def loop(self, d_idx, d_m_mat, DWIJ, HIJ):
i, j, n, nt = declare('int', 4)
n = self.dim
nt = n + 1
# Note that we allocate enough for a 3D case but may only use a
# part of the matrix.
temp = declare('matrix(12)')
res = declare('matrix(3)')
eps = 1.0e-04 * HIJ
for i in range(n):
for j in range(n):
temp[nt * i + j] = d_m_mat[9 * d_idx + 3 * i + j]
# Augmented part of matrix
temp[nt * i + n] = DWIJ[i]
gj_solve(temp, n, 1, res)
res_mag = 0.0
dwij_mag = 0.0
for i in range(n):
res_mag += abs(res[i])
dwij_mag += abs(DWIJ[i])
change = abs(res_mag - dwij_mag) / (dwij_mag + eps)
if change < self.tol:
for i in range(n):
DWIJ[i] = res[i]
def test_symmetric_matrix(self):
n = 3
mat = [[0.96, 4.6, -3.7], [4.6, 4.3, -0.67], [-3.7, -0.67, -5.]]
b = [2.4, 3.6, -5.8]
result = [0.0] * n
gj_solve(np.ravel(mat), b, n, result)
mat = np.matrix(mat)
new_b = mat * np.transpose(np.matrix(result))
new_b = np.ravel(np.array(new_b))
assert np.allclose(new_b, np.array(b))
def test_band_matrix(self):
n = 3
mat = [[1., -2., 0.], [1., -1., 3.], [2., 5., 0.]]
b = [-3., 1., 0.5]
result = [0.0] * n
gj_solve(np.ravel(mat), b, n, result)
mat = np.matrix(mat)
new_b = mat * np.transpose(np.matrix(result))
new_b = np.ravel(np.array(new_b))
assert np.allclose(new_b, np.array(b))
def test_symmetric_positivedefinite_Matrix(self):
n = 4
mat = [[1., 1., 4., -1.], [1., 5., 0., -1.], [4., 0., 21., -4.],
[-1., -1., -4., 10.]]
b = [2.4, 3.6, -5.8, 0.5]
result = [0.0] * n
gj_solve(np.ravel(mat), b, n, result)
mat = np.matrix(mat)
new_b = mat * np.transpose(np.matrix(result))
new_b = np.ravel(np.array(new_b))
assert np.allclose(new_b, np.array(b))
def test_tridiagonal_matrix(self):
n = 4
mat = [[-2., 1., 0., 0.], [1., -2., 1., 0.], [0., 1., -2., 0.],
[0., 0., 1., -2.]]
b = [-1., 0., 0., -5.]
result = [0.0] * n
gj_solve(np.ravel(mat), b, n, result)
mat = np.matrix(mat)
new_b = mat * np.transpose(np.matrix(result))
new_b = np.ravel(np.array(new_b))
assert np.allclose(new_b, np.array(b))
def loop(self, d_idx, d_m_mat, DWIJ, HIJ):
i, j, n = declare('int', 3)
n = self.dim
temp = declare('matrix(9)')
res = declare('matrix(3)')
eps = 1.0e-04 * HIJ
for i in range(n):
for j in range(n):
temp[n * i + j] = d_m_mat[9 * d_idx + 3 * i + j]
gj_solve(temp, DWIJ, n, res)
change = 0.0
for i in range(n):
change += abs(DWIJ[i] - res[i]) / (abs(DWIJ[i]) + eps)
if change <= self.tol:
for i in range(n):
DWIJ[i] = res[i]
def test_general_matrix(self):
"""
This is a general matrix which needs partial pivoting to be
solved.
References
----------
http://web.mit.edu/10.001/Web/Course_Notes/GaussElimPivoting.html
"""
n = 4
mat = [[0.02, 0.01, 0., 0.], [1., 2., 1., 0.], [0., 1., 2., 1.],
[0., 0., 100., 200.]]
b = [0.02, 1., 4., 800.]
result = [0.0] * n
gj_solve(np.ravel(mat), b, n, result)
mat = np.matrix(mat)
new_b = mat * np.transpose(np.matrix(result))
new_b = np.ravel(np.array(new_b))
assert np.allclose(new_b, np.array(b))
def loop(self, d_idx, d_m_mat, d_dw_gamma, d_cwij, DWIJ, HIJ):
i, j, n, nt = declare('int', 4)
n = self.dim
nt = n + 1
temp = declare('matrix(12)') # The augmented matrix
res = declare('matrix(3)')
dwij = declare('matrix(3)')
eps = 1.0e-04 * HIJ
for i in range(n):
dwij[i] = (DWIJ[i] - d_dw_gamma[3 * d_idx + i]) / d_cwij[d_idx]
for j in range(n):
temp[nt * i + j] = d_m_mat[9 * d_idx + 3 * i + j]
temp[nt * i + n] = dwij[i]
gj_solve(temp, n, 1, res)
res_mag = 0.0
dwij_mag = 0.0
for i in range(n):
res_mag += abs(res[i])
dwij_mag += abs(dwij[i])
change = abs(res_mag - dwij_mag) / (dwij_mag + eps)
if change < self.tol:
for i in range(n):
DWIJ[i] = res[i]