Source code for sympy.matrices.expressions.trace

from __future__ import print_function, division

from sympy import Basic, Expr, sympify, S
from sympy.matrices.matrices import MatrixBase
from .matexpr import ShapeError


[docs]class Trace(Expr): """Matrix Trace Represents the trace of a matrix expression. Examples ======== >>> from sympy import MatrixSymbol, Trace, eye >>> A = MatrixSymbol('A', 3, 3) >>> Trace(A) Trace(A) """ is_Trace = True is_commutative = True def __new__(cls, mat): mat = sympify(mat) if not mat.is_Matrix: raise TypeError("input to Trace, %s, is not a matrix" % str(mat)) if not mat.is_square: raise ShapeError("Trace of a non-square matrix") return Basic.__new__(cls, mat) def _eval_transpose(self): return self def _eval_derivative(self, v): from sympy.matrices.expressions.matexpr import _matrix_derivative return _matrix_derivative(self, v) def _eval_derivative_matrix_lines(self, x): r = self.args[0]._eval_derivative_matrix_lines(x) for lr in r: if lr.higher == 1: lr.higher *= lr.first * lr.second.T else: # This is not a matrix line: lr.higher *= Trace(lr.first * lr.second.T) lr.first = S.One lr.second = S.One return r @property def arg(self): return self.args[0] def doit(self, **kwargs): if kwargs.get('deep', True): arg = self.arg.doit(**kwargs) try: return arg._eval_trace() except (AttributeError, NotImplementedError): return Trace(arg) else: # _eval_trace would go too deep here if isinstance(self.arg, MatrixBase): return trace(self.arg) else: return Trace(self.arg) def _eval_rewrite_as_Sum(self, expr, **kwargs): from sympy import Sum, Dummy i = Dummy('i') return Sum(self.arg[i, i], (i, 0, self.arg.rows-1)).doit()
def trace(expr): """Trace of a Matrix. Sum of the diagonal elements. Examples ======== >>> from sympy import trace, Symbol, MatrixSymbol, pprint, eye >>> n = Symbol('n') >>> X = MatrixSymbol('X', n, n) # A square matrix >>> trace(2*X) 2*Trace(X) >>> trace(eye(3)) 3 """ return Trace(expr).doit()