o Ebt@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>/usr/lib/python3/dist-packages/scipy/linalg/_matfuncs_sqrtm.pyr sr )within_block_loop@c CsJt|}t|ot|dk}|s%tj|tjdd}tj|tjd}ntj|tjdd}tj|tjd}tt|}|j\}}t ||d}t ||\}}|d} ||} | ||| |krgt dg} d} | |f|| ffD]\} }t | D]}| | | |f| |7} q{qsz t||| |Wnty}zt|j|d}~wwt |D]v}| |\}}t |dddD]e}| |\}}|||||f}||dkr||||||f|||||f}|||||f}|||||f}|r t|||\}}}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. rC)dtypeZorder)rrzinternal inconsistencyN)npZdiag isrealobjminZasarrayZ complex128Zfloat64Zsqrtshapemaxdivmod Exceptionrangeappendr RuntimeErrorr argsdotrr)T blocksizeZT_diag keep_it_realRnZnblocksZbsmallZnlargeZblargeZnsmallZstart_stop_pairsstartcountsizeiejZjstartZjstopZistartZistopSZRiiZRjjxZscaleinforrr _sqrtm_triusZ          r/Tc Cs>t|ddd}t|jdkrtd|dkrtdt|}|r8t|\}}t|t|s7t ||\}}nt|dd\}}d }zt ||d }t |j }| | |} Wntynd}t|} | tjYnw|ry|rwtd | Szt| | |d dt|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` 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 -------- >>> 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$Non-matrix input to matrix function.rz#The blocksize should be at least 1.complex)outputF)r"zFailed to find a square root.Zfro)rlenr ValueErrorrrrZ array_equalZtriur r/ conjugater!r r Z empty_likefillnanprintrinf) AZdispr"r#r!ZZfailflagr$ZZHXZarg2rrrrusB,      $ )r)Tr)__doc____all__ZnumpyrZscipy._lib._utilrZ_miscrZlapackrrZ _decomp_schurrr ZlinalgZ LinAlgErrorr Z_matfuncs_sqrtm_triurr/rrrrrs    Z