CdD@0ddlmZddlZddlZddlmZddlmZmZm Z ddl m Z m Z ddl ZddlmZmZmZddlmZddlmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$dd l%m&Z&m'Z'm(Z(m)Z)m*Z*dd l+m,Z,dd l-m.Z.dd l/m0Z0m1Z1dd l2m3Z3m4Z4m5Z5m6Z6m7Z7ddl8m9Z9ddl:m;Z;mZ>ddl?m@Z@mAZAddlBmCZCddlDmEZEmFZFmGZGmHZHmIZIeJZKeFeddddZLeFedZMeFedZNeFedZOeFedZPeFeddZQeFeddZReFeddZSeFedZTeFeddZUdd ZVeFed!ZWeFed"ZXeFedd%ZYd&ZZd'Z[eFedd)Z\eFed*g+d,Z]eFed-Z^dd.Z_dd/Z`d0ZaeFed1ZbeFed2Zcd3ZdeFeddd4d5ZeeFed6ZfeFedd7ZgeFedd9ZheFedd:Zid;ZjeFedd<d=Zkd>ZleFedd?ZmeFedd@ZndAZoeFeddCZpddEZqddFZrddGZsddIZtdJZudKZvddLZweFeddMZxeFeddNZye ejzej{eFeddOZze ej|eFedPZ|e ej}eFedQZ}ddRZ~ ddSZeFeddTZddUZe6eedVdddWZeFeddXZeFedYZeFedZZeFed[ZeFed\ZeFedd]ZeFedd^ZeFed_ZeFedd`ZdaZeFeddbZdcZddZdeZeFeddhZeFeddiZdjZeFedkZdlZejeegmZdnZeFedoZeFeddpZeFeddqZeFedrZeFedsZdtZeFeddvZe ejddxZdyZeFedzZd{ZeFedd|ZddZddZe ejddZddZeFedZeFedZeFeddZ ddZeFeddZeFeddZeFeddZeFeddZeFeddZeFeddZeFeddZdS)) annotationsN)Iterable)partialreducewraps)IntegralReal)concat interleavesliding_window)chunk)Array asanyarrayasarray blockwisebroadcast_arraysbroadcast_shapes broadcast_to concatenateelemwise from_array implementsis_scalar_for_elemwise map_blocksstacktensordot_lookup)arangediagemptyindicestri)einsum) reduction)multiplysqrt) array_safe asarray_safemeta_from_array safe_wraps validate_axis)ones)is_dask_collectiontokenize)flatten)Delayedunpack_collections)HighLevelGraph)apply derived_fromfuncname is_arraylike is_cupy_typelikect||}|$|j|kr|dddf}| |j|k| |j|kr||}|S)Nr7)rndimdtypeastype)xr;ndminr8s 3lib/python3.11/site-packages/dask/array/routines.pyarrayr@4smA   dAAAgJ   QW-- HHUOO Hc6d|D}tj|S)Nc>g|]}t|r|n|jS)rr;).0as r? zresult_type..@s, F F FA'** 7AA F F FrA)np result_type)argss r?rIrI>s" F F F F FD >4  rAc g}|D]m}t|}|jdkr |d}n3|jdkr|ddddf}n|jdkr|dddddf}||nt|dkr|dS|S)NrNNNrr:appendlenarysnew_arysr=s r? atleast_3drUDsH    qMM 6Q;;"#AA Vq[[$4- AA Vq[[!!!QQQ* A 8}}{rAcg}|D]Q}t|}|jdkr |d}n|jdkr |dddf}||Rt|dkr|dS|S)NrNNrMrOrRs r? atleast_2drXXsH  qMM 6Q;;* AA Vq[[$' A 8}}{rAcg}|D]9}t|}|jdkr|d}||:t|dkr|dS|S)NrrMrOrRs r? atleast_1drZjsjH  qMM 6Q;;$A 8}}{rAFct|trtdtd|D}t |d|S)Nz=``vstack`` expects a sequence of arrays as the first argumentc34K|]}t|VdSN)rXrEr=s r? zvstack..(++! 1 ++++++rAraxisallow_unknown_chunksizes isinstancerNotImplementedErrortuplertuprcs r?vstackrjz]#u ! 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Nrz `axis` of z invalid for z-D array) rr:sliceryrer IndexErrorrstrrg)mrbslaxes r?fliprs" 1 A 5;;- B |QV}} dH % %w + +B4r**BrFF +  FT F FQV F F F    rB R5LsA11 B6;6B11B6c"t|dSNrrrs r?flipudr 1::rAc"t|dSNrMrrs r?fliplrrrrArMrrMct|}t|dkrtdt|}|d|dks,t j|d|dz |jkrtd|d|jks5|d|j ks#|d|jks|d|j krtd|d|jd|d z}|dkr |ddS|dkr*tt||d|dSttd|j}||d||dc||d<||d<|dkr$tt||d|Stt|||dS) NrNzlen(axes) must be 2.rrMzAxes must be different.zAxes=z out of range for array of ndim=.) rgrQrrrHabsoluter:rrxryr)rkr axes_lists r?rot90rs ;;D 4yyA~~/0001 A Aw$q'R[a47):;;qvEE2333 Aw!&DGqvg--aAF1B1Bd1gQRQWPWFWFWPPPqvPPPQQQFAAvvt AvvDDG$$d1g...U1af%%&&I09$q'0BIdSTgDV,YtAw47+Avvaa))9555Ia++T!W555rAc~t||gd}tjt|}||||}|rt |ddkr|St ddg|jz}t|dD]}||d|t|}|S)Nc|jSr])__array_priority__r=s r?z_tensordot.. s !"6rA)keyrrrM) maxrdispatchtyperQrr:sortedinsertrg)rFbr is_sparser= tensordotr{s r? _tensordotr s QF66777A )$q''22I !QT"""ASa\\Q&&T4  !AF*Q  A JJq$     eCjjMrAcdtt|jv}|r#dtt|jv}|S)Nsparsezsparse._coo.core.COO)rr_meta)r=rs r?_tensordot_is_sparsersECQW ...IE*#d17mm2D2DD rArNc t|tst|}t|tst|}t|tr|\}}nGt t |j|z |j}t t d|}t|tr|f}t|tr|f}t|trt |}t|trt |}t|pt|}|rt|dkrd}nd}tj |j |j }tt |j}tt |j|j|jz} || z} i} t||D]U\} } | | | || | | <|r| || Id| || <Vt!t"| |||| ||| ||f| }|r|S||S)NrrMTFcdSrrD)cs r?rztensordot..DsQrA)r;r adjust_chunksrrrb)rerrrrgryr:rrxrrQrH promote_typesr;zipremoverrsum)lhsrhsr left_axes right_axesrrdt left_index right_index out_indexrlr intermediates r?rr sr c5 ! !oo c5 ! !oo$!!+ $ ::%4::;; 5D>>** )X&&!L *h''# ] )T""%)$$ *d##':&& $S))F-A#-F-FIS^^q((  #)SY / /BeCHoo&&JuSXsx#(':;;< ? ? ??rAct||Sr])rconjravelrs r?vdotr]s, qvvxx~~ + ++rAct|tur*tttj||}n|}|r|S||dS)Nr;r)rrxrrrHaddsqueeze)rFrbr;keepdimsr|s r? _chunk_sumrbs[ Aww$WRV5111155$ {{47###rAc|Attjd|jdt }|j|dkr||St|tt||dS)NrMrr;F)rbr;r) getattrrHzerosr;robjectshaperr#r)rFrbr;s r? _sum_wo_catrvsz }!'2226688'6JJwt}yy  :zEu   rAct}t|rddl}|}|||}|d|jddfS)Nr.)rHr6cupymatmulnewaxis)rFrxprr s r?_matmulrsP BA   IIaOOE bj!!!# $$rAc t|}t|}|jdks |jdkrtdd}|jdkrd}|tjddf}d}|jdkrd}|ddtjf}|j|jkr$||j|jz tjfz}n3|j|jkr#||j|jz tjfz}t t |jdz}t t |j}t t |jdz |d|jfz}tt||||||ddit||d }t|d }|r| d }|r| d}|S) Nrz"`matmul` does not support scalars.FrMTrNr)rr;rr) rr:rrHrrgryrrrIrr)rFra_is_1db_is_1dout_indlhs_indrhs_indr|s r?rrs1 A1 Av{{afkk=>>>Gv{{ bj!!!m Gv{{ aaam v qv2:-/ 0 !& qv2:-/ 0 E!&1*%%&&GE!&MM""GE!&1*%%&&'"+qv)>>G   r{A&!Q   C$ c # # #Ckk"ookk"oo JrAc "|}|}tj|j|jj}t tjd|d|d|S)Nijijr)r.rHouterr;rr)rFrr;s r?rrsc A A HQW\\^^QW\\^^ 4 4 :E RXtQQ5 A A AArAc0tj|||g|Ri|Sr])rHapply_along_axis)arrfunc1d func1d_axis func1d_args func1d_kwargss r?_inner_apply_along_axisrs' v{C W+ W W W W WWrA)r;rct|}t|jd|}||Ktjd|j}tj||g|Ri|}||j}||j}||jd||j||dzfz|j|dzdz}| tt|dz||jd||z|j|dzdz|tt||t|zd|||| } | S)aj This is a blocked variant of :func:`numpy.apply_along_axis` implemented via :func:`dask.array.map_blocks` Notes ----- If either of `dtype` or `shape` are not provided, Dask attempts to determine them by calling `func1d` on a dummy array. This may produce incorrect values for `dtype` or `shape`, so we recommend providing them. NrMrrMz -along-axis) namer;chunks drop_axisnew_axisrrrr)rrQrrHr+r;r@rechunkrrrr4rxry) rrbrr;rrJkwargs test_data test_resultresults r?rrsj #,,C sy$ D } GD 222 hvviA$AAA&AABB =%E =%E ++ 5D5SYtdQh799CJtaxzz>> ;!  MMEE$K_VU5\\::F 8}}q $ ' ' 6U4[[M !D 6U4[[M !Dq$DJtRDJ ;;D ;;D A 1XX dGag  HrAc6t|}|}|dd|ddz }|g}|%t|g|z}|%|t|gz}t|}|S)NrMr)rr.r)aryto_endto_beginaryfrs r?ediff1drhs #,,C ;;==D QRR49A A X   & & ( ( )A -  ((**+ +AA HrAc||}|"||d||d|}tj||fd|i|}|S)aU x: nd-array array of one block coord: 1d-array or scalar coordinate along which the gradient is computed. axis: int axis along which the gradient is computed array_locs: actual location along axis. 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Rechunk to proceed.z(dask array coordinated is not supported.rrc&i|] }||krdndS)rMrrD)rErrs r? zgradient..s'EEE!qqBww!!AEEErAnone)r;depthboundaryrrbrr)#rmathceilgetrrgryr:rerr*rQsetr issubclassr;rrHbool_r<floatr itemsize enumeraterrformatisscalarrrfr@cumsumrP map_overlapr ) r$rbvarargsrdrop_result_listresultsrrrr array_loc_stoparray_loc_startrs ` @r?rrsb A9VZZ a%@%@AAF< laFGGG |U16]]## D( # #w qv & &D 4yyCD NN""5666 ,,,,t,,, , ,D"}} 7||qd))g% 7||s4yy   U   !',8 455 HHUOO AGL$ ' 'AG,:J MM gEEEEuQV}}EEEaj%"    !* NrAc t|ts|Sttt|}t j|d||}|D]!}|dt |xx|z cc<"|S)Nr)rr;)rerxrmaprQrH zeros_like) bincountsr;rr r|rs r? _bincount_aggr@s i & & CY    A - ! AU ; ; ;C  Hc!ffH  JrAc 6|jdkrtd||j|jkrtdt|||}|dg}|Lt t jdgdgt|}||dgn0t t jgt|}|dkrt j f}n|f}ttt j|dg|R||d }|t|jdzg|jddR|_ dd lm} | |tt |j d d |j|d} |g|jddR| _ || _| S)NrMz8Input array must be one dimensional. Try using x.ravel()z/Chunks of input array x and weights must match.r)weightsr7r) minlength)tokenmeta) _tree_reducerrTF) aggregaterbrr; split_everyr)r:rrr-r&rHbincountr(extendnanrrrQ_chunksdask.array.reductionsrFr@r;r) r=rBrCrIrDrJrE output_sizechunked_countsrFoutputs r?rJrJsv{{STTT >QX % %NOO O Q + +E s8D"+qcA3777oa>P>PQQQ WcN####"+b//0B0BCCCA~~vi  l  y11139=EJQUN c./2333  qrr "N 322222 \-tz::: jF">N$9!""$=>>FNFL MrAct|t|}tjtdg||dj}|tj|||S)Nr7rF)right)r;binsrS)r'r(rHdigitizer;r)rFrTrSr;s r?rUrUs` ?1#5#5 6 6 6D K aSt444d% H H H NE << 5t5< I IIrAcntj|||}d||dk<|tjddfS)N)siderr)rH searchsortedr)r=yrWress r?_searchsorted_blockr[s< /!QT * * *CCqM rz111} rAleftc|jdkrtd|tdtj|j|j}t ttt|jdz|dg|ttd|jdz|d|ddi }tdg|j dRt|}tj |dd}|tf|jtjfzz}t!|d}t#|dk|||z}|d }d||dk<|S) NrMz%Input array a must be one dimensionalz7da.searchsorted with a sorter argument is not supportedr)rErr7rrr)r:rrfrHrXrrr[rxryr&rr(r5Ellipsisrrwherer) rFvrWsorterrEr| a_chunk_sizesa_chunk_offsets a_offsetss r?rXrX#sgv{{@AAA ! E   ?17AG , ,D  U16A:     U1afqj ! !""  !f   C0AHQK00q7I7IJJJMi ..ss3O%xkAFbj]4J&JKO222I acIo . .C ''q'//CCr N JrA2cxdt|||z}t|||g\\}}}}t|dkrtj|||S|dftj|||fi}t j|||} t|rtjffn|ff} t| || tS)Nz linspace-r)num dependenciesr) r-r0rQrHlinspacer1from_collectionsr,rLrr0) startstoprh linspace_name start_refstop_refnum_refdeps linspace_dsklinspace_graphrs r?_linspace_from_delayedrvMs(5$"<"<P+Q+Q("Y'D 4yyA~~{5$C0000"A&i7(STL#4|$N044 Crvi\\C6)F e D D DDrAc^tj||||dtjS)NryrBr)rH histogramr)r=rTryrBs r? _block_histrz\s' <4ug > > >q A"* MMrAct|tr |jdk}nBt|tr|jdup |jdk}nt j|dk}||r|t d||j|jkrt d|durt d|r-|r+t|ttfrtdd |fd |fd |ffD]S\}}t|ttfs2t|r#td ||T| t|d kr t dt|dt|tt j fr"|jdkrt d|jn!#t$rtd|dwxYwt|||||} d| z|r!t!|d|d|dz}nRt|tt j fst#|}|jdkrt d|jt%||g\\} |\fdt't)|D} t jgdj} ntt)|} t)|}fdt't1| |D} |j} |f| z} || |fz } t3j| | }tt7t)|}|jdz }d|z|ff}t||| }|d}|b|r\t#t j|t@|j}||z |z |fS||fS||fS)aW Blocked variant of :func:`numpy.histogram`. Parameters ---------- a : dask.array.Array Input data; the histogram is computed over the flattened array. If the ``weights`` argument is used, the chunks of ``a`` are accessed to check chunking compatibility between ``a`` and ``weights``. If ``weights`` is ``None``, a :py:class:`dask.dataframe.Series` object can be passed as input data. bins : int or sequence of scalars, optional Either an iterable specifying the ``bins`` or the number of ``bins`` and a ``range`` argument is required as computing ``min`` and ``max`` over blocked arrays is an expensive operation that must be performed explicitly. If `bins` is an int, it defines the number of equal-width bins in the given range (10, by default). If `bins` is a sequence, it defines a monotonically increasing array of bin edges, including the rightmost edge, allowing for non-uniform bin widths. range : (float, float), optional The lower and upper range of the bins. If not provided, range is simply ``(a.min(), a.max())``. Values outside the range are ignored. The first element of the range must be less than or equal to the second. `range` affects the automatic bin computation as well. While bin width is computed to be optimal based on the actual data within `range`, the bin count will fill the entire range including portions containing no data. normed : bool, optional This is equivalent to the ``density`` argument, but produces incorrect results for unequal bin widths. It should not be used. weights : dask.array.Array, optional A dask.array.Array of weights, of the same block structure as ``a``. Each value in ``a`` only contributes its associated weight towards the bin count (instead of 1). If ``density`` is True, the weights are normalized, so that the integral of the density over the range remains 1. density : bool, optional If ``False``, the result will contain the number of samples in each bin. If ``True``, the result is the value of the probability *density* function at the bin, normalized such that the *integral* over the range is 1. Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability *mass* function. Overrides the ``normed`` keyword if given. If ``density`` is True, ``bins`` cannot be a single-number delayed value. It must be a concrete number, or a (possibly-delayed) array/sequence of the bin edges. Returns ------- hist : dask Array The values of the histogram. See `density` and `weights` for a description of the possible semantics. bin_edges : dask Array of dtype float Return the bin edges ``(length(hist)+1)``. Examples -------- Using number of bins and range: >>> import dask.array as da >>> import numpy as np >>> x = da.from_array(np.arange(10000), chunks=10) >>> h, bins = da.histogram(x, bins=10, range=[0, 10000]) >>> bins array([ 0., 1000., 2000., 3000., 4000., 5000., 6000., 7000., 8000., 9000., 10000.]) >>> h.compute() array([1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]) Explicitly specifying the bins: >>> h, bins = da.histogram(x, bins=np.array([0, 5000, 10000])) >>> bins array([ 0, 5000, 10000]) >>> h.compute() array([5000, 5000]) rNrMzudask.array.histogram requires either specifying bins as an iterable or specifying both a range and the number of binsz.s>   11aL;8Y?   rAc<i|]\}\}}|dft||fSrGr~)rErrwrrrs r?r&zhistogram..sD   6Aq1aL;8YB   rArirrrr^)!rerr:r/_lengthrHrrrfr,rr3rQndarrayrr-rvrr0r2r. __dask_keys__ryr;rr1rlrxsizerrr<r0)rFrTrynormedrBdensity scalar_binsargnamevalrDrsdskr;a_keysw_keysgraphnchunksnbinsrmappedr dbrrrs @@@r?ryry`sb$)i1n D' " ")ld*?dla.? gdmmq(  | |  !   w~99WXXX U F    ; :dUG4D#E#E ! `   !$'5)9Iw;OP $ 011 6H6N6N @@FwPS@T@T    5zzQ `cRWjj```%%!455 %+:M:M pchcnpp   FuFF   QeWg 6 6E e #D %eAha$(CC$ 344 !4==D 9>>YTZYY #5dE]"C"CXy4      !'!//*;*;"<"<==    R  #)**++..0011      &s66':':;;     4$;D    +D#D I I IE$wq00112233G IMEWnuh 'F 5$e 4 4 4F   A  --e44QXFFFBr6AEEGG#T) )d7N$ws A6F88G cXt||f|||||\}}||d|dfS)aBlocked variant of :func:`numpy.histogram2d`. Parameters ---------- x : dask.array.Array An array containing the `x`-coordinates of the points to be histogrammed. y : dask.array.Array An array containing the `y`-coordinates of the points to be histogrammed. bins : sequence of arrays describing bin edges, int, or sequence of ints The bin specification. See the `bins` argument description for :py:func:`histogramdd` for a complete description of all possible bin configurations (this function is a 2D specific version of histogramdd). range : tuple of pairs, optional. The leftmost and rightmost edges of the bins along each dimension when integers are passed to `bins`; of the form: ((xmin, xmax), (ymin, ymax)). normed : bool, optional An alias for the density argument that behaves identically. To avoid confusion with the broken argument in the `histogram` function, `density` should be preferred. weights : dask.array.Array, optional An array of values weighing each sample in the input data. The chunks of the weights must be identical to the chunking along the 0th (row) axis of the data sample. density : bool, optional If False (the default) return the number of samples in each bin. If True, the returned array represents the probability density function at each bin. Returns ------- dask.array.Array The values of the histogram. dask.array.Array The edges along the `x`-dimension. dask.array.Array The edges along the `y`-dimension. See Also -------- histogram histogramdd Examples -------- >>> import dask.array as da >>> x = da.array([2, 4, 2, 4, 2, 4]) >>> y = da.array([2, 2, 4, 4, 2, 4]) >>> bins = 2 >>> range = ((0, 6), (0, 6)) >>> h, xedges, yedges = da.histogram2d(x, y, bins=bins, range=range) >>> h dask.array >>> xedges dask.array >>> h.compute() array([[2., 1.], [1., 2.]]) )rTryrrBrrrM) histogramdd) r=rYrTryrrBrcountsedgess r? histogram2dr sJ~ A  MFE 58U1X %%rAcBtj||||ddS)aOCall numpy.histogramdd for a blocked/chunked calculation. Slurps the result into an additional outer axis; this new axis will be used to stack chunked calls of the numpy function and add them together later. Returns ------- :py:object:`np.ndarray` NumPy array with an additional outer dimension. rxrrMrHr)samplerTryrBs r?_block_histogramdd_rectrjs& >&$eW E E Eac JJrAcr|dd\}}}|dd}tj||||ddS)axCall numpy.histogramdd for a multi argument blocked/chunked calculation. Slurps the result into an additional outer axis; this new axis will be used to stack chunked calls of the numpy function and add them together later. The last three arguments _must be_ (bins, range, weights). The difference between this function and _block_histogramdd_rect is that here we expect the sample to be composed of multiple arguments (multiple 1D arrays, each one representing a coordinate), while _block_histogramdd_rect expects a single rectangular (2D array where columns are coordinates) sample. N)rTryrBrrMr)rJrTryrBrs r?_block_histogramdd_multiargrzsG" 9D% #2#YF >&t5' J J J1Q3 OOrAc ||d}n||}ntdt}tttfr|pt dD}t dDnd}|s|rt dt||}d|tdrptj d krtd j \} j d } d } j d dj d dkrtdntttfrcd} td j d } td D]-} | jd jkrtd.ntddfdfd|ffD]S\} }tt t"fs2tr#td| |T|O| r+|jd jd krtd| s |j d | krtdtttfr"tkrtdJtkrtdt'dDstdtt(rfzt'dDr4t'dDrdt+D}n dD}| rf}nt }|/t-|}||fz }|j}n$d| z}t3jgd j}t d tD| rNt-fd!t7t+|D}npfd"ttDfd#t| D}fd$t7t+||D}t9j||%}t d&|D}d'| zg|R}t!|||(}|d )}|rt3j|j }tD]\} t3jt(}|j | || <|t3j || !|z}]tE||j*}||z |z |fS|d+|DfS),aBlocked variant of :func:`numpy.histogramdd`. Chunking of the input data (``sample``) is only allowed along the 0th (row) axis (the axis corresponding to the total number of samples). Data chunked along the 1st axis (column) axis is not compatible with this function. If weights are used, they must be chunked along the 0th axis identically to the input sample. An example setup for a three dimensional histogram, where the sample shape is ``(8, 3)`` and weights are shape ``(8,)``, sample chunks would be ``((4, 4), (3,))`` and the weights chunks would be ``((4, 4),)`` a table of the structure: +-------+-----------------------+-----------+ | | sample (8 x 3) | weights | +=======+=====+=====+=====+=====+=====+=====+ | chunk | row | `x` | `y` | `z` | row | `w` | +-------+-----+-----+-----+-----+-----+-----+ | | 0 | 5 | 6 | 6 | 0 | 0.5 | | +-----+-----+-----+-----+-----+-----+ | | 1 | 8 | 9 | 2 | 1 | 0.8 | | 0 +-----+-----+-----+-----+-----+-----+ | | 2 | 3 | 3 | 1 | 2 | 0.3 | | +-----+-----+-----+-----+-----+-----+ | | 3 | 2 | 5 | 6 | 3 | 0.7 | +-------+-----+-----+-----+-----+-----+-----+ | | 4 | 3 | 1 | 1 | 4 | 0.3 | | +-----+-----+-----+-----+-----+-----+ | | 5 | 3 | 2 | 9 | 5 | 1.3 | | 1 +-----+-----+-----+-----+-----+-----+ | | 6 | 8 | 1 | 5 | 6 | 0.8 | | +-----+-----+-----+-----+-----+-----+ | | 7 | 3 | 5 | 3 | 7 | 0.7 | +-------+-----+-----+-----+-----+-----+-----+ If the sample 0th dimension and weight 0th (row) dimension are chunked differently, a ``ValueError`` will be raised. If coordinate groupings ((x, y, z) trios) are separated by a chunk boundry, then a ``ValueError`` will be raised. We suggest that you rechunk your data if it is of that form. The chunks property of the data (and optional weights) are used to check for compatibility with the blocked algorithm (as described above); therefore, you must call `to_dask_array` on a collection from ``dask.dataframe``, i.e. :class:`dask.dataframe.Series` or :class:`dask.dataframe.DataFrame`. The function is also compatible with `x`, `y`, and `z` being individual 1D arrays with equal chunking. In that case, the data should be passed as a tuple: ``histogramdd((x, y, z), ...)`` Parameters ---------- sample : dask.array.Array (N, D) or sequence of dask.array.Array Multidimensional data to be histogrammed. Note the unusual interpretation of a sample when it is a sequence of dask Arrays: * When a (N, D) dask Array, each row is an entry in the sample (coordinate in D dimensional space). * When a sequence of dask Arrays, each element in the sequence is the array of values for a single coordinate. bins : sequence of arrays describing bin edges, int, or sequence of ints The bin specification. The possible binning configurations are: * A sequence of arrays describing the monotonically increasing bin edges along each dimension. * A single int describing the total number of bins that will be used in each dimension (this requires the ``range`` argument to be defined). * A sequence of ints describing the total number of bins to be used in each dimension (this requires the ``range`` argument to be defined). When bins are described by arrays, the rightmost edge is included. Bins described by arrays also allows for non-uniform bin widths. range : sequence of pairs, optional A sequence of length D, each a (min, max) tuple giving the outer bin edges to be used if the edges are not given explicitly in `bins`. If defined, this argument is required to have an entry for each dimension. Unlike :func:`numpy.histogramdd`, if `bins` does not define bin edges, this argument is required (this function will not automatically use the min and max of of the value in a given dimension because the input data may be lazy in dask). normed : bool, optional An alias for the density argument that behaves identically. To avoid confusion with the broken argument to `histogram`, `density` should be preferred. weights : dask.array.Array, optional An array of values weighing each sample in the input data. The chunks of the weights must be identical to the chunking along the 0th (row) axis of the data sample. density : bool, optional If ``False`` (default), the returned array represents the number of samples in each bin. If ``True``, the returned array represents the probability density function at each bin. See Also -------- histogram Returns ------- dask.array.Array The values of the histogram. list(dask.array.Array) Sequence of arrays representing the bin edges along each dimension. Examples -------- Computing the histogram in 5 blocks using different bin edges along each dimension: >>> import dask.array as da >>> x = da.random.uniform(0, 1, size=(1000, 3), chunks=(200, 3)) >>> edges = [ ... np.linspace(0, 1, 5), # 4 bins in 1st dim ... np.linspace(0, 1, 6), # 5 in the 2nd ... np.linspace(0, 1, 4), # 3 in the 3rd ... ] >>> h, edges = da.histogramdd(x, bins=edges) >>> result = h.compute() >>> result.shape (4, 5, 3) Defining the bins by total number and their ranges, along with using weights: >>> bins = (4, 5, 3) >>> ranges = ((0, 1),) * 3 # expands to ((0, 1), (0, 1), (0, 1)) >>> w = da.random.uniform(0, 1, size=(1000,), chunks=x.chunksize[0]) >>> h, edges = da.histogramdd(x, bins=bins, range=ranges, weights=w) >>> np.isclose(h.sum().compute(), w.sum().compute()) True Using a sequence of 1D arrays as the input: >>> x = da.array([2, 4, 2, 4, 2, 4]) >>> y = da.array([2, 2, 4, 4, 2, 4]) >>> z = da.array([4, 2, 4, 2, 4, 2]) >>> bins = ([0, 3, 6],) * 3 >>> h, edges = da.histogramdd((x, y, z), bins) >>> h dask.array >>> edges[0] dask.array >>> h.compute() array([[[0., 2.], [0., 1.]], [[1., 0.], [2., 0.]]]) >>> edges[0].compute() array([0, 3, 6]) >>> edges[1].compute() array([0, 3, 6]) >>> edges[2].compute() array([0, 3, 6]) NFz*Cannot specify both 'normed' and 'density'c,g|]}t|SrDr,rErs r?rGzhistogramdd..Es!!F!F!FA"4Q"7"7!F!F!FrAc,g|]}t|SrDrrErs r?rGzhistogramdd..Gs! 2 2 2q  " " 2 2 2rAzCPassing dask collections to bins=... or range=... is not supported.zhistogramdd-sum-rrNz4Single array input to histogramdd should be columnarrTrMz3Input array can only be chunked along the 0th axis.z2All coordinate arrays must be chunked identically.zCIncompatible sample. Must be a 2D array or a sequence of 1D arrays.rTryrBzfDask types besides Array and Delayed are not supported for `histogramdd`. 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MKLL L$w{ , ,t , , ,,,.4P4P%4P4P4P1P1P.MMCeDS[[>Q>Q        AGAQAQ          's+>'G'GHH      +D#D I I IE33U33333IXo2 22N 5$e < <  >AGAsOOE$*1-E!H RWU1X..66u== =MM ah??? = 15577*E11 115111 11rAc|"|t|krtdt|}| tj|tj}n/t|}tj||tj}t |d|}|jddkrd}|r|jd}d}n|jd}d}| |dkrd}nd}t||z } | dkrtj dtd} |$t |d|}t||f|}|| d|z d z }|sr;rrMz!Degrees of freedom <= 0 for slicegT)rbr)r rrrHrIfloat64r@rr0warningswarnRuntimeWarningrmeanrTrr) rrYrowvarbiasddofr;XNrbfacts r?covrs  DCII--/000  Ayq"*-- AJJq!RZ00 aq&&&AwqzQ  GAJ GAJ | 199DDD T??D qyy 9>JJJ} !1E * * * A % % AFFD4F 0 00A 5AC""T)22444Aqsxxzz""T)22444rAct|||}|jdkr||z St|}||jddf}t |}||z |jz S)NrDrrM)rrrrr%r)r=rYrrrsqr_ds r?corrcoefrsi Aq&Aw"}}1u  QA 171:q/""A GGE I  rAcP|tj||jS)N)decimalsr;)rrHroundr;)rFrs r?rr!s  <<817< C CCrAc|jSr]rorFs r?r:r:'s  6MrAcJt|jjtjSr])r.r;rrHcomplexfloatingrs r? iscomplexobjr-s aglB$6 7 77rAc|du}|du}tj|}d|jfg}|r!|dtjf|r!|dtjf|r!|dtjftj|j|}||d<|r0tjt|tj|d<|s|rt|dD]k\} } || k} |r.||  d|d| | dz |r.||  d|d| | dz l|S) a Helper/wrapper function for :func:`numpy.unique`. Uses :func:`numpy.unique` to find the unique values for the array chunk. Given this chunk may not represent the whole array, also take the ``indices`` and ``counts`` that are in 1-to-1 correspondence to ``ar`` and reduce them in the same fashion as ``ar`` is reduced. Namely sum any counts that correspond to the same value and take the smallest index that corresponds to the same value. To handle the inverse mapping from the unique values to the original array, simply return a NumPy array created with ``arange`` with enough values to correspond 1-to-1 to the unique values. While there is more work needed to be done to create the full inverse mapping for the original array, this provides enough information to generate the inverse mapping in Dask. Given Dask likes to have one array returned from functions like ``blockwise``, some formatting is done to stuff all of the resulting arrays into one big NumPy structured array. Dask is then able to handle this object and can split it apart into the separate results on the Dask side, which then can be passed back to this function in concatenated chunks for further reduction or can be return to the user to perform other forms of analysis. By handling the problem in this way, it does not matter where a chunk is in a larger array or how big it is. The chunk can still be computed on the same way. Also it does not matter if the chunk is the result of other chunks being run through this function multiple times. The end result will still be just as accurate using this strategy. 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