ó ~9­\c@ s‚ddlmZmZddlmZddlmZmZmZddl m Z defd„ƒYZ defd„ƒYZ d S( i˙˙˙˙(tprint_functiontdivision(t MatrixExpr(tStEqtGe(tKroneckerDeltatDiagonalMatrixcB sDeZdZed„ƒZed„ƒZed„ƒZd„ZRS(sDiagonalMatrix(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 s |jdS(Ni(targs(tself((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyt1tcC s |jjS(N(targtshape(R ((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyR 3R cC sħ|j\}}|jr3|jr3t||ƒ}nz|jrO|j rO|}n^|jrk|j rk|}nB||kr€|}n-yt||ƒ}Wntk rĴd}nX|S(N(R t is_Integertmint TypeErrortNone(R trtctm((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pytdiagonal_length5s      cC sı|jdk rVt||jƒtjkr1tjSt||jƒtjkrVtjSnt||ƒ}|tjkr…|j||fS|tjkr›tjS|j||ft ||ƒS(N( RRRRttruetZeroRR tfalseR(R titjteq((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyt_entryGs (t__name__t __module__t__doc__tpropertyR R RR(((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyRs (t DiagonalOfcB sDeZdZed„ƒZed„ƒZed„ƒZd„ZRS(s™DiagonalOf(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 cC s |jdS(Ni(R(R ((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyR R cC s½|jj\}}|jr6|jr6t||ƒ}nz|jrR|j rR|}n^|jrn|j rn|}nB||krƒ|}n-yt||ƒ}Wntk rŻd}nX|tjfS(N(R R RRRRRtOne(R RRR((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyR ‚s      cC s |jdS(Ni(R (R ((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyR”scC s|j||fS(N(R (R RR((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyR˜s(RRRR R R RR(((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyR!Us +N( t __future__RRtsympy.matrices.expressionsRt sympy.coreRRRt(sympy.functions.special.tensor_functionsRRR!(((sBlib/python2.7/site-packages/sympy/matrices/expressions/diagonal.pyts M