U Hv f@sdZdgZddlZddlmZddlmZddlm Z m Z ddl m Z m Z Gd d d ejjZdd lmZdd dZdddZdS)zz Matrix square root for general matrices and for upper triangular matrices. This module exists to avoid cyclic imports. sqrtmN)_asarray_validated)norm)ztrsyldtrsyl)schurrsf2csfc@s eZdZdS) SqrtmErrorN)__name__ __module__ __qualname__rr@/tmp/pip-unpacked-wheel-96ln3f52/scipy/linalg/_matfuncs_sqrtm.pyr sr )within_block_loop@c Cs\t|}t|o t|dk}|sJtj|tjdd}tj|tjd}n"tj|tjdd}tj|tjd}tt|}|j\}}t ||d}t ||\}}|d} ||} | ||| |krt dg} d} | |f|| ffD]0\} }t | D]}| | | |f| |7} qqzt||| |Wn0tk rZ}zt|j|W5d}~XYnXt |D]}| |\}}t |dddD]}| |\}}|||||f}||dkr||||||f|||||f}|||||f}|||||f}|r&t|||\}}}nt|||\}}}|||||||f<qqd|S) a Matrix square root of an upper triangular matrix. This is a helper function for `sqrtm` and `logm`. Parameters ---------- T : (N, N) array_like upper triangular Matrix whose square root to evaluate blocksize : int, optional If the blocksize is not degenerate with respect to the size of the input array, then use a blocked algorithm. (Default: 64) Returns ------- sqrtm : (N, N) ndarray Value of the sqrt function at `T` References ---------- .. [1] Edvin Deadman, Nicholas J. Higham, Rui Ralha (2013) "Blocked Schur Algorithms for Computing the Matrix Square Root, Lecture Notes in Computer Science, 7782. pp. 171-182. rC)dtypeorder)rrzinternal inconsistencyN)npZdiag isrealobjminasarrayZ complex128Zfloat64sqrtshapemaxdivmod Exceptionrangeappendr RuntimeErrorr argsdotrr)T blocksizeZT_diag keep_it_realRnZnblocksZbsmallZnlargeZblargeZnsmallZstart_stop_pairsstartcountsizeiejZjstartZjstopistartistopSZRiiZRjjxZscaleinforrr _sqrtm_triusT         r4Tc Cst|jj}t|ddd}t|jdkr2td|dkrBtdt|}|r~t |\}}t |t |st ||\}}nt |dd\}}d }zt ||d }t|j} ||| } t| s| jd t|dd d d } nRttdr| jdt|dddd d } n"| jdt|ddd d d } Wn0tk rjd}t|} | tjYnX|r|rtd| Sz&t| | |ddt|d} Wntk rtj} YnX| | fSdS)a Matrix square root. Parameters ---------- A : (N, N) array_like Matrix whose square root to evaluate disp : bool, optional Print warning if error in the result is estimated large instead of returning estimated error. (Default: True) blocksize : integer, optional If the blocksize is not degenerate with respect to the size of the input array, then use a blocked algorithm. (Default: 64) Returns ------- sqrtm : (N, N) ndarray Value of the sqrt function at `A`. The dtype is float or complex. The precision (data size) is determined based on the precision of input `A`. When the dtype is float, the precision is same as `A`. When the dtype is complex, the precition is double as `A`. The precision might be cliped by each dtype precision range. errest : float (if disp == False) Frobenius norm of the estimated error, ||err||_F / ||A||_F References ---------- .. [1] Edvin Deadman, Nicholas J. Higham, Rui Ralha (2013) "Blocked Schur Algorithms for Computing the Matrix Square Root, Lecture Notes in Computer Science, 7782. pp. 171-182. Examples -------- >>> import numpy as np >>> from scipy.linalg import sqrtm >>> a = np.array([[1.0, 3.0], [1.0, 4.0]]) >>> r = sqrtm(a) >>> r array([[ 0.75592895, 1.13389342], [ 0.37796447, 1.88982237]]) >>> r.dot(r) array([[ 1., 3.], [ 1., 4.]]) T)Z check_finiteZ as_inexactz$Non-matrix input to matrix function.rz#The blocksize should be at least 1.complex)outputF)r%f)copyZ complex256c zFailed to find a square root.ZfroN)rrritemsizerlenr ValueErrorrrZ array_equalZtriur r4 conjugater$r#Z iscomplexobjZastypeZcliphasattrr Z empty_likefillnanprintrinf) AZdispr%Z byte_sizer&r$ZZfailflagr'ZZHXZarg2rrrrusF1       $& & )r)Tr)__doc____all__ZnumpyrZscipy._lib._utilrZ_miscrZlapackrrZ _decomp_schurrr ZlinalgZ LinAlgErrorr Z_matfuncs_sqrtm_triurr4rrrrrs    Z