*h nSSKJr SSKJrJr SSKJr SSKJrJ r SSK J r SSK J r Jr "SS \5rg ) ) MatrixExpr) FunctionClassLambda)Dummy)_sympifysympify)Matrix)reimc^^\rSrSrSrU4Sjr\S5r\S5rSr Sr Sr S r U=r $) FunctionMatrix a*Represents a matrix using a function (``Lambda``) which gives outputs according to the coordinates of each matrix entries. Parameters ========== rows : nonnegative integer. Can be symbolic. cols : nonnegative integer. Can be symbolic. lamda : Function, Lambda or str If it is a SymPy ``Function`` or ``Lambda`` instance, it should be able to accept two arguments which represents the matrix coordinates. If it is a pure string containing Python ``lambda`` semantics, it is interpreted by the SymPy parser and casted into a SymPy ``Lambda`` instance. Examples ======== Creating a ``FunctionMatrix`` from ``Lambda``: >>> from sympy import FunctionMatrix, symbols, Lambda, MatPow >>> i, j, n, m = symbols('i,j,n,m') >>> FunctionMatrix(n, m, Lambda((i, j), i + j)) FunctionMatrix(n, m, Lambda((i, j), i + j)) Creating a ``FunctionMatrix`` from a SymPy function: >>> from sympy import KroneckerDelta >>> X = FunctionMatrix(3, 3, KroneckerDelta) >>> X.as_explicit() Matrix([ [1, 0, 0], [0, 1, 0], [0, 0, 1]]) Creating a ``FunctionMatrix`` from a SymPy undefined function: >>> from sympy import Function >>> f = Function('f') >>> X = FunctionMatrix(3, 3, f) >>> X.as_explicit() Matrix([ [f(0, 0), f(0, 1), f(0, 2)], [f(1, 0), f(1, 1), f(1, 2)], [f(2, 0), f(2, 1), f(2, 2)]]) Creating a ``FunctionMatrix`` from Python ``lambda``: >>> FunctionMatrix(n, m, 'lambda i, j: i + j') FunctionMatrix(n, m, Lambda((i, j), i + j)) Example of lazy evaluation of matrix product: >>> Y = FunctionMatrix(1000, 1000, Lambda((i, j), i + j)) >>> isinstance(Y*Y, MatPow) # this is an expression object True >>> (Y**2)[10,10] # So this is evaluated lazily 342923500 Notes ===== This class provides an alternative way to represent an extremely dense matrix with entries in some form of a sequence, in a most sparse way. c>[U5[U5p!URU5 URU5 [U5n[U[[ 45(d[ SRU55eSUR;a[ SRU55e[U[ 5(d([S5[S5pT[ XE4U"XE55n[TU]-XX#5$)Nz4{} 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 b/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/matrices/expressions/funcmatrix.pyrFunctionMatrix.__new__Psd^Xd^d t t%-!899F   EKK :AA%HJ J%((:uSzqA65;/Ews$66c URSS$)Nrrargsselfs r shapeFunctionMatrix.shapeesyy1~r"c URS$)Nrr$r&s r rFunctionMatrix.lamdaisyy|r"c $URX5$N)r)r'rrkwargss r _entryFunctionMatrix._entrymszz!r"cdSSKJn SSKJn U"U5R U5R 5$)Nr)Trace)Sum) sympy.matrices.expressions.tracer2sympy.concrete.summationsr3rewritedoit)r'r2r3s r _eval_traceFunctionMatrix._eval_traceps&:1T{""3',,..r"cR[[U55[[U554$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/r8r;__static_attributes__ __classcell__)rs@r rr sKEL7* / 44r"rN)matexprrsympy.core.functionrrsympy.core.symbolrsympy.core.sympifyrr sympy.matricesr $sympy.functions.elementary.complexesr r rr=r"r rLs%5#0!7m4Zm4r"