def test_kspace_precond_simple_cart(self):
# Check identity
mps_shape = [1, 1]
mps = np.ones(mps_shape, dtype=np.complex)
p = precond.kspace_precond(mps)
npt.assert_allclose(p, np.ones(mps_shape),
atol=1e-6, rtol=1e-6)
# Check scaling
mps_shape = [1, 3]
mps = np.ones(mps_shape, dtype=np.complex)
p = precond.kspace_precond(mps)
npt.assert_allclose(p, np.ones(mps_shape),
atol=1e-6, rtol=1e-6)
# Check 2d
mps_shape = [1, 3, 3]
mps = np.ones(mps_shape, dtype=np.complex)
p = precond.kspace_precond(mps)
npt.assert_allclose(p, np.ones(mps_shape),
atol=1e-6, rtol=1e-6)
# Check weights
mps_shape = [1, 3]
mps = np.ones(mps_shape, dtype=np.complex)
weights = np.array([1, 0, 1], dtype=np.complex)
p = precond.kspace_precond(mps, weights=weights)
npt.assert_allclose(p, [[1, 1, 1]],
atol=1e-6, rtol=1e-6)
def test_kspace_precond_simple_noncart(self):
# Check identity
mps_shape = [1, 1]
mps = np.ones(mps_shape, dtype=np.complex)
coord = np.array([[0.0]])
p = precond.kspace_precond(mps, coord=coord)
npt.assert_allclose(p, [[1.0]], atol=1, rtol=1e-1)
mps_shape = [1, 3]
mps = np.ones(mps_shape, dtype=np.complex)
coord = np.array([[0.0], [-1], [1]])
p = precond.kspace_precond(mps, coord=coord)
npt.assert_allclose(p, [[1.0, 1.0, 1.0]], atol=1, rtol=1e-1)
def test_kspace_precond_noncart(self):
n = 10
nc = 3
shape = [nc, n]
mps = sp.randn(shape, dtype=np.complex)
mps /= np.linalg.norm(mps, axis=0, keepdims=True)
coord = sp.randn([n, 1], dtype=np.float)
A = linop.Sense(mps, coord=coord)
AAH = np.zeros((nc, n, nc, n), np.complex)
for d in range(nc):
for j in range(n):
x = np.zeros(shape, np.complex)
x[d, j] = 1.0
AAHx = A(A.H(x))
for c in range(nc):
for i in range(n):
AAH[c, i, d, j] = AAHx[c, i]
p_expected = np.zeros([nc, n], np.complex)
for c in range(nc):
for i in range(n):
p_expected_inv_ic = 0
for d in range(nc):
for j in range(n):
p_expected_inv_ic += abs(AAH[c, i, d, j]
)**2 / abs(AAH[c, i, c, i])
p_expected[c, i] = 1 / p_expected_inv_ic
p = precond.kspace_precond(mps, coord=coord)
npt.assert_allclose(p, p_expected, atol=1e-2, rtol=1e-2)
def test_kspace_precond_cart(self):
nc = 4
n = 10
shape = (nc, n)
mps = sp.randn(shape, dtype=np.complex)
mps /= np.linalg.norm(mps, axis=0, keepdims=True)
weights = sp.randn([n]) >= 0
A = sp.linop.Multiply(shape, weights**0.5) * linop.Sense(mps)
AAH = np.zeros((nc, n, nc, n), np.complex)
for d in range(nc):
for j in range(n):
x = np.zeros((nc, n), np.complex)
x[d, j] = 1.0
AAHx = A(A.H(x))
for c in range(nc):
for i in range(n):
AAH[c, i, d, j] = AAHx[c, i]
p_expected = np.ones((nc, n), np.complex)
for c in range(nc):
for i in range(n):
if weights[i]:
p_expected_inv_ic = 0
for d in range(nc):
for j in range(n):
p_expected_inv_ic += abs(AAH[c, i, d, j])**2 / abs(
AAH[c, i, c, i])
p_expected[c, i] = 1 / p_expected_inv_ic
p = precond.kspace_precond(mps, weights=weights)
npt.assert_allclose(p[:, weights == 1], p_expected[:, weights == 1])