Source code for sympy.matrices.expressions.trace

from __future__ import print_function, division

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

[docs]class Trace(Expr): """Matrix Trace Represents the trace of a matrix expression. >>> from sympy import MatrixSymbol, Trace, eye >>> A = MatrixSymbol('A', 3, 3) >>> Trace(A) Trace(A) See Also: trace """ is_Trace = 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 import Dummy, MatrixExpr, Sum if not isinstance(v, MatrixExpr): return None t1 = Dummy("t_1") m = Dummy("m") n = Dummy("n") return MatrixExpr.from_index_summation( Sum(self.args[0][t1, t1].diff(v[m, n]), (t1, 0, self.args[0].shape[0]-1)), m ) @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): 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 >>> 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 See Also: Trace """ return Trace(expr).doit()