninCandlinkedtostand- ardfastimplementationsoflinearalgebra3,4 .Oneofitsearliestuseswas to steer C++ applications for inertial confinement fusion research at LawrenceLivermoreNationalLaboratory5 .Tohandlelargeastronomi- calimagescomingfromtheHubbleSpaceTelescope,areimplementa- tionofNumeric,calledNumarray,addedsupportforstructuredarrays, flexibleindexing,memorymapping,byte-ordervariants,moreefficient memoryuse,flexibleIEEE754-standarderror-handlingcapabilities,and bettertype-castingrules6 .AlthoughNumarraywashighlycompatible withNumeric,thetwopackageshadenoughdifferencesthatitdivided the community; however, in 2005 NumPy emerged as a ‘best of both worlds’ unification7 —combining the features of Numarray with the small-array performance of Numeric and its rich C API. Now, 15 years later, NumPy underpins almost every Python library that does scientific or numerical computation8–11 , including SciPy12 , Matplotlib13 , pandas14 , scikit-learn15 and scikit-image16 . NumPy is a community-developed, open-source library, which provides a mul- tidimensional Python array object along with array-aware functions thatoperateonit.Becauseofitsinherentsimplicity,theNumPyarray is the de facto exchange format for array data in Python. NumPyoperatesonin-memoryarraysusingthecentralprocessing unit(CPU).Toutilizemodern,specializedstorageandhardware,there has been a recent proliferation of Python array packages. Unlike with the Numarray–Numeric divide, it is now much harder for these new libraries to fracture the user community—given how much work is alreadybuiltontopofNumPy.However,toprovidethecommunitywith access to new and exploratory technologies, NumPy is transitioning into a central coordinating mechanism that specifies a well defined array programming API and dispatches it, as appropriate, to special- ized array implementations. NumPyarrays TheNumPyarrayisadatastructurethatefficientlystoresandaccesses multidimensionalarrays17 (alsoknownastensors),andenablesawide variety of scientific computation. It consists of a pointer to memory, along with metadata used to interpret the data stored there, notably ‘data type’, ‘shape’ and ‘strides’ (Fig. 1a). https://doi.org/10.1038/s41586-020-2649-2 Received: 21 February 2020 Accepted: 17 June 2020 Published online: 16 September 2020 Open access Check for updates 1 Independent researcher, Logan, UT, USA. 2 Brain Imaging Center, University of California, Berkeley, Berkeley, CA, USA. 3 Division of Biostatistics, University of California, Berkeley, Berkeley, CA, USA. 4 Berkeley Institute for Data Science, University of California, Berkeley, Berkeley, CA, USA. 5 Applied Mathematics, Stellenbosch University, Stellenbosch, South Africa. 6 Quansight, Austin, TX, USA. 7 Department of Physics, University of Jyväskylä, Jyväskylä, Finland. 8 Nanoscience Center, University of Jyväskylä, Jyväskylä, Finland. 9 Mercari JP, Tokyo, Japan. 10 Department of Engineering, University of Cambridge, Cambridge, UK. 11 Independent researcher, Karlsruhe, Germany. 12 Independent researcher, Berkeley, CA, USA. 13 Enthought, Austin, TX, USA. 14 Google Research, Mountain View, CA, USA. 15 Department of Astronomy and Astrophysics, University of Toronto, Toronto, Ontario, Canada. 16 School of Psychology, University of Birmingham, Edgbaston, Birmingham, UK. 17 Department of Physics, Temple University, Philadelphia, PA, USA. 18 Google, Zurich, Switzerland. 19 Department of Physics and Astronomy, The University of British Columbia, Vancouver, British Columbia, Canada. 20 Amazon, Seattle, WA, USA. 21 Independent researcher, Saue, Estonia. 22 Department of Mechanics and Applied Mathematics, Institute of Cybernetics at Tallinn Technical University, Tallinn, Estonia. 23 Department of Biological and Agricultural Engineering, University of Georgia, Athens, GA, USA. 24 France-IX Services, Paris, France. 25 Department of Economics, University of Oxford, Oxford, UK. 26 CCS-7, Los Alamos National Laboratory, Los Alamos, NM, USA. 27 Laboratory for Fluorescence Dynamics, Biomedical Engineering Department, University of California, Irvine, Irvine, CA, USA. ✉e-mail: millman@berkeley.edu; stefanv@berkeley.edu; ralf.gommers@gmail.com
358 | Nature | Vol 585 | 17 September 2020 Review The data type describes the nature of elements stored in an array. Anarrayhasasingledatatype,andeachelementofanarrayoccupies thesamenumberofbytesinmemory.Examplesofdatatypesinclude real and complex numbers (of lower and higher precision), strings, timestamps and pointers to Python objects. The shape of an array determines the number of elements along each axis, and the number of axes is the dimensionality of the array. For example, a vector of numbers can be stored as a one-dimensional array of shape N, whereas colour videos are four-dimensional arrays of shape (T, M, N, 3). Strides are necessary to interpret computer memory, which stores elementslinearly,asmultidimensionalarrays.Theydescribethenum- berofbytestomoveforwardinmemorytojumpfromrowtorow,col- umntocolumn,andsoforth.Consider,forexample,atwo-dimensional arrayoffloating-pointnumberswithshape(4, 3),whereeachelement occupies 8 bytes in memory. To move between consecutive columns, weneedtojumpforward8 bytesinmemory,andtoaccessthenextrow, 3 × 8 = 24 bytes. The strides of that array are therefore (24, 8). NumPy canstorearraysineitherCorFortranmemoryorder,iteratingfirstover either rows or columns. This allows external libraries written in those languages to access NumPy array data in memory directly. Users interact with NumPy arrays using ‘indexing’ (to access sub- arrays or individual elements), ‘operators’ (for example, +, − and × for vectorized operations and @ for matrix multiplication), as well as‘array-awarefunctions’;together,theseprovideaneasilyreadable, expressive, high-level API for array programming while NumPy deals with the underlying mechanics of making operations fast. Indexing an array returns single elements, subarrays or elements that satisfy a specific condition (Fig. 1b). Arrays can even be indexed usingotherarrays(Fig. 1c).Whereverpossible,indexingthatretrievesa subarrayreturnsa‘view’ontheoriginalarraysuchthatdataareshared between the two arrays. This provides a powerful way to operate on subsets of array data while limiting memory usage. To complement the array syntax, NumPy includes functions that perform vectorized calculations on arrays, including arithmetic, statistics and trigonometry (Fig. 1d). Vectorization—operating on entirearraysratherthantheirindividualelements—isessentialtoarray programming.Thismeansthatoperationsthatwouldtakemanytens oflinestoexpressinlanguagessuchasCcanoftenbeimplementedas asingle,clearPythonexpression.Thisresultsinconcisecodeandfrees users to focus on the details of their analysis, while NumPy handles looping over array elements near-optimally—for example, taking strides into consideration to best utilize the computer’s fast cache memory. Whenperformingavectorizedoperation(suchasaddition)ontwo arrays with the same shape, it is clear what should happen. Through ‘broadcasting’ NumPy allows the dimensions to differ, and produces results that appeal to intuition. A trivial example is the addition of a scalarvaluetoanarray,butbroadcastingalsogeneralizestomorecom- plex examples such as scaling each column of an array or generating agridofcoordinates.Inbroadcasting,oneorbotharraysarevirtually duplicated (that is, without copying any data in memory), so that the shapes of the operands match (Fig. 1d). Broadcasting is also applied when an array is indexed using arrays of indices (Fig. 1c). Other array-aware functions, such as sum, mean and maximum, performelement-by-element‘reductions’,aggregatingresultsacross one, multiple or all axes of a single array. For example, summing an n-dimensional array over d axes results in an array of dimension n − d (Fig. 1f). NumPyalsoincludesarray-awarefunctionsforcreating,reshaping, concatenating and padding arrays; searching, sorting and counting data; and reading and writing files. It provides extensive support for generatingpseudorandomnumbers,includesanassortmentofprob- ability distributions, and performs accelerated linear algebra, using oneofseveralbackendssuchasOpenBLAS18,19 orIntelMKLoptimized for the CPUs at hand (see Supplementary Methods for more details). Altogether, the combination of a simple in-memory array repre- sentation, a syntax that closely mimics mathematics, and a variety of array-aware utility functions forms a productive and powerfully expressive array programming language. In [1]: import numpy as np In [2]: x = np.arange(12) In [3]: x = x.reshape(4, 3) In [4]: x Out[4]: array([[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11]]) In [5]: np.mean(x, axis=0) Out[5]: array([4.5, 5.5, 6.5]) In [6]: x = x - np.mean(x, axis=0) In [7]: x Out[7]: array([[-4.5, -4.5, -4.5], [-1.5, -1.5, -1.5], [ 1.5, 1.5, 1.5], [ 4.5, 4.5, 4.5]]) a Data structure g Example x = 0 1 2 3 4 5 6 7 8 9 10 11 data data type shape strides 8-byte integer (4, 3) (24, 8) 1 2 3 4 5 6 70 8 9 10 11 8 bytes per element 3 × 8 = 24 bytes to jump one row down b Indexing (view) 10 1199 x[:,1:] → with slices 1 2 4 5 7 8 00 33 66 x[:,::2]→ with slices with steps 0 2 3 5 6 8 9 11 0 11 2 3 44 5 6 77 8 9 1010 11 Slices are start:end:step, any of which can be left blank d Vectorization + → 0 1 3 4 6 7 9 10 1 1 1 1 1 1 1 1 1 2 4 5 7 8 10 11 e Broadcasting × 3 6 0 9 1 2 → 0 0 3 6 6 12 9 18 f Reduction 0 1 3 4 6 7 9 10 2 5 8 11 3 12 21 30 sum axis 1 18 22 26 sum axis 0 66 sum axis (0,1) c Indexing (copy) 4 3 7 6 with arrays with broadcasting →x → ,2 1 1 0 x , 1 1 2 2 1 0 1 0 x with arraysx[0,1],x[1,2] 1 5→ →0 1 1 2 , x[x > 9] with masks10 11→→ 5 with scalarsx[1,2] Fig.1|TheNumPyarrayincorporatesseveralfundamentalarrayconcepts. a,TheNumPyarraydatastructureanditsassociatedmetadatafields. b,Indexinganarraywithslicesandsteps.Theseoperationsreturna‘view’of theoriginaldata.c,Indexinganarraywithmasks,scalarcoordinatesorother arrays,sothatitreturnsa‘copy’oftheoriginaldata.Inthebottomexample,an arrayisindexedwithotherarrays;thisbroadcaststheindexingarguments beforeperformingthelookup.d,Vectorizationefficientlyappliesoperations togroupsofelements.e,Broadcastinginthemultiplicationoftwo-dimensional arrays.f,Reductionoperationsactalongoneormoreaxes.Inthisexample, anarrayissummedalongselectaxestoproduceavector,oralongtwoaxes consecutivelytoproduceascalar.g,ExampleNumPycode,illustratingsomeof theseconcepts.
Nature | Vol 585 | 17 September 2020 | 359 ScientificPythonecosystem Pythonisanopen-source,general-purposeinterpretedprogramming languagewellsuitedtostandardprogrammingtaskssuchascleaning data,interactingwithwebresourcesandparsingtext.Addingfastarray operations and linear algebra enables scientists to do all their work withinasingleprogramminglanguage—onethathastheadvantageof being famously easy to learn and teach, as witnessed by its adoption as a primary learning language in many universities. Even though NumPy is not part of Python’s standard library, it ben- efits from a good relationship with the Python developers. Over the years,thePythonlanguagehasaddednewfeaturesandspecialsyntax so that NumPy would have a more succinct and easier-to-read array notation.However,becauseitisnotpartofthestandardlibrary,NumPy is able to dictate its own release policies and development patterns. SciPyandMatplotlibaretightlycoupledwithNumPyintermsofhis- tory,developmentanduse.SciPyprovidesfundamentalalgorithmsfor scientificcomputing,includingmathematical,scientificandengineer- ingroutines.Matplotlibgeneratespublication-readyfiguresandvisu- alizations.ThecombinationofNumPy,SciPyandMatplotlib,together with an advanced interactive environment such as IPython20 or Jupy- ter21 ,providesasolidfoundationforarrayprogramminginPython.The scientificPythonecosystem(Fig. 2)buildsontopofthisfoundationto provide several, widely used technique-specific libraries15,16,22 , that in turn underlie numerous domain-specific projects23–28 . NumPy, at the base of the ecosystem of array-aware libraries, sets documentation standards, provides array testing infrastructure and adds build sup- port for Fortran and other compilers. Manyresearchgroupshavedesignedlarge,complexscientificlibrar- ies that add application-specific functionality to the ecosystem. For example, the eht-imaging library29 , developed by the Event Horizon Telescope collaboration for radio interferometry imaging, analysis andsimulation,reliesonmanylower-levelcomponentsofthescientific Pythonecosystem.Inparticular,theEHTcollaborationusedthislibrary forthefirstimagingofablackhole.Withineht-imaging,NumPyarrays are used to store and manipulate numerical data at every step in the processingchain:fromrawdatathroughcalibrationandimagerecon- struction.SciPysuppliestoolsforgeneralimage-processingtaskssuch asfilteringandimagealignment,andscikit-image,animage-processing library that extends SciPy, provides higher-level functionality such as edge filters and Hough transforms. The ‘scipy.optimize’ module performsmathematicaloptimization.NetworkX22 ,apackageforcom- plexnetworkanalysis,isusedtoverifyimagecomparisonconsistency. Astropy23,24 handlesstandardastronomicalfileformatsandcomputes time–coordinatetransformations.Matplotlibisusedtovisualizedata and to generate the final image of the black hole. Theinteractiveenvironmentcreatedbythearray programmingfoun- dation and the surrounding ecosystem of tools—inside of IPython or Jupyter—isideallysuitedtoexploratorydataanalysis.Userscanfluidly inspect,manipulateandvisualizetheirdata,andrapidlyiteratetorefine programmingstatements.Thesestatementsarethenstitchedtogether intoimperativeorfunctionalprograms,ornotebookscontainingboth computationandnarrative.Scientificcomputingbeyondexploratory workisoftendoneinatexteditororanintegrateddevelopmentenvi- ronment (IDE) such as Spyder. This rich and productive environment has made Python popular for scientific research. To complement this facility for exploratory work and rapid proto- typing,NumPyhasdevelopedacultureofusingtime-testedsoftware engineeringpracticestoimprovecollaborationandreduceerror30 .This culture is not only adopted by leaders in the project but also enthusi- astically taught to newcomers. The NumPy team was early to adopt distributedrevisioncontrolandcodereviewtoimprovecollaboration cantera Chemistry Biopython Biology Astropy Astronomy simpeg Geophysics NLTK Linguistics QuantEcon Economics SciPy Algorithms Matplotlib Plots scikit-learn Machine learning NetworkX Network analysis pandas, statsmodels Statistics scikit-image Image processing PsychoPykhmer Qiime2 FiPy deepchem librosaPyWavelets SunPy QuTiP yt nibabel yellowbrickmne-python scikit-HEP eht-imagingMDAnalysis iriscesium PyChrono Foundation Application-specific Domain-specific Technique-specific Array ProtocolsNumPy API Python Language IPython / Jupyter Interactive environments NumPy Arrays New array implementations Fig.2|NumPyisthebaseofthescientificPythonecosystem.EssentiallibrariesandprojectsthatdependonNumPy’sAPIgainaccesstonewarray implementationsthatsupportNumPy’sarrayprotocols(Fig. 3).
360 | Nature | Vol 585 | 17 September 2020 Review oncode,andcontinuoustestingthatrunsanextensivebatteryofauto- mated tests for every proposed change to NumPy. The project also hascomprehensive,high-qualitydocumentation,integratedwiththe source code31–33 . Thiscultureofusingbestpracticesforproducingreliablescientific softwarehasbeenadoptedbytheecosystemoflibrariesthatbuildon NumPy.Forexample,inarecentawardgivenbytheRoyalAstronomi- cal Society to Astropy, they state: “The Astropy Project has provided hundredsofjuniorscientistswithexperienceinprofessional-standard softwaredevelopmentpracticesincludinguseofversioncontrol,unit testing, code review and issue tracking procedures. This is a vital skill setformodernresearchersthatisoftenmissingfromformaluniversity educationinphysicsorastronomy”34 .Communitymembersexplicitly work to address this lack of formal education through courses and workshops35–37 . Therecentrapidgrowthofdatascience,machinelearningandarti- ficial intelligence has further and dramatically boosted the scientific use of Python. Examples of its important applications, such as the eht-imaging library, now exist in almost every discipline in the natu- ralandsocialsciences.Thesetoolshavebecometheprimarysoftware environmentinmanyfields.NumPyanditsecosystemarecommonly taught in university courses, boot camps and summer schools, and are the focus of community conferences and workshops worldwide. NumPy and its API have become truly ubiquitous. Arrayproliferationandinteroperability NumPyprovidesin-memory,multidimensional,homogeneouslytyped (thatis,single-pointerandstrided)arraysonCPUs.Itrunsonmachines rangingfromembeddeddevicestotheworld’slargestsupercomputers, withperformanceapproachingthatofcompiledlanguages.Formost its existence, NumPy addressed the vast majority of array computa- tion use cases. However,scientificdatasetsnowroutinelyexceedthememorycapac- ity of a single machine and may be stored on multiple machines or in thecloud.Inaddition,therecentneedtoacceleratedeep-learningand artificialintelligenceapplicationshasledtotheemergenceofspecial- izedacceleratorhardware,includinggraphicsprocessingunits(GPUs), tensor processing units (TPUs) and field-programmable gate arrays (FPGAs).Owingtoitsin-memorydatamodel,NumPyiscurrentlyunable to directly utilize such storage and specialized hardware. However, both distributed data and also the parallel execution of GPUs, TPUs andFPGAsmapwelltotheparadigmofarrayprogramming:therefore leadingtoagapbetweenavailablemodernhardwarearchitecturesand the tools necessary to leverage their computational power. Thecommunity’seffortstofillthisgapledtoaproliferationofnew array implementations. For example, each deep-learning framework created its own arrays; the PyTorch38 , Tensorflow39 , Apache MXNet40 and JAX arrays all have the capability to run on CPUs and GPUs in a distributed fashion, using lazy evaluation to allow for additional per- formanceoptimizations.SciPyandPyData/Sparsebothprovidesparse arrays,whichtypicallycontainfewnon-zerovaluesandstoreonlythose in memory for efficiency. In addition, there are projects that build on NumPy arrays as data containers, and extend its capabilities. Distrib- uted arrays are made possible that way by Dask, and labelled arrays— referring to dimensions of an array by name rather than by index for clarity, compare x[:, 1] versus x.loc[:, 'time']—by xarray41 . Such libraries often mimic the NumPy API, because this lowers the barriertoentryfornewcomersandprovidesthewidercommunitywith astablearray programminginterface.This,inturn,preventsdisruptive schisms such as the divergence between Numeric and Numarray. But exploring new ways of working with arrays is experimental by nature and,infact,severalpromisinglibraries(suchasTheanoandCaffe)have alreadyceaseddevelopment.Andeachtimethatauserdecidestotrya newtechnology,theymustchangeimportstatementsandensurethatthe newlibraryimplementsallthepartsoftheNumPyAPItheycurrentlyuse. Ideally, operating on specialized arrays using NumPy functions or semantics would simply work, so that users could write code once, and would then benefit from switching between NumPy arrays, GPU arrays,distributedarraysandsoforthasappropriate.Tosupportarray operations between external array objects, NumPy therefore added the capability to act as a central coordination mechanism with a well specified API (Fig. 2). To facilitate this interoperability, NumPy provides ‘protocols’ (or contractsofoperation),thatallowforspecializedarraystobepassedto NumPyfunctions(Fig. 3).NumPy,inturn,dispatchesoperationstothe originatinglibrary,asrequired.Overfourhundredofthemostpopular NumPy functions are supported. The protocols are implemented by widely used libraries such as Dask, CuPy, xarray and PyData/Sparse. Thankstothesedevelopments,userscannow,forexample,scaletheir computationfromasinglemachinetodistributedsystemsusingDask. The protocols also compose well, allowing users to redeploy NumPy codeatscaleondistributed,multi-GPUsystemsvia,forinstance,CuPy arrays embedded in Dask arrays. Using NumPy’s high-level API, users can leverage highly parallel code execution on multiple systems with millions of cores, all with minimal code changes42 . These array protocols are now a key feature of NumPy, and are expected to only increase in importance. The NumPy developers— many of whom are authors of this Review—iteratively refine and add protocol designs to improve utility and simplify adoption. Output arrays Input arrays NumPy API np.stack np.reshape np.transpose np.argmin np.mean np.std np.max np.cos np.arctan np.log np.cumsum np.diff ... NumPy array protocols In [1]: import numpy as np In [2]: import dask.array as da In [3]: x = da.arange(12) In [4]: x = np.reshape(x, (4, 3)) In [5]: x Out[5]: dask.array<..., shape=(4, 3), ...> In [6]: np.mean(x, axis=0) Out[6]: dask.array<..., shape=(3,), ...> In [7]: x = x - np.mean(x, axis=0) In [8]: x Out[8]: dask.array<..., shape=(4, 3), ...> Array implementation NumPy Dask CuPy PyData/ Sparse ... ... Dask NumPy CuPy PyData Sparse ... Dask NumPy CuPy PyData Sparse Fig.3|NumPy’sAPIandarrayprotocolsexposenewarraystothe ecosystem.Inthisexample,NumPy’s‘mean’functioniscalledonaDaskarray. Thecallsucceedsbydispatchingtotheappropriatelibraryimplementation(in thiscase,Dask)andresultsinanewDaskarray.Comparethiscodetothe examplecodeinFig. 1g.
Nature | Vol 585 | 17 September 2020 | 361 Discussion NumPy combines the expressive power of array programming, the performanceofC,andthereadability,usabilityandversatilityofPython inamature,welltested,welldocumentedandcommunity-developed library.LibrariesinthescientificPythonecosystemprovidefastimple- mentations of most important algorithms. Where extreme optimiza- tion is warranted, compiled languages can be used, such as Cython43 , Numba44 and Pythran45 ; these languages extend Python and trans- parently accelerate bottlenecks. Owing to NumPy’s simple memory model, it is easy to write low-level, hand-optimized code, usually in C orFortran,tomanipulateNumPyarraysandpassthembacktoPython. Furthermore, using array protocols, it is possible to utilize the full spectrumofspecializedhardwareaccelerationwithminimalchanges to existing code. NumPywasinitiallydevelopedbystudents,facultyandresearchers to provide an advanced, open-source array programming library for Python,whichwasfreetouseandunencumberedbylicenseserversand softwareprotectiondongles.Therewasasenseofbuildingsomething consequential together for the benefit of many others. Participating in such an endeavour, within a welcoming community of like-minded individuals, held a powerful attraction for many early contributors. These user–developers frequently had to write code from scratch to solve their own or their colleagues’ problems—often in low-level languages that preceded Python, such as Fortran46 and C. To them, theadvantagesofaninteractive,high-levelarraylibrarywereevident. Thedesignofthisnewtoolwasinformedbyotherpowerfulinteractive programming languages for scientific computing such as Basis47–50 , Yorick51 , R52 and APL53 , as well as commercial languages and environ- ments such as IDL (Interactive Data Language) and MATLAB. WhatbeganasanattempttoaddanarrayobjecttoPythonbecame thefoundationofavibrantecosystemoftools.Now,alargeamountof scientific work depends on NumPy being correct, fast and stable. It is nolongerasmallcommunityproject,butcorescientificinfrastructure. Thedeveloperculturehasmatured:althoughinitialdevelopmentwas highlyinformal,NumPynowhasaroadmapandaprocessforpropos- ing and discussing large changes. The project has formal governance structures and is fiscally sponsored by NumFOCUS, a nonprofit that promotes open practices in research, data and scientific computing. Overthepastfewyears,theprojectattracteditsfirstfundeddevelop- ment, sponsored by the Moore and Sloan Foundations, and received anawardaspartoftheChanZuckerbergInitiative’sEssentialsofOpen Source Software programme. With this funding, the project was (and is) able to have sustained focus over multiple months to implement substantial new features and improvements. That said, the develop- mentofNumPystilldependsheavilyoncontributionsmadebygradu- ate students and researchers in their free time (see Supplementary Methods for more details). NumPyisnolongermerelythefoundationalarraylibraryunderlying thescientificPythonecosystem,butithasbecomethestandardAPIfor tensor computation and a central coordinating mechanism between arraytypesandtechnologiesinPython.Workcontinuestoexpandon and improve these interoperability features. Overthenextdecade,NumPydeveloperswillfaceseveralchallenges. Newdeviceswillbedeveloped,andexistingspecializedhardwarewill evolvetomeetdiminishingreturnsonMoore’slaw.Therewillbemore, andawidervarietyof,datasciencepractitioners,alargeproportionof whom will use NumPy. The scale of scientific data gathering will con- tinue to increase, with the adoption of devices and instruments such as light-sheet microscopes and the Large Synoptic Survey Telescope (LSST)54 .Newgenerationlanguages,interpretersandcompilers,suchas Rust55 ,Julia56 andLLVM57 ,willcreatenewconceptsanddatastructures, and determine their viability. ThroughthemechanismsdescribedinthisReview,NumPyispoised to embrace such a changing landscape, and to continue playing a leading part in interactive scientific computation, although to do so willrequiresustainedfundingfromgovernment,academiaandindus- try.But,importantly,forNumPytomeettheneedsofthenextdecade ofdatascience,itwillalsoneedanewgenerationofgraduatestudents and community contributors to drive it forward. 1. Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016). 2. Chael, A. et al. High-resolution linear polarimetric imaging for the Event Horizon Telescope. Astrophys. J. 286, 11 (2016). 3. Dubois, P. F., Hinsen, K. & Hugunin, J. Numerical Python. Comput. Phys. 10, 262–267 (1996). 4. Ascher, D., Dubois, P. F., Hinsen, K., Hugunin, J. & Oliphant, T. E. An Open Source Project: Numerical Python (Lawrence Livermore National Laboratory, 2001). 5. Yang, T.-Y., Furnish, G. & Dubois, P. F. Steering object-oriented scientific computations. In Proc. TOOLS USA 97. Intl Conf. Technology of Object Oriented Systems and Languages (eds Ege, R., Singh, M. & Meyer, B.) 112–119 (IEEE, 1997). 6. Greenfield, P., Miller, J. T., Hsu, J. & White, R. L. numarray: a new scientific array package for Python. In PyCon DC 2003 http://citeseerx.ist.psu.edu/viewdoc/download?d oi=10.1.1.112.9899 (2003). 7. Oliphant, T. E. Guide to NumPy 1st edn (Trelgol Publishing, 2006). 8. Dubois, P. F. Python: batteries included. Comput. Sci. Eng. 9, 7–9 (2007). 9. Oliphant, T. E. Python for scientific computing. Comput. Sci. Eng. 9, 10–20 (2007). 10. Millman, K. J. & Aivazis, M. Python for scientists and engineers. Comput. Sci. Eng. 13, 9–12 (2011). 11. Pérez, F., Granger, B. E. & Hunter, J. D. Python: an ecosystem for scientific computing. Comput. Sci. Eng. 13, 13–21 (2011). Explains why the scientific Python ecosystem is a highly productive environment for research. 12. Virtanen, P. et al. SciPy 1.0—fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020); correction 17, 352 (2020). Introduces the SciPy library and includes a more detailed history of NumPy and SciPy. 13. Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007). 14. McKinney, W. Data structures for statistical computing in Python. In Proc. 9th Python in Science Conf. (eds van der Walt, S. & Millman, K. J.) 56–61 (2010). 15. Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011). 16. van der Walt, S. et al. scikit-image: image processing in Python. PeerJ 2, e453 (2014). 17. van der Walt, S., Colbert, S. C. & Varoquaux, G. The NumPy array: a structure for efficient numerical computation. Comput. Sci. Eng. 13, 22–30 (2011). Discusses the NumPy array data structure with a focus on how it enables efficient computation. 18. Wang, Q., Zhang, X., Zhang, Y. & Yi, Q. AUGEM: automatically generate high performance dense linear algebra kernels on x86 CPUs. In SC’13: Proc. Intl Conf. High Performance Computing, Networking, Storage and Analysis 25 (IEEE, 2013). 19. Xianyi, Z., Qian, W. & Yunquan, Z. Model-driven level 3 BLAS performance optimization on Loongson 3A processor. In 2012 IEEE 18th Intl Conf. Parallel and Distributed Systems 684–691 (IEEE, 2012). 20. Pérez, F. & Granger, B. E. IPython: a system for interactive scientific computing. Comput. Sci. Eng. 9, 21–29 (2007). 21. Kluyver, T. et al. Jupyter Notebooks—a publishing format for reproducible computational workflows. In Positioning and Power in Academic Publishing: Players, Agents and Agendas (eds Loizides, F. & Schmidt, B.) 87–90 (IOS Press, 2016). 22. Hagberg, A. A., Schult, D. A. & Swart, P. J. Exploring network structure, dynamics, and function using NetworkX. In Proc. 7th Python in Science Conf. (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 11–15 (2008). 23. Astropy Collaboration et al. Astropy: a community Python package for astronomy. Astron. Astrophys. 558, A33 (2013). 24. Price-Whelan, A. M. et al. The Astropy Project: building an open-science project and status of the v2.0 core package. Astron. J. 156, 123 (2018). 25. Cock, P. J. et al. Biopython: freely available Python tools for computational molecular biology and bioinformatics. Bioinformatics 25, 1422–1423 (2009). 26. Millman, K. J. & Brett, M. Analysis of functional magnetic resonance imaging in Python. Comput. Sci. Eng. 9, 52–55 (2007). 27. The SunPy Community et al. SunPy—Python for solar physics. Comput. Sci. Discov. 8, 014009 (2015). 28. Hamman, J., Rocklin, M. & Abernathy, R. Pangeo: a big-data ecosystem for scalable Earth system science. In EGU General Assembly Conf. Abstracts 12146 (2018). 29. Chael, A. A. et al. ehtim: imaging, analysis, and simulation software for radio interferometry. Astrophysics Source Code Library https://ascl.net/1904.004 (2019). 30. Millman, K. J. & Pérez, F. Developing open source scientific practice. In Implementing Reproducible Research (eds Stodden, V., Leisch, F. & Peng, R. D.) 149–183 (CRC Press, 2014). Describes the software engineering practices embraced by the NumPy and SciPy communities with a focus on how these practices improve research. 31. van der Walt, S. The SciPy Documentation Project (technical overview). In Proc. 7th Python in Science Conf. (SciPy 2008) (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 27–28 (2008). 32. Harrington, J. The SciPy Documentation Project. In Proc. 7th Python in Science Conference (SciPy 2008) (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 33–35 (2008). 33. Harrington, J. & Goldsmith, D. Progress report: NumPy and SciPy documentation in 2009. In Proc. 8th Python in Science Conf. (SciPy 2009) (eds Varoquaux, G., van der Walt, S. & Millman, K. J.) 84–87 (2009). 34. Royal Astronomical Society Report of the RAS ‘A’ Awards Committee 2020: Astropy Project: 2020 Group Achievement Award (A) https://ras.ac.uk/sites/default/files/2020-01/ Group%20Award%20-%20Astropy.pdf (2020). 35. Wilson, G. Software carpentry: getting scientists to write better code by making them more productive. Comput. Sci. Eng. 8, 66–69 (2006).
362 | Nature | Vol 585 | 17 September 2020 Review 36. Hannay, J. E. et al. How do scientists develop and use scientific software? In Proc. 2009 ICSE Workshop on Software Engineering for Computational Science and Engineering 1–8 (IEEE, 2009). 37. Millman, K. J., Brett, M., Barnowski, R. & Poline, J.-B. Teaching computational reproducibility for neuroimaging. Front. Neurosci. 12, 727 (2018). 38. Paszke, A. et al. Pytorch: an imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32 (eds Wallach, H. et al.) 8024–8035 (Neural Information Processing Systems, 2019). 39. Abadi, M. et al. TensorFlow: a system for large-scale machine learning. In OSDI’16: Proc. 12th USENIX Conf. Operating Systems Design and Implementation (chairs Keeton, K. & Roscoe, T.) 265–283 (USENIX Association, 2016). 40. Chen, T. et al. MXNet: a flexible and efficient machine learning library for heterogeneous distributed systems. Preprint at http://www.arxiv.org/abs/1512.01274 (2015). 41. Hoyer, S. & Hamman, J. xarray: N–D labeled arrays and datasets in Python. J. Open Res. Softw. 5, 10 (2017). 42. Entschev, P. Distributed multi-GPU computing with Dask, CuPy and RAPIDS. In EuroPython 2019 https://ep2019.europython.eu/media/conference/slides/ fX8dJsD-distributed-multi-gpu-computing-with-dask-cupy-and-rapids.pdf (2019). 43. Behnel, S. et al. Cython: the best of both worlds. Comput. Sci. Eng. 13, 31–39 (2011). 44. Lam, S. K., Pitrou, A. & Seibert, S. Numba: a LLVM-based Python JIT compiler. In Proc. Second Workshop on the LLVM Compiler Infrastructure in HPC, LLVM ’15 7:1–7:6 (ACM, 2015). 45. Guelton, S. et al. Pythran: enabling static optimization of scientific Python programs. Comput. Sci. Discov. 8, 014001 (2015). 46. Dongarra, J., Golub, G. H., Grosse, E., Moler, C. & Moore, K. Netlib and NA-Net: building a scientific computing community. IEEE Ann. Hist. Comput. 30, 30–41 (2008). 47. Barrett, K. A., Chiu, Y. H., Painter, J. F., Motteler, Z. C. & Dubois, P. F. Basis System, Part I: Running a Basis Program—A Tutorial for Beginners UCRL-MA-118543, Vol. 1 (Lawrence Livermore National Laboratory 1995). 48. Dubois, P. F. & Motteler, Z. Basis System, Part II: Basis Language Reference Manual UCRL-MA-118543, Vol. 2 (Lawrence Livermore National Laboratory, 1995). 49. Chiu, Y. H. & Dubois, P. F. Basis System, Part III: EZN User Manual UCRL-MA-118543, Vol. 3 (Lawrence Livermore National Laboratory, 1995). 50. Chiu, Y. H. & Dubois, P. F. Basis System, Part IV: EZD User Manual UCRL-MA-118543, Vol. 4 (Lawrence Livermore National Laboratory, 1995). 51. Munro, D. H. & Dubois, P. F. Using the Yorick interpreted language. Comput. Phys. 9, 609–615 (1995). 52. Ihaka, R. & Gentleman, R. R: a language for data analysis and graphics. J. Comput. Graph. Stat. 5, 299–314 (1996). 53. Iverson, K. E. A programming language. In Proc. 1962 Spring Joint Computer Conf. 345–351 (1962). 54. Jenness, T. et al. LSST data management software development practices and tools. In Proc. SPIE 10707, Software and Cyberinfrastructure for Astronomy V 1070709 (SPIE and International Society for Optics and Photonics, 2018). 55. Matsakis, N. D. & Klock, F. S. The Rust language. Ada Letters 34, 103–104 (2014). 56. Bezanson, J., Edelman, A., Karpinski, S. & Shah, V. B. Julia: a fresh approach to numerical computing. SIAM Rev. 59, 65–98 (2017). 57. Lattner, C. & Adve, V. LLVM: a compilation framework for lifelong program analysis and transformation. In Proc. 2004 Intl Symp. Code Generation and Optimization (CGO’04) 75–88 (IEEE, 2004). Acknowledgements We thank R. Barnowski, P. Dubois, M. Eickenberg, and P. Greenfield, who suggested text and provided helpful feedback on the manuscript. K.J.M. and S.J.v.d.W. were funded in part by the Gordon and Betty Moore Foundation through grant GBMF3834 and by the Alfred P. Sloan Foundation through grant 2013-10-27 to the University of California, Berkeley. S.J.v.d.W., S.B., M.P. and W.W. were funded in part by the Gordon and Betty Moore Foundation through grant GBMF5447 and by the Alfred P. Sloan Foundation through grant G-2017-9960 to the University of California, Berkeley. Author contributions K.J.M. and S.J.v.d.W. composed the manuscript with input from others. S.B., R.G., K.S., W.W., M.B. and T.R. contributed text. All authors contributed substantial code, documentation and/or expertise to the NumPy project. All authors reviewed the manuscript. Competing interests The authors declare no competing interests. Additional information Supplementary information is available for this paper at https://doi.org/10.1038/s41586-020- 2649-2. Correspondence and requests for materials should be addressed to K.J.M., S.J.v.W. or R.G. Peer review information Nature thanks Edouard Duchesnay, Alan Edelman and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Reprints and permissions information is available at http://www.nature.com/reprints. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. © The Author(s) 2020
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Array programming with Numpy

  • 1. Nature | Vol 585 | 17 September 2020 | 357 Review ArrayprogrammingwithNumPy Charles R. Harris1 , K. Jarrod Millman2,3,4 ✉, Stéfan J. van der Walt2,4,5 ✉, Ralf Gommers6 ✉, Pauli Virtanen7,8 , David Cournapeau9 , Eric Wieser10 , Julian Taylor11 , Sebastian Berg4 , Nathaniel J. Smith12 , Robert Kern13 , Matti Picus4 , Stephan Hoyer14 , Marten H. van Kerkwijk15 , Matthew Brett2,16 , Allan Haldane17 , Jaime Fernández del Río18 , Mark Wiebe19,20 , Pearu Peterson6,21,22 , Pierre Gérard-Marchant23,24 , Kevin Sheppard25 , Tyler Reddy26 , Warren Weckesser4 , Hameer Abbasi6 , Christoph Gohlke27 & Travis E. Oliphant6 Arrayprogrammingprovidesapowerful,compactandexpressivesyntaxfor accessing,manipulatingandoperatingondatainvectors,matricesand higher-dimensionalarrays.NumPyistheprimaryarrayprogramminglibraryforthe Pythonlanguage.Ithasanessentialroleinresearchanalysispipelinesinfieldsas diverseasphysics,chemistry,astronomy,geoscience,biology,psychology,materials science,engineering,financeandeconomics.Forexample,inastronomy,NumPywas animportantpartofthesoftwarestackusedinthediscoveryofgravitationalwaves1 andinthefirstimagingofablackhole2 .Herewereviewhowafewfundamentalarray conceptsleadtoasimpleandpowerfulprogrammingparadigmfororganizing, exploringandanalysingscientificdata.NumPyisthefoundationuponwhichthe scientificPythonecosystemisconstructed.Itissopervasivethatseveralprojects, targetingaudienceswithspecializedneeds,havedevelopedtheirownNumPy-like interfacesandarrayobjects.Owingtoitscentralpositionintheecosystem,NumPy increasinglyactsasaninteroperabilitylayerbetweensucharraycomputation librariesand,togetherwithitsapplicationprogramminginterface(API),providesa flexibleframeworktosupportthenextdecadeofscientificandindustrialanalysis. TwoPythonarraypackagesexistedbeforeNumPy.TheNumericpack- age was developed in the mid-1990s and provided array objects and array-awarefunctionsinPython.ItwaswritteninCandlinkedtostand- ardfastimplementationsoflinearalgebra3,4 .Oneofitsearliestuseswas to steer C++ applications for inertial confinement fusion research at LawrenceLivermoreNationalLaboratory5 .Tohandlelargeastronomi- calimagescomingfromtheHubbleSpaceTelescope,areimplementa- tionofNumeric,calledNumarray,addedsupportforstructuredarrays, flexibleindexing,memorymapping,byte-ordervariants,moreefficient memoryuse,flexibleIEEE754-standarderror-handlingcapabilities,and bettertype-castingrules6 .AlthoughNumarraywashighlycompatible withNumeric,thetwopackageshadenoughdifferencesthatitdivided the community; however, in 2005 NumPy emerged as a ‘best of both worlds’ unification7 —combining the features of Numarray with the small-array performance of Numeric and its rich C API. Now, 15 years later, NumPy underpins almost every Python library that does scientific or numerical computation8–11 , including SciPy12 , Matplotlib13 , pandas14 , scikit-learn15 and scikit-image16 . NumPy is a community-developed, open-source library, which provides a mul- tidimensional Python array object along with array-aware functions thatoperateonit.Becauseofitsinherentsimplicity,theNumPyarray is the de facto exchange format for array data in Python. NumPyoperatesonin-memoryarraysusingthecentralprocessing unit(CPU).Toutilizemodern,specializedstorageandhardware,there has been a recent proliferation of Python array packages. Unlike with the Numarray–Numeric divide, it is now much harder for these new libraries to fracture the user community—given how much work is alreadybuiltontopofNumPy.However,toprovidethecommunitywith access to new and exploratory technologies, NumPy is transitioning into a central coordinating mechanism that specifies a well defined array programming API and dispatches it, as appropriate, to special- ized array implementations. NumPyarrays TheNumPyarrayisadatastructurethatefficientlystoresandaccesses multidimensionalarrays17 (alsoknownastensors),andenablesawide variety of scientific computation. It consists of a pointer to memory, along with metadata used to interpret the data stored there, notably ‘data type’, ‘shape’ and ‘strides’ (Fig. 1a). https://doi.org/10.1038/s41586-020-2649-2 Received: 21 February 2020 Accepted: 17 June 2020 Published online: 16 September 2020 Open access Check for updates 1 Independent researcher, Logan, UT, USA. 2 Brain Imaging Center, University of California, Berkeley, Berkeley, CA, USA. 3 Division of Biostatistics, University of California, Berkeley, Berkeley, CA, USA. 4 Berkeley Institute for Data Science, University of California, Berkeley, Berkeley, CA, USA. 5 Applied Mathematics, Stellenbosch University, Stellenbosch, South Africa. 6 Quansight, Austin, TX, USA. 7 Department of Physics, University of Jyväskylä, Jyväskylä, Finland. 8 Nanoscience Center, University of Jyväskylä, Jyväskylä, Finland. 9 Mercari JP, Tokyo, Japan. 10 Department of Engineering, University of Cambridge, Cambridge, UK. 11 Independent researcher, Karlsruhe, Germany. 12 Independent researcher, Berkeley, CA, USA. 13 Enthought, Austin, TX, USA. 14 Google Research, Mountain View, CA, USA. 15 Department of Astronomy and Astrophysics, University of Toronto, Toronto, Ontario, Canada. 16 School of Psychology, University of Birmingham, Edgbaston, Birmingham, UK. 17 Department of Physics, Temple University, Philadelphia, PA, USA. 18 Google, Zurich, Switzerland. 19 Department of Physics and Astronomy, The University of British Columbia, Vancouver, British Columbia, Canada. 20 Amazon, Seattle, WA, USA. 21 Independent researcher, Saue, Estonia. 22 Department of Mechanics and Applied Mathematics, Institute of Cybernetics at Tallinn Technical University, Tallinn, Estonia. 23 Department of Biological and Agricultural Engineering, University of Georgia, Athens, GA, USA. 24 France-IX Services, Paris, France. 25 Department of Economics, University of Oxford, Oxford, UK. 26 CCS-7, Los Alamos National Laboratory, Los Alamos, NM, USA. 27 Laboratory for Fluorescence Dynamics, Biomedical Engineering Department, University of California, Irvine, Irvine, CA, USA. ✉e-mail: [email protected]; [email protected]; [email protected]
  • 2. 358 | Nature | Vol 585 | 17 September 2020 Review The data type describes the nature of elements stored in an array. Anarrayhasasingledatatype,andeachelementofanarrayoccupies thesamenumberofbytesinmemory.Examplesofdatatypesinclude real and complex numbers (of lower and higher precision), strings, timestamps and pointers to Python objects. The shape of an array determines the number of elements along each axis, and the number of axes is the dimensionality of the array. For example, a vector of numbers can be stored as a one-dimensional array of shape N, whereas colour videos are four-dimensional arrays of shape (T, M, N, 3). Strides are necessary to interpret computer memory, which stores elementslinearly,asmultidimensionalarrays.Theydescribethenum- berofbytestomoveforwardinmemorytojumpfromrowtorow,col- umntocolumn,andsoforth.Consider,forexample,atwo-dimensional arrayoffloating-pointnumberswithshape(4, 3),whereeachelement occupies 8 bytes in memory. To move between consecutive columns, weneedtojumpforward8 bytesinmemory,andtoaccessthenextrow, 3 × 8 = 24 bytes. The strides of that array are therefore (24, 8). NumPy canstorearraysineitherCorFortranmemoryorder,iteratingfirstover either rows or columns. This allows external libraries written in those languages to access NumPy array data in memory directly. Users interact with NumPy arrays using ‘indexing’ (to access sub- arrays or individual elements), ‘operators’ (for example, +, − and × for vectorized operations and @ for matrix multiplication), as well as‘array-awarefunctions’;together,theseprovideaneasilyreadable, expressive, high-level API for array programming while NumPy deals with the underlying mechanics of making operations fast. Indexing an array returns single elements, subarrays or elements that satisfy a specific condition (Fig. 1b). Arrays can even be indexed usingotherarrays(Fig. 1c).Whereverpossible,indexingthatretrievesa subarrayreturnsa‘view’ontheoriginalarraysuchthatdataareshared between the two arrays. This provides a powerful way to operate on subsets of array data while limiting memory usage. To complement the array syntax, NumPy includes functions that perform vectorized calculations on arrays, including arithmetic, statistics and trigonometry (Fig. 1d). Vectorization—operating on entirearraysratherthantheirindividualelements—isessentialtoarray programming.Thismeansthatoperationsthatwouldtakemanytens oflinestoexpressinlanguagessuchasCcanoftenbeimplementedas asingle,clearPythonexpression.Thisresultsinconcisecodeandfrees users to focus on the details of their analysis, while NumPy handles looping over array elements near-optimally—for example, taking strides into consideration to best utilize the computer’s fast cache memory. Whenperformingavectorizedoperation(suchasaddition)ontwo arrays with the same shape, it is clear what should happen. Through ‘broadcasting’ NumPy allows the dimensions to differ, and produces results that appeal to intuition. A trivial example is the addition of a scalarvaluetoanarray,butbroadcastingalsogeneralizestomorecom- plex examples such as scaling each column of an array or generating agridofcoordinates.Inbroadcasting,oneorbotharraysarevirtually duplicated (that is, without copying any data in memory), so that the shapes of the operands match (Fig. 1d). Broadcasting is also applied when an array is indexed using arrays of indices (Fig. 1c). Other array-aware functions, such as sum, mean and maximum, performelement-by-element‘reductions’,aggregatingresultsacross one, multiple or all axes of a single array. For example, summing an n-dimensional array over d axes results in an array of dimension n − d (Fig. 1f). NumPyalsoincludesarray-awarefunctionsforcreating,reshaping, concatenating and padding arrays; searching, sorting and counting data; and reading and writing files. It provides extensive support for generatingpseudorandomnumbers,includesanassortmentofprob- ability distributions, and performs accelerated linear algebra, using oneofseveralbackendssuchasOpenBLAS18,19 orIntelMKLoptimized for the CPUs at hand (see Supplementary Methods for more details). Altogether, the combination of a simple in-memory array repre- sentation, a syntax that closely mimics mathematics, and a variety of array-aware utility functions forms a productive and powerfully expressive array programming language. In [1]: import numpy as np In [2]: x = np.arange(12) In [3]: x = x.reshape(4, 3) In [4]: x Out[4]: array([[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11]]) In [5]: np.mean(x, axis=0) Out[5]: array([4.5, 5.5, 6.5]) In [6]: x = x - np.mean(x, axis=0) In [7]: x Out[7]: array([[-4.5, -4.5, -4.5], [-1.5, -1.5, -1.5], [ 1.5, 1.5, 1.5], [ 4.5, 4.5, 4.5]]) a Data structure g Example x = 0 1 2 3 4 5 6 7 8 9 10 11 data data type shape strides 8-byte integer (4, 3) (24, 8) 1 2 3 4 5 6 70 8 9 10 11 8 bytes per element 3 × 8 = 24 bytes to jump one row down b Indexing (view) 10 1199 x[:,1:] → with slices 1 2 4 5 7 8 00 33 66 x[:,::2]→ with slices with steps 0 2 3 5 6 8 9 11 0 11 2 3 44 5 6 77 8 9 1010 11 Slices are start:end:step, any of which can be left blank d Vectorization + → 0 1 3 4 6 7 9 10 1 1 1 1 1 1 1 1 1 2 4 5 7 8 10 11 e Broadcasting × 3 6 0 9 1 2 → 0 0 3 6 6 12 9 18 f Reduction 0 1 3 4 6 7 9 10 2 5 8 11 3 12 21 30 sum axis 1 18 22 26 sum axis 0 66 sum axis (0,1) c Indexing (copy) 4 3 7 6 with arrays with broadcasting →x → ,2 1 1 0 x , 1 1 2 2 1 0 1 0 x with arraysx[0,1],x[1,2] 1 5→ →0 1 1 2 , x[x > 9] with masks10 11→→ 5 with scalarsx[1,2] Fig.1|TheNumPyarrayincorporatesseveralfundamentalarrayconcepts. a,TheNumPyarraydatastructureanditsassociatedmetadatafields. b,Indexinganarraywithslicesandsteps.Theseoperationsreturna‘view’of theoriginaldata.c,Indexinganarraywithmasks,scalarcoordinatesorother arrays,sothatitreturnsa‘copy’oftheoriginaldata.Inthebottomexample,an arrayisindexedwithotherarrays;thisbroadcaststheindexingarguments beforeperformingthelookup.d,Vectorizationefficientlyappliesoperations togroupsofelements.e,Broadcastinginthemultiplicationoftwo-dimensional arrays.f,Reductionoperationsactalongoneormoreaxes.Inthisexample, anarrayissummedalongselectaxestoproduceavector,oralongtwoaxes consecutivelytoproduceascalar.g,ExampleNumPycode,illustratingsomeof theseconcepts.
  • 3. Nature | Vol 585 | 17 September 2020 | 359 ScientificPythonecosystem Pythonisanopen-source,general-purposeinterpretedprogramming languagewellsuitedtostandardprogrammingtaskssuchascleaning data,interactingwithwebresourcesandparsingtext.Addingfastarray operations and linear algebra enables scientists to do all their work withinasingleprogramminglanguage—onethathastheadvantageof being famously easy to learn and teach, as witnessed by its adoption as a primary learning language in many universities. Even though NumPy is not part of Python’s standard library, it ben- efits from a good relationship with the Python developers. Over the years,thePythonlanguagehasaddednewfeaturesandspecialsyntax so that NumPy would have a more succinct and easier-to-read array notation.However,becauseitisnotpartofthestandardlibrary,NumPy is able to dictate its own release policies and development patterns. SciPyandMatplotlibaretightlycoupledwithNumPyintermsofhis- tory,developmentanduse.SciPyprovidesfundamentalalgorithmsfor scientificcomputing,includingmathematical,scientificandengineer- ingroutines.Matplotlibgeneratespublication-readyfiguresandvisu- alizations.ThecombinationofNumPy,SciPyandMatplotlib,together with an advanced interactive environment such as IPython20 or Jupy- ter21 ,providesasolidfoundationforarrayprogramminginPython.The scientificPythonecosystem(Fig. 2)buildsontopofthisfoundationto provide several, widely used technique-specific libraries15,16,22 , that in turn underlie numerous domain-specific projects23–28 . NumPy, at the base of the ecosystem of array-aware libraries, sets documentation standards, provides array testing infrastructure and adds build sup- port for Fortran and other compilers. Manyresearchgroupshavedesignedlarge,complexscientificlibrar- ies that add application-specific functionality to the ecosystem. For example, the eht-imaging library29 , developed by the Event Horizon Telescope collaboration for radio interferometry imaging, analysis andsimulation,reliesonmanylower-levelcomponentsofthescientific Pythonecosystem.Inparticular,theEHTcollaborationusedthislibrary forthefirstimagingofablackhole.Withineht-imaging,NumPyarrays are used to store and manipulate numerical data at every step in the processingchain:fromrawdatathroughcalibrationandimagerecon- struction.SciPysuppliestoolsforgeneralimage-processingtaskssuch asfilteringandimagealignment,andscikit-image,animage-processing library that extends SciPy, provides higher-level functionality such as edge filters and Hough transforms. The ‘scipy.optimize’ module performsmathematicaloptimization.NetworkX22 ,apackageforcom- plexnetworkanalysis,isusedtoverifyimagecomparisonconsistency. Astropy23,24 handlesstandardastronomicalfileformatsandcomputes time–coordinatetransformations.Matplotlibisusedtovisualizedata and to generate the final image of the black hole. Theinteractiveenvironmentcreatedbythearray programmingfoun- dation and the surrounding ecosystem of tools—inside of IPython or Jupyter—isideallysuitedtoexploratorydataanalysis.Userscanfluidly inspect,manipulateandvisualizetheirdata,andrapidlyiteratetorefine programmingstatements.Thesestatementsarethenstitchedtogether intoimperativeorfunctionalprograms,ornotebookscontainingboth computationandnarrative.Scientificcomputingbeyondexploratory workisoftendoneinatexteditororanintegrateddevelopmentenvi- ronment (IDE) such as Spyder. This rich and productive environment has made Python popular for scientific research. To complement this facility for exploratory work and rapid proto- typing,NumPyhasdevelopedacultureofusingtime-testedsoftware engineeringpracticestoimprovecollaborationandreduceerror30 .This culture is not only adopted by leaders in the project but also enthusi- astically taught to newcomers. The NumPy team was early to adopt distributedrevisioncontrolandcodereviewtoimprovecollaboration cantera Chemistry Biopython Biology Astropy Astronomy simpeg Geophysics NLTK Linguistics QuantEcon Economics SciPy Algorithms Matplotlib Plots scikit-learn Machine learning NetworkX Network analysis pandas, statsmodels Statistics scikit-image Image processing PsychoPykhmer Qiime2 FiPy deepchem librosaPyWavelets SunPy QuTiP yt nibabel yellowbrickmne-python scikit-HEP eht-imagingMDAnalysis iriscesium PyChrono Foundation Application-specific Domain-specific Technique-specific Array ProtocolsNumPy API Python Language IPython / Jupyter Interactive environments NumPy Arrays New array implementations Fig.2|NumPyisthebaseofthescientificPythonecosystem.EssentiallibrariesandprojectsthatdependonNumPy’sAPIgainaccesstonewarray implementationsthatsupportNumPy’sarrayprotocols(Fig. 3).
  • 4. 360 | Nature | Vol 585 | 17 September 2020 Review oncode,andcontinuoustestingthatrunsanextensivebatteryofauto- mated tests for every proposed change to NumPy. The project also hascomprehensive,high-qualitydocumentation,integratedwiththe source code31–33 . Thiscultureofusingbestpracticesforproducingreliablescientific softwarehasbeenadoptedbytheecosystemoflibrariesthatbuildon NumPy.Forexample,inarecentawardgivenbytheRoyalAstronomi- cal Society to Astropy, they state: “The Astropy Project has provided hundredsofjuniorscientistswithexperienceinprofessional-standard softwaredevelopmentpracticesincludinguseofversioncontrol,unit testing, code review and issue tracking procedures. This is a vital skill setformodernresearchersthatisoftenmissingfromformaluniversity educationinphysicsorastronomy”34 .Communitymembersexplicitly work to address this lack of formal education through courses and workshops35–37 . Therecentrapidgrowthofdatascience,machinelearningandarti- ficial intelligence has further and dramatically boosted the scientific use of Python. Examples of its important applications, such as the eht-imaging library, now exist in almost every discipline in the natu- ralandsocialsciences.Thesetoolshavebecometheprimarysoftware environmentinmanyfields.NumPyanditsecosystemarecommonly taught in university courses, boot camps and summer schools, and are the focus of community conferences and workshops worldwide. NumPy and its API have become truly ubiquitous. Arrayproliferationandinteroperability NumPyprovidesin-memory,multidimensional,homogeneouslytyped (thatis,single-pointerandstrided)arraysonCPUs.Itrunsonmachines rangingfromembeddeddevicestotheworld’slargestsupercomputers, withperformanceapproachingthatofcompiledlanguages.Formost its existence, NumPy addressed the vast majority of array computa- tion use cases. However,scientificdatasetsnowroutinelyexceedthememorycapac- ity of a single machine and may be stored on multiple machines or in thecloud.Inaddition,therecentneedtoacceleratedeep-learningand artificialintelligenceapplicationshasledtotheemergenceofspecial- izedacceleratorhardware,includinggraphicsprocessingunits(GPUs), tensor processing units (TPUs) and field-programmable gate arrays (FPGAs).Owingtoitsin-memorydatamodel,NumPyiscurrentlyunable to directly utilize such storage and specialized hardware. However, both distributed data and also the parallel execution of GPUs, TPUs andFPGAsmapwelltotheparadigmofarrayprogramming:therefore leadingtoagapbetweenavailablemodernhardwarearchitecturesand the tools necessary to leverage their computational power. Thecommunity’seffortstofillthisgapledtoaproliferationofnew array implementations. For example, each deep-learning framework created its own arrays; the PyTorch38 , Tensorflow39 , Apache MXNet40 and JAX arrays all have the capability to run on CPUs and GPUs in a distributed fashion, using lazy evaluation to allow for additional per- formanceoptimizations.SciPyandPyData/Sparsebothprovidesparse arrays,whichtypicallycontainfewnon-zerovaluesandstoreonlythose in memory for efficiency. In addition, there are projects that build on NumPy arrays as data containers, and extend its capabilities. Distrib- uted arrays are made possible that way by Dask, and labelled arrays— referring to dimensions of an array by name rather than by index for clarity, compare x[:, 1] versus x.loc[:, 'time']—by xarray41 . Such libraries often mimic the NumPy API, because this lowers the barriertoentryfornewcomersandprovidesthewidercommunitywith astablearray programminginterface.This,inturn,preventsdisruptive schisms such as the divergence between Numeric and Numarray. But exploring new ways of working with arrays is experimental by nature and,infact,severalpromisinglibraries(suchasTheanoandCaffe)have alreadyceaseddevelopment.Andeachtimethatauserdecidestotrya newtechnology,theymustchangeimportstatementsandensurethatthe newlibraryimplementsallthepartsoftheNumPyAPItheycurrentlyuse. Ideally, operating on specialized arrays using NumPy functions or semantics would simply work, so that users could write code once, and would then benefit from switching between NumPy arrays, GPU arrays,distributedarraysandsoforthasappropriate.Tosupportarray operations between external array objects, NumPy therefore added the capability to act as a central coordination mechanism with a well specified API (Fig. 2). To facilitate this interoperability, NumPy provides ‘protocols’ (or contractsofoperation),thatallowforspecializedarraystobepassedto NumPyfunctions(Fig. 3).NumPy,inturn,dispatchesoperationstothe originatinglibrary,asrequired.Overfourhundredofthemostpopular NumPy functions are supported. The protocols are implemented by widely used libraries such as Dask, CuPy, xarray and PyData/Sparse. Thankstothesedevelopments,userscannow,forexample,scaletheir computationfromasinglemachinetodistributedsystemsusingDask. The protocols also compose well, allowing users to redeploy NumPy codeatscaleondistributed,multi-GPUsystemsvia,forinstance,CuPy arrays embedded in Dask arrays. Using NumPy’s high-level API, users can leverage highly parallel code execution on multiple systems with millions of cores, all with minimal code changes42 . These array protocols are now a key feature of NumPy, and are expected to only increase in importance. The NumPy developers— many of whom are authors of this Review—iteratively refine and add protocol designs to improve utility and simplify adoption. Output arrays Input arrays NumPy API np.stack np.reshape np.transpose np.argmin np.mean np.std np.max np.cos np.arctan np.log np.cumsum np.diff ... NumPy array protocols In [1]: import numpy as np In [2]: import dask.array as da In [3]: x = da.arange(12) In [4]: x = np.reshape(x, (4, 3)) In [5]: x Out[5]: dask.array<..., shape=(4, 3), ...> In [6]: np.mean(x, axis=0) Out[6]: dask.array<..., shape=(3,), ...> In [7]: x = x - np.mean(x, axis=0) In [8]: x Out[8]: dask.array<..., shape=(4, 3), ...> Array implementation NumPy Dask CuPy PyData/ Sparse ... ... Dask NumPy CuPy PyData Sparse ... Dask NumPy CuPy PyData Sparse Fig.3|NumPy’sAPIandarrayprotocolsexposenewarraystothe ecosystem.Inthisexample,NumPy’s‘mean’functioniscalledonaDaskarray. Thecallsucceedsbydispatchingtotheappropriatelibraryimplementation(in thiscase,Dask)andresultsinanewDaskarray.Comparethiscodetothe examplecodeinFig. 1g.
  • 5. Nature | Vol 585 | 17 September 2020 | 361 Discussion NumPy combines the expressive power of array programming, the performanceofC,andthereadability,usabilityandversatilityofPython inamature,welltested,welldocumentedandcommunity-developed library.LibrariesinthescientificPythonecosystemprovidefastimple- mentations of most important algorithms. Where extreme optimiza- tion is warranted, compiled languages can be used, such as Cython43 , Numba44 and Pythran45 ; these languages extend Python and trans- parently accelerate bottlenecks. Owing to NumPy’s simple memory model, it is easy to write low-level, hand-optimized code, usually in C orFortran,tomanipulateNumPyarraysandpassthembacktoPython. Furthermore, using array protocols, it is possible to utilize the full spectrumofspecializedhardwareaccelerationwithminimalchanges to existing code. NumPywasinitiallydevelopedbystudents,facultyandresearchers to provide an advanced, open-source array programming library for Python,whichwasfreetouseandunencumberedbylicenseserversand softwareprotectiondongles.Therewasasenseofbuildingsomething consequential together for the benefit of many others. Participating in such an endeavour, within a welcoming community of like-minded individuals, held a powerful attraction for many early contributors. These user–developers frequently had to write code from scratch to solve their own or their colleagues’ problems—often in low-level languages that preceded Python, such as Fortran46 and C. To them, theadvantagesofaninteractive,high-levelarraylibrarywereevident. Thedesignofthisnewtoolwasinformedbyotherpowerfulinteractive programming languages for scientific computing such as Basis47–50 , Yorick51 , R52 and APL53 , as well as commercial languages and environ- ments such as IDL (Interactive Data Language) and MATLAB. WhatbeganasanattempttoaddanarrayobjecttoPythonbecame thefoundationofavibrantecosystemoftools.Now,alargeamountof scientific work depends on NumPy being correct, fast and stable. It is nolongerasmallcommunityproject,butcorescientificinfrastructure. Thedeveloperculturehasmatured:althoughinitialdevelopmentwas highlyinformal,NumPynowhasaroadmapandaprocessforpropos- ing and discussing large changes. The project has formal governance structures and is fiscally sponsored by NumFOCUS, a nonprofit that promotes open practices in research, data and scientific computing. Overthepastfewyears,theprojectattracteditsfirstfundeddevelop- ment, sponsored by the Moore and Sloan Foundations, and received anawardaspartoftheChanZuckerbergInitiative’sEssentialsofOpen Source Software programme. With this funding, the project was (and is) able to have sustained focus over multiple months to implement substantial new features and improvements. That said, the develop- mentofNumPystilldependsheavilyoncontributionsmadebygradu- ate students and researchers in their free time (see Supplementary Methods for more details). NumPyisnolongermerelythefoundationalarraylibraryunderlying thescientificPythonecosystem,butithasbecomethestandardAPIfor tensor computation and a central coordinating mechanism between arraytypesandtechnologiesinPython.Workcontinuestoexpandon and improve these interoperability features. Overthenextdecade,NumPydeveloperswillfaceseveralchallenges. Newdeviceswillbedeveloped,andexistingspecializedhardwarewill evolvetomeetdiminishingreturnsonMoore’slaw.Therewillbemore, andawidervarietyof,datasciencepractitioners,alargeproportionof whom will use NumPy. The scale of scientific data gathering will con- tinue to increase, with the adoption of devices and instruments such as light-sheet microscopes and the Large Synoptic Survey Telescope (LSST)54 .Newgenerationlanguages,interpretersandcompilers,suchas Rust55 ,Julia56 andLLVM57 ,willcreatenewconceptsanddatastructures, and determine their viability. ThroughthemechanismsdescribedinthisReview,NumPyispoised to embrace such a changing landscape, and to continue playing a leading part in interactive scientific computation, although to do so willrequiresustainedfundingfromgovernment,academiaandindus- try.But,importantly,forNumPytomeettheneedsofthenextdecade ofdatascience,itwillalsoneedanewgenerationofgraduatestudents and community contributors to drive it forward. 1. Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016). 2. Chael, A. et al. High-resolution linear polarimetric imaging for the Event Horizon Telescope. Astrophys. J. 286, 11 (2016). 3. Dubois, P. F., Hinsen, K. & Hugunin, J. Numerical Python. Comput. Phys. 10, 262–267 (1996). 4. Ascher, D., Dubois, P. F., Hinsen, K., Hugunin, J. & Oliphant, T. E. An Open Source Project: Numerical Python (Lawrence Livermore National Laboratory, 2001). 5. Yang, T.-Y., Furnish, G. & Dubois, P. F. Steering object-oriented scientific computations. In Proc. TOOLS USA 97. Intl Conf. Technology of Object Oriented Systems and Languages (eds Ege, R., Singh, M. & Meyer, B.) 112–119 (IEEE, 1997). 6. Greenfield, P., Miller, J. T., Hsu, J. & White, R. L. numarray: a new scientific array package for Python. In PyCon DC 2003 http://citeseerx.ist.psu.edu/viewdoc/download?d oi=10.1.1.112.9899 (2003). 7. Oliphant, T. E. Guide to NumPy 1st edn (Trelgol Publishing, 2006). 8. Dubois, P. F. Python: batteries included. Comput. Sci. Eng. 9, 7–9 (2007). 9. Oliphant, T. E. Python for scientific computing. Comput. Sci. Eng. 9, 10–20 (2007). 10. Millman, K. J. & Aivazis, M. Python for scientists and engineers. Comput. Sci. Eng. 13, 9–12 (2011). 11. Pérez, F., Granger, B. E. & Hunter, J. D. Python: an ecosystem for scientific computing. Comput. Sci. Eng. 13, 13–21 (2011). Explains why the scientific Python ecosystem is a highly productive environment for research. 12. Virtanen, P. et al. SciPy 1.0—fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020); correction 17, 352 (2020). Introduces the SciPy library and includes a more detailed history of NumPy and SciPy. 13. Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007). 14. McKinney, W. Data structures for statistical computing in Python. In Proc. 9th Python in Science Conf. (eds van der Walt, S. & Millman, K. J.) 56–61 (2010). 15. Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011). 16. van der Walt, S. et al. scikit-image: image processing in Python. PeerJ 2, e453 (2014). 17. van der Walt, S., Colbert, S. C. & Varoquaux, G. The NumPy array: a structure for efficient numerical computation. Comput. Sci. Eng. 13, 22–30 (2011). Discusses the NumPy array data structure with a focus on how it enables efficient computation. 18. Wang, Q., Zhang, X., Zhang, Y. & Yi, Q. AUGEM: automatically generate high performance dense linear algebra kernels on x86 CPUs. In SC’13: Proc. Intl Conf. High Performance Computing, Networking, Storage and Analysis 25 (IEEE, 2013). 19. Xianyi, Z., Qian, W. & Yunquan, Z. Model-driven level 3 BLAS performance optimization on Loongson 3A processor. In 2012 IEEE 18th Intl Conf. Parallel and Distributed Systems 684–691 (IEEE, 2012). 20. Pérez, F. & Granger, B. E. IPython: a system for interactive scientific computing. Comput. Sci. Eng. 9, 21–29 (2007). 21. Kluyver, T. et al. Jupyter Notebooks—a publishing format for reproducible computational workflows. In Positioning and Power in Academic Publishing: Players, Agents and Agendas (eds Loizides, F. & Schmidt, B.) 87–90 (IOS Press, 2016). 22. Hagberg, A. A., Schult, D. A. & Swart, P. J. Exploring network structure, dynamics, and function using NetworkX. In Proc. 7th Python in Science Conf. (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 11–15 (2008). 23. Astropy Collaboration et al. Astropy: a community Python package for astronomy. Astron. Astrophys. 558, A33 (2013). 24. Price-Whelan, A. M. et al. The Astropy Project: building an open-science project and status of the v2.0 core package. Astron. J. 156, 123 (2018). 25. Cock, P. J. et al. Biopython: freely available Python tools for computational molecular biology and bioinformatics. Bioinformatics 25, 1422–1423 (2009). 26. Millman, K. J. & Brett, M. Analysis of functional magnetic resonance imaging in Python. Comput. Sci. Eng. 9, 52–55 (2007). 27. The SunPy Community et al. SunPy—Python for solar physics. Comput. Sci. Discov. 8, 014009 (2015). 28. Hamman, J., Rocklin, M. & Abernathy, R. Pangeo: a big-data ecosystem for scalable Earth system science. In EGU General Assembly Conf. Abstracts 12146 (2018). 29. Chael, A. A. et al. ehtim: imaging, analysis, and simulation software for radio interferometry. Astrophysics Source Code Library https://ascl.net/1904.004 (2019). 30. Millman, K. J. & Pérez, F. Developing open source scientific practice. In Implementing Reproducible Research (eds Stodden, V., Leisch, F. & Peng, R. D.) 149–183 (CRC Press, 2014). Describes the software engineering practices embraced by the NumPy and SciPy communities with a focus on how these practices improve research. 31. van der Walt, S. The SciPy Documentation Project (technical overview). In Proc. 7th Python in Science Conf. (SciPy 2008) (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 27–28 (2008). 32. Harrington, J. The SciPy Documentation Project. In Proc. 7th Python in Science Conference (SciPy 2008) (eds Varoquaux, G., Vaught, T. & Millman, K. J.) 33–35 (2008). 33. Harrington, J. & Goldsmith, D. Progress report: NumPy and SciPy documentation in 2009. In Proc. 8th Python in Science Conf. (SciPy 2009) (eds Varoquaux, G., van der Walt, S. & Millman, K. J.) 84–87 (2009). 34. Royal Astronomical Society Report of the RAS ‘A’ Awards Committee 2020: Astropy Project: 2020 Group Achievement Award (A) https://ras.ac.uk/sites/default/files/2020-01/ Group%20Award%20-%20Astropy.pdf (2020). 35. Wilson, G. Software carpentry: getting scientists to write better code by making them more productive. Comput. Sci. Eng. 8, 66–69 (2006).
  • 6. 362 | Nature | Vol 585 | 17 September 2020 Review 36. Hannay, J. E. et al. How do scientists develop and use scientific software? In Proc. 2009 ICSE Workshop on Software Engineering for Computational Science and Engineering 1–8 (IEEE, 2009). 37. Millman, K. J., Brett, M., Barnowski, R. & Poline, J.-B. Teaching computational reproducibility for neuroimaging. Front. Neurosci. 12, 727 (2018). 38. Paszke, A. et al. Pytorch: an imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32 (eds Wallach, H. et al.) 8024–8035 (Neural Information Processing Systems, 2019). 39. Abadi, M. et al. TensorFlow: a system for large-scale machine learning. In OSDI’16: Proc. 12th USENIX Conf. Operating Systems Design and Implementation (chairs Keeton, K. & Roscoe, T.) 265–283 (USENIX Association, 2016). 40. Chen, T. et al. MXNet: a flexible and efficient machine learning library for heterogeneous distributed systems. Preprint at http://www.arxiv.org/abs/1512.01274 (2015). 41. Hoyer, S. & Hamman, J. xarray: N–D labeled arrays and datasets in Python. J. Open Res. Softw. 5, 10 (2017). 42. Entschev, P. Distributed multi-GPU computing with Dask, CuPy and RAPIDS. In EuroPython 2019 https://ep2019.europython.eu/media/conference/slides/ fX8dJsD-distributed-multi-gpu-computing-with-dask-cupy-and-rapids.pdf (2019). 43. Behnel, S. et al. Cython: the best of both worlds. Comput. Sci. Eng. 13, 31–39 (2011). 44. Lam, S. K., Pitrou, A. & Seibert, S. Numba: a LLVM-based Python JIT compiler. In Proc. Second Workshop on the LLVM Compiler Infrastructure in HPC, LLVM ’15 7:1–7:6 (ACM, 2015). 45. Guelton, S. et al. Pythran: enabling static optimization of scientific Python programs. Comput. Sci. Discov. 8, 014001 (2015). 46. Dongarra, J., Golub, G. H., Grosse, E., Moler, C. & Moore, K. Netlib and NA-Net: building a scientific computing community. IEEE Ann. Hist. Comput. 30, 30–41 (2008). 47. Barrett, K. A., Chiu, Y. H., Painter, J. F., Motteler, Z. C. & Dubois, P. F. Basis System, Part I: Running a Basis Program—A Tutorial for Beginners UCRL-MA-118543, Vol. 1 (Lawrence Livermore National Laboratory 1995). 48. Dubois, P. F. & Motteler, Z. Basis System, Part II: Basis Language Reference Manual UCRL-MA-118543, Vol. 2 (Lawrence Livermore National Laboratory, 1995). 49. Chiu, Y. H. & Dubois, P. F. Basis System, Part III: EZN User Manual UCRL-MA-118543, Vol. 3 (Lawrence Livermore National Laboratory, 1995). 50. Chiu, Y. H. & Dubois, P. F. Basis System, Part IV: EZD User Manual UCRL-MA-118543, Vol. 4 (Lawrence Livermore National Laboratory, 1995). 51. Munro, D. H. & Dubois, P. F. Using the Yorick interpreted language. Comput. Phys. 9, 609–615 (1995). 52. Ihaka, R. & Gentleman, R. R: a language for data analysis and graphics. J. Comput. Graph. Stat. 5, 299–314 (1996). 53. Iverson, K. E. A programming language. In Proc. 1962 Spring Joint Computer Conf. 345–351 (1962). 54. Jenness, T. et al. LSST data management software development practices and tools. In Proc. SPIE 10707, Software and Cyberinfrastructure for Astronomy V 1070709 (SPIE and International Society for Optics and Photonics, 2018). 55. Matsakis, N. D. & Klock, F. S. The Rust language. Ada Letters 34, 103–104 (2014). 56. Bezanson, J., Edelman, A., Karpinski, S. & Shah, V. B. Julia: a fresh approach to numerical computing. SIAM Rev. 59, 65–98 (2017). 57. Lattner, C. & Adve, V. LLVM: a compilation framework for lifelong program analysis and transformation. In Proc. 2004 Intl Symp. Code Generation and Optimization (CGO’04) 75–88 (IEEE, 2004). Acknowledgements We thank R. Barnowski, P. Dubois, M. Eickenberg, and P. Greenfield, who suggested text and provided helpful feedback on the manuscript. K.J.M. and S.J.v.d.W. were funded in part by the Gordon and Betty Moore Foundation through grant GBMF3834 and by the Alfred P. Sloan Foundation through grant 2013-10-27 to the University of California, Berkeley. S.J.v.d.W., S.B., M.P. and W.W. were funded in part by the Gordon and Betty Moore Foundation through grant GBMF5447 and by the Alfred P. Sloan Foundation through grant G-2017-9960 to the University of California, Berkeley. Author contributions K.J.M. and S.J.v.d.W. composed the manuscript with input from others. S.B., R.G., K.S., W.W., M.B. and T.R. contributed text. All authors contributed substantial code, documentation and/or expertise to the NumPy project. All authors reviewed the manuscript. Competing interests The authors declare no competing interests. Additional information Supplementary information is available for this paper at https://doi.org/10.1038/s41586-020- 2649-2. Correspondence and requests for materials should be addressed to K.J.M., S.J.v.W. or R.G. Peer review information Nature thanks Edouard Duchesnay, Alan Edelman and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Reprints and permissions information is available at http://www.nature.com/reprints. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 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