def solve(self):
one_domain = w1_one_domain.one_domain(self.n)
one_domain.solve()
u_simple = one_domain.get_solution()
A = self.get_a() # A Global
b = self.get_b() # b global
self.A1 = self.get_A1() # D and N block matrix 2 by 2 for Omega 1
self.A2 = self.get_A2() # D and N block matrix 2 by 2 for Omega 2
solvetime = timeit.default_timer()
for i in range(self.iterations):
if i == 0:
u1_itr = scipy.sparse.linalg.spsolve(self.A1,self.b11) #u1^0, ur^0 & u2^0 = 0 initial guess
else:
u1_itr = scipy.sparse.linalg.spsolve(self.A1,(self.b11+bl1))
u1 = u1_itr[:(self.n-2)**2]
uG1 = u1_itr[(self.n-2)**2:]
bl2 = self.get_bl2(u1,uG1)
u2_itr = scipy.sparse.linalg.spsolve(self.A2,(self.b22+bl2))
uG2 = u2_itr[:(self.n-2)]
u2 = u2_itr[(self.n-2):]
bl1 = self.get_bl1(uG2,u2)
self.set_solution(u1,uG2,u2)
self.difference[i] = np.linalg.norm(self.get_solution()-u_simple,ord='fro')
solvetime = timeit.default_timer() - solvetime
print("iteration took {} seconds.".format(solvetime))
self.set_solution(u1, uG2, u2)
def solve(self):
one_domain = w1_one_domain.one_domain(self.n)
one_domain.solve()
u_simple = one_domain.get_solution()
A1 = self.get_a("Neumann")
A2 = self.get_a("Dirichlet")
solvetime = timeit.default_timer()
for i in range(self.iterations):
b1 = self.get_b("Neumann")
u1_itr = np.reshape(scipy.sparse.linalg.spsolve(A1, b1),
(self.n - 1, self.n - 2))
u1_itr = self.relax(i, "Neumann", u1_itr)
self.u_gamma = u1_itr[-1, :]
b2 = self.get_b("Dirichlet")
u2_itr = np.reshape(scipy.sparse.linalg.spsolve(A2, b2),
(self.n - 1, self.n - 2))
u2_itr = self.relax(i, "Dirichlet", u2_itr)
self.aj = (u2_itr[1:, 0] - self.u_gamma)
self.set_solution(u1_itr[:-1, :], u2_itr[1:, :])
#self.error[i] = np.linalg.norm(self.utrue - self.u_gamma,ord=inf)
self.difference[i] = np.linalg.norm(self.solution - u_simple,
ord='fro')
#res1 = np.reshape(A1 * np.asarray(u1_itr).reshape(-1)-b1,(self.n-2,self.n-1))
#res2 = np.reshape(A2 * np.asarray(u2_itr).reshape(-1)-b2, (self.n - 2, self.n - 2))
#self.residual[i,0] = np.linalg.norm(res1[:,-1],ord=inf)
#self.residual[i, 1] = np.linalg.norm(res2[:, 0], ord=inf)
solvetime = timeit.default_timer() - solvetime
print("It took {} seconds to iterate a solution.".format(solvetime))
self.set_solution(u1_itr[:-1, :], u2_itr[1:, :])
This script runs the overdetermined system solving using constrained least squares constraining internal points ''' n = 40 itr = 300 relaxation = 1 # iterated domain initialization and solving itr_domain = w07_ConstrainedLQ_Internal_2d.two_domain(n, itr, relaxation) itr_domain.solve() u_itr = itr_domain.get_solution() # single domain comparison one_domain = w1_one_domain.one_domain(n) one_domain.solve() u_simple = one_domain.get_solution() # calculating difference iterated and single domain diff = u_itr - u_simple # get residuals from iterated domain residuals = itr_domain.get_residual() # get difference ||u_itr(i)-u_simple||fro difference = itr_domain.get_difference() # plotting plt.figure(figsize=(16, 8))
import matplotlib.pyplot as plt
from week_03 import w03_2d_block
from week_two import w1_one_domain
import numpy as np
N = 30
itr = 300
rel = 0.2
onedomain = w1_one_domain.one_domain(n = N)
onedomain.solve()
od = onedomain.get_solution()
twodomain = w03_2d_block.two_domain(n = N, iterations=itr, relaxation=rel)
twodomain.set_utrue(np.flipud(od[1:-1,N-1]))
twodomain.solve()
td = twodomain.get_solution()
err = twodomain.get_error()
diff = td-od
plt.subplot(221)
plt.title("Iterated Domain solution, %d itr %g relax" % (itr,rel))
plt.pcolor(td)
plt.colorbar()
plt.subplot(222)
plt.title("Simple Domain solution")
plt.pcolor(od)
plt.colorbar()
def solve(self):
one_domain = w1_one_domain.one_domain(self.n)
one_domain.solve()
u_simple = one_domain.get_solution()
A = self.get_a() # A Global
b = self.get_b() # b global
self.initiate_constrained_matrices()
solvetime = timeit.default_timer()
for i in range(self.iterations):
if i == 0:
u1_itr = scipy.sparse.linalg.spsolve(
self.A1_constr, self.get_constrained_b1_0())
#u1_residual = u1_itr[1]
#u1_itr = u1_itr[0]
else:
u1_itr = scipy.sparse.linalg.spsolve(
self.A1_constr, self.get_constrained_b1(bl1))
#u1_residual = u1_itr[1]
#u1_itr = u1_itr[0]
u1_itr = u1_itr[:(self.n - 2)**2 + (self.n - 2)]
# Temporär residual
if i > 0:
temp_res_top = self.A1 * u1_itr - (self.b11 + bl1)
u1 = u1_itr[:(self.n - 2)**2]
uG1 = u1_itr[(self.n - 2)**2:(self.n - 2)**2 + (self.n - 2)]
# Relaxation
if i > 0:
uG1 = self.relaxation * uG1 + (1 - self.relaxation) * uG1_old
uG1_old = uG1
bl2 = self.get_bl2(u1, uG1)
u2_itr = scipy.sparse.linalg.spsolve(self.A2_constr,
self.get_constrained_b2(bl2))
u2_itr = u2_itr[:(self.n - 2)**2 + (self.n - 2)]
#Temporär residual
temp_res_bot = self.A2 * u2_itr - (self.b22 + bl2)
uG2 = u2_itr[:(self.n - 2)]
u2 = u2_itr[(self.n - 2):(self.n - 2)**2 + (self.n - 2)]
# Relaxation
if i > 0:
uG2 = self.relaxation * uG2 + (1 - self.relaxation) * uG2_old
uG2_old = uG2
bl1 = self.get_bl1(uG2, u2)
#self.residual[i, 0] = u1_residual
#self.residual[i, 1] = u2_residual
self.set_solution(u1, uG2, u2)
self.difference[i] = np.linalg.norm(self.solution - u_simple,
ord='fro')
'''
if i == 20 or i == 50 or i == 100:
plt.subplot(311)
plt.plot(temp_res_top,'.')
plt.title("Iteration %d" % i)
plt.subplot(312)
plt.plot(temp_res_bot, '.')
plt.title("Residual $\Omega_2$")
plt.subplot(325)
plt.title("Current iterated solution")
plt.pcolor(self.solution)
plt.subplot(326)
plt.title("Difference current iterated exact discrete")
plt.pcolor(self.solution-u_simple)
plt.colorbar()
plt.show()
'''
'''
if i == 20:
plt.figure(figsize=(10,4))
plt.subplot(211)
plt.plot(temp_res_top, '.')
plt.title("Residual over $\Omega_1$")
plt.subplot(212)
plt.plot(temp_res_bot, '.')
plt.title("Residual over $\Omega_2$")
savefig('residual.pdf')
plt.show()
'''
solvetime = timeit.default_timer() - solvetime
print("iteration took {} seconds.".format(solvetime))
self.set_solution(u1, uG2, u2)
def solve(self):
one_domain = w1_one_domain.one_domain(self.n)
one_domain.solve()
u_simple = one_domain.get_solution()
A = self.get_a() # A Global
b = self.get_b() # b global
self.A1 = self.get_A1() # D and N block matrix 2 by 2 for Omega 1
self.A2 = self.get_A2() # D and N block matrix 2 by 2 for Omega 2
solvetime = timeit.default_timer()
for i in range(self.iterations):
if i == 0:
#u1_itr = scipy.sparse.linalg.spsolve(self.A1,self.b11) #u1^0, ur^0 & u2^0 = 0 initial guess
u1_itr = np.linalg.lstsq(self.A1.toarray(), self.b11)
u1_residual = u1_itr[1]
u1_itr = u1_itr[0]
else:
u1_itr = np.linalg.lstsq(self.A1.toarray(), (self.b11 + bl1))
u1_residual = u1_itr[1]
u1_itr = u1_itr[0]
u1 = u1_itr[:(self.n - 2)**2]
uG1 = u1_itr[(self.n - 2)**2:]
if i > 0:
uG1 = self.relaxation * uG1 + (1 - self.relaxation) * uG1_old
uG1_old = uG1
bl2 = self.get_bl2(u1, uG1)
u2_itr = np.linalg.lstsq(self.A2.toarray(), (self.b22 + bl2))
u2_residual = u2_itr[1]
u2_itr = u2_itr[0]
uG2 = u2_itr[:(self.n - 2)]
u2 = u2_itr[(self.n - 2):]
if i > 0:
uG2 = self.relaxation * uG2 + (1 - self.relaxation) * uG2_old
uG2_old = uG2
bl1 = self.get_bl1(uG2, u2)
self.residual[i, 0] = u1_residual
self.residual[i, 1] = u2_residual
self.set_solution(u1, uG2, u2)
self.difference[i] = np.linalg.norm(self.solution - u_simple,
ord='fro')
if i == 20 or i == 50 or i == 100:
temp_res_top = self.A1 * u1_itr - (self.b11 + bl1)
temp_res_bot = self.A2 * u2_itr - (self.b22 + bl2)
plt.subplot(311)
plt.plot(temp_res_top, '.')
plt.title("Iteration %d" % i)
plt.subplot(312)
plt.plot(temp_res_bot, '.')
plt.title("Residual $\Omega_2$")
plt.subplot(325)
plt.title("Current iterated solution")
plt.pcolor(self.solution)
plt.subplot(326)
plt.title("Difference current iterated exact discrete")
plt.pcolor(self.solution - u_simple)
plt.colorbar()
plt.show()
solvetime = timeit.default_timer() - solvetime
print("iteration took {} seconds.".format(solvetime))
self.set_solution(u1, uG2, u2)