def test_single_values(self):
# Test with ints
a = np.ndarray((1, 1))
a[0, 0] = 2
b = np.ndarray((1, 1))
b[0, 0] = 10
x = gauss_elimination(a, b)
self.assertAlmostEqual(x[0, 0], 5, 'Failed for scalar values')
# Test with float result
a[0, 0] = 2
b[0, 0] = 3
x = gauss_elimination(a, b)
self.assertAlmostEqual(x[0, 0], 1.5, 'Failed for scalar values')
def test_nominal_01(self):
# Given
A = np.array([[ 3, 2, -3, 1, 6], \
[ 6, 2, 4, 0, 5], \
[-3, 1, 0, 2, 3], \
[ 5, -8, 1, 2, 6], \
[ 5, -8, 1, 4, 6]],\
dtype=np.float64)
B = np.array([[-24, 5 ], \
[-6, 3 ], \
[-9, 8 ], \
[ 24, 2 ], \
[ 36, 12]], \
dtype=np.float64 )
#
# True solution
xtru = np.linalg.solve(A, B)
# Computed solution
[x_soln, A_aug] = gauss_elimination(A, B, True)
# Check x solution
precision = 1e-12
for i in range(0, xtru.shape[0]):
for j in range(0, xtru.shape[1]):
assert abs(xtru[i, j] -
x_soln[i, j]) < precision, 'Wrong solution'
#
# Check that the triangular matrix is returned correctly
for j in range(0, i):
assert not A_aug[
i, j], 'Non-zero element in lower triangular area'
def test_gauss_elimination_00(self):
n = 2
mat_a = m.get_random_mat(n, n)
vec_x = m.get_random_vector(n)
vec_b = m.mul_mat_vec(mat_a, vec_x)
vec_x_sol = ge.gauss_elimination(mat_a, vec_x_sol)
del vec_x_sol
del vec_x
del vec_b
del mat_a[:]
del mat_a
def test_gauss_elimination_01(self):
for n in range(3, 10):
mat_a = m.get_random_mat(n, n)
vec_x = m.get_random_vector(n)
vec_b = m.mul_mat_vec(mat_a, vec_x)
vec_x_sol = ge.gauss_elimination(mat_a, vec_b)
del mat_a[:]
del mat_a
del vec_x_sol
del vec_x
del vec_b
def test_gauss_elimination_01(self):
for n in range(3, 10):
mat_a = m.get_random_mat(n, n)
vec_x = m.get_random_vector(n)
vec_b = m.mul_mat_vec(mat_a, vec_x)
vec_x_sol = ge.gauss_elimination(mat_a, vec_b)
self.assertSequenceAlmostEqual(vec_x, vec_x_sol)
del mat_a[:]
del mat_a
del vec_x_sol
del vec_x
del vec_b
def test_nominal_02(self):
# Given
A = np.array([[1, 1, 1], [2, 2, 1], [3, 4, 2]])
B = np.array([[1], [2], [2]])
# True solution
xtru = np.linalg.solve(A, B)
# Computed solution
[x_soln, A_aug] = gauss_elimination(A, B, True)
# Check x solution
precision = 1e-12
for i in range(0, xtru.shape[0]):
for j in range(0, xtru.shape[1]):
assert abs(xtru[i, j] -
x_soln[i, j]) < precision, 'Wrong solution'
#
# Check that the triangular matrix is returned correctly
for j in range(0, i):
assert not A_aug[
i, j], 'Non-zero element in lower triangular area'
def finite_difference(yhist, h, n=1, customge=False):
'''
Forward, Central, Backwards finite difference calculation of derivative
This function uses the Central Finite Difference method to compute the
derivative for the given data vector. At the ends of the array, central
difference doesn't work, so the forward difference method and backwards
difference methods are used instead.
Note that this function decides for you to use forward and bakwards
differencing functions at either end of the dataset. This cannot be
turned off or changed.
@arg
yhist - M x N numpy.ndarray
Function value time history, where N is the length of the
dataset and M is the number different things to take the
derivative of. M is usually 1. N corresponds to the number
of samples in the time history of the dataset.
h - double
Time step
n - double (optional)
Order of finite difference
customge - bool (optional)
Specify to use the custom gauss elimination function.
True to use the function, False use numpy's built in function.
False by default.
@return
ydothist - N x M numpy.ndarray
Finite difference derivative time history
@dependencies
python 3.6.0
numpy
scipy
@author: Matt Marti
@date: 2019-06-14
'''
# Raise Type Errors on bad input
if type(yhist) != np.ndarray:
raise TypeError("Argument 'yhist' is not of type numpy.ndarray")
#
if type(h) not in [int, float]:
raise TypeError("Argument 'h' is not of type [int, float]")
elif type(h) == int:
h = h + 0.0
#
if type(n) != int:
raise TypeError("Argument 'n' is not of type int")
#
# Check yhist shape
assert n > 0, "Argument 'n' is not greater than zero"
if yhist.shape.__len__() == 1:
M = 1
yhistold = yhist.copy()
yhist = np.ndarray((1, yhistold.shape[0]))
for i in range(0, yhistold.shape[0]):
yhist[0, i] = yhistold[i]
#
else:
M = yhist.shape[0]
#
N = yhist.shape[1]
assert N >= n + 1, 'Not enough data points for given order'
# Preallocate output
ydothist = np.zeros(yhist.shape, np.float64)
hmat = np.zeros((n, n), np.float64)
# Forward difference method
for i in range(0, n):
# Delta t matrix
for j in range(1, n + 1):
d = 1.0
hj = h * j
for k in range(1, n + 1):
d = d * k
hmat[j - 1, k - 1] = (hj**k) / d
#
#
# Forward finite difference
k = 0
yfvec = np.ndarray((M, n))
for j in range(i + 1, i + n + 1):
yfvec[:, k] = yhist[:, j] - yhist[:, i]
k += 1
#
# Compute derivative
if customge:
ydoti = gauss_elimination(hmat, yfvec.transpose())
else:
ydoti = spla.solve(hmat, yfvec.transpose())
#
# Assign output
for j in range(ydothist.shape[0]):
ydothist[j, i] = ydoti[0, j]
#
#
# Central difference method
for i in range(n, N - n):
# Delta t matrix
for j in range(1, n + 1):
d = 1.0
hj = h * j
for k in range(1, n + 1):
d = d * k
hmat[j - 1, k - 1] = (hj**k) / d
#
#
# Forward finite difference
k = 0
yfvec = np.ndarray((M, n))
for j in range(i + 1, i + n + 1):
yfvec[:, k] = yhist[:, j] - yhist[:, i]
k += 1
#
# Backward finite difference
k = 0
ybvec = np.ndarray((M, n))
for j in range(i - 1, i - n - 1, -1):
ybvec[:, k] = yhist[:, i] - yhist[:, j]
k += 1
#
# Compute derivative
if customge:
ydoti_f = gauss_elimination(hmat, yfvec.transpose())
ydoti_b = gauss_elimination(hmat, ybvec.transpose())
ydoti = 0.5 * (ydoti_f + ydoti_b)
else:
ydoti_f = spla.solve(hmat, yfvec.transpose())
ydoti_b = spla.solve(hmat, ybvec.transpose())
ydoti = 0.5 * (ydoti_f + ydoti_b)
#
# Assign output
for j in range(ydothist.shape[0]):
ydothist[j, i] = ydoti[0, j]
#
#
# Backwards difference method
for i in range(N - n, N):
# Delta t matrix
for j in range(1, n + 1):
d = 1.0
hj = h * j
for k in range(1, n + 1):
d = d * k
hmat[j - 1, k - 1] = (hj**k) / d
#
#
# Backward finite difference
k = 0
ybvec = np.ndarray((M, n))
for j in range(i - 1, i - n - 1, -1):
ybvec[:, k] = yhist[:, i] - yhist[:, j]
k += 1
#
# Compute derivative
if customge:
ydoti = gauss_elimination(hmat, ybvec.transpose())
else:
ydoti = spla.solve(hmat, ybvec.transpose())
#
# Assign output
for j in range(ydothist.shape[0]):
ydothist[j, i] = ydoti[0, j]
#
#
return ydothist