def check_random_complex_exact(self):
n = 20
a = random([n, n]) + 1j * random([n, n])
for i in range(n):
a[i, i] = 20 * (0.1 + a[i, i])
for i in range(2):
b = random([n, 3])
x = lstsq(a, b)[0]
assert_array_almost_equal(numpy.dot(a, x), b)
def check_random_overdet_large(self):
# bug report: Nils Wagner
n = 200
a = random([n, 2])
for i in range(2):
a[i, i] = 20 * (0.1 + a[i, i])
b = random([n, 3])
x = lstsq(a, b)[0]
assert_array_almost_equal(x, direct_lstsq(a, b))
def check_random_complex_overdet(self):
n = 20
m = 15
a = random([n, m]) + 1j * random([n, m])
for i in range(m):
a[i, i] = 20 * (0.1 + a[i, i])
for i in range(2):
b = random([n, 3])
x, res, r, s = lstsq(a, b)
assert r == m, "unexpected efficient rank"
# XXX: check definition of res
assert_array_almost_equal(x, direct_lstsq(a, b, 1))
def test_lstsq(self):
from linalg import lstsq
shapes = ([10, 3], [3, 10])
for shape in shapes:
for b2d in True, False:
A = (np.random.rand(np.prod(shape))-.5).reshape(shape)
if b2d:
b = np.random.randn(shape[0],2)
else:
b = np.random.randn(shape[0])
x1, residuals1, rank1, s1 = lstsq(A, b)
x2, residuals2, rank2, s2 = np.linalg.lstsq(A, b)
#print(x1.r)
#print(x2)
#print(residuals1.r)
#print(residuals2)
self.assertTrue(np.max(np.abs(x1.r-x2)) < 1e-14)
if len(residuals2) > 0:
self.assertTrue(np.max(np.abs(residuals1.r-residuals2)) < 1e-14)
def test_lstsq(self):
from linalg import lstsq
shapes = ([10, 3], [3, 10])
for shape in shapes:
for b2d in True, False:
A = (np.random.rand(np.prod(shape))-.5).reshape(shape)
if b2d:
b = np.random.randn(shape[0],2)
else:
b = np.random.randn(shape[0])
x1, residuals1, rank1, s1 = lstsq(A, b)
x2, residuals2, rank2, s2 = np.linalg.lstsq(A, b)
#print x1.r
#print x2
#print residuals1.r
#print residuals2
self.assertTrue(np.max(np.abs(x1.r-x2)) < 1e-14)
if len(residuals2) > 0:
self.assertTrue(np.max(np.abs(residuals1.r-residuals2)) < 1e-14)
def check_simple_underdet(self):
a = [[1, 2, 3], [4, 5, 6]]
b = [1, 2]
x, res, r, s = lstsq(a, b)
# XXX: need independent check
assert_array_almost_equal(x, [[-0.05555556], [0.11111111], [0.27777778]])
def check_simple_overdet(self):
a = [[1, 2], [4, 5], [3, 4]]
b = [1, 2, 3]
x, res, r, s = lstsq(a, b)
# XXX: check defintion of res
assert_array_almost_equal(x, direct_lstsq(a, b))
def check_simple_exact(self):
a = [[1, 20], [-30, 4]]
for b in ([[1, 0], [0, 1]], [1, 0], [[2, 1], [-30, 4]]):
x = lstsq(a, b)[0]
assert_array_almost_equal(numpy.dot(a, x), b)
