Otj vddlmZddlmZmZddlmZddlmZm Z ddl m Z ddl m Z mZGdd eZd S) ) MatrixExpr) FunctionClassLambda)Dummy)_sympifysympify)Matrix)reimc`eZdZdZfdZedZedZdZdZ dZ xZ S)FunctionMatrixaRepresents 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. cjt|t|}}||||t|}t|tt fs"t d|d|jvr"t d|t|t s:tdtd}}t ||f|||}t ||||S)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 c/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/matrices/expressions/funcmatrix.pyrzFunctionMatrix.__new__Psd^^Xd^^d t t%-!899 F    EK  :AA%HHJJ J%(( 0::uSzzqAAq655A;;//EwwsD$666c |jddS)Nrrargsselfs rshapezFunctionMatrix.shapeesy1~r c|jdS)Nrr"r$s rrzFunctionMatrix.lamdaisy|r c .|||SN)r)r%rrkwargss r_entryzFunctionMatrix._entrymszz!Qr czddlm}ddlm}|||S)Nr)Trace)Sum) sympy.matrices.expressions.tracer-sympy.concrete.summationsr.rewritedoit)r%r-r.s r _eval_tracezFunctionMatrix._eval_tracepsN::::::111111uT{{""3'',,...r crtt|tt|fSr))r r r r$s r_eval_as_real_imagz!FunctionMatrix._eval_as_real_imagus)6$<<  "VD\\"2"233r ) __name__ __module__ __qualname____doc__rpropertyr&rr+r3r5 __classcell__)rs@rrr sEEL77777*XX   /// 4444444r rN)matexprrsympy.core.functionrrsympy.core.symbolrsympy.core.sympifyrr sympy.matricesr $sympy.functions.elementary.complexesr r rr rrCs55555555######00000000!!!!!!77777777m4m4m4m4m4Zm4m4m4m4m4r