+ i p^RIHt^RIHtHt^RIHt^RIHtH t ^RI H t ^RI H t Ht!RR]4tR #) ) MatrixExpr) FunctionClassLambda)Dummy)_sympifysympify)Matrix)reimchaa]tRt^ toRtV3Rlt]R4t]R4tRt Rt Rt Rt Vt V;t#) FunctionMatrixa*Represents a matrix using a function (``Lambda``) which gives outputs according to the coordinates of each matrix entries. Parameters ========== rows : nonnegative integer. Can be symbolic. cols : nonnegative integer. Can be symbolic. lamda : Function, Lambda or str If it is a SymPy ``Function`` or ``Lambda`` instance, it should be able to accept two arguments which represents the matrix coordinates. If it is a pure string containing Python ``lambda`` semantics, it is interpreted by the SymPy parser and casted into a SymPy ``Lambda`` instance. Examples ======== Creating a ``FunctionMatrix`` from ``Lambda``: >>> from sympy import FunctionMatrix, symbols, Lambda, MatPow >>> i, j, n, m = symbols('i,j,n,m') >>> FunctionMatrix(n, m, Lambda((i, j), i + j)) FunctionMatrix(n, m, Lambda((i, j), i + j)) Creating a ``FunctionMatrix`` from a SymPy function: >>> from sympy import KroneckerDelta >>> X = FunctionMatrix(3, 3, KroneckerDelta) >>> X.as_explicit() Matrix([ [1, 0, 0], [0, 1, 0], [0, 0, 1]]) Creating a ``FunctionMatrix`` from a SymPy undefined function: >>> from sympy import Function >>> f = Function('f') >>> X = FunctionMatrix(3, 3, f) >>> X.as_explicit() Matrix([ [f(0, 0), f(0, 1), f(0, 2)], [f(1, 0), f(1, 1), f(1, 2)], [f(2, 0), f(2, 1), f(2, 2)]]) Creating a ``FunctionMatrix`` from Python ``lambda``: >>> FunctionMatrix(n, m, 'lambda i, j: i + j') FunctionMatrix(n, m, Lambda((i, j), i + j)) Example of lazy evaluation of matrix product: >>> Y = FunctionMatrix(1000, 1000, Lambda((i, j), i + j)) >>> isinstance(Y*Y, MatPow) # this is an expression object True >>> (Y**2)[10,10] # So this is evaluated lazily 342923500 Notes ===== This class provides an alternative way to represent an extremely dense matrix with entries in some form of a sequence, in a most sparse way. c<\V4\V4r!VPV4VPV4\V4p\V\\ 34'g\ RPV44h^VP9d\ RPV44h\V\ 4'g)\R4\R4rT\ WE3V!WE44p\SV`-WW#4#)z4{} should be compatible with SymPy function classes.z({} should be able to accept 2 arguments.ij) r _check_dimr isinstancerr ValueErrorformatnargsrsuper__new__)clsrowscolslamdarr __class__s&&&& څ/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/matrices/expressions/funcmatrix.pyrFunctionMatrix.__new__Psd^Xd^d t t%-!899F   EKK :AA%HJ J%((:uSzqA65;/Ews$66c(VPR,#):Nargsselfs&rshapeFunctionMatrix.shapeesyy~rc(VP^,#)r"r#r%s&rrFunctionMatrix.lamdaisyy|rc $VPW4#N)r)r&rrkwargss&&&,r_entryFunctionMatrix._entrymszz!rcd^RIHp^RIHpV!V4P V4P 4#)r!)Trace)Sum) sympy.matrices.expressions.tracer1sympy.concrete.summationsr2rewritedoit)r&r1r2s& r _eval_traceFunctionMatrix._eval_traceps&:1T{""3',,..rcR\\V44\\V443#r,)r r r r%s&r_eval_as_real_imag!FunctionMatrix._eval_as_real_imagus6$< "VD\"233r)__name__ __module__ __qualname____firstlineno____doc__rpropertyr'rr.r7r:__static_attributes____classdictcell__ __classcell__)r __classdict__s@@rr r sMEL7* / 44rr N)matexprrsympy.core.functionrrsympy.core.symbolrsympy.core.sympifyrrsympy.matricesr $sympy.functions.elementary.complexesr r r r<rrrMs%5#0!7m4Zm4r