def test_basic3(self):
# b is a 3-d matrix.
c = np.array([1, 2, -3, -5])
b = np.arange(24).reshape(4, 3, 2)
x = solve_circulant(c, b)
y = solve(circulant(c), b)
assert_allclose(x, y)
def test_complex(self):
# Complex b and c
c = np.array([1+2j, -3, 4j, 5])
b = np.arange(8).reshape(4, 2) + 0.5j
x = solve_circulant(c, b)
y = solve(circulant(c), b)
assert_allclose(x, y)
def test_complex(self):
# Complex b and c
c = np.array([1 + 2j, -3, 4j, 5])
b = np.arange(8).reshape(4, 2) + 0.5j
x = solve_circulant(c, b)
y = solve(circulant(c), b)
assert_allclose(x, y)
def test_basic3(self):
# b is a 3-d matrix.
c = np.array([1, 2, -3, -5])
b = np.arange(24).reshape(4, 3, 2)
x = solve_circulant(c, b)
y = solve(circulant(c), b)
assert_allclose(x, y)
def test_singular(self):
# c gives a singular circulant matrix.
c = np.array([1, 1, 0, 0])
b = np.array([1, 2, 3, 4])
x = solve_circulant(c, b, singular='lstsq')
y, res, rnk, s = lstsq(circulant(c), b)
assert_allclose(x, y)
assert_raises(LinAlgError, solve_circulant, x, y)
def test_random_b_and_c(self):
# Random b and c
np.random.seed(54321)
c = np.random.randn(50)
b = np.random.randn(50)
x = solve_circulant(c, b)
y = solve(circulant(c), b)
assert_allclose(x, y)
def test_singular(self):
# c gives a singular circulant matrix.
c = np.array([1, 1, 0, 0])
b = np.array([1, 2, 3, 4])
x = solve_circulant(c, b, singular='lstsq')
y, res, rnk, s = lstsq(circulant(c), b)
assert_allclose(x, y)
assert_raises(LinAlgError, solve_circulant, x, y)
def test_random_b_and_c(self):
# Random b and c
np.random.seed(54321)
c = np.random.randn(50)
b = np.random.randn(50)
x = solve_circulant(c, b)
y = solve(circulant(c), b)
assert_allclose(x, y)
def test_axis_args(self):
# Test use of caxis, baxis and outaxis.
# c has shape (2, 1, 4)
c = np.array([[[-1, 2.5, 3, 3.5]], [[1, 6, 6, 6.5]]])
# b has shape (3, 4)
b = np.array([[0, 0, 1, 1], [1, 1, 0, 0], [1, -1, 0, 0]])
x = solve_circulant(c, b, baxis=1)
assert_equal(x.shape, (4, 2, 3))
expected = np.empty_like(x)
expected[:, 0, :] = solve(circulant(c[0]), b.T)
expected[:, 1, :] = solve(circulant(c[1]), b.T)
assert_allclose(x, expected)
x = solve_circulant(c, b, baxis=1, outaxis=-1)
assert_equal(x.shape, (2, 3, 4))
assert_allclose(np.rollaxis(x, -1), expected)
# np.swapaxes(c, 1, 2) has shape (2, 4, 1); b.T has shape (4, 3).
x = solve_circulant(np.swapaxes(c, 1, 2), b.T, caxis=1)
assert_equal(x.shape, (4, 2, 3))
assert_allclose(x, expected)
def test_axis_args(self):
# Test use of caxis, baxis and outaxis.
# c has shape (2, 1, 4)
c = np.array([[[-1, 2.5, 3, 3.5]], [[1, 6, 6, 6.5]]])
# b has shape (3, 4)
b = np.array([[0, 0, 1, 1], [1, 1, 0, 0], [1, -1, 0, 0]])
x = solve_circulant(c, b, baxis=1)
assert_equal(x.shape, (4, 2, 3))
expected = np.empty_like(x)
expected[:, 0, :] = solve(circulant(c[0]), b.T)
expected[:, 1, :] = solve(circulant(c[1]), b.T)
assert_allclose(x, expected)
x = solve_circulant(c, b, baxis=1, outaxis=-1)
assert_equal(x.shape, (2, 3, 4))
assert_allclose(np.rollaxis(x, -1), expected)
# np.swapaxes(c, 1, 2) has shape (2, 4, 1); b.T has shape (4, 3).
x = solve_circulant(np.swapaxes(c, 1, 2), b.T, caxis=1)
assert_equal(x.shape, (4, 2, 3))
assert_allclose(x, expected)
def BTCS(x, t, phiold, c):
nx = len(x)
nt = len(t)
M = np.zeros(nt)
V = np.zeros(nt)
TV = np.zeros(nt)
"We are going to solve a linear system of equations, where the matrix of "
"coefficients is a circulant matrix, which is only defined by its first"
"column that we will represent as a vector named 'q' "
q = np.zeros(nx)
q[0] = 1
q[1] = -c / 2
q[-1] = c / 2
for it in range(nt):
phiold = linalg.solve_circulant(q, phiold)
M[it] = first_mom(phiold)
V[it] = second_mom(phiold)
TV[it] = tot_var(phiold)
return phiold, M, V, TV
def test_basic1(self):
c = np.array([1, 2, 3, 5])
b = np.array([1, -1, 1, 0])
x = solve_circulant(c, b)
y = solve(circulant(c), b)
assert_allclose(x, y)
# Sistemas de ecuaciones lineales
linalg.solve(
matriz, vector
) # Resolver sistema de ecuaciones (resuelve por matriz triangular superior)
linalg.solve(
matriz, vector, lower=True
) # Resolver sistema de ecuaciones (resuelve por matriz triangular inferior)
linalg.solve(
matriz, vector, overwrite_a=True
) # Resolver sistema de ecuaciones (Sobrescribe la matriz para optimizar)
linalg.solve(
matriz, vector, overwrite_b=True
) # Resolver sistema de ecuaciones (Sobrescribe el vector para optimizar)
linalg.solve_circulant(
coeficientes, vector
) # Resolver sistema de ecuaciones con coeficiente de una Matriz circular
linalg.solve_triangular(
matriz, vector
) # Resolver sistema de ecuaciones asumiendo Matriz Triangular Superior
linalg.solve_triangular(
matriz, vector, lower=True
) # Resolver sistema de ecuaciones asumiendo Matriz Triangular Inferior
linalg.solve_triangular(
(columnas, filas), vector
) # Resolver sistema de ecuaciones con la primera fila y columna de la Matriz de Toeplitz usando la recursion de Levinson
linalg.lu_solve(
(lu, piv), vector
) # Resolver sistema de ecuaciones dada la decomposición LU (lu: Matriz que contiene a L y U, piv: Indices que representan los unos de la matriz P en filas)
linalg.lu_solve(linalg.lu_factor(matriz),
vector) # Resolver sistema de ecuaciones por decomposición LU
def test_basic1(self):
c = np.array([1, 2, 3, 5])
b = np.array([1, -1, 1, 0])
x = solve_circulant(c, b)
y = solve(circulant(c), b)
assert_allclose(x, y)