o ?Hh|@sdZdgZddlZddlmZddlmZddlm Z m Z ddl m Z m Z dd lmZGd d d ejjZdd lmZdddZdddZdS)zz Matrix square root for general matrices and for upper triangular matrices. This module exists to avoid cyclic imports. sqrtmN)_asarray_validated)norm)ztrsyldtrsyl)schurrsf2csf)_ensure_dtype_cdszc@s eZdZdS) SqrtmErrorN)__name__ __module__ __qualname__rr\/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/scipy/linalg/_matfuncs_sqrtm.pyr sr )within_block_loop@c CsNt|}t|otj|dddk}|s'tj|tjdd}tj|tjd}ntj|tjdd}tj|tjd}tt|}|j\}}t ||d}t ||\}}|d} ||} | ||| |krit dg} d} | |f|| ffD]\} }t | D]}| | | |f| |7} q}quz t||| |Wnty}zt|j|d }~wwt |D]v}| |\}}t |dd d D]e}| |\}}|||||f}||dkr||||||f|||||f}|||||f}|||||f}|rt|||\}}}n t|||\}}}|||||||f<qq|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. g)initialrC)dtypeorder)rrzinternal inconsistencyN)npdiag isrealobjminasarray complex128float64sqrtshapemaxdivmod Exceptionrangeappendr RuntimeErrorr argsdotrr)T blocksizeT_diag keep_it_realRnnblocksbsmallnlargeblargensmallstart_stop_pairsstartcountsizeiejjstartjstopistartistopSRiiRjjxscaleinforrr _sqrtm_triusZ          rETcCst|ddd}t|jdkrtd|dkrtdt|\}t|}|r`t|\}}t|}t|d}t |j j }t ||t |ddt |ddk} | r_t||\}}nt|d d \}}d } z+t||d } t|j} || | } t|j t| rd nd}| j|d d} Wntyd} t|} | tjYnw|r| rtd| Szt| | |ddt|d}W| |fStytj}Y| |fSw)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`. 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) check_finite as_inexactz$Non-matrix input to matrix function.rz#The blocksize should be at least 1.rNcomplex)outputF)r*y?)copyzFailed to find a square root.fro)rlenr ValueErrorr rrrdiagonalfinforepsabsanyr rE conjugater)r( result_type iscomplexobjastyper empty_likefillnanprintrinf)Adispr*r,r)Zd0d1rQneeds_conversionfailflagr-ZHXrarg2rrrrvsP/     ,    $ )r)Tr)__doc____all__numpyrscipy._lib._utilr_miscrlapackrr _decomp_schurrr _basicr linalg LinAlgErrorr _matfuncs_sqrtm_triurrErrrrrs     Z