def M2(H0, W, v, start, stop, step):
v0 = 93536.7
n = 10.3
print('H0: ', H0)
print('W: ', W)
print('v:', v)
print('start=', start, ' end=', stop, ' step=', step)
def f_prof(t):
return v0 * np.exp(-1 * n * t)
section = np.linspace(start,
stop,
num=int((stop - start) // step),
endpoint=False)
Y = v
for i, t in enumerate(section):
print("---------", i, "---------", t, "----------")
A = -step * (H0 + f_prof(t + step / 2) * W)
Y = exp(A, Y, -1.0)
print_more_info(Y)
return Y
def Cf4(H0, W, v, step):
v0 = 93536.7
n = 10.3
def f_prof(t):
return v0 * np.exp(-1 * n * t)
section = np.arange(0, 1 + step, step)
Y = v
c1 = 0.5 - np.sqrt(3) / 6
c2 = 0.5 + np.sqrt(3) / 6
alfa1 = (3 - 2 * np.sqrt(3)) / 12
alfa2 = (3 + 2 * np.sqrt(3)) / 12
for i, t in enumerate(section):
# print('-'*10, f' {i} ', '-'*10,)
A1 = H0 + f_prof(t + c1 * step) * W
A2 = H0 + f_prof(t + c2 * step) * W
omega = 123 #???????????????????
Y = exp(omega, Y, 1)
# print(Y)
# print('norm ', la.norm(Y))
# print('-'*10, ' final ', '-'*10,)
# print(1Y)
return Y
def M4(H0, W, v, start, stop, step):
v0 = 93536.7
n = 10.3
def f_prof(t):
return v0 * np.exp(-1 * n * t)
def commutator(A1, A2):
return A1.dot(A2) - A2.dot(A1)
section = np.linspace(start,
stop,
num=int((stop - start) // step),
endpoint=False)
Y = v
c1 = 0.5 - np.sqrt(3) / 6
c2 = 0.5 + np.sqrt(3) / 6
for i, t in enumerate(section):
print("---------", i, "---------", t, "----------")
A1 = H0 + f_prof(t + c1 * step) * W
A2 = H0 + f_prof(t + c2 * step) * W
omega = -step / 2 * (A1 + A2) + 1j * (np.sqrt(3) / 12 *
step**2) * commutator(A2, A1)
Y = exp(omega, Y, 1.0)
#print(Y)
#print('norm ', 1-la.norm(Y))
#print('-'*10, ' final ', '-'*10,)
#print(Y)
return Y
def M6(H0, W, v, start, stop, step):
v0 = 93536.7
n = 10.3
def f_prof(t):
return v0 * np.exp(-1 * n * t)
def commutator(A1, A2):
return A1.dot(A2) - A2.dot(A1)
section = np.linspace(start,
stop,
num=int((stop - start) // step),
endpoint=False)
Y = v
c1 = 0.5 - np.sqrt(15) / 10
c2 = 0.5
c3 = 0.5 + np.sqrt(15) / 10
for i, t in enumerate(section):
#print('-'*10, f' {i} ', '-'*10,)
A1 = H0 + f_prof(t + c1 * step) * W
A2 = H0 + f_prof(t + c2 * step) * W
A3 = H0 + f_prof(t + c3 * step) * W
B1 = step * A2
B2 = (np.sqrt(15) * step / 3) * (A3 - A1)
B3 = (10 * step / 3) * (A3 - 2 * A2 + A1)
omega = B1 + 0.5 * B3 + 1 / 240 * commutator(
-20 * B1 - B3 + commutator(B1, B2),
B2 - 1 / 60 * commutator(B1, 2 * B3 + commutator(B1, B2)))
Y = exp(omega, Y, 1.0)
#print(Y)
#print('norm ', la.norm(Y))
#print('-'*10, ' final ', '-'*10,)
#print(Y)
return Y
# (np.cosh(1.0) + A2*np.sinh(1)).dot(v2)
# print('A2 v2: ', delta)
#
# delta = exp(A2, leja_points, div_diff, v=v3) -\
# (np.cosh(1.0) + A2*np.sinh(1)).dot(v3)
# print('A2 v3: ', delta)
# print('--------------')
#
#
# # --- Third mtrx ---
# delta = exp(A3, leja_points, div_diff, v=v1) -\
# (A2*np.exp(2.0)).dot(v1)
# print('A3 v1: ', delta)
#
# delta = exp(A3, leja_points, div_diff, v=v2) -\
# (A2*np.exp(2.0)).dot(v2)
# print('A3 v2: ', delta)
#
# delta = exp(A3, leja_points, div_diff, v=v3) -\
# (A2*np.exp(2.0)).dot(v3)
# print('A3 v3: ', delta)
# print('--------------')
from exponentiation.exp import matrix_exp_puzzer as exp
A1 = np.matrix([[1., 2., 3.], [2., 1., -1.], [3., -1., 1.]])
v = np.array([[1.0], [0.0], [0.0]])
a = exp(A1, v, 1.0)
print('#' * 30)
print(a)