0PhPdZddlZddlmZddlmZddlZddlm Z m Z ddl m Z m Z mZdd lmZmZmZmZmZdd lmZdd lmZmZd Zd7dZdZdZd ddZddddZeej dge edddge edddge eddde dhge hdgde dhgdgdge ddhgd d d!ddddddd"d#Z!d!ddd$dd%d&Z"dd'd(Z#d8d)Z$d9d*Z%d9d+Z&d:d,Z'd-Z( d8d.Z)d/Z*d;d2Z+d8d3Z,dd4d5Z-d6Z.dS)ir axis) rissparsetocsrrrsqrtrr asarrayeinsumsummultiply)Xsquarednormsxp_s r" row_normsr4/s(q# GGIIa   #GENNEa  A r " " 6 1 AIj!Q//EJJu%%EEFF2;;q!,,1F55E #GGENNE Lr$ct|\}}|j|\}}|dks|j S|S)aCompute logarithm of determinant of a square matrix. The (natural) logarithm of the determinant of a square matrix is returned if det(A) is non-negative and well defined. If the determinant is zero or negative returns -Inf. Equivalent to : np.log(np.det(A)) but more robust. Parameters ---------- A : array_like of shape (n, n) The square matrix. Returns ------- logdet : float When det(A) is strictly positive, log(det(A)) is returned. When det(A) is non-positive or not defined, then -inf is returned. See Also -------- numpy.linalg.slogdet : Compute the sign and (natural) logarithm of the determinant of an array. Examples -------- >>> import numpy as np >>> from sklearn.utils.extmath import fast_logdet >>> a = np.array([[5, 1], [2, 8]]) >>> fast_logdet(a) np.float64(3.6375861597263857) r)rrslogdetinf)Ar2r3signlds r" fast_logdetr;UsFB !  EBy  ##HD" !88w Ir$ct|dr1t|j|jd|jdzz }n1|dn,t|dk|jz }|S)aCompute density of a sparse vector. Parameters ---------- w : {ndarray, sparse matrix} The input data can be numpy ndarray or a sparse matrix. Returns ------- float The density of w, between 0 and 1. Examples -------- >>> from scipy import sparse >>> from sklearn.utils.extmath import density >>> X = sparse.random(10, 10, density=0.25, random_state=0) >>> density(X) 0.25 toarrayrr )hasattrfloatnnzshaper-size)wds r"densityrE}sh*q)? !%LLAGAJ3 4AAqAvllnn 5 5 > Hr$) dense_outputct||\}}|jdks |jdkrtj|rct j|d}||jddf}||z}|j|jdg|jddR}ntj|rN|d|jd}||z}|jg|jdd|jdR}n/|jdkrdnd} |||d| g}n||z}tj|r:tj|r&|r$t|dr| S|S) a%Dot product that handle the sparse matrix case correctly. Parameters ---------- a : {ndarray, sparse matrix} b : {ndarray, sparse matrix} dense_output : bool, default=False When False, ``a`` and ``b`` both being sparse will yield sparse output. When True, output will always be a dense array. Returns ------- dot_product : {ndarray, sparse matrix} Sparse if ``a`` and ``b`` are sparse and ``dense_output=False``. Examples -------- >>> from scipy.sparse import csr_matrix >>> from sklearn.utils.extmath import safe_sparse_dot >>> X = csr_matrix([[1, 2], [3, 4], [5, 6]]) >>> dot_product = safe_sparse_dot(X, X.T) >>> dot_product.toarray() array([[ 5, 11, 17], [11, 25, 39], [17, 39, 61]]) rrr N)axesr=) rndimrr(rrollaxisreshaperA tensordotr>r=) abrFr2r3b_b_2dreta_2db_axiss r"safe_sparse_dotrVs6 !Q  EBvzzQVaZZ ?1   8Q##B::qwr{B/00Dd(C#+agaj828ABB<888CC _Q   899R--D(C#+8qwss|8QWQZ888CC 6Q;;RRBF,,q!2v,,77CC!e  OA    C # #  {{}} Jr$auto)power_iteration_normalizer random_statec|t|\}}t|}|||jd|f}t |dr9||jdr|||jd}|r$||t|}|d kr%|d krd }n3|rtj d d }nd}n|dkr|rtd|rt|jjd}nttjdd}|d kr|} n&|dkrttjdd} nd} t#|D])} | ||z\}} | |j|z\}} *|||z\}} |S)aCompute an orthonormal matrix whose range approximates the range of A. Parameters ---------- A : 2D array The input data matrix. size : int Size of the return array. n_iter : int Number of power iterations used to stabilize the result. power_iteration_normalizer : {'auto', 'QR', 'LU', 'none'}, default='auto' Whether the power iterations are normalized with step-by-step QR factorization (the slowest but most accurate), 'none' (the fastest but numerically unstable when `n_iter` is large, e.g. typically 5 or larger), or 'LU' factorization (numerically stable but can lose slightly in accuracy). The 'auto' mode applies no normalization if `n_iter` <= 2 and switches to LU otherwise. .. versionadded:: 0.18 random_state : int, RandomState instance or None, default=None The seed of the pseudo random number generator to use when shuffling the data, i.e. getting the random vectors to initialize the algorithm. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. Returns ------- Q : ndarray A (size x size) projection matrix, the range of which approximates well the range of the input matrix A. Notes ----- Follows Algorithm 4.3 of :arxiv:`"Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions" <0909.4061>` Halko, et al. (2009) An implementation of a randomized algorithm for principal component analysis A. Szlam et al. 2014 Examples -------- >>> import numpy as np >>> from sklearn.utils.extmath import randomized_range_finder >>> A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) >>> randomized_range_finder(A, size=2, n_iter=2, random_state=42) array([[-0.21..., 0.88...], [-0.52..., 0.24...], [-0.82..., -0.38...]]) r )rBrz real floating)kindFcopyrrWrnonezArray API does not support LU factorization, falling back to QR instead. Set `power_iteration_normalizer='QR'` explicitly to silence this warning.QRLUz[Array API does not support LU factorization. Set `power_iteration_normalizer='QR'` instead.reduced)modeeconomic)rc check_finiteT) permute_lrec |dfSNr s r"z)randomized_range_finder..Js 4yr$)rrr+normalrAr>isdtyperastyperrr ValueErrorrrqrlurangeT) r8rBn_iterrXrYr2is_array_api_compliantQ qr_normalizer normalizerr3s r"randomized_range_finderrxsz"/q!1!1B%l33L <&&QWQZ,>&??@@Aq'.rzz!'zHH. IIauI - -, JJqJ + +"V++ Q;;)/ & & # . M!    *. & &)- & & #t + +0F + 9   P 9===   OOO !T))" #t + +VY$UKKK (( 6]]##z!a%  1z!#'""11 =Q  DAq Hr$z sparse matrixleft)closed>rar`rWr_booleanrYgesddgesvd) M n_components n_oversamplesrsrX transpose flip_signrYsvd_lapack_driverT)prefer_skip_nested_validation )rrsrXrrrYrcbtj|rM|jdvrDtjdt |jtjt|}||z} |j \} } |dkr|dt|j zkrdnd}|dkr| | k}|r|j }t|| |||} | j |z} t| \}}|r!|j| d \}}}ntj| d| \}}}~ | |z}|r+|st!||\}}nt!||d \}}|r/|d |d d fj |d ||d d d |fj fS|d d d |f|d ||d |d d ffS) akCompute a truncated randomized SVD. This method solves the fixed-rank approximation problem described in [1]_ (problem (1.5), p5). Refer to :ref:`sphx_glr_auto_examples_applications_wikipedia_principal_eigenvector.py` for a typical example where the power iteration algorithm is used to rank web pages. This algorithm is also known to be used as a building block in Google's PageRank algorithm. Parameters ---------- M : {ndarray, sparse matrix} Matrix to decompose. n_components : int Number of singular values and vectors to extract. n_oversamples : int, default=10 Additional number of random vectors to sample the range of `M` so as to ensure proper conditioning. The total number of random vectors used to find the range of `M` is `n_components + n_oversamples`. Smaller number can improve speed but can negatively impact the quality of approximation of singular vectors and singular values. Users might wish to increase this parameter up to `2*k - n_components` where k is the effective rank, for large matrices, noisy problems, matrices with slowly decaying spectrums, or to increase precision accuracy. See [1]_ (pages 5, 23 and 26). n_iter : int or 'auto', default='auto' Number of power iterations. It can be used to deal with very noisy problems. When 'auto', it is set to 4, unless `n_components` is small (< .1 * min(X.shape)) in which case `n_iter` is set to 7. This improves precision with few components. Note that in general users should rather increase `n_oversamples` before increasing `n_iter` as the principle of the randomized method is to avoid usage of these more costly power iterations steps. When `n_components` is equal or greater to the effective matrix rank and the spectrum does not present a slow decay, `n_iter=0` or `1` should even work fine in theory (see [1]_ page 9). .. versionchanged:: 0.18 power_iteration_normalizer : {'auto', 'QR', 'LU', 'none'}, default='auto' Whether the power iterations are normalized with step-by-step QR factorization (the slowest but most accurate), 'none' (the fastest but numerically unstable when `n_iter` is large, e.g. typically 5 or larger), or 'LU' factorization (numerically stable but can lose slightly in accuracy). The 'auto' mode applies no normalization if `n_iter` <= 2 and switches to LU otherwise. .. versionadded:: 0.18 transpose : bool or 'auto', default='auto' Whether the algorithm should be applied to M.T instead of M. The result should approximately be the same. The 'auto' mode will trigger the transposition if M.shape[1] > M.shape[0] since this implementation of randomized SVD tend to be a little faster in that case. .. versionchanged:: 0.18 flip_sign : bool, default=True The output of a singular value decomposition is only unique up to a permutation of the signs of the singular vectors. If `flip_sign` is set to `True`, the sign ambiguity is resolved by making the largest loadings for each component in the left singular vectors positive. random_state : int, RandomState instance or None, default='warn' The seed of the pseudo random number generator to use when shuffling the data, i.e. getting the random vectors to initialize the algorithm. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. .. versionchanged:: 1.2 The default value changed from 0 to None. svd_lapack_driver : {"gesdd", "gesvd"}, default="gesdd" Whether to use the more efficient divide-and-conquer approach (`"gesdd"`) or more general rectangular approach (`"gesvd"`) to compute the SVD of the matrix B, which is the projection of M into a low dimensional subspace, as described in [1]_. .. versionadded:: 1.2 Returns ------- u : ndarray of shape (n_samples, n_components) Unitary matrix having left singular vectors with signs flipped as columns. s : ndarray of shape (n_components,) The singular values, sorted in non-increasing order. vh : ndarray of shape (n_components, n_features) Unitary matrix having right singular vectors with signs flipped as rows. Notes ----- This algorithm finds a (usually very good) approximate truncated singular value decomposition using randomization to speed up the computations. It is particularly fast on large matrices on which you wish to extract only a small number of components. In order to obtain further speed up, `n_iter` can be set <=2 (at the cost of loss of precision). To increase the precision it is recommended to increase `n_oversamples`, up to `2*k-n_components` where k is the effective rank. Usually, `n_components` is chosen to be greater than k so increasing `n_oversamples` up to `n_components` should be enough. References ---------- .. [1] :arxiv:`"Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions" <0909.4061>` Halko, et al. (2009) .. [2] A randomized algorithm for the decomposition of matrices Per-Gunnar Martinsson, Vladimir Rokhlin and Mark Tygert .. [3] An implementation of a randomized algorithm for principal component analysis A. Szlam et al. 2014 Examples -------- >>> import numpy as np >>> from sklearn.utils.extmath import randomized_svd >>> a = np.array([[1, 2, 3, 5], ... [3, 4, 5, 6], ... [7, 8, 9, 10]]) >>> U, s, Vh = randomized_svd(a, n_components=2, random_state=0) >>> U.shape, s.shape, Vh.shape ((3, 2), (2,), (2, 4)) )lildokzCCalculating SVD of a {} is expensive. csr_matrix is more efficient.rWg?)rBrsrXrYF) full_matrices)r lapack_driver)u_based_decisionN)rr(formatrrtype__name__SparseEfficiencyWarningrrAminrrrxrrsvdsvd_flip)r~rrrsrXrrrYrn_random n_samples n_featuresruBr2rtUhatsVtUs r"randomized_svdrYs.zq ah.88  ,,2F4773C,D,D  *   &l33Lm+HGIz #S3qw<<%777QF *  C #=!    A aA"/q!1!1B immAUm;; a j U2C   a  DA< <QOOEArrQU;;;EArK-<-"#%q,'7111m|m;K9L9NNNM\M!"Am|m$4b,9I6JJJr$module)rrsrX selectionrYc V|dkrt|dkrzt|||||d|\}}} |ddd|f} |d|} tjd| d|ddf|ddd|f} tj| } | | z} nt d|z| | fS)aComputes a truncated eigendecomposition using randomized methods This method solves the fixed-rank approximation problem described in the Halko et al paper. The choice of which components to select can be tuned with the `selection` parameter. .. versionadded:: 0.24 Parameters ---------- M : ndarray or sparse matrix Matrix to decompose, it should be real symmetric square or complex hermitian n_components : int Number of eigenvalues and vectors to extract. n_oversamples : int, default=10 Additional number of random vectors to sample the range of M so as to ensure proper conditioning. The total number of random vectors used to find the range of M is n_components + n_oversamples. Smaller number can improve speed but can negatively impact the quality of approximation of eigenvectors and eigenvalues. Users might wish to increase this parameter up to `2*k - n_components` where k is the effective rank, for large matrices, noisy problems, matrices with slowly decaying spectrums, or to increase precision accuracy. See Halko et al (pages 5, 23 and 26). n_iter : int or 'auto', default='auto' Number of power iterations. It can be used to deal with very noisy problems. When 'auto', it is set to 4, unless `n_components` is small (< .1 * min(X.shape)) in which case `n_iter` is set to 7. This improves precision with few components. Note that in general users should rather increase `n_oversamples` before increasing `n_iter` as the principle of the randomized method is to avoid usage of these more costly power iterations steps. When `n_components` is equal or greater to the effective matrix rank and the spectrum does not present a slow decay, `n_iter=0` or `1` should even work fine in theory (see Halko et al paper, page 9). power_iteration_normalizer : {'auto', 'QR', 'LU', 'none'}, default='auto' Whether the power iterations are normalized with step-by-step QR factorization (the slowest but most accurate), 'none' (the fastest but numerically unstable when `n_iter` is large, e.g. typically 5 or larger), or 'LU' factorization (numerically stable but can lose slightly in accuracy). The 'auto' mode applies no normalization if `n_iter` <= 2 and switches to LU otherwise. selection : {'value', 'module'}, default='module' Strategy used to select the n components. When `selection` is `'value'` (not yet implemented, will become the default when implemented), the components corresponding to the n largest eigenvalues are returned. When `selection` is `'module'`, the components corresponding to the n eigenvalues with largest modules are returned. random_state : int, RandomState instance, default=None The seed of the pseudo random number generator to use when shuffling the data, i.e. getting the random vectors to initialize the algorithm. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. Notes ----- This algorithm finds a (usually very good) approximate truncated eigendecomposition using randomized methods to speed up the computations. This method is particularly fast on large matrices on which you wish to extract only a small number of components. In order to obtain further speed up, `n_iter` can be set <=2 (at the cost of loss of precision). To increase the precision it is recommended to increase `n_oversamples`, up to `2*k-n_components` where k is the effective rank. Usually, `n_components` is chosen to be greater than k so increasing `n_oversamples` up to `n_components` should be enough. Strategy 'value': not implemented yet. Algorithms 5.3, 5.4 and 5.5 in the Halko et al paper should provide good candidates for a future implementation. Strategy 'module': The principle is that for diagonalizable matrices, the singular values and eigenvalues are related: if t is an eigenvalue of A, then :math:`|t|` is a singular value of A. This method relies on a randomized SVD to find the n singular components corresponding to the n singular values with largest modules, and then uses the signs of the singular vectors to find the true sign of t: if the sign of left and right singular vectors are different then the corresponding eigenvalue is negative. Returns ------- eigvals : 1D array of shape (n_components,) containing the `n_components` eigenvalues selected (see ``selection`` parameter). eigvecs : 2D array of shape (M.shape[0], n_components) containing the `n_components` eigenvectors corresponding to the `eigvals`, in the corresponding order. Note that this follows the `scipy.linalg.eigh` convention. See Also -------- :func:`randomized_svd` References ---------- * :arxiv:`"Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions" (Algorithm 4.3 for strategy 'module') <0909.4061>` Halko, et al. (2009) valuerF)rrrsrXrrYNzji,ij->jzInvalid `selection`: %r)NotImplementedErrorrrr,r9rn)r~rrrsrXrrYrSreigvecseigvalsdiag_VtUsignss r"_randomized_eigshr4snG!### h  " %''A%   1bAAA} }$%M\M"9ZM\M111,<)=qM\MAQ?RSS!!E/2Y>??? G r$r&c|+tj|}tj|}d}n(tj|}tj|}|j|jkr!tj|j||j}tjtj|}t|j}d||<tj|}tj|}|D]}tj|j}||k} || || <tj tj |||} tj | |k||} tj | |}| }| |fS)aReturn an array of the weighted modal (most common) value in the passed array. If there is more than one such value, only the first is returned. The bin-count for the modal bins is also returned. This is an extension of the algorithm in scipy.stats.mode. Parameters ---------- a : array-like of shape (n_samples,) Array of which values to find mode(s). w : array-like of shape (n_samples,) Array of weights for each value. axis : int, default=0 Axis along which to operate. Default is 0, i.e. the first axis. Returns ------- vals : ndarray Array of modal values. score : ndarray Array of weighted counts for each mode. See Also -------- scipy.stats.mode: Calculates the Modal (most common) value of array elements along specified axis. Examples -------- >>> from sklearn.utils.extmath import weighted_mode >>> x = [4, 1, 4, 2, 4, 2] >>> weights = [1, 1, 1, 1, 1, 1] >>> weighted_mode(x, weights) (array([4.]), array([3.])) The value 4 appears three times: with uniform weights, the result is simply the mode of the distribution. >>> weights = [1, 3, 0.5, 1.5, 1, 2] # deweight the 4's >>> weighted_mode(x, weights) (array([2.]), array([3.5])) The value 2 has the highest score: it appears twice with weights of 1.5 and 2: the sum of these is 3.5. Nrrr ) rrr+rAfullruniquelistzeros expand_dimsr-wheremaximum) rOrCr'scores testshape oldmostfreq oldcountsscoretemplateindcounts mostfrequents r" weighted_modersG^ | HQKK HQKK JqMM JqMMw!' GAGQag . . . Yrx{{ # #FQW IIdO(9%%K##I##8AG$$5j# x 6 6==x 2E;GG Jvy11 "  ""r$cbd|D}d|D}tj|}|t|dj}|$tj|}tj||}t|D]$\}}|||dd|f|dd|f<%|S)aGenerate a cartesian product of input arrays. Parameters ---------- arrays : list of array-like 1-D arrays to form the cartesian product of. out : ndarray of shape (M, len(arrays)), default=None Array to place the cartesian product in. Returns ------- out : ndarray of shape (M, len(arrays)) Array containing the cartesian products formed of input arrays. If not provided, the `dtype` of the output array is set to the most permissive `dtype` of the input arrays, according to NumPy type promotion. .. versionadded:: 1.2 Add support for arrays of different types. Notes ----- This function may not be used on more than 32 arrays because the underlying numpy functions do not support it. Examples -------- >>> from sklearn.utils.extmath import cartesian >>> cartesian(([1, 2, 3], [4, 5], [6, 7])) array([[1, 4, 6], [1, 4, 7], [1, 5, 6], [1, 5, 7], [2, 4, 6], [2, 4, 7], [2, 5, 6], [2, 5, 7], [3, 4, 6], [3, 4, 7], [3, 5, 6], [3, 5, 7]]) c6g|]}tj|Sri)rr+.0r!s r" zcartesian..Ds , , ,bjmm , , ,r$c34K|]}t|VdSrh)lenrs r" zcartesian..Es( $ $SVV $ $ $ $ $ $r$rINr)rindicesrMrrr result_type empty_like enumerate)arraysoutrAixrnarrs r" cartesianrsV- ,V , , ,F $ $V $ $ $E E  B CKK $ $ &B {'mBe,,,F##((31IbAh'AAAqD Jr$ctd||fD\}}|r|||jd}||jjdt |}|||jjdzz}||| |jd|d}||tj ddfz}|||ddtj fz}n|||d} ||jdt |}| ||jdzz}||| |d|d}|||tj ddfz}||ddtj fz}||fS)aSign correction to ensure deterministic output from SVD. Adjusts the columns of u and the rows of v such that the loadings in the columns in u that are largest in absolute value are always positive. If u_based_decision is False, then the same sign correction is applied to so that the rows in v that are largest in absolute value are always positive. Parameters ---------- u : ndarray Parameters u and v are the output of `linalg.svd` or :func:`~sklearn.utils.extmath.randomized_svd`, with matching inner dimensions so one can compute `np.dot(u * s, v)`. u can be None if `u_based_decision` is False. v : ndarray Parameters u and v are the output of `linalg.svd` or :func:`~sklearn.utils.extmath.randomized_svd`, with matching inner dimensions so one can compute `np.dot(u * s, v)`. The input v should really be called vt to be consistent with scipy's output. v can be None if `u_based_decision` is True. u_based_decision : bool, default=True If True, use the columns of u as the basis for sign flipping. Otherwise, use the rows of v. The choice of which variable to base the decision on is generally algorithm dependent. Returns ------- u_adjusted : ndarray Array u with adjusted columns and the same dimensions as u. v_adjusted : ndarray Array v with adjusted rows and the same dimensions as v. cg|]}||Srhri)rrOs r"rzsvd_flip..zs???!Ar$r r&rr^)rIN) rargmaxabsrrarangerArr9takerMrnewaxis) uvrr2r3max_abs_u_colsshiftrrmax_abs_v_rowss r"rrTsL ??1v??? @EB"266!#;;Q77 !#)A,vayy 99 5139Q<#77 13 6 6aHHII U2:qqq= !! = qqq"*}% %A266!99155 !'!*VAYY 77 5171:#55 1e 4 4gAFFGG = rz111}% %A U111bj= !! a4Kr$ct|\}}|r||d}|||dd}||z}t |r)t j|t j|n||}|||dd}||z}|S)a@ Calculate the softmax function. The softmax function is calculated by np.exp(X) / np.sum(np.exp(X), axis=1) This will cause overflow when large values are exponentiated. Hence the largest value in each row is subtracted from each data point to prevent this. Parameters ---------- X : array-like of float of shape (M, N) Argument to the logistic function. copy : bool, default=True Copy X or not. Returns ------- out : ndarray of shape (M, N) Softmax function evaluated at every point in x. Tr\r r&)rIr )r)rr+rMmaxr rexpr-)r/r]r2rtmax_probsum_probs r"softmaxrs0"/q!1!1B % JJqtJ $ $zz"&&&++W55HMA2 qbjmm$$$$$ FF1IIzz"&&&++W55HMA Hr$c|}||kr+tj|rtd|||z z}|S)aEEnsure `X.min()` >= `min_value`. Parameters ---------- X : array-like The matrix to make non-negative. min_value : float, default=0 The threshold value. Returns ------- array-like The thresholded array. Raises ------ ValueError When X is sparse. z{Cannot make the data matrix nonnegative because it is sparse. Adding a value to every entry would make it no longer sparse.)rrr(rn)r/ min_valuemin_s r"make_nonnegativers[( 5577D i ?1   -  T! " Hr$ctj|jtjr+|jjdkr||g|Ri|dtji}n ||g|Ri|}|S)a This function provides numpy accumulator functions with a float64 dtype when used on a floating point input. This prevents accumulator overflow on smaller floating point dtypes. Parameters ---------- op : function A numpy accumulator function such as np.mean or np.sum. x : ndarray A numpy array to apply the accumulator function. *args : positional arguments Positional arguments passed to the accumulator function after the input x. **kwargs : keyword arguments Keyword arguments passed to the accumulator function. Returns ------- result The output of the accumulator function passed to this function. r)rrrfloatingitemsizefloat64)opr!argskwargsresults r"_safe_accumulator_oprs}. }QWbk**(qw/?!/C/CA999999bj999A'''''' Mr$c ||z}tj|}tj|r tj}n tj}|Zt tj|tj|d|}t tj|dddf|zd} n8t ||d}|jd} | tj|dz } || z} ||z| z } |d} n || z }||z }|dt tj|tj|d|}|dz}t tj|tj|d|}n)t ||d}|dz}t ||d}||dz| z z}||z}tj dd5|| z }||z|| z ||z |z dzzz}dddn #1swxYwY|dk}||||<|| z } | | | fS)aCalculate mean update and a Youngs and Cramer variance update. If sample_weight is given, the weighted mean and variance is computed. Update a given mean and (possibly) variance according to new data given in X. last_mean is always required to compute the new mean. If last_variance is None, no variance is computed and None return for updated_variance. From the paper "Algorithms for computing the sample variance: analysis and recommendations", by Chan, Golub, and LeVeque. Parameters ---------- X : array-like of shape (n_samples, n_features) Data to use for variance update. last_mean : array-like of shape (n_features,) last_variance : array-like of shape (n_features,) last_sample_count : array-like of shape (n_features,) The number of samples encountered until now if sample_weight is None. If sample_weight is not None, this is the sum of sample_weight encountered. sample_weight : array-like of shape (n_samples,) or None Sample weights. If None, compute the unweighted mean/variance. Returns ------- updated_mean : ndarray of shape (n_features,) updated_variance : ndarray of shape (n_features,) None if last_variance was None. updated_sample_count : ndarray of shape (n_features,) Notes ----- NaNs are ignored during the algorithm. References ---------- T. Chan, G. Golub, R. LeVeque. Algorithms for computing the sample variance: recommendations, The American Statistician, Vol. 37, No. 3, pp. 242-247 Also, see the sparse implementation of this in `utils.sparsefuncs.incr_mean_variance_axis` and `utils.sparsefuncs_fast.incr_mean_variance_axis0` Nrr&rignore)divideinvalid) risnananynansumr-rmatmulrrAerrstate)r/ last_mean last_variancelast_sample_count sample_weightlast_sum X_nan_masksum_opnew_sumnew_sample_countrupdated_sample_count updated_meanupdated_variancerrtemp correctionnew_unnormalized_variancelast_unnormalized_variancelast_over_new_countupdated_unnormalized_variancers r"_incremental_mean_and_varr st,,H!J vj ' I}bhz1a&@&@  0 FM!!!T'*zk:   'vqq999GAJ $rvjq'A'A'AA,/??w&*>>L & &1u  $. ="(:q$*G*GJ QJD(< ="(:q$*G*G)) % %.fdCCCJ QJD(:0yE>ctj||tj}tj||tj}tj|d||||dst jdt|S)aUse high precision for cumsum and check that final value matches sum. Warns if the final cumulative sum does not match the sum (up to the chosen tolerance). Parameters ---------- arr : array-like To be cumulatively summed as flat. axis : int, default=None Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array. rtol : float, default=1e-05 Relative tolerance, see ``np.allclose``. atol : float, default=1e-08 Absolute tolerance, see ``np.allclose``. Returns ------- out : ndarray Array with the cumulative sums along the chosen axis. )r'rrIr&T)rtolatol equal_nanzLcumsum was found to be unstable: its last element does not correspond to sum) rcumsumrr-allcloserrrRuntimeWarning)rr'rrrexpecteds r" stable_cumsumrs. )Cd"* 5 5 5CvcBJ777H ; $44       >      Jr$ct|\}}|jddkr|jS||}||r|jS|t ||S||}||||}} t||S#t$rt|cYSwxYw)a5Compute the weighted average, ignoring NaNs. Parameters ---------- a : ndarray Array containing data to be averaged. weights : array-like, default=None An array of weights associated with the values in a. Each value in a contributes to the average according to its associated weight. The weights array can either be 1-D of the same shape as a. If `weights=None`, then all data in a are assumed to have a weight equal to one. Returns ------- weighted_average : float The weighted average. Notes ----- This wrapper to combine :func:`numpy.average` and :func:`numpy.nanmean`, so that :func:`np.nan` values are ignored from the average and weights can be passed. Note that when possible, we delegate to the prime methods. rN)r2)weights) rrAnanrallrr+r ZeroDivisionError)rOrr2r3masks r" _nanaveragers0 !  EBwqzQv 88A;;D vvd||v b!!!!jj!!GD57D5>wA7++++ {{sB((CCr\ct|gdd}tj|r'|r|}|xjdzc_n |r|dz}n|dz}|S)aElement wise squaring of array-likes and sparse matrices. Parameters ---------- X : {array-like, ndarray, sparse matrix} copy : bool, default=True Whether to create a copy of X and operate on it or to perform inplace computation (default behaviour). Returns ------- X ** 2 : element wise square Return the element-wise square of the input. Examples -------- >>> from sklearn.utils import safe_sqr >>> safe_sqr([1, 2, 3]) array([1, 4, 9]) )csrcsccooF) accept_sparse ensure_2dr)rrr(r]data)r/r]s r"safe_sqrr&sx, A%:%:%:eLLLA q  A 1   1AA !GA Hr$cNt|}||z |z}tj|}t ||z }|dkr||z }tjtj|ddd}|D]n}tj||k\} tt| |} | | | d} || xxdz cc<|| z}|dkrno| tS)aComputes approximate mode of multivariate hypergeometric. This is an approximation to the mode of the multivariate hypergeometric given by class_counts and n_draws. It shouldn't be off by more than one. It is the mostly likely outcome of drawing n_draws many samples from the population given by class_counts. Parameters ---------- class_counts : ndarray of int Population per class. n_draws : int Number of draws (samples to draw) from the overall population. rng : random state Used to break ties. Returns ------- sampled_classes : ndarray of int Number of samples drawn from each class. np.sum(sampled_classes) == n_draws Examples -------- >>> import numpy as np >>> from sklearn.utils.extmath import _approximate_mode >>> _approximate_mode(class_counts=np.array([4, 2]), n_draws=3, rng=0) array([2, 1]) >>> _approximate_mode(class_counts=np.array([5, 2]), n_draws=4, rng=0) array([3, 1]) >>> _approximate_mode(class_counts=np.array([2, 2, 2, 1]), ... n_draws=2, rng=0) array([0, 1, 1, 0]) >>> _approximate_mode(class_counts=np.array([2, 2, 2, 1]), ... n_draws=2, rng=42) array([1, 1, 0, 0]) rNrIF)rBreplacer ) rr-rfloorintsortrrrrchoicerm) class_countsn_drawsrng continuousfloored need_to_add remaindervaluesrindsadd_nows r"_approximate_moder7s-P S ! !C 0 0 2 22W>#  r$)Frh)T)r)Nr r)/__doc__r functoolsrnumbersrnumpyrscipyrrutils._param_validationrr r _array_apir r rrrsparsefuncs_fastr validationrrr#r4r;rErVrxndarrayrrrrrrrrr r rrr&r7rir$r"rBsKK  KKKKKKKKKKVVVVVVVVVVVVVV++++++777777778####L%%%P   8+0;;;;;~4:     Dj/ *!(AtFCCCD"(8QVDDDE8Haf===zz6(?S?ST'1z2N2N2N'O'O&PVH!5!56['((j'7);<<=  #'   $ %JKJKJKJK  JKb %XXXXXv!"G#G#G#G#G#T8888v::::z' ' ' ' T    H>CG{@{@{@{@|   ,####L))))X      FBBBBBr$