>qj8 rdZgZddlZddlmZGddej jZddl m Z d dZ y) zz Matrix square root for general matrices and for upper triangular matrices. This module exists to avoid cyclic imports. N)get_lapack_funcsc eZdZy) SqrtmErrorN)__name__ __module__ __qualname__[/opt/rentech/trading_bot/.venv/lib/python3.12/site-packages/scipy/linalg/_matfuncs_sqrtm.pyrrsr r)within_block_loopc tj|}tj|xrtj|ddk\}|sLtj|tj d}tj|tj }nKtj|tj d}tj|tj }tjtj|}td|fd }|j\}}t||zd }t||\}} |d z} || z } | |z| | zz|k7r td g} d} | |f| | ffD]0\}}t|D]}| j| | |zf| |z } 2 t||| |t|D]}| |\}}t|d z d d D]u}| |\}}|||||f}||z d kDr&||||||fj'|||||fz }|||||f}|||||f}||||\}}}||z|||||f<w|S#t $r}t#|j$|d }~wwxYw)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)rtrsyl preferred)ilp64rzinternal inconsistencyN)npdiag isrealobjminasarray complex128float64sqrtrshapemaxdivmod Exceptionrangeappendr RuntimeErrorrargsdot)T blocksizeT_diag keep_it_realRrnnblocksbsmallnlargeblargensmallstart_stop_pairsstartcountsizeiejjstartjstopistartistopSRiiRjjxscaleinfos r _sqrtm_triurDs4WWQZF<<?Frvvfb'AQ'FL  JJq S 9F"--8 JJq # 6F"**5  A Wqd+ >E 77DAq!y.!$GAw'NFF aZF v F &(A-011 E(66*:; tu A  # #UEDL$9 : TME  )!Q 0': 7^6(+ qsB# 6A,Q/MFE&,u ,-A1uqy&,f 4599!E&LrMs: % && 4V r