def test_dot_as_in_kalman(self):
# a specific test for a problem that occured in KalmanFilter.bayes()
A = array([[1., -0.5], [1., 0.]])
R = array([[200., 0.], [0., 200.]])
R = nw.dot(nw.dot(A, R), A.T)
R_exp = array([[250., 200.], [200., 200.]])
self.assertApproxEqual(R, R_exp)
def test_dotmv_dimensions(self):
A = array([[1., 2.]])
B = array([[1., 2.],
[3., 4.],
[5., 6.]])
# while AT.T = A, its internal is dirrefent and sometimes causes problems. we try to detect them
AT = array([[1.],
[2.]])
BT = array([[1., 3., 5.],
[2., 4., 6.]])
x = array([-123., -345.])
self.assertApproxEqual(nw.dot(A, x), dot(A, x)) # second dot call is from numpy
self.assertApproxEqual(nw.dot(B, x), dot(B, x))
self.assertApproxEqual(nw.dot(AT.T, x), dot(AT.T, x))
self.assertApproxEqual(nw.dot(BT.T, x), dot(BT.T, x))
def test_dot(self):
# test data
A = array([[1., 2.], [3., -4.]])
B = array([[2., 1.], [3., 2.]])
x = array([-4., -7.])
# precomputed restults
AB = array([[ 8., 5.], [-6., -5.]])
BA = array([[ 5., 0.], [ 9., -2.]])
Ax = array([-18., 16.])
Bx = array([-15., -26.])
# do the check!
for (left, right, exp) in [(A, B, AB), (B, A, BA), (A, x, Ax), (B, x, Bx)]:
res = nw.dot(left, right)
self.assertApproxEqual(res, exp)
def test_dot_transposed(self):
# transposed optimised dot made problems in the past. Test it!
# source data
A = array([[1., -2.], [3., 4.]])
B = array([[0.5, 1.], [-1., 2.]])
C = array([[-2.]])
x = array([-7., -6.])
y = array([-.5])
# precomputed results
Atx = array([-25., -10.])
Atxt = array([-25., -10.])
AtB = array([[-2.5, 7.], [-5., 6.]])
ABt = array([[-1.5, -5.], [5.5, 5.]])
AtBt = array([[3.5, 5.], [3., 10.]])
Cty = array([1.])
# do the test!
for (left, right, exp) in [(A.T, x, Atx), (A.T, x.T, Atxt), (A.T, B, AtB),
(A, B.T, ABt), (A.T, B.T, AtBt), (C.T, y, Cty)]:
res = nw.dot(left, right)
self.assertApproxEqual(res, exp)
def test_dot_dimensions(self):
"""Test that dot(a, b) works with different combinations of matrix dimensions"""
A = array([[1., 2.]])
B = array([[1., 2., 3.],
[4., 5., 6.]])
self.assertApproxEqual(nw.dot(A, B), dot(A, B)) # second dot call is from NumPy
self.assertApproxEqual(nw.dot(B.T, A.T), dot(B.T, A.T))
with self.assertRaises(ValueError):
nw.dot(A.T, B.T)
with self.assertRaises(ValueError):
nw.dot(B, A)
C = array([[1., 2.],
[3., 4.],
[5., 6.]])
D = array([[1.],
[2.]])
self.assertApproxEqual(nw.dot(C, D), dot(C, D))
self.assertApproxEqual(nw.dot(D.T, C.T), dot(D.T, C.T))
with self.assertRaises(ValueError):
nw.dot(C.T, D.T)
with self.assertRaises(ValueError):
nw.dot(D, C)
# test all (transposed, smaller-dimension first) combinations
self.assertApproxEqual(nw.dot(D.T, B), dot(D.T, B))
self.assertApproxEqual(nw.dot(B.T, D), dot(B.T, D))
self.assertApproxEqual(nw.dot(A, C.T), dot(A, C.T))
self.assertApproxEqual(nw.dot(C, A.T), dot(C, A.T))
with self.assertRaises(ValueError):
nw.dot(D, B.T)
with self.assertRaises(ValueError):
nw.dot(B, D.T)
with self.assertRaises(ValueError):
nw.dot(A.T, C)
with self.assertRaises(ValueError):
nw.dot(C.T, A)
