def test_inv_nonsquare(use_numpy_inv):
use_numpy = linalg._USE_NUMPY_LINALG_INV
linalg._USE_NUMPY_LINALG_INV = use_numpy_inv
with pytest.raises(np.linalg.LinAlgError):
try:
linalg.inv(np.empty((1, 2)))
finally:
linalg._USE_NUMPY_LINALG_INV = use_numpy
def test_inv_nan(use_numpy_inv):
use_numpy = linalg._USE_NUMPY_LINALG_INV
linalg._USE_NUMPY_LINALG_INV = use_numpy_inv
arr = np.array([[1.0, 1.0, -1.], [2.0, -2.1, 4.0], [-1.0, np.nan, 1.0]])
with pytest.raises(np.linalg.LinAlgError):
try:
linalg.inv(arr)
finally:
linalg._USE_NUMPY_LINALG_INV = use_numpy
def test_inv_singular(use_numpy_inv):
use_numpy = linalg._USE_NUMPY_LINALG_INV
linalg._USE_NUMPY_LINALG_INV = use_numpy_inv
arr = np.array([[1.0, 1.0], [2.0, 2.0]])
with pytest.raises(np.linalg.LinAlgError):
try:
linalg.inv(arr)
finally:
linalg._USE_NUMPY_LINALG_INV = use_numpy
def test_inv_high_dim():
use_numpy = linalg._USE_NUMPY_LINALG_INV
linalg._USE_NUMPY_LINALG_INV = False
arr = np.random.random((4, 4, 4))
with pytest.raises(np.linalg.LinAlgError):
try:
linalg.inv(arr)
finally:
linalg._USE_NUMPY_LINALG_INV = use_numpy
def test_inv_order2():
feps = 1000 * np.finfo(np.float64).eps
# Generate a 2D rotation/scale/skew matrix + some random noise.
# The reason for this complicated approach is to avoid creating
# singular matrices.
angle1 = 360 * np.random.random()
angle2 = angle1 + 50 * (np.random.random() - 0.5)
scale1 = 0.7 + 0.6 * np.random.random()
scale2 = 0.7 + 0.6 * np.random.random()
a = linearfit.build_fit_matrix((angle1, angle2), (scale1, scale2))
# invert using numpy.linalg:
use_numpy = linalg._USE_NUMPY_LINALG_INV
linalg._USE_NUMPY_LINALG_INV = True
try:
x = linalg.inv(a)
r = np.identity(2) - np.dot(a, x)
# Use Morris Newman's formula to asses the quality of the inversion
# (see https://nvlpubs.nist.gov/nistpubs/jres/78B/jresv78Bn2p65_A1b.pdf
# January 3, 1974).
err = 2.0 * np.abs(np.dot(x, r)).max() / (1.0 - np.abs(r).max())
assert err < feps
finally:
linalg._USE_NUMPY_LINALG_INV = use_numpy
# invert using tweakwcs.linalg:
linalg._USE_NUMPY_LINALG_INV = False
try:
x = linalg.inv(a)
r = np.identity(2) - np.dot(a, x)
# Use Morris Newman's formula to asses the quality of the inversion
# (see https://nvlpubs.nist.gov/nistpubs/jres/78B/jresv78Bn2p65_A1b.pdf
# January 3, 1974).
err = 2.0 * np.abs(np.dot(x, r)).max() / (1.0 - np.abs(r).max())
assert err < feps
finally:
linalg._USE_NUMPY_LINALG_INV = use_numpy
