def _derivatives_close(x, y):
"""
Returns True iff the AffineScalarFunc objects x and y have
derivatives that are close to each other (they must depend
on the same variables).
"""
# x and y must depend on the same variables:
if set(x.derivatives) != set(y.derivatives):
return False # Not the same variables
return all(_numbers_close(x.derivatives[var], y.derivatives[var])
for var in x.derivatives)
def _derivatives_close(x, y):
"""
Returns True iff the AffineScalarFunc objects x and y have
derivatives that are close to each other (they must depend
on the same variables).
"""
# x and y must depend on the same variables:
if set(x.derivatives) != set(y.derivatives):
return False # Not the same variables
return all(_numbers_close(x.derivatives[var], y.derivatives[var])
for var in x.derivatives)
def test_inverse():
"Tests of the matrix inverse"
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))]])
m_nominal_values = unumpy.nominal_values(m)
# "Regular" inverse matrix, when uncertainties are not taken
# into account:
m_no_uncert_inv = m_nominal_values.I
# The matrix inversion should not yield numbers with uncertainties:
assert m_no_uncert_inv.dtype == numpy.dtype(float)
# Inverse with uncertainties:
m_inv_uncert = m.I # AffineScalarFunc elements
# The inverse contains uncertainties: it must support custom
# operations on matrices with uncertainties:
assert isinstance(m_inv_uncert, unumpy.matrix)
assert type(m_inv_uncert[0, 0]) == uncertainties.AffineScalarFunc
# Checks of the numerical values: the diagonal elements of the
# inverse should be the inverses of the diagonal elements of
# m (because we started with a triangular matrix):
assert _numbers_close(1/m_nominal_values[0, 0],
m_inv_uncert[0, 0].nominal_value), "Wrong value"
assert _numbers_close(1/m_nominal_values[1, 1],
m_inv_uncert[1, 1].nominal_value), "Wrong value"
####################
# Checks of the covariances between elements:
x = ufloat((10, 1))
m = unumpy.matrix([[x, x],
[0, 3+2*x]])
m_inverse = m.I
# Check of the properties of the inverse:
m_double_inverse = m_inverse.I
# The initial matrix should be recovered, including its
# derivatives, which define covariances:
assert _numbers_close(m_double_inverse[0, 0].nominal_value,
m[0, 0].nominal_value)
assert _numbers_close(m_double_inverse[0, 0].std_dev(),
m[0, 0].std_dev())
assert matrices_close(m_double_inverse, m)
# Partial test:
assert _derivatives_close(m_double_inverse[0, 0], m[0, 0])
assert _derivatives_close(m_double_inverse[1, 1], m[1, 1])
####################
# Tests of covariances during the inversion:
# There are correlations if both the next two derivatives are
# not zero:
assert m_inverse[0, 0].derivatives[x]
assert m_inverse[0, 1].derivatives[x]
# Correlations between m and m_inverse should create a perfect
# inversion:
assert matrices_close(m * m_inverse, numpy.eye(m.shape[0]))
def test_inverse():
"Tests of the matrix inverse"
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))]])
m_nominal_values = unumpy.nominal_values(m)
# "Regular" inverse matrix, when uncertainties are not taken
# into account:
m_no_uncert_inv = m_nominal_values.I
# The matrix inversion should not yield numbers with uncertainties:
assert m_no_uncert_inv.dtype == numpy.dtype(float)
# Inverse with uncertainties:
m_inv_uncert = m.I # AffineScalarFunc elements
# The inverse contains uncertainties: it must support custom
# operations on matrices with uncertainties:
assert isinstance(m_inv_uncert, unumpy.matrix)
assert type(m_inv_uncert[0, 0]) == uncertainties.AffineScalarFunc
# Checks of the numerical values: the diagonal elements of the
# inverse should be the inverses of the diagonal elements of
# m (because we started with a triangular matrix):
assert _numbers_close(1/m_nominal_values[0, 0],
m_inv_uncert[0, 0].nominal_value), "Wrong value"
assert _numbers_close(1/m_nominal_values[1, 1],
m_inv_uncert[1, 1].nominal_value), "Wrong value"
####################
# Checks of the covariances between elements:
x = ufloat((10, 1))
m = unumpy.matrix([[x, x],
[0, 3+2*x]])
m_inverse = m.I
# Check of the properties of the inverse:
m_double_inverse = m_inverse.I
# The initial matrix should be recovered, including its
# derivatives, which define covariances:
assert _numbers_close(m_double_inverse[0, 0].nominal_value,
m[0, 0].nominal_value)
assert _numbers_close(m_double_inverse[0, 0].std_dev(),
m[0, 0].std_dev())
assert matrices_close(m_double_inverse, m)
# Partial test:
assert _derivatives_close(m_double_inverse[0, 0], m[0, 0])
assert _derivatives_close(m_double_inverse[1, 1], m[1, 1])
####################
# Tests of covariances during the inversion:
# There are correlations if both the next two derivatives are
# not zero:
assert m_inverse[0, 0].derivatives[x]
assert m_inverse[0, 1].derivatives[x]
# Correlations between m and m_inverse should create a perfect
# inversion:
assert matrices_close(m * m_inverse, numpy.eye(m.shape[0]))
