def test_pseudo_inverse():
"Tests of the pseudo-inverse"
# Numerical version of the pseudo-inverse:
pinv_num = core.wrap_array_func(numpy.linalg.pinv)
##########
# Full rank rectangular matrix:
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))],
[1, -3.1]])
# Numerical and package (analytical) pseudo-inverses: they must be
# the same:
rcond = 1e-8 # Test of the second argument to pinv()
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
##########
# Example with a non-full rank rectangular matrix:
vector = [ufloat((10, 1)), -3.1, 11]
m = unumpy.matrix([vector, vector])
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
##########
# Example with a non-full-rank square matrix:
m = unumpy.matrix([[ufloat((10, 1)), 0], [3, 0]])
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
def test_pseudo_inverse():
"Tests of the pseudo-inverse"
# Numerical version of the pseudo-inverse:
pinv_num = core.wrap_array_func(numpy.linalg.pinv)
##########
# Full rank rectangular matrix:
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))],
[1, -3.1]])
# Numerical and package (analytical) pseudo-inverses: they must be
# the same:
rcond = 1e-8 # Test of the second argument to pinv()
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
##########
# Example with a non-full rank rectangular matrix:
vector = [ufloat((10, 1)), -3.1, 11]
m = unumpy.matrix([vector, vector])
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
##########
# Example with a non-full-rank square matrix:
m = unumpy.matrix([[ufloat((10, 1)), 0], [3, 0]])
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
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]))
