ó ʽ÷Xc@`sÛdZddlmZmZmZddlZddlmZdgZ dde e d„Z d „Z e d „ƒZ e d „ƒZd „Zd „Zd„Zd„Zdd„Zd„Zd„Zd„Zd„ZdS(sSparse block 1-norm estimator. i(tdivisiontprint_functiontabsolute_importN(taslinearoperatort onenormestiicC`s§t|ƒ}|jd|jdkr5tdƒ‚n|jd}||kr3tjt|ƒjtj|ƒƒƒ}|j||fkr©tddt|jƒƒ‚nt |ƒj ddƒ}|j|fkròtddt|jƒƒ‚ntj |ƒ}t ||ƒ} |dd…|f} ||} n't ||j||ƒ\} } } } } |sf|rŸ| f}|r…|| f7}n|r›|| f7}n|S| SdS(s! Compute a lower bound of the 1-norm of a sparse matrix. Parameters ---------- A : ndarray or other linear operator A linear operator that can be transposed and that can produce matrix products. t : int, optional A positive parameter controlling the tradeoff between accuracy versus time and memory usage. Larger values take longer and use more memory but give more accurate output. itmax : int, optional Use at most this many iterations. compute_v : bool, optional Request a norm-maximizing linear operator input vector if True. compute_w : bool, optional Request a norm-maximizing linear operator output vector if True. Returns ------- est : float An underestimate of the 1-norm of the sparse matrix. v : ndarray, optional The vector such that ||Av||_1 == est*||v||_1. It can be thought of as an input to the linear operator that gives an output with particularly large norm. w : ndarray, optional The vector Av which has relatively large 1-norm. It can be thought of as an output of the linear operator that is relatively large in norm compared to the input. Notes ----- This is algorithm 2.4 of [1]. In [2] it is described as follows. "This algorithm typically requires the evaluation of about 4t matrix-vector products and almost invariably produces a norm estimate (which is, in fact, a lower bound on the norm) correct to within a factor 3." .. versionadded:: 0.13.0 References ---------- .. [1] Nicholas J. Higham and Francoise Tisseur (2000), "A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra." SIAM J. Matrix Anal. Appl. Vol. 21, No. 4, pp. 1185-1201. .. [2] Awad H. Al-Mohy and Nicholas J. Higham (2009), "A new scaling and squaring algorithm for the matrix exponential." SIAM J. Matrix Anal. Appl. Vol. 31, No. 3, pp. 970-989. iis1expected the operator to act like a square matrixsinternal error: sunexpected shape taxisN(Rtshapet ValueErrortnptasarraytmatmattidentityt Exceptiontstrtabstsumtargmaxtelementary_vectort_onenormest_coretH(tAtttitmaxt compute_vt compute_wtnt A_explicitt col_abs_sumstargmax_jtvtwtesttnmultst nresamplestresult((s>/tmp/pip-build-7oUkmx/scipy/scipy/sparse/linalg/_onenormest.pyR s4<   ' '  c`sd‰‡‡fd†}|S(s‘ Decorator for an elementwise function, to apply it blockwise along first dimension, to avoid excessive memory usage in temporaries. iic`sµ|jdˆkrˆ|ƒSˆ|ˆ ƒ}tj|jdf|jdd|jƒ}||ˆ*~xCtˆ|jdˆƒD](}ˆ|||ˆ!ƒ|||ˆ+qW|SdS(Niitdtype(RRtzerosR#trange(txty0tytj(t block_sizetfunc(s>/tmp/pip-build-7oUkmx/scipy/scipy/sparse/linalg/_onenormest.pytwrapperts -  &i((R+R,((R*R+s>/tmp/pip-build-7oUkmx/scipy/scipy/sparse/linalg/_onenormest.pyt_blocked_elementwisems cC`s3|jƒ}d||dk<|tj|ƒ}|S(s9 This should do the right thing for both real and complex matrices. 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