*hSSKJr SSKJr SSKJrJrJr SSKJ r SSK J r "SS\5r "SS \5r "S S \5rS rg ))_sympify) MatrixExpr)SEqGe)Mul)KroneckerDeltacR\rSrSrSr\"S5r\"S5r\S5rSr Sr g) DiagonalMatrix aDiagonalMatrix(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 c URS$Nrargsselfs `/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/matrices/expressions/diagonal.pyDiagonalMatrix.2  ! c.URR$N)argshapers rrr4s $((..rchURupUR(aUR(a [X5nU$UR(aUR(dUnU$UR(aUR(dUnU$X:XaUnU$[X5nU$![a SnU$f=fr)r is_Integermin TypeErrorrrcms rdiagonal_lengthDiagonalMatrix.diagonal_length6szz < ! 177]66Mxx~nQ222rN __name__ __module__ __qualname____firstlineno____doc__propertyrrr$r.__static_attributes__r0rrr r s7'P , -C 0 1E " 3rr cP\rSrSrSr\"S5r\S5r\S5rSr Sr g) DiagonalOfVaDiagonalOf(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 c URS$rrrs rrDiagonalOf.rrcURRupUR(aUR(a [X5nO^UR(aUR(dUnO9UR(aUR(dUnOX:XaUnO [X5nU[ R 4$![a SnN f=fr)rrrrrrOner s rrDiagonalOf.shapesxx~~ <>\\((A88F\\((A88F 6 nQ* *F rcU$rr0rs r_eval_transposeDiagMatrix._eval_transposes rcZSSKJn U"[URR 556$)Nr)diag)sympy.matrices.denser\listrM as_explicit)rr\s rr_DiagMatrix.as_explicits"-T$,,224566rc *SSKJnJn SSKJn SSKJn SSKJn SSK J n URnU"URU55(aU$[X5(aSU"[UR55n [!U RS5H n XXU 4'M [#U5"U 5$UR$(aUR&V s/sHoR((dMU PM n n UR&V s/sH oU ;dM U PM n n U (aM[*R,"U 5[/UR-U 5R155R15-$[X5(a UR2n[/U5$s sn fs sn f)Nr)askQ)MatMul) Transpose)eye) MatrixBase)sympy.assumptionsrbrc!sympy.matrices.expressions.matmulrd$sympy.matrices.expressions.transposerer]rfsympy.matrices.matrixbasergrMdiagonal isinstancemaxrrangetype is_MatMulr is_MatrixrfromiterrFdoitr)rhintsrbrcrdrerfrgrOretr*rmatricesscalarss rrtDiagMatrix.doits%,<B,8 qzz&! " "M f ) )c&,,'(C399Q<("IqD )<$ $   '-{{D{mm{HD&,kkIks5HskGI||G,Z8Q8V8V8X-Y-^-^-``` f ( (ZZF&!! EIs F %F ; FFr0N) r2r3r4r5r6rJr7rr.rYr_rtr8r0rrrFrFs4 7"rrFc4[U5R5$r)rFrt)rOs rdiagonalize_vectorr{s f  " " $$rN)sympy.core.sympifyrsympy.matrices.expressionsr sympy.corerrrsympy.core.mulr(sympy.functions.special.tensor_functionsr r r:rFr{r0rrrsG'1 CJ3ZJ3ZD/D/N;";"|%r