U f{jZ@sdZddlZddlZedddZedddZejfddZdd d Z edd d Z dddZ dddZ dddZ dS)aUtility functions to speed up linear algebraic operations. In general, things like np.dot and linalg.svd should be used directly because they are smart about checking for bad values. However, in cases where things are done repeatedly (e.g., thousands of times on tiny matrices), the overhead can become problematic from a performance standpoint. Examples: - Optimization routines: - Dipole fitting - Sparse solving - cHPI fitting - Inverse computation - Beamformers (LCMV/DICS) - eLORETA minimum norm Significant performance gains can be achieved by ensuring that inputs are Fortran contiguous because that's what LAPACK requires. Without this, inputs will be memcopied. NcCs"ddlm}||td|fSNrlinalg)scipyrZget_blas_funcsnpempty)dtypenamesrr O/var/www/html/bwave/python/venv/lib/python3.8/site-packages/mne/utils/linalg.py_get_blas_funcs!s r cCs:ddlm}|tjtjfks ttd|}|||fSr)rrrfloat64 complex128AssertionErrorrget_lapack_funcs)rr rxr r r _get_lapack_funcs's  rcCsxddlm}z |j}Wntk r0|j}YnXt|d\}}|j|f|ddd}|j|f|ddd}||fS)zESet up SVD calculations on identical-shape float64/complex128 arrays.rr) gesdd_lwork gesvd_lworkTF) compute_uv full_matrices)rrZ _decomp_svdAttributeErrorZ decomp_svdrZ_compute_lwork)shaperrZdsrrZ sdd_lworkZ svd_lworkr r r _svd_lwork2s4   rFc Cst|jd\}}||d|dddd\}}}}|dkrT||d|dd|d\}}}}|dkrhtjd|dkr~td| |||fS) zBMimic scipy.linalg.svd, avoid lwork and get_lapack_funcs overhead.)gesddgesvdTrF)rlworkr overwrite_azSVD did not convergez1illegal value in %d-th argument of internal gesdd)rrrr LinAlgError ValueError) rrrrrusvinfor r r _repeated_svdBs(   r%cCsTddlm}td|}|tjkr(d}n|tjks6td}||f|f\}||fS)NrrZsyevdZheevd)rrrrr rrr)rrrdriverZevrr r r _get_evdXs   r'Tc Csddlm}ddlm}|r(|||d}t|j\}}||d|d\}}} | dkrZ||fS| dkrvtd| |fn |d| d S) aEfficient wrapper for eigh. Parameters ---------- a : ndarray, shape (n_components, n_components) The symmetric array operate on. overwrite_a : bool If True, the contents of a can be overwritten for efficiency. check_finite : bool If True, check that all elements are finite. Returns ------- w : ndarray, shape (n_components,) The N eigenvalues, in ascending order, each repeated according to its multiplicity. v : ndarray, shape (n_components, n_components) The normalized eigenvector corresponding to the eigenvalue ``w[i]`` is the column ``v[:, i]``. r)r)_asarray_validated) check_finiter)lowerrz+illegal value in argument %d of internal %szinternal fortran routine failed to converge: %i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.N)Z scipy.linalgrZscipy._lib._utilr(r'rr ) arr)rr(Zevdr&wr#r$r r r eighes   r-Hz>cCst||r dnd|ddS)aVCompute the sqrt of a positive, semi-definite matrix (or its inverse). Parameters ---------- A : ndarray, shape (..., n, n) The array to take the square root of. rcond : float The relative condition number used during reconstruction. inv : bool If True, compute the inverse of the square root rather than the square root itself. Returns ------- A_sqrt : ndarray, shape (..., n, n) The (possibly inverted) square root of A. s : ndarray, shape (..., n) The original square root singular values (not inverted). ?T)return_s) _sym_mat_pow)Arcondinvr r r sqrtm_symsr6c Cs|dks ttj|\}}|dddf|}|| ksFtd|dkrTtjnd|||k<|rntj|d<|dkrtj||d |dkrd |n|}t||dtj ddf| d d } |r| |f} | S) z=Exponentiate Hermitian matrices with optional rank reduction.)r0r/.r7Nz$Matrix is not positive semi-definiter).r)r/r0)outg?) rrrr-allr infsqrtmatmulZnewaxisZswapaxesZconj) r3powerr4Z reduce_rankr1r"r!limitZuse_sr8r r r r2s  ,r2)F)FT)r.F)r.FF)__doc__ functoolsnumpyr lru_cacher rr rr%r'r-r6r2r r r r s    (