o oÇ hÀ ã@shddlmZddlmZmZddlmZddlmZm Z ddl m Z ddl m Z mZGdd „d eƒZd S) é)Ú MatrixExpré)Ú FunctionClassÚLambda)ÚDummy)Ú_sympifyÚsympify)ÚMatrix)ÚreÚimcsPeZdZdZ‡fdd„Zedd„ƒZedd„ƒZdd „Zd d „Z d d „Z ‡Z S)ÚFunctionMatrixaöRepresents 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. cs¤t|ƒt|ƒ}}| |¡| |¡t|ƒ}t|ttfƒs%td |¡ƒ‚d|jvr1td |¡ƒ‚t|tƒsIt dƒt dƒ}}t||f|||ƒƒ}t ƒ  ||||¡S)Nz4{} should be compatible with SymPy function classes.éz({} should be able to accept 2 arguments.ÚiÚj) rÚ _check_dimrÚ isinstancerrÚ ValueErrorÚformatÚnargsrÚsuperÚ__new__)ÚclsÚrowsÚcolsÚlamdarr©Ú __class__©úy/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/matrices/expressions/funcmatrix.pyrPs"  þ ÿ zFunctionMatrix.__new__cCs|jdd…S)Nrr ©Úargs©ÚselfrrrÚshapeeszFunctionMatrix.shapecCs |jdS)Nr rr!rrrris zFunctionMatrix.lamdacKs | ||¡S©N)r)r"rrÚkwargsrrrÚ_entryms zFunctionMatrix._entrycCs*ddlm}ddlm}||ƒ |¡ ¡S)Nr)ÚTrace)ÚSum)Ú sympy.matrices.expressions.tracer'Úsympy.concrete.summationsr(ÚrewriteÚdoit)r"r'r(rrrÚ _eval_traceps  zFunctionMatrix._eval_tracecCstt|ƒƒtt|ƒƒfSr$)r r r r!rrrÚ_eval_as_real_imagusz!FunctionMatrix._eval_as_real_imag) Ú__name__Ú __module__Ú __qualname__Ú__doc__rÚpropertyr#rr&r-r.Ú __classcell__rrrrr s F  r N)ÚmatexprrÚsympy.core.functionrrÚsympy.core.symbolrÚsympy.core.sympifyrrÚsympy.matricesr Ú$sympy.functions.elementary.complexesr r r rrrrÚs