def matrices_close(m1, m2, precision=1e-4):
"""
Returns True iff m1 and m2 are almost equal, where elements
can be either floats or AffineScalarFunc objects.
m1, m2 -- NumPy matrices.
precision -- precision passed through to
uncertainties.test_uncertainties._numbers_close().
"""
# ! numpy.allclose() is similar to this function, but does not
# work on arrays that contain numbers with uncertainties, because
# of the isinf() function.
for (elmt1, elmt2) in zip(m1.flat, m2.flat):
# For a simpler comparison, both elements are
# converted to AffineScalarFunc objects:
elmt1 = to_affine_scalar(elmt1)
elmt2 = to_affine_scalar(elmt2)
if not _numbers_close(elmt1.nominal_value,
elmt2.nominal_value, precision):
return False
if not _numbers_close(elmt1.std_dev(),
elmt2.std_dev(), precision):
return False
return True
def frexp(x):
"""
Version of frexp that works for numbers with uncertainty, and also
for regular numbers.
"""
# The code below is inspired by wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
aff_func = to_affine_scalar(x)
if aff_func.derivatives:
result = math.frexp(aff_func.nominal_value)
# With frexp(x) = (m, e), dm/dx = 1/(2**e):
factor = 1 / (2**result[1])
return (
AffineScalarFunc(
result[0],
# Chain rule:
dict((var, factor * deriv)
for (var, deriv) in aff_func.derivatives.iteritems())),
# The exponent is an integer and is supposed to be
# continuous (small errors):
result[1])
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
return math.frexp(x)
def ldexp(x, y):
# The code below is inspired by wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
# Another approach would be to add an additional argument to
# wrap() so that some arguments are automatically
# considered as constants.
aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp
if aff_func.derivatives:
factor = 2**y
return AffineScalarFunc(
math.ldexp(aff_func.nominal_value, y),
# Chain rule:
dict((var, factor * deriv)
for (var, deriv) in aff_func.derivatives.iteritems()))
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
# aff_func.nominal_value is not passed instead of x, because
# we do not have to care about the type of the return value of
# math.ldexp, this way (aff_func.nominal_value might be the
# value of x coerced to a difference type [int->float, for
# instance]):
return math.ldexp(x, y)
def frexp(x):
"""
Version of frexp that works for numbers with uncertainty, and also
for regular numbers.
"""
# The code below is inspired by wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
aff_func = to_affine_scalar(x)
if aff_func.derivatives:
result = math.frexp(aff_func.nominal_value)
# With frexp(x) = (m, e), dm/dx = 1/(2**e):
factor = 1/(2**result[1])
return (
AffineScalarFunc(
result[0],
# Chain rule:
dict((var, factor*deriv)
for (var, deriv) in aff_func.derivatives.iteritems())),
# The exponent is an integer and is supposed to be
# continuous (small errors):
result[1])
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
return math.frexp(x)
def ldexp(x, y):
# The code below is inspired by wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
# Another approach would be to add an additional argument to
# wrap() so that some arguments are automatically
# considered as constants.
aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp
if aff_func.derivatives:
factor = 2**y
return AffineScalarFunc(
math.ldexp(aff_func.nominal_value, y),
# Chain rule:
dict((var, factor*deriv)
for (var, deriv) in aff_func.derivatives.iteritems()))
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
# aff_func.nominal_value is not passed instead of x, because
# we do not have to care about the type of the return value of
# math.ldexp, this way (aff_func.nominal_value might be the
# value of x coerced to a difference type [int->float, for
# instance]):
return math.ldexp(x, y)
def modf(x):
"""
Version of modf that works for numbers with uncertainty, and also
for regular numbers.
"""
# The code below is inspired by wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
aff_func = to_affine_scalar(x)
(frac_part, int_part) = math.modf(aff_func.nominal_value)
if aff_func.derivatives:
# The derivative of the fractional part is simply 1: the
# derivatives of modf(x)[0] are the derivatives of x:
return (AffineScalarFunc(frac_part, aff_func.derivatives), int_part)
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
return (frac_part, int_part)
def modf(x):
"""
Version of modf that works for numbers with uncertainty, and also
for regular numbers.
"""
# The code below is inspired by wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
aff_func = to_affine_scalar(x)
(frac_part, int_part) = math.modf(aff_func.nominal_value)
if aff_func.derivatives:
# The derivative of the fractional part is simply 1: the
# derivatives of modf(x)[0] are the derivatives of x:
return (AffineScalarFunc(frac_part, aff_func.derivatives), int_part)
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
return (frac_part, int_part)
