Pg3 ZdZddlmZmZddlZddlmZdZdZdeeded efd Zd edeed ed efd Z deedefdZ dZ ddedee d eeeffdZ dddd efdZdddeded eeeffdZdddeded eeeffdZ dddd eeeffdZ dddddede d eeeffdZy) z8Various linear algebra utility methods for internal use.)OptionalTupleN)Tensorct|tjr|jtjk(Sd}tj j s|dt|z }t|)z$Check if tensor A is a sparse tensorzexpected Tensorz but got ) isinstancetorchrlayout sparse_coojit is_scriptingtype TypeError)A error_strs Z/var/www/html/suriana-translation/venv/lib/python3.12/site-packages/torch/_linalg_utils.py is_sparser sZ!U\\"xx5++++!I 99 ! ! #ya ** I c|j}|tjtjtjfvr|StjS)zTReturn the floating point dtype of tensor A. Integer types map to float32. )dtyperfloat16float32float64)rrs rget_floating_dtypers7 GGE  u}}== ==rrBreturnc||St|r tjj||Stj||S)ziMultiply two matrices. If A is None, return B. A can be sparse or dense. B is always dense. )rrsparsemmmatmul)rrs rrr s;  y|||q!$$ <<1 rXYcBt|jt||S)z2Return bilinear form of matrices: :math:`X^T A Y`.)rmT)r rr!s rbformr$-s !$$q! %%rSct|||S)z&Return quadratic form :math:`S^T A S`.)r$)rr%s rqformr'2s Aq>rcTtjj|jS)z%Return orthogonal basis of A columns.)rlinalgqrQ)rs rbasisr,7s < n. In torch.linalg.lstsq, the residuals are in the field 'residuals' of the returned named tuple. The unpacking of the solution, as in X, _ = torch.lstsq(B, A).solution[:A.size(1)] should be replaced with: X = torch.linalg.lstsq(A, B).solutionr:rAs rlstsqrD^s  0  rctd)NaThis function was deprecated since version 1.9 and is now removed. The default behavior has changed from using the upper triangular portion of the matrix by default to using the lower triangular portion. L, _ = torch.symeig(A, upper=upper) should be replaced with: L = torch.linalg.eigvalsh(A, UPLO='U' if upper else 'L') and L, V = torch.symeig(A, eigenvectors=True) should be replaced with: L, V = torch.linalg.eigh(A, UPLO='U' if upper else 'L')r:)r< eigenvectorsupperr8s r_symeigrHos  B  r)evselfrFctd)NaThis function was deprecated since version 1.9 and is now removed. `torch.linalg.eig` returns complex tensors of dtype `cfloat` or `cdouble` rather than real tensors mimicking complex tensors. L, _ = torch.eig(A) should be replaced with: L_complex = torch.linalg.eigvals(A) and L, V = torch.eig(A, eigenvectors=True) should be replaced with: L_complex, V_complex = torch.linalg.eig(A)r:)rKrFrIrJs reigrMs  5  r)F)NF)FT)__doc__typingrrrrrrrr$r'r,boolr7r?rBrDrHrMrrrRsk>"  hv 6 f &V&(&V&& Xf &  f x~ %:O &,0  F E&&.4I ,0FE&&.4I&    66> .     66> r