def eval_power(parse_result):
"""
Exponentiate a list of numbers, right to left. Can also have minus signs
interspersed, which means to flip the sign of the exponent.
Arguments:
parse_result: A list of numbers and "-" strings, to be read as exponentiated
[a, b, c, d] = a^b^c^d
[a, "-", c, d] = a^(-(c^d))
Usage
=====
>>> MathExpression.eval_power([4,3,2]) # Evaluate 4^3^2
262144
>>> MathExpression.eval_power([2,"-",2,2]) # Evaluate 2^(-(2^2))
0.0625
"""
data = parse_result[:]
result = data.pop()
while data:
# Result contains the current exponent
working = data.pop()
if isinstance(working, six.text_type) and working == "-":
result = -result
else:
# working is base, result is exponent
result = robust_pow(working, result)
return result
def __rpow__(self, other):
if is_numberlike_array(self) and isinstance(other, Number):
return robust_pow(other, self.item())
if isinstance(other, Number):
raise ShapeError("Cannot raise a scalar to power of a {self.shape_name}."
.format(self=self))
raise TypeError("Cannot raise {type} to power of {self.shape_name}."
.format(type=type(other), self=self))
def __pow__(self, other):
"""
Matrix powers for MathArrays of dimension 0 and 2.
"""
if is_numberlike_array(self):
if isinstance(other, Number):
return robust_pow(self.item(), other)
elif isinstance(other, MathArray):
return other.__rpow__(self.item())
else:
raise TypeError("Cannot raise a scalar to a {type} power".format(type=type(other)))
elif not self.ndim == 2:
raise ShapeError("Cannot raise a {self.shape_name} to powers.".format(
self=self))
elif not is_square(self):
raise ShapeError("Cannot raise a non-square matrix to powers.")
# Henceforth, self is a square matrix.
if isinstance(other, Number):
exponent = other
elif isinstance(other, MathArray):
if is_numberlike_array(other):
exponent = other.item()
else:
raise ShapeError("Cannot raise a matrix to {other.shape_name} powers.".format(
other=other))
else:
raise TypeError("Cannot raise matrix to power of type {type}.".format(
type=type(other)))
# Henceforth:
# - self is a square matrix, AND
# - exponent is a number
integer_like = (isinstance(exponent, int) or
isinstance(exponent, float) and exponent.is_integer())
if not integer_like:
raise MathArrayError("Cannot raise a matrix to non-integer powers.")
elif exponent < 0 and not MathArray._negative_powers:
raise MathArrayError('Negative matrix powers have been disabled.')
else:
# just in case it had been an integer-like float
exponent = int(exponent)
try:
return np.linalg.matrix_power(self, exponent)
except np.linalg.linalg.LinAlgError as error:
if error.message.startswith('Singular'):
raise MathArrayError('Cannot raise singular matrix to negative powers.')
else:
# Not sure what could cause this...
raise # pragma: no cover