B [ @s`ddlmZmZddlmZddlmZmZmZddl m Z GdddeZ GdddeZ d S) )print_functiondivision) 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 cCs |jdS)Nr)args)selfr Blib/python3.7/site-packages/sympy/matrices/expressions/diagonal.py1szDiagonalMatrix.cCs|jjS)N)argshape)r r r r r3scCs|j\}}|jr"|jr"t||}nZ|jr4|js4|}nH|jrF|jsF|}n6||krT|}n(yt||}Wntk rzd}YnX|S)N)r is_Integermin TypeError)r rcmr r r diagonal_length5s      zDiagonalMatrix.diagonal_lengthcCs|jdk r:t||jtjkr"tjSt||jtjkr:tjSt||}|tjkr\|j||fS|tjkrltjS|j||ft||S)N) rrrtrueZZerorrZfalser)r ijeqr r r _entryGs    zDiagonalMatrix._entryN) __name__ __module__ __qualname____doc__propertyrrrrr r r r r 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 |jdS)Nr)r )r r r r rszDiagonalOf.cCs|jj\}}|jr$|jr$t||}nZ|jr6|js6|}nH|jrH|jsH|}n6||krV|}n(yt||}Wntk r|d}YnX|tjfS)N)rrrrrrZOne)r rrrr r r rs      zDiagonalOf.shapecCs |jdS)Nr)r)r r r r rszDiagonalOf.diagonal_lengthcCs|j||fS)N)r)r rrr r r rszDiagonalOf._entryN) rrrr r!rrrrr r r r r"Us +   r"N) Z __future__rrZsympy.matrices.expressionsrZ sympy.corerrrZ(sympy.functions.special.tensor_functionsrr r"r r r r s   M