o Uݢg @s`dZddlmZddlZddlZddlmZdddZ ddZ d d Z   ddddZ dS)a9Copyright 2013 Michael Kane and Bryan Lewis. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ) annotationsNFcCs|jdksJt|r2|r t||dddfS|t|dddfS|r@t|| St|| S)Nr) ndimspissparse csr_matrixdot transposetoarraynpasarrayravel)Axtrg/oak/stanford/groups/akundaje/marinovg/programs/cellranger-9.0.1/lib/python/cellranger/analysis/irlb.pymults $$rcCs||}|t||S)zOrthogonalize a vector or matrix Y against the columns of the matrix X. This function requires that the column dimension of Y is less than X and that Y and X have the same number of rows. )rr)YXZdotYrrrorthog)s rcCs.dttj}||krd|StddS)Ng?z9Ill-conditioning encountered, result accuracy may be poorg)r finfofloatepswarningswarn)rZeps2rrrinvcheck4s  r-C6?2r np.ndarrayninttolrmaxitcenternp.ndarray | Nonescalereturn3tuple[np.ndarray, np.ndarray, np.ndarray, int, int]c Cstj|}|durt|tjstd|dur"t|tjs"td|}|jd} |jd}t| |dkr9tdt|dd |t|jf} d} d} d} |}d}t || f}t | | f}t |df}t | | f}| ||dddf<|dddftj ||dddf<| |kr| dkr|} |dd| f}|dur||}t |||dd| f<| d7} |dur|dd| ft|||dd| f<| dkrt|dd| f|ddd| f|dd| f<tj |dd| f}t|}||dd| f|dd| f<| | krCt ||dd| fd d }| d7} |dur*||}|durIt|dd| f|}|durE||}||}|||dd| f}t||ddd| df}tj |}t|}||}| | dkr4||dd| df<||| | f<||| | df<|dd| df}|dur||}t |||dd| df<| d7} |dur|dd| dft|||dd| df<|dd| df||dd| f|dd| df<t|dd| df|ddd| df|dd| df<tj |dd| df}t|}||dd| df|dd| df<n||| | f<| d7} | | kstj |}||d| dddf}| dkrc|dd}n t|dd|f}tt|d|||k}||krt|||}t|| d }nnu|ddd| f|dddd|f|ddd|f<||dd|f<t | | f}t|D] }|d||||f<q|d||d||f<|ddd| f|dddd|f|ddd|f<| d7} | |ks|ddd| f|dddd|f}|ddd| f|dddd|f}||dd||| | fS) aEstimate a few of the largest singular values and corresponding singular. vectors of matrix using the implicitly restarted Lanczos bidiagonalization method of Baglama and Reichel, see: Augmented Implicitly Restarted Lanczos Bidiagonalization Methods, J. Baglama and L. Reichel, SIAM J. Sci. Comput. 2005 Keyword Arguments: tol -- An estimation tolerance. Smaller means more accurate estimates. maxit -- Maximum number of Lanczos iterations allowed. Given an input matrix A of dimension j * k, and an input desired number of singular values n, the function returns a tuple X with five entries: X[0] A j * nu matrix of estimated left singular vectors. X[1] A vector of length nu of estimated singular values. X[2] A k * nu matrix of estimated right singular vectors. X[3] The number of Lanczos iterations run. X[4] The number of matrix-vector products run. The algorithm estimates the truncated singular value decomposition: A.dot(X[2]) = X[0]*X[1]. Nzcenter must be a numpy.ndarrayzscale must be a numpy.ndarrayrrrz&The input matrix must be at least 2x2.T)r)r random RandomState isinstancendarray TypeErrorshapemin ValueErrorzerosrandnlinalgnormrrrrsumsvdmaxabsr range) rr!r#r$r%r' random_statersnumZm_bZmproditjksmaxVWFBZVJsZsinvsubfnZfninvZVJp1SRconvlUrrrirlb=s !  ( (2         08>*  2  B >.f2rQ)F)rrNNr)rr r!r"r#rr$r"r%r&r'r&r(r)) __doc__ __future__rrnumpyr scipy.sparsesparserrrrrQrrrrs