U L?h @shddlmZddlmZmZddlmZddlmZm Z ddl m Z ddl m Z mZGdd d eZd S) ) MatrixExpr) FunctionClassLambda)Dummy)_sympifysympify)Matrix)reimcsPeZdZdZfddZeddZeddZdd Zd d Z d d Z Z 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. cst|t|}}||||t|}t|ttfsJtd|d|jkrbtd|t|tst dt d}}t||f|||}t ||||S)Nz4{} should be compatible with SymPy function classes.z({} should be able to accept 2 arguments.ij) rZ _check_dimr isinstancerr ValueErrorformatnargsrsuper__new__)clsrowscolslamdarr __class__W/var/www/html/venv/lib/python3.8/site-packages/sympy/matrices/expressions/funcmatrix.pyrPs$    zFunctionMatrix.__new__cCs|jddS)Nrr argsselfrrrshapeeszFunctionMatrix.shapecCs |jdS)Nr rr rrrriszFunctionMatrix.lamdacKs |||SN)r)r!rrkwargsrrr_entrymszFunctionMatrix._entrycCs*ddlm}ddlm}|||S)Nr)Trace)Sum)Z sympy.matrices.expressions.tracer&Zsympy.concrete.summationsr'ZrewriteZdoit)r!r&r'rrr _eval_traceps  zFunctionMatrix._eval_tracecCstt|tt|fSr#)r r r r rrr_eval_as_real_imagusz!FunctionMatrix._eval_as_real_imag) __name__ __module__ __qualname____doc__rpropertyr"rr%r(r) __classcell__rrrrr sF   r N)ZmatexprrZsympy.core.functionrrZsympy.core.symbolrZsympy.core.sympifyrrZsympy.matricesr Z$sympy.functions.elementary.complexesr r r rrrrs