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test.py
133 lines (114 loc) · 3.9 KB
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test.py
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import math
from matrixandvectors import matrix
from matrixandvectors import vector
def real_u(x, y, k):
if k == 0:
return math.sin(math.pi*x)*math.sin(math.pi*y)
else:
if k == 1:
return (1 - x)*x*(1 - y)*y
def real_wx(x, y, k):
if k == 0:
return math.pi*math.cos(math.pi*x)*math.sin(math.pi*y)
else:
if k == 1:
return (1 - 2*x)*(1 - y)*y
def real_wy(x, y, k):
if k == 0:
return math.pi*math.sin(math.pi*x)*math.cos(math.pi*y)
else:
if k == 1:
return (1 - 2*y)*(1 - x)*x
def def_real_u(u, k):
u.clear()
for i in xrange(u.line):
for j in xrange(u.col):
u.data[i][j] = real_u(hx*j+hx/2, hy*i+hy/2, k)
def def_real_wx(u, k):
u.clear()
for i in xrange(u.line):
for j in xrange(u.col):
u.data[i][j] = real_wx(hx*j+hx/2, hy*i+hy/2, k)
def def_real_wy(u, k):
u.clear()
for i in xrange(u.line):
for j in xrange(u.col):
u.data[i][j] = real_wy(hx*j+hx/2, hy*i+hy/2, k)
def corrector_x(u, b1, b2, a1, a2):
Bu = matrix(u.line, u.col + 1)
Bu.clear()
for i in xrange(Bu.line):
Bu.data[i][0] = u.data[i][0] * b1
Bu.data[i][Bu.col - 1] = u.data[i][u.col - 1]*b2
for j in xrange(1, Bu.col - 1):
Bu.data[i][j] = u.data[i][j]*b1 + u.data[i][j-1]*b2
#progonka A
y = matrix(Bu.line, Bu.col)
y.clear()
gradu = matrix(Bu.line, Bu.col)
gradu.clear()
alpha = vector(Bu.col)
beta = vector(Bu.col)
for i in xrange(y.line):
alpha.data[0] = a1
beta.data[0] = a2/alpha.data[0]
y.data[i][0] = Bu.data[i][0]/alpha.data[0]
for j in xrange(1, y.col - 1):
alpha.data[j] = 2*a1 - a2*beta.data[j - 1]
beta.data[j] = a2/alpha.data[j]
y.data[i][j] = (Bu.data[i][j] - a2*y.data[i][j -1])/alpha.data[j]
alpha.data[y.col - 1] = a1 - a2*beta.data[y.col - 2]
y.data[i][y.col - 1] = (Bu.data[i][y.col - 1] - a2*y.data[i][y.col - 2])/alpha.data[y.col - 1]
gradu.data[i][y.col - 1] = y.data[i][y.col - 1]
for j in range(y.col - 2, -1, -1):
gradu.data[i][j] = y.data[i][j] - beta.data[j]*gradu.data[i][j + 1]
gradu.printmatrix()
return gradu
def corrector_y(u, b1, b2, a1, a2):
Bu = matrix(u.line + 1, u.col + 1)
Bu.clear()
for i in xrange(Bu.line):
Bu.data[i][0] = u.data[i][0] * b1
Bu.data[i][Bu.col - 1] = u.data[i][u.col - 1]*b2
for j in xrange(1, Bu.col - 1):
Bu.data[i][j] = u.data[i][j]*b1 + u.data[i][j-1]*b2
#progonka A
y = matrix(Bu.line, Bu.col)
y.clear()
gradu = matrix(Bu.line, Bu.col)
gradu.clear()
alpha = vector(Bu.col)
beta = vector(Bu.col)
for i in xrange(y.line):
alpha.data[0] = a1
beta.data[0] = a2/alpha.data[0]
y.data[i][0] = Bu.data[i][0]/alpha.data[0]
for j in xrange(1, y.col - 1):
alpha.data[j] = 2*a1 - a2*beta.data[j - 1]
beta.data[j] = a2/alpha.data[j]
y.data[i][j] = (Bu.data[i][j] - a2*y.data[i][j -1])/alpha.data[j]
alpha.data[y.col - 1] = a1 - a2*beta.data[y.col - 2]
y.data[i][y.col - 1] = (Bu.data[i][y.col - 1] - a2*y.data[i][y.col - 2])/alpha.data[y.col - 1]
gradu.data[i][y.col - 1] = y.data[i][y.col - 1]
for j in range(y.col - 2, -1, -1):
gradu.data[i][j] = y.data[i][j] - beta.data[j]*gradu.data[i][j + 1]
gradu.printmatrix()
return gradu
solution_number =1 #input()
amntx =4 #input()
amnty = 4#input()
amntt =4 #input()
hx = 1/float(amntx)
hy = 1/float(amnty)
teta =0.3 #input()
tao = 1/float(amntt)
w_x = matrix(amnty, amntx + 1)
w_y = matrix(amnty + 1, amntx)
u = matrix(amnty, amntx)
realu = matrix(amnty, amntx)
realw_x = matrix(amnty, amntx + 1)
realw_y = matrix(amnty + 1, amntx)
def_real_u(u, solution_number)
print "U"
u.printmatrix()
w_x.copy(corrector_x(u,-hy,hy,hx*hy/3,hx*hy/6))