o 8Va@stddlmZddlmZddlmZmZmZddlm Z GdddeZ GdddeZ Gd d d eZ d d Z d S))_sympify) MatrixExpr)SEqGe)KroneckerDeltac@s<eZdZdZeddZeddZeddZddZd S) DiagonalMatrixaDiagonalMatrix(M) will create a matrix expression that behaves as though all off-diagonal elements, `M[i, j]` where `i != j`, are zero. Examples ======== >>> from sympy import MatrixSymbol, DiagonalMatrix, Symbol >>> n = Symbol('n', integer=True) >>> m = Symbol('m', integer=True) >>> D = DiagonalMatrix(MatrixSymbol('x', 2, 3)) >>> D[1, 2] 0 >>> D[1, 1] x[1, 1] The length of the diagonal -- the lesser of the two dimensions of `M` -- is accessed through the `diagonal_length` property: >>> D.diagonal_length 2 >>> DiagonalMatrix(MatrixSymbol('x', n + 1, n)).diagonal_length n When one of the dimensions is symbolic the other will be treated as though it is smaller: >>> tall = DiagonalMatrix(MatrixSymbol('x', n, 3)) >>> tall.diagonal_length 3 >>> tall[10, 1] 0 When the size of the diagonal is not known, a value of None will be returned: >>> DiagonalMatrix(MatrixSymbol('x', n, m)).diagonal_length is None True cC |jdSNrargsselfrE/usr/lib/python3/dist-packages/sympy/matrices/expressions/diagonal.py1 zDiagonalMatrix.cCs|jjSN)argshaper rrrr3scCs|j\}}|jr|jrt||}|S|jr|js|}|S|jr&|js&|}|S||kr.|}|Szt||}W|StyBd}Y|Swr)r is_Integermin TypeErrorrrcmrrrdiagonal_length5s(       zDiagonalMatrix.diagonal_lengthcKs|jdurt||jtjurtjSt||jtjurtjSt||}|tjur.|j||fS|tjur6tjS|j||ft||Sr) rrrtrueZZerorrZfalser)rijkwargseqrrr_entryGs    zDiagonalMatrix._entryN __name__ __module__ __qualname____doc__propertyrrrr#rrrrrs (   rc@s<eZdZdZeddZeddZeddZdd Zd S) DiagonalOfaDiagonalOf(M) will create a matrix expression that is equivalent to the diagonal of `M`, represented as a single column matrix. Examples ======== >>> from sympy import MatrixSymbol, DiagonalOf, Symbol >>> n = Symbol('n', integer=True) >>> m = Symbol('m', integer=True) >>> x = MatrixSymbol('x', 2, 3) >>> diag = DiagonalOf(x) >>> diag.shape (2, 1) The diagonal can be addressed like a matrix or vector and will return the corresponding element of the original matrix: >>> diag[1, 0] == diag[1] == x[1, 1] True The length of the diagonal -- the lesser of the two dimensions of `M` -- is accessed through the `diagonal_length` property: >>> diag.diagonal_length 2 >>> DiagonalOf(MatrixSymbol('x', n + 1, n)).diagonal_length n When only one of the dimensions is symbolic the other will be treated as though it is smaller: >>> dtall = DiagonalOf(MatrixSymbol('x', n, 3)) >>> dtall.diagonal_length 3 When the size of the diagonal is not known, a value of None will be returned: >>> DiagonalOf(MatrixSymbol('x', n, m)).diagonal_length is None True cCr r r r rrrrrzDiagonalOf.cCs|jj\}}|jr|jrt||}n,|jr|js|}n#|jr$|js$|}n||kr+|}nzt||}Wn ty=d}Ynw|tjfSr)rrrrrrZOnerrrrrs       zDiagonalOf.shapecCr r )rr rrrrs zDiagonalOf.diagonal_lengthcKs|jj||fi|Sr)rr#)rrr r!rrrr#szDiagonalOf._entryNr$rrrrr*Us +   r*c@sDeZdZdZddZeddZddZdd Zd d Z d d Z dS) DiagMatrixz/ Turn a vector into a diagonal matrix. cCsft|}t||}|j}|ddkr|dn|d}|jddkr&d|_nd|_||f|_||_|S)NrTF)rr__new__r _iscolumn_shape_vector)clsvectorobjrZdimrrrr-s  zDiagMatrix.__new__cCs|jSr)r/r rrrrszDiagMatrix.shapecKsN|jr|jj|dfi|}n |jjd|fi|}||kr%|t||9}|Sr )r.r0r#r)rrr r!resultrrrr#s zDiagMatrix._entrycCs|Srrr rrr_eval_transposeszDiagMatrix._eval_transposecCsddlm}|t|jS)Nr)diag)sympyr6listr0 as_explicit)rr6rrrr9s zDiagMatrix.as_explicitc  sddlm}m}ddlm}m}m}ddlm}m}|j } || | r&| St | |rJ|t | j } t| j dD] } | | | | | f<q9t| | S| jrqdd| jDfdd| jD} | rq|| t|St | |ry| j} t| S)Nr)askQ) TransposeMulMatMul) MatrixBaseeyecSsg|]}|jr|qSr)Z is_Matrix.0rrrr sz#DiagMatrix.doit..csg|]}|vr|qSrrrAZmatricesrrrCs)Zsympy.assumptionsr:r;r7r<r=r>r?r@r0Zdiagonal isinstancemaxrrangetypeZ is_MatMulr Zfromiterr+doitr) rZhintsr:r;r<r=r>r?r@r2retrZscalarsrrDrrIs&    zDiagMatrix.doitN) r%r&r'r(r-r)rr#r5r9rIrrrrr+s   r+cCs t|Sr)r+rI)r2rrrdiagonalize_vectors rKN)Zsympy.core.sympifyrZsympy.matrices.expressionsrZ sympy.corerrrZ(sympy.functions.special.tensor_functionsrrr*r+rKrrrrs  MG <