a >> 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 cCs |jdSNrargsselfrs/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/matrices/expressions/diagonal.py2zDiagonalMatrix.cCs|jjSN)argshaper rrrr4rcCs~|j\}}|jr"|jr"t||}nX|jr4|js4|}nF|jrF|jsF|}n4||krT|}n&zt||}Wntyxd}Yn0|Sr)r is_Integermin TypeErrorrrcmrrrdiagonal_length6s       zDiagonalMatrix.diagonal_lengthcKs|jdur:t||jtjur"tjSt||jtjur:tjSt||}|tjur\|j||fS|tjurltjS|j||ft||Sr) rrrtrueZZerorrfalser)rijkwargseqrrr_entryHs    zDiagonalMatrix._entryN __name__ __module__ __qualname____doc__propertyrrrr$rrrrr s (   r c@s<eZdZdZeddZeddZeddZdd Zd S) DiagonalOfaDiagonalOf(M) will create a matrix expression that is equivalent to the diagonal of `M`, represented as a single column matrix. Examples ======== >>> from sympy import MatrixSymbol, DiagonalOf, Symbol >>> n = Symbol('n', integer=True) >>> m = Symbol('m', integer=True) >>> x = MatrixSymbol('x', 2, 3) >>> diag = DiagonalOf(x) >>> diag.shape (2, 1) The diagonal can be addressed like a matrix or vector and will return the corresponding element of the original matrix: >>> diag[1, 0] == diag[1] == x[1, 1] True The length of the diagonal -- the lesser of the two dimensions of `M` -- is accessed through the `diagonal_length` property: >>> diag.diagonal_length 2 >>> DiagonalOf(MatrixSymbol('x', n + 1, n)).diagonal_length n When only one of the dimensions is symbolic the other will be treated as though it is smaller: >>> dtall = DiagonalOf(MatrixSymbol('x', n, 3)) >>> dtall.diagonal_length 3 When the size of the diagonal is not known, a value of None will be returned: >>> DiagonalOf(MatrixSymbol('x', n, m)).diagonal_length is None True cCs |jdSr r r rrrrrzDiagonalOf.cCs|jj\}}|jr$|jr$t||}nX|jr6|js6|}nF|jrH|jsH|}n4||krV|}n&zt||}Wntyzd}Yn0|tjfSr)rrrrrrZOnerrrrrs       zDiagonalOf.shapecCs |jdSr )rr rrrrszDiagonalOf.diagonal_lengthcKs|jj||fi|Sr)rr$)rr r!r"rrrr$szDiagonalOf._entryNr%rrrrr+Vs+   r+c@sDeZdZdZddZeddZddZdd Zd d Z d d Z dS) DiagMatrixz/ Turn a vector into a diagonal matrix. cCsft|}t||}|j}|ddkr.|dn|d}|jddkrLd|_nd|_||f|_||_|S)NrTF)rr__new__r _iscolumn_shape_vector)clsvectorobjrZdimrrrr.s  zDiagMatrix.__new__cCs|jSr)r0r rrrrszDiagMatrix.shapecKsN|jr|jj|dfi|}n|jjd|fi|}||krJ|t||9}|Sr )r/r1r$r)rr r!r"resultrrrr$s zDiagMatrix._entrycCs|Srrr rrr_eval_transposeszDiagMatrix._eval_transposecCsddlm}|t|jS)Nr)diag)sympy.matrices.denser7listr1 as_explicit)rr7rrrr:s zDiagMatrix.as_explicitc  sddlm}m}ddlm}ddlm}ddlm}ddl m }|j }|| |rX|St ||r|t|j} t| jdD]} || | | | f<q~t|| S|jrdd|jDfd d|jD} | rt| t|St ||r|j}t|S) Nr)askQ)MatMul) Transpose)eye) MatrixBasecSsg|]}|jr|qSr)Z is_Matrix.0rrrr rz#DiagMatrix.doit..csg|]}|vr|qSrrrAZmatricesrrrCr)Zsympy.assumptionsr;r<Z!sympy.matrices.expressions.matmulr=Z$sympy.matrices.expressions.transposer>r8r?Zsympy.matrices.matricesr@r1Zdiagonal isinstancemaxrrangetypeZ is_MatMulr rZfromiterr,doitr) rhintsr;r<r=r>r?r@r3retr ZscalarsrrDrrIs*        zDiagMatrix.doitN) r&r'r(r)r.r*rr$r6r:rIrrrrr,s   r,cCs t|Sr)r,rI)r3rrrdiagonalize_vectorsrLN)Zsympy.core.sympifyrZsympy.matrices.expressionsrZ sympy.corerrrZsympy.core.mulrZ(sympy.functions.special.tensor_functionsrr r+r,rLrrrrs    MG>