def wathen_test07():
#*****************************************************************************80
#
## WATHEN_TEST06 assembles, factor and solves using WATHEN_CSC + CG_CSC.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 04 September 2014
#
# Author:
#
# John Burkardt
#
import numpy as np
from cg_csc import cg_csc
from numpy.linalg import norm
from r8vec_uniform_01 import r8vec_uniform_01
from wathen_csc import wathen_csc
from wathen_order import wathen_order
print ''
print 'WATHEN_TEST07'
print ' Assemble, factor and solve a Wathen system'
print ' defined by WATHEN_CSC and CG_CSC.'
print ''
nx = 2
ny = 2
print ' Elements in X direction NX = %d' % (nx)
print ' Elements in Y direction NY = %d' % (ny)
print ' Number of elements = %d' % (nx * ny)
#
# Compute the number of unknowns.
#
n = wathen_order(nx, ny)
print ' Number of nodes N = %d' % (n)
#
# Set up a random solution X1.
#
seed = 123456789
x1, seed = r8vec_uniform_01(n, seed)
#
# Compute the matrix.
#
seed = 123456789
a, seed = wathen_csc(nx, ny, seed)
#
# Compute the corresponding right hand side B.
#
b = a.dot(x1)
#
# Solve the linear system.
#
x2 = np.ones(n)
x2 = cg_csc(n, a, b, x2)
#
# Compute the maximum solution error.
#
e = norm(x1 - x2)
print ' Maximum solution error is %g' % (e)
return
def wathen_test04 ( ):
#*****************************************************************************80
#
## WATHEN_TEST04 times WATHEN_CSC assembly and solution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 04 September 2014
#
# Author:
#
# John Burkardt
#
import numpy as np
import scipy.sparse.linalg as ssl
import time
from numpy.linalg import norm
from r8vec_uniform_01 import r8vec_uniform_01
from wathen_csc import wathen_csc
from wathen_order import wathen_order
print ''
print 'WATHEN_TEST04'
print ' For various problem sizes,'
print ' time the assembly and factorization of a Wathen system'
print ' using the WATHEN_CSC function.'
print ''
print ' NX Elements Nodes Assembly ',
print 'Factor Error'
print ''
nx = 1
ny = 1
for test in range ( 0, 7 ):
#
# Compute the number of unknowns.
#
n = wathen_order ( nx, ny )
#
# Set up a random solution X1.
#
seed = 123456789
x1, seed = r8vec_uniform_01 ( n, seed )
#
# Compute the matrix.
#
seed = 123456789
t0 = time.clock ( )
a, seed = wathen_csc ( nx, ny, seed )
t1 = ( time.clock ( ) - t0 )
#
# Compute the corresponding right hand side B.
#
b = a.dot ( x1 )
#
# Solve the system.
#
t0 = time.clock ( )
x2 = ssl.spsolve ( a, b )
t2 = ( time.clock ( ) - t0 )
#
# Compute the norm of the solution error.
#
e = norm ( x1 - x2 )
#
# Report.
#
print ' %4d %4d %6d %10.2e %10.2e %10.2e' % \
( nx, nx * ny, n, t1, t2, e )
#
# Ready for next iteration.
#
nx = nx * 2
ny = ny * 2
return
def wathen_test07 ( ): #*****************************************************************************80 # ## WATHEN_TEST06 assembles, factor and solves using WATHEN_CSC + CG_CSC. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 04 September 2014 # # Author: # # John Burkardt # import numpy as np from cg_csc import cg_csc from numpy.linalg import norm from r8vec_uniform_01 import r8vec_uniform_01 from wathen_csc import wathen_csc from wathen_order import wathen_order print '' print 'WATHEN_TEST07' print ' Assemble, factor and solve a Wathen system' print ' defined by WATHEN_CSC and CG_CSC.' print '' nx = 2 ny = 2 print ' Elements in X direction NX = %d' % ( nx ) print ' Elements in Y direction NY = %d' % ( ny ) print ' Number of elements = %d' % ( nx * ny ) # # Compute the number of unknowns. # n = wathen_order ( nx, ny ) print ' Number of nodes N = %d' % ( n ) # # Set up a random solution X1. # seed = 123456789 x1, seed = r8vec_uniform_01 ( n, seed ) # # Compute the matrix. # seed = 123456789 a, seed = wathen_csc ( nx, ny, seed ) # # Compute the corresponding right hand side B. # b = a.dot ( x1 ) # # Solve the linear system. # x2 = np.ones ( n ) x2 = cg_csc ( n, a, b, x2 ) # # Compute the maximum solution error. # e = norm ( x1 - x2 ) print ' Maximum solution error is %g' % ( e ) return
def wathen_test04():
#*****************************************************************************80
#
## WATHEN_TEST04 times WATHEN_CSC assembly and solution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 04 September 2014
#
# Author:
#
# John Burkardt
#
import numpy as np
import scipy.sparse.linalg as ssl
import time
from numpy.linalg import norm
from r8vec_uniform_01 import r8vec_uniform_01
from wathen_csc import wathen_csc
from wathen_order import wathen_order
print ''
print 'WATHEN_TEST04'
print ' For various problem sizes,'
print ' time the assembly and factorization of a Wathen system'
print ' using the WATHEN_CSC function.'
print ''
print ' NX Elements Nodes Assembly ',
print 'Factor Error'
print ''
nx = 1
ny = 1
for test in range(0, 7):
#
# Compute the number of unknowns.
#
n = wathen_order(nx, ny)
#
# Set up a random solution X1.
#
seed = 123456789
x1, seed = r8vec_uniform_01(n, seed)
#
# Compute the matrix.
#
seed = 123456789
t0 = time.clock()
a, seed = wathen_csc(nx, ny, seed)
t1 = (time.clock() - t0)
#
# Compute the corresponding right hand side B.
#
b = a.dot(x1)
#
# Solve the system.
#
t0 = time.clock()
x2 = ssl.spsolve(a, b)
t2 = (time.clock() - t0)
#
# Compute the norm of the solution error.
#
e = norm(x1 - x2)
#
# Report.
#
print ' %4d %4d %6d %10.2e %10.2e %10.2e' % \
( nx, nx * ny, n, t1, t2, e )
#
# Ready for next iteration.
#
nx = nx * 2
ny = ny * 2
return