def sphere_fibonacci_grid_points_test():
#*****************************************************************************80
#
#% SPHERE_FIBONACCI_GRID_POINTS_TEST tests SPHERE_FIBONACCI_GRID_POINTS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 16 May 2015
#
# Author:
#
# John Burkardt
#
import platform
from r8mat_print_some import r8mat_print_some
from r8mat_write import r8mat_write
print('')
print('SPHERE_FIBONACCI_GRID_POINTS_TEST')
print(' Python version: %s' % (platform.python_version()))
print(' SPHERE_FIBONACCI_GRID_POINTS computes points on a sphere')
print(' that lie on a Fibonacci spiral.')
ng = 1000
print('')
print(' Number of points NG = %d' % (ng))
xg = sphere_fibonacci_grid_points(ng)
r8mat_print_some(ng, 3, xg, 0, 0, 19, 2, ' Part of the grid array:')
#
# Write the nodes to a file.
#
filename = 'sphere_fibonacci_grid_points.xyz'
r8mat_write(filename, ng, 3, xg)
#
# Terminate.
#
print('')
print('SPHERE_FIBONACCI_GRID_POINTS_TEST:')
print(' Normal end of execution.')
return
def sphere_fibonacci_grid_points_test ( ): #*****************************************************************************80 # #% SPHERE_FIBONACCI_GRID_POINTS_TEST tests SPHERE_FIBONACCI_GRID_POINTS. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 16 May 2015 # # Author: # # John Burkardt # from r8mat_print_some import r8mat_print_some from r8mat_write import r8mat_write print '' print 'SPHERE_FIBONACCI_GRID_POINTS_TEST' print ' SPHERE_FIBONACCI_GRID_POINTS computes points on a sphere' print ' that lie on a Fibonacci spiral.' ng = 1000 print '' print ' Number of points NG = %d' % ( ng ) xg = sphere_fibonacci_grid_points ( ng ) r8mat_print_some ( ng, 3, xg, 0, 0, 19, 2, ' Part of the grid array:' ) # # Write the nodes to a file. # filename = 'sphere_fibonacci_grid_points.xyz' r8mat_write ( filename, ng, 3, xg ) # # Terminate. # print '' print 'SPHERE_FIBONACCI_GRID_POINTS_TEST:' print ' Normal end of execution.' return
def polygon_grid_points_test01 ( ):
#*****************************************************************************80
#
## POLYGON_GRID_POINTS_TEST01 tests POLYGON_GRID_POINTS
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 10 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from polygon_grid_count import polygon_grid_count
from polygon_grid_display import polygon_grid_display
from r8mat_print import r8mat_print
from r8mat_write import r8mat_write
print ''
print 'POLYGON_GRID_POINTS_TEST01:'
print ' POLYGON_GRID_POINTS returns grid points for a polygon'
print ' of NV vertices, with N+1 points on a side'
print ''
print ' For this test, the polygon is a triangle.'
#
# Define the polygon.
#
nv = 3
v = np.array ( [ \
[ 0.0, 0.0 ], \
[ 1.0, 0.0 ], \
[ 0.5, 0.86602540378443860 ] ] )
r8mat_print ( nv, 2, v, ' Polygon vertices:' )
#
# Count the grid points.
#
n = 5
ng = polygon_grid_count ( n, nv )
print ''
print ' N = %d' % ( n )
print ' Number of grid points will be NG = %d' % ( ng )
#
# Compute the grid points.
#
xg = polygon_grid_points ( n, nv, v, ng )
r8mat_print ( ng, 2, xg, ' The grid point array:' )
#
# Display the points.
#
filename = 'triangle.png'
polygon_grid_display ( n, nv, v, ng, xg, filename )
#
# Write the points to a file.
#
filename = 'triangle.xy'
r8mat_write ( filename, ng, 2, xg )
print ''
print ' Data written to the file "%s"' % ( filename )
#
# Terminate.
#
print ''
print 'POLYGON_GRID_POINTS_TEST01:'
print ' Normal end of execution.'
return
def fem1d_heat_explicit_test02 ( ):
#*****************************************************************************80
#
## FEM1D_HEAT_EXPLICIT_TEST02 does a problem with known solution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 November 2014
#
# Author:
#
# John Burkardt
#
from assemble_mass import assemble_mass
from fem1d_heat_explicit import fem1d_heat_explicit
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
import numpy as np
from math import sqrt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
print ''
print 'FEM1D_HEAT_EXPLICIT_TEST02:'
print ' Using the finite element method,'
print ' compute an approximate solution to the time-dependent'
print ' one dimensional heat equation for a problem where we'
print ' know the exact solution.'
print ''
print ' dH/dt - K * d2H/dx2 = f(x,t)'
#
# Set the nodes.
#
x_num = 21
x_min = 0.0
x_max = 1.0
dx = ( x_max - x_min ) / ( x_num - 1 )
x = np.linspace ( x_min, x_max, x_num )
#
# Set the times.
#
t_num = 51
t_min = 0.0
t_max = 10.0
dt = ( t_max - t_min ) / ( t_num - 1 )
t = np.linspace ( t_min, t_max, t_num )
#
# Set finite element information.
#
element_num = x_num - 1
element_node = np.zeros ( ( 2, element_num ) )
for j in range ( 0, element_num ):
element_node[0,j] = j
element_node[1,j] = j + 1
quad_num = 3
mass = assemble_mass ( x_num, x, element_num, element_node, quad_num )
print ''
print ' Number of X nodes = %d' % ( x_num )
print ' X interval = [ %f, %f ]' % ( x_min, x_max )
print ' X step size = %f' % ( dx )
print ' Number of T steps = %d' % ( t_num )
print ' T interval = [ %f, %f ]' % ( t_min, t_max )
print ' T step size = %f' % ( dt )
print ' Number of elements = %d' % ( element_num )
print ' Number of quadrature points = %d' % ( quad_num )
#
# Running the code produces an array H of temperatures H(t,x),
# and vectors x and t.
#
g_mat = np.zeros ( ( x_num, t_num ) )
h_mat = np.zeros ( ( x_num, t_num ) )
print ''
print ' Step Time RMS Error'
print ''
for j in range ( 0, t_num ):
if ( j == 0 ):
h = ic_test02 ( x_num, x, t[j] )
h = bc_test02 ( x_num, x, t[j], h )
else:
h = fem1d_heat_explicit ( x_num, x, t[j-1], dt, k_test02, \
rhs_test02, bc_test02, element_num, element_node, quad_num, mass, h )
g = exact_test02 ( x_num, x, t[j] )
e = 0.0
for i in range ( 0, x_num ):
e = e + ( h[i] - g[i] ) ** 2
e = sqrt ( e / x_num )
print ' %4d %14.6g %14.6g' % ( j, t[j], e )
for i in range ( 0, x_num ):
g_mat[i,j] = g[i]
h_mat[i,j] = h[i]
#
# Make a product grid of T and X for plotting.
#
t_mat, x_mat = np.meshgrid ( t, x )
#
# Plot the data.
#
fig = plt.figure ( )
ax = fig.add_subplot ( 111, projection = '3d' )
surf = ax.plot_surface ( x_mat, t_mat, h_mat )
plt.xlabel ( '<---X--->' )
plt.ylabel ( '<---T--->' )
plt.title ( 'U(X,T)' )
plt.savefig ( 'plot_test02.png' )
plt.show ( )
#
# Write the data to files.
#
r8mat_write ( 'g_test02.txt', x_num, t_num, g_mat )
r8mat_write ( 'h_test02.txt', x_num, t_num, h_mat )
r8vec_write ( 't_test02.txt', t_num, t )
r8vec_write ( 'x_test02.txt', x_num, x )
print ''
print ' G(X,T) written to "g_test02.txt"'
print ' H(X,T) written to "h_test02.txt"'
print ' T values written to "t_test02.txt"'
print ' X values written to "x_test02.txt"'
print ''
print 'FEM1D_HEAT_EXPLICIT_TEST02:'
print ' Normal end of execution.'
return
def polygon_grid_points_test01():
#*****************************************************************************80
#
## POLYGON_GRID_POINTS_TEST01 tests POLYGON_GRID_POINTS
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 10 May 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from polygon_grid_count import polygon_grid_count
from polygon_grid_display import polygon_grid_display
from r8mat_print import r8mat_print
from r8mat_write import r8mat_write
print ''
print 'POLYGON_GRID_POINTS_TEST01:'
print ' POLYGON_GRID_POINTS returns grid points for a polygon'
print ' of NV vertices, with N+1 points on a side'
print ''
print ' For this test, the polygon is a triangle.'
#
# Define the polygon.
#
nv = 3
v = np.array ( [ \
[ 0.0, 0.0 ], \
[ 1.0, 0.0 ], \
[ 0.5, 0.86602540378443860 ] ] )
r8mat_print(nv, 2, v, ' Polygon vertices:')
#
# Count the grid points.
#
n = 5
ng = polygon_grid_count(n, nv)
print ''
print ' N = %d' % (n)
print ' Number of grid points will be NG = %d' % (ng)
#
# Compute the grid points.
#
xg = polygon_grid_points(n, nv, v, ng)
r8mat_print(ng, 2, xg, ' The grid point array:')
#
# Display the points.
#
filename = 'triangle.png'
polygon_grid_display(n, nv, v, ng, xg, filename)
#
# Write the points to a file.
#
filename = 'triangle.xy'
r8mat_write(filename, ng, 2, xg)
print ''
print ' Data written to the file "%s"' % (filename)
#
# Terminate.
#
print ''
print 'POLYGON_GRID_POINTS_TEST01:'
print ' Normal end of execution.'
return
def fd1d_heat_implicit_test03():
#*****************************************************************************80
#
## FD1D_HEAT_IMPLICIT_TEST03 does a simple test problem.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 17 November 2014
#
# Author:
#
# John Burkardt
#
from fd1d_heat_implicit import fd1d_heat_implicit
from fd1d_heat_implicit_cfl import fd1d_heat_implicit_cfl
from fd1d_heat_implicit_matrix import fd1d_heat_implicit_matrix
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
from mpl_toolkits.mplot3d import axes3d, Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
print ''
print 'FD1D_HEAT_IMPLICIT_TEST03:'
print ' Compute an approximate solution to the time-dependent'
print ' one dimensional heat equation:'
print ' dH/dt - K * d2H/dx2 = f(x,t)'
print ' Run a simple test case.'
#
# Heat coefficient.
#
k = k_test03()
#
# X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
x_num = 21
x_min = -5.0
x_max = +5.0
dx = (x_max - x_min) / (x_num - 1)
x = np.linspace(x_min, x_max, x_num)
#
# T_NUM is the number of equally spaced time points between 0 and 10.0.
#
t_num = 81
t_min = 0.0
t_max = 4.0
dt = (t_max - t_min) / (t_num - 1)
t = np.linspace(t_min, t_max, t_num)
#
# Get the CFL coefficient.
#
cfl = fd1d_heat_implicit_cfl(k, t_num, t_min, t_max, x_num, x_min, x_max)
print ''
print ' Number of X nodes = %d' % (x_num)
print ' X interval is [%f,%f]' % (x_min, x_max)
print ' X spacing is %f' % (dx)
print ' Number of T values = %d' % (t_num)
print ' T interval is [%f,%f]' % (t_min, t_max)
print ' T spacing is %f' % (dt)
print ' Constant K = %g' % (k)
print ' CFL coefficient = %g' % (cfl)
#
# Get the system matrix.
#
a = fd1d_heat_implicit_matrix(x_num, cfl)
hmat = np.zeros((x_num, t_num))
for j in range(0, t_num):
if (j == 0):
h = ic_test03(x_num, x, t[j])
h = bc_test03(x_num, x, t[j], h)
else:
h = fd1d_heat_implicit(a, x_num, x, t[j - 1], dt, cfl, rhs_test03,
bc_test03, h)
for i in range(0, x_num):
hmat[i, j] = h[i]
#
# Plot the data.
#
tmat, xmat = np.meshgrid(t, x)
fig = plt.figure()
ax = Axes3D(fig)
surf = ax.plot_surface(xmat, tmat, hmat)
plt.xlabel('<---X--->')
plt.ylabel('<---T--->')
plt.title('H(X,T)')
plt.savefig('plot_test03.png')
plt.show()
#
# Write the data to files.
#
r8mat_write('h_test03.txt', x_num, t_num, hmat)
r8vec_write('t_test03.txt', t_num, t)
r8vec_write('x_test03.txt', x_num, x)
print ''
print ' H(X,T) written to "h_test03.txt"'
print ' T values written to "t_test03.txt"'
print ' X values written to "x_test3.txt"'
print ''
print 'FD1D_HEAT_IMPLICIT_TEST03:'
print ' Normal end of execution.'
return
def fd1d_heat_explicit_test02 ( ):
# FD1D_HEAT_EXPLICIT_TEST03 does a simple test problem.
from fd1d_heat_explicit import fd1d_heat_explicit
from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
from math import sqrt
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
print ''
print 'FD1D_HEAT_EXPLICIT_TEST03:'
print ' Compute an approximate solution to the time-dependent'
print ' one dimensional heat equation:'
print ''
print ' dH/dt - K * d2H/dx2 = f(x,t)'
print ''
print ' Run a simple test case.'
#
# Heat coefficient.
#
k = k_test02 ( )
#
# X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
x_num = 21
x_min = -5.0
x_max = +5.0
dx = ( x_max - x_min ) / ( x_num - 1 )
x = np.linspace ( x_min, x_max, x_num )
#
# T_NUM is the number of equally spaced time points between 0 and 10.0.
#
t_num = 81
t_min = 0.0
t_max = 4.0
dt = ( t_max - t_min ) / ( t_num - 1 )
t = np.linspace ( t_min, t_max, t_num )
#
# Get the CFL coefficient.
#
cfl = fd1d_heat_explicit_cfl ( k, t_num, t_min, t_max, x_num, x_min, x_max )
print ''
print ' Number of X nodes = %d' % ( x_num )
print ' X interval is [%f,%f]' % ( x_min, x_max )
print ' X spacing is %f' % ( dx )
print ' Number of T values = %d' % ( t_num )
print ' T interval is [%f,%f]' % ( t_min, t_max )
print ' T spacing is %f' % ( dt )
print ' Constant K = %g' % ( k )
print ' CFL coefficient = %g' % ( cfl )
#
# Running the code produces an array H of temperatures H(t,x),
# and vectors x and t.
#
hmat = np.zeros ( ( x_num, t_num ) )
for j in range ( 0, t_num ):
if ( j == 0 ):
h = ic_test02 ( x_num, x, t[j] )
h = bc_test02 ( x_num, x, t[j], h )
else:
h = fd1d_heat_explicit ( x_num, x, t[j-1], dt, cfl, rhs_test02, bc_test02, h )
for i in range ( 0, x_num ):
hmat[i,j] = h[i]
#
# Plot the data.
#
tmat, xmat = np.meshgrid ( t, x )
fig = plt.figure ( )
ax = Axes3D ( fig )
surf = ax.plot_surface ( xmat, tmat, hmat )
plt.xlabel ( '<---X--->' )
plt.ylabel ( '<---T--->' )
plt.title ( 'U(X,T)' )
plt.savefig ( 'plot_test02.png' )
plt.show ( )
#
# Write the data to files.
#
r8mat_write ( 'h_test02.txt', x_num, t_num, hmat )
r8vec_write ( 't_test02.txt', t_num, t )
r8vec_write ( 'x_test02.txt', x_num, x )
print ''
print ' H(X,T) written to "h_test02.txt"'
print ' T values written to "t_test02.txt"'
print ' X values written to "x_test3.txt"'
return
def triangle_grid_points_test ( n ):
#*****************************************************************************80
#
## TRIANGLE_GRID_POINTS_TEST tests TRIANGLE_GRID_POINTS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 April 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r82col_print_part import r82col_print_part
from r8mat_print import r8mat_print
from r8mat_write import r8mat_write
from triangle_grid_count import triangle_grid_count
from triangle_grid_display import triangle_grid_display
print ''
print 'TRIANGLE_GRID_POINTS_TEST:'
print ' TRIANGLE_GRID_POINTS defines a triangular grid'
print ' with N+1 points on a side, based on any triangle.'
print ''
print ' Input value of N is %d' % ( n )
ng = triangle_grid_count ( n )
print ' Number of grid points will be %d' % ( ng )
t = np.array ( [ \
[ 0.0, 0.0 ], \
[ 1.0, 0.0 ], \
[ 0.5, 0.86602540378443860 ] ] )
r8mat_print ( 3, 2, t, ' Triangle vertices:' )
tg = triangle_grid_points ( n, t )
r82col_print_part ( ng, tg, 20, ' Part of the grid point array:' );
#
# Write the data to a file.
#
filename = 'triangle_grid_points.xy'
r8mat_write ( filename, ng, 2, tg )
#
# Plot the data.
#
print ''
print ' Data written to the file "%s".' % ( filename )
filename = 'triangle_grid_points.png'
triangle_grid_display ( t, ng, tg, filename )
print ''
print 'TRIANGLE_GRID_POINTS_TEST:'
print ' Normal end of execution.'
return
def burgers_viscous_time_exact1_test02():
#*****************************************************************************80
#
## BURGERS_VISCOUS_TIME_EXACT1_TEST02 tests sets up a finer test case.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 24 September 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
import platform
from r8mat_print import r8mat_print
from r8mat_write import r8mat_write
from r8vec_print import r8vec_print
vtn = 41
vxn = 41
nu = 0.01 / np.pi
print('')
print('BURGERS_VISCOUS_TIME_EXACT1_TEST02')
print(' Python version: %s' % (platform.python_version()))
print(' BURGERS_VISCOUS_TIME_EXACT1 computes solution #1')
print(' to the Burgers equation.')
print('')
print(' Viscosity NU = %g' % (nu))
print(' NX = %d' % (vxn))
print(' NT = %d' % (vtn))
xlo = -1.0
xhi = +1.0
vx = np.linspace(xlo, xhi, vxn)
r8vec_print(vxn, vx, ' X grid points:')
tlo = 0.0
thi = 3.0 / np.pi
vt = np.linspace(tlo, thi, vtn)
r8vec_print(vtn, vt, ' T grid points:')
vu = burgers_viscous_time_exact1(nu, vxn, vx, vtn, vt)
filename = 'burgers_solution_test02.txt'
r8mat_write(filename, vxn, vtn, vu)
print('')
print(' Data written to file "%s"' % (filename))
#
# Terminate
#
print('')
print('BURGERS_VISCOUS_TIME_EXACT1_TEST02')
print(' Normal end of execution.')
return
def fd1d_heat_explicit_test02():
#*****************************************************************************80
#
## FD1D_HEAT_EXPLICIT_TEST02 does a problem with known solution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 06 November 2014
#
# Author:
#
# John Burkardt
#
from fd1d_heat_explicit import fd1d_heat_explicit
from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
from math import sqrt
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
print ''
print 'FD1D_HEAT_EXPLICIT_TEST02:'
print ' Compute an approximate solution to the time-dependent'
print ' one dimensional heat equation for a problem where we'
print ' know the exact solution.'
print ''
print ' dH/dt - K * d2H/dx2 = f(x,t)'
print ''
print ' Run a simple test case.'
#
# Heat coefficient.
#
k = k_test02()
#
# X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
x_num = 21
x_min = 0.0
x_max = 1.0
dx = (x_max - x_min) / (x_num - 1)
x = np.linspace(x_min, x_max, x_num)
#
# T_NUM is the number of equally spaced time points between 0 and 10.0.
#
t_num = 26
t_min = 0.0
t_max = 10.0
dt = (t_max - t_min) / (t_num - 1)
t = np.linspace(t_min, t_max, t_num)
#
# Get the CFL coefficient.
#
cfl = fd1d_heat_explicit_cfl(k, t_num, t_min, t_max, x_num, x_min, x_max)
print ''
print ' Number of X nodes = %d' % (x_num)
print ' X interval is [%f,%f]' % (x_min, x_max)
print ' X spacing is %f' % (dx)
print ' Number of T values = %d' % (t_num)
print ' T interval is [%f,%f]' % (t_min, t_max)
print ' T spacing is %f' % (dt)
print ' Constant K = %g' % (k)
print ' CFL coefficient = %g' % (cfl)
#
# Running the code produces an array H of temperatures H(t,x),
# and vectors x and t.
#
gmat = np.zeros((x_num, t_num))
hmat = np.zeros((x_num, t_num))
print ''
print ' Step Time RMS Error'
print ''
for j in range(0, t_num):
if (j == 0):
h = ic_test02(x_num, x, t[j])
h = bc_test02(x_num, x, t[j], h)
else:
h = fd1d_heat_explicit(x_num, x, t[j - 1], dt, cfl, rhs_test02,
bc_test02, h)
g = exact_test02(x_num, x, t[j])
e = 0.0
for i in range(0, x_num):
e = e + (h[i] - g[i])**2
e = sqrt(e) / sqrt(x_num)
print ' %4d %14.6g %14.6g' % (j, t[j], e)
for i in range(0, x_num):
gmat[i, j] = g[i]
hmat[i, j] = h[i]
#
# Plot the data.
#
tmat, xmat = np.meshgrid(t, x)
fig = plt.figure()
ax = Axes3D(fig)
surf = ax.plot_surface(xmat, tmat, hmat)
plt.xlabel('<---X--->')
plt.ylabel('<---T--->')
plt.title('U(X,T)')
plt.savefig('plot_test02.png')
plt.show()
#
# Write the data to files.
#
r8mat_write('g_test02.txt', x_num, t_num, gmat)
r8mat_write('h_test02.txt', x_num, t_num, hmat)
r8vec_write('t_test02.txt', t_num, t)
r8vec_write('x_test02.txt', x_num, x)
print ''
print ' G(X,T) written to "g_test02.txt"'
print ' H(X,T) written to "h_test02.txt"'
print ' T values written to "t_test02.txt"'
print ' X values written to "x_test02.txt"'
return
def square_grid_points_test ( m, n ):
#*****************************************************************************80
#
## SQUARE_GRID_POINTS_TEST tests SQUARE_GRID_POINTS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 13 April 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r82col_print_part import r82col_print_part
from r8mat_print import r8mat_print
from r8mat_write import r8mat_write
from square_grid_count import square_grid_count
from square_grid_display import square_grid_display
print ''
print 'SQUARE_GRID_POINTS_TEST:'
print ' SQUARE_GRID_POINTS defines a grid'
print ' with M*N points on a side, based on a quadrilateral.'
print ''
print ' Input value of M is %d' % ( m )
print ' Input value of N is %d' % ( n )
ns = np.zeros ( 2, dtype = np.int32 );
ns[0] = m
ns[1] = n
ng = square_grid_count ( ns )
print ''
print ' Number of grid points will be %d' % ( ng )
xv = np.array ( [ \
[ 0.0, 1.0 ], \
[ 3.0, 2.0 ], \
[ 4.0, 5.0 ], \
[ 1.0, 3.0 ] ] )
r8mat_print ( 4, 2, xv, ' Quadrilateral vertices:' )
xg = square_grid_points ( ns, xv, ng )
r82col_print_part ( ng, xg, 20, ' Part of the grid point array:' );
#
# Write the data to a file.
#
filename = 'square_grid_points.xy'
r8mat_write ( filename, ng, 2, xg )
print ''
print ' Data written to the file "%s".' % ( filename )
#
# Plot the data.
#
filename = 'square_grid_points.png'
square_grid_display ( xv, ng, xg, filename )
#
# Terminate.
#
print ''
print 'SQUARE_GRID_POINTS_TEST:'
print ' Normal end of execution.'
return
def ball_grid_points_test():
#*****************************************************************************80
#
#% BALL_GRID_POINTS_TEST tests BALL_GRID_POINTS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 11 April 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from ball_grid_count import ball_grid_count
from ball_grid_display import ball_grid_display
from r83col_print_part import r83col_print_part
from r8mat_write import r8mat_write
print ''
print 'BALL_GRID_POINTS_TEST:'
print ' BALL_GRID_POINTS can define a grid of points'
print ' with N+1 points on a horizontal or vertical radius,'
print ' based on any ball.'
n = 4
r = 2.0
c = np.array([1.0, 5.0, 2.0])
print ''
print ' We use N = %d' % (n)
print ' Radius R = %g' % (r)
print ' Center C = (%g,%g,%g)' % (c[0], c[1], c[2])
ng = ball_grid_count(n, r, c)
print ''
print ' Number of grid points will be %d' % (ng)
xg = ball_grid_points(n, r, c, ng)
r83col_print_part(ng, xg, 20, ' Part of the grid point array:')
filename = 'ball_grid_points.xyz'
r8mat_write(filename, ng, 3, xg)
print ''
print ' Data written to the file "%s".' % (filename)
#
# Plot the grid.
#
filename = 'ball_grid_points.png'
ball_grid_display(r, c, ng, xg, filename)
print ''
print ' Plot written to the file "%s".' % (filename)
#
# Terminate.
#
print ''
print 'BALL_GRID_POINTS_TEST:'
print ' Normal end of execution.'
return
def fem1d_heat_explicit_test01 ( ):
#*****************************************************************************80
#
## FEM1D_HEAT_EXPLICIT_TEST01 runs a simple test.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 06 November 2014
#
# Author:
#
# John Burkardt
#
from assemble_mass import assemble_mass
from fem1d_heat_explicit import fem1d_heat_explicit
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
print ''
print 'FEM1D_HEAT_EXPLICIT_TEST01:'
print ' The time dependent 1D heat equation is'
print ''
print ' Ut - k * Uxx = f(x,t)'
print ''
print ' for space interval A <= X <= B with boundary conditions'
print ''
print ' U(A,t) = UA(t)'
print ' U(B,t) = UB(t)'
print ''
print ' and time interval T0 <= T <= T1 with initial condition'
print ''
print ' U(X,T0) = U0(X).'
print ''
print ' To compute an approximate solution:'
print ' the interval [A,B] is replace by a discretized mesh Xi'
print ' a set of finite element functions PSI(X) are determined,'
print ' the solution U is written as a weighted sum of the basis functions,'
print ' the weak form of the differential equation is written,'
print ' a time grid Tj is imposed, and time derivatives replaced by'
print ' an explicit forward Euler first difference,'
print ''
print ' The continuous PDE has now been transformed into a set of algebraic'
print ' equations for the coefficients C(Xi,Tj).'
#
# Set the nodes.
#
x_num = 21
x_min = 0.0
x_max = 1.0
dx = ( x_max - x_min ) / ( x_num - 1 )
x = np.linspace ( x_min, x_max, x_num )
#
# Set the times.
#
t_num = 401
t_min = 0.0
t_max = 80.0
dt = ( t_max - t_min ) / ( t_num - 1 )
t = np.linspace ( t_min, t_max, t_num )
#
# Set finite element information.
#
element_num = x_num - 1
element_node = np.zeros ( ( 2, element_num ) )
for j in range ( 0, element_num ):
element_node[0,j] = j
element_node[1,j] = j + 1
quad_num = 3
mass = assemble_mass ( x_num, x, element_num, element_node, quad_num )
print ''
print ' Number of X nodes = %d' % ( x_num )
print ' X interval = [ %f, %f ]' % ( x_min, x_max )
print ' X step size = %f' % ( dx )
print ' Number of T steps = %d' % ( t_num )
print ' T interval = [ %f, %f ]' % ( t_min, t_max )
print ' T step size = %f' % ( dt )
print ' Number of elements = %d' % ( element_num )
print ' Number of quadrature points = %d' % ( quad_num )
u_mat = np.zeros ( ( x_num, t_num ) )
for j in range ( 0, t_num ):
if ( j == 0 ):
u = ic_test01 ( x_num, x, t[j] )
u = bc_test01 ( x_num, x, t[j], u )
else:
u = fem1d_heat_explicit ( x_num, x, t[j-1], dt, k_test01, \
rhs_test01, bc_test01, element_num, element_node, quad_num, mass, u )
for i in range ( 0, x_num ):
u_mat[i,j] = u[i]
#
# Make a product grid of T and X for plotting.
#
t_mat, x_mat = np.meshgrid ( t, x )
#
# Make a mesh plot of the solution.
#
fig = plt.figure ( )
ax = fig.add_subplot ( 111, projection = '3d' )
surf = ax.plot_surface ( x_mat, t_mat, u_mat )
plt.xlabel ( '<---X--->' )
plt.ylabel ( '<---T--->' )
plt.title ( 'U(X,T)' )
plt.savefig ( 'plot_test01.png' )
plt.show ( )
#
# Write the data to files.
#
r8mat_write ( 'h_test01.txt', x_num, t_num, u_mat )
r8vec_write ( 't_test01.txt', t_num, t )
r8vec_write ( 'x_test01.txt', x_num, x )
print ''
print ' H(X,T) written to "h_test01.txt"'
print ' T values written to "t_test01.txt"'
print ' X values written to "x_test01.txt"'
print ''
print 'FEM1D_HEAT_EXPLICIT_TEST01:'
print ' Normal end of execution.'
return
def fd1d_heat_explicit_test02 ( ):
#*****************************************************************************80
#
## FD1D_HEAT_EXPLICIT_TEST02 does a problem with known solution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 06 November 2014
#
# Author:
#
# John Burkardt
#
from fd1d_heat_explicit import fd1d_heat_explicit
from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
from math import sqrt
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
print ''
print 'FD1D_HEAT_EXPLICIT_TEST02:'
print ' Compute an approximate solution to the time-dependent'
print ' one dimensional heat equation for a problem where we'
print ' know the exact solution.'
print ''
print ' dH/dt - K * d2H/dx2 = f(x,t)'
print ''
print ' Run a simple test case.'
#
# Heat coefficient.
#
k = k_test02 ( )
#
# X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
x_num = 21
x_min = 0.0
x_max = 1.0
dx = ( x_max - x_min ) / ( x_num - 1 )
x = np.linspace ( x_min, x_max, x_num )
#
# T_NUM is the number of equally spaced time points between 0 and 10.0.
#
t_num = 26
t_min = 0.0
t_max = 10.0
dt = ( t_max - t_min ) / ( t_num - 1 )
t = np.linspace ( t_min, t_max, t_num )
#
# Get the CFL coefficient.
#
cfl = fd1d_heat_explicit_cfl ( k, t_num, t_min, t_max, x_num, x_min, x_max )
print ''
print ' Number of X nodes = %d' % ( x_num )
print ' X interval is [%f,%f]' % ( x_min, x_max )
print ' X spacing is %f' % ( dx )
print ' Number of T values = %d' % ( t_num )
print ' T interval is [%f,%f]' % ( t_min, t_max )
print ' T spacing is %f' % ( dt )
print ' Constant K = %g' % ( k )
print ' CFL coefficient = %g' % ( cfl )
#
# Running the code produces an array H of temperatures H(t,x),
# and vectors x and t.
#
gmat = np.zeros ( ( x_num, t_num ) )
hmat = np.zeros ( ( x_num, t_num ) )
print ''
print ' Step Time RMS Error'
print ''
for j in range ( 0, t_num ):
if ( j == 0 ):
h = ic_test02 ( x_num, x, t[j] )
h = bc_test02 ( x_num, x, t[j], h )
else:
h = fd1d_heat_explicit ( x_num, x, t[j-1], dt, cfl, rhs_test02, bc_test02, h )
g = exact_test02 ( x_num, x, t[j] )
e = 0.0
for i in range ( 0, x_num ):
e = e + ( h[i] - g[i] ) ** 2
e = sqrt ( e ) / sqrt ( x_num )
print ' %4d %14.6g %14.6g' % ( j, t[j], e )
for i in range ( 0, x_num ):
gmat[i,j] = g[i]
hmat[i,j] = h[i]
#
# Plot the data.
#
tmat, xmat = np.meshgrid ( t, x )
fig = plt.figure ( )
ax = Axes3D ( fig )
surf = ax.plot_surface ( xmat, tmat, hmat )
plt.xlabel ( '<---X--->' )
plt.ylabel ( '<---T--->' )
plt.title ( 'U(X,T)' )
plt.savefig ( 'plot_test02.png' )
plt.show ( )
#
# Write the data to files.
#
r8mat_write ( 'g_test02.txt', x_num, t_num, gmat )
r8mat_write ( 'h_test02.txt', x_num, t_num, hmat )
r8vec_write ( 't_test02.txt', t_num, t )
r8vec_write ( 'x_test02.txt', x_num, x )
print ''
print ' G(X,T) written to "g_test02.txt"'
print ' H(X,T) written to "h_test02.txt"'
print ' T values written to "t_test02.txt"'
print ' X values written to "x_test02.txt"'
return
def fem1d_heat_explicit_test02():
#*****************************************************************************80
#
## FEM1D_HEAT_EXPLICIT_TEST02 does a problem with known solution.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 November 2014
#
# Author:
#
# John Burkardt
#
from assemble_mass import assemble_mass
from fem1d_heat_explicit import fem1d_heat_explicit
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
import numpy as np
from math import sqrt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
print ''
print 'FEM1D_HEAT_EXPLICIT_TEST02:'
print ' Using the finite element method,'
print ' compute an approximate solution to the time-dependent'
print ' one dimensional heat equation for a problem where we'
print ' know the exact solution.'
print ''
print ' dH/dt - K * d2H/dx2 = f(x,t)'
#
# Set the nodes.
#
x_num = 21
x_min = 0.0
x_max = 1.0
dx = (x_max - x_min) / (x_num - 1)
x = np.linspace(x_min, x_max, x_num)
#
# Set the times.
#
t_num = 51
t_min = 0.0
t_max = 10.0
dt = (t_max - t_min) / (t_num - 1)
t = np.linspace(t_min, t_max, t_num)
#
# Set finite element information.
#
element_num = x_num - 1
element_node = np.zeros((2, element_num))
for j in range(0, element_num):
element_node[0, j] = j
element_node[1, j] = j + 1
quad_num = 3
mass = assemble_mass(x_num, x, element_num, element_node, quad_num)
print ''
print ' Number of X nodes = %d' % (x_num)
print ' X interval = [ %f, %f ]' % (x_min, x_max)
print ' X step size = %f' % (dx)
print ' Number of T steps = %d' % (t_num)
print ' T interval = [ %f, %f ]' % (t_min, t_max)
print ' T step size = %f' % (dt)
print ' Number of elements = %d' % (element_num)
print ' Number of quadrature points = %d' % (quad_num)
#
# Running the code produces an array H of temperatures H(t,x),
# and vectors x and t.
#
g_mat = np.zeros((x_num, t_num))
h_mat = np.zeros((x_num, t_num))
print ''
print ' Step Time RMS Error'
print ''
for j in range(0, t_num):
if (j == 0):
h = ic_test02(x_num, x, t[j])
h = bc_test02(x_num, x, t[j], h)
else:
h = fem1d_heat_explicit ( x_num, x, t[j-1], dt, k_test02, \
rhs_test02, bc_test02, element_num, element_node, quad_num, mass, h )
g = exact_test02(x_num, x, t[j])
e = 0.0
for i in range(0, x_num):
e = e + (h[i] - g[i])**2
e = sqrt(e / x_num)
print ' %4d %14.6g %14.6g' % (j, t[j], e)
for i in range(0, x_num):
g_mat[i, j] = g[i]
h_mat[i, j] = h[i]
#
# Make a product grid of T and X for plotting.
#
t_mat, x_mat = np.meshgrid(t, x)
#
# Plot the data.
#
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
surf = ax.plot_surface(x_mat, t_mat, h_mat)
plt.xlabel('<---X--->')
plt.ylabel('<---T--->')
plt.title('U(X,T)')
plt.savefig('plot_test02.png')
plt.show()
#
# Write the data to files.
#
r8mat_write('g_test02.txt', x_num, t_num, g_mat)
r8mat_write('h_test02.txt', x_num, t_num, h_mat)
r8vec_write('t_test02.txt', t_num, t)
r8vec_write('x_test02.txt', x_num, x)
print ''
print ' G(X,T) written to "g_test02.txt"'
print ' H(X,T) written to "h_test02.txt"'
print ' T values written to "t_test02.txt"'
print ' X values written to "x_test02.txt"'
print ''
print 'FEM1D_HEAT_EXPLICIT_TEST02:'
print ' Normal end of execution.'
return
def fd1d_heat_implicit_test01 ( ):
#*****************************************************************************80
#
## FD1D_HEAT_IMPLICIT_TEST01 does a simple test problem.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 17 November 2014
#
# Author:
#
# John Burkardt
#
from fd1d_heat_implicit import fd1d_heat_implicit
from fd1d_heat_implicit_cfl import fd1d_heat_implicit_cfl
from fd1d_heat_implicit_matrix import fd1d_heat_implicit_matrix
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
from mpl_toolkits.mplot3d import axes3d, Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
print ''
print 'FD1D_HEAT_IMPLICIT_TEST01:'
print ' Compute an approximate solution to the time-dependent'
print ' one dimensional heat equation:'
print ' dH/dt - K * d2H/dx2 = f(x,t)'
print ' Run a simple test case.'
#
# Heat coefficient.
#
k = k_test01 ( )
#
# X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
x_num = 21
x_min = 0.0
x_max = 1.0
dx = ( x_max - x_min ) / ( x_num - 1 )
x = np.linspace ( x_min, x_max, x_num )
#
# T_NUM is the number of equally spaced time points between 0 and 10.0.
#
t_num = 201
t_min = 0.0
t_max = 80.0
dt = ( t_max - t_min ) / ( t_num - 1 )
t = np.linspace ( t_min, t_max, t_num )
#
# Get the CFL coefficient.
#
cfl = fd1d_heat_implicit_cfl ( k, t_num, t_min, t_max, x_num, x_min, x_max )
print ''
print ' Number of X nodes = %d' % ( x_num )
print ' X interval is [%f,%f]' % ( x_min, x_max )
print ' X spacing is %f' % ( dx )
print ' Number of T values = %d' % ( t_num )
print ' T interval is [%f,%f]' % ( t_min, t_max )
print ' T spacing is %f' % ( dt )
print ' Constant K = %g' % ( k )
print ' CFL coefficient = %g' % ( cfl )
#
# Get the system matrix.
#
a = fd1d_heat_implicit_matrix ( x_num, cfl )
hmat = np.zeros ( ( x_num, t_num ) )
for j in range ( 0, t_num ):
if ( j == 0 ):
h = ic_test01 ( x_num, x, t[j] )
h = bc_test01 ( x_num, x, t[j], h )
else:
h = fd1d_heat_implicit ( a, x_num, x, t[j-1], dt, cfl, rhs_test01, bc_test01, h )
for i in range ( 0, x_num ):
hmat[i,j] = h[i]
#
# Plot the data.
#
tmat, xmat = np.meshgrid ( t, x )
fig = plt.figure ( )
ax = Axes3D ( fig )
surf = ax.plot_surface ( xmat, tmat, hmat )
plt.xlabel ( '<---X--->' )
plt.ylabel ( '<---T--->' )
plt.title ( 'H(X,T)' )
plt.savefig ( 'plot_test01.png' )
plt.show ( )
#
# Write the data to files.
#
r8mat_write ( 'h_test01.txt', x_num, t_num, hmat )
r8vec_write ( 't_test01.txt', t_num, t )
r8vec_write ( 'x_test01.txt', x_num, x )
print ''
print ' H(X,T) written to "h_test01.txt"'
print ' T values written to "t_test01.txt"'
print ' X values written to "x_test01.txt"'
print ''
print 'FD1D_HEAT_IMPLICIT_TEST01:'
print ' Normal end of execution.'
return
def fd1d_heat_explicit_test01(path,mode,weightsFile):
"""fd1d_heat_explicit_test01 does a simple test problem"""
from fd1d_heat_explicit import fd1d_heat_explicit
from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
print ''
print 'FD1D_HEAT_EXPLICIT_TEST01:'
print ' Compute an approximate solution to the time-dependent'
print ' one dimensional heat equation:'
print ''
print ' dH/dt - K * d2H/dx2 = f(x,t)'
print ''
print ' Run a simple test case.'
"""Heat coefficient"""
k = k_test01 ( )
#
# X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
x_num = 21
x_min = 0.0
x_max = 1.0
dx = ( x_max - x_min ) / ( x_num - 1 )
x = np.linspace ( x_min, x_max, x_num )
#
# T_NUM is the number of equally spaced time points between 0 and 10.0.
#
t_num = 201
t_min = 0.0
t_max = 80.0
dt = ( t_max - t_min ) / ( t_num - 1 )
t = np.linspace ( t_min, t_max, t_num )
#
# Get the CFL coefficient.
#
cfl = fd1d_heat_explicit_cfl ( k, t_num, t_min, t_max, x_num, x_min, x_max )
print ''
print ' Number of X nodes = %d' % ( x_num )
print ' X interval is [%f,%f]' % ( x_min, x_max )
print ' X spacing is %f' % ( dx )
print ' Number of T values = %d' % ( t_num )
print ' T interval is [%f,%f]' % ( t_min, t_max )
print ' T spacing is %f' % ( dt )
print ' Constant K = %g' % ( k )
print ' CFL coefficient = %g' % ( cfl )
#
# Running the code produces an array H of temperatures H(t,x),
# and vectors x and t.
#
hmat = np.zeros ( ( x_num, t_num ) )
for j in range ( 0, t_num ):
if ( j == 0 ):
h = ic_test01 ( x_num, x, t[j] ,mode)
h = bc_test01 ( x_num, x, t[j], h ,mode)
else:
h = fd1d_heat_explicit ( x_num, x, t[j-1], dt, cfl, rhs_test01, bc_test01, h, mode, weightsFile )
for i in range ( 0, x_num ):
hmat[i,j] = h[i]
#
# Plot the data.
#
tmat, xmat = np.meshgrid ( t, x )
fig = plt.figure ( )
ax = fig.add_subplot ( 111, projection = '3d' )
ax = Axes3D ( fig )
surf = ax.plot_surface ( xmat, tmat, hmat )
plt.xlabel ( '<---X--->' )
plt.ylabel ( '<---T--->' )
plt.title ( 'U(X,T)' )
save_at = path.strip()
print path, save_at
filename = str(save_at) + 'plot_test_' + str(mode) + '.png'
print filename
plt.savefig (filename)
#plt.show ( )
#
# Write the data to files.
#
filename = str(save_at) + 'h_test01.txt'
r8mat_write ( filename, x_num, t_num, hmat )
#filename = str(save_at) + 't_test01.txt'
#r8vec_write ( filename, t_num, t )
#filename = str(save_at) + 'x_test01.txt'
#r8vec_write ( filename, x_num, x )
print ''
print ' H(X,T) written to "h_test01.txt"'
print ' T values written to "t_test01.txt"'
print ' X values written to "x_test01.txt"'
#
# Terminate.
#
print ''
print 'FD1D_HEAT_EXPLICIT_TEST01:'
print ' Normal end of execution.'
return
def square_grid_points_test(m, n):
#*****************************************************************************80
#
## SQUARE_GRID_POINTS_TEST tests SQUARE_GRID_POINTS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 13 April 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r82col_print_part import r82col_print_part
from r8mat_print import r8mat_print
from r8mat_write import r8mat_write
from square_grid_count import square_grid_count
from square_grid_display import square_grid_display
print ''
print 'SQUARE_GRID_POINTS_TEST:'
print ' SQUARE_GRID_POINTS defines a grid'
print ' with M*N points on a side, based on a quadrilateral.'
print ''
print ' Input value of M is %d' % (m)
print ' Input value of N is %d' % (n)
ns = np.zeros(2, dtype=np.int32)
ns[0] = m
ns[1] = n
ng = square_grid_count(ns)
print ''
print ' Number of grid points will be %d' % (ng)
xv = np.array ( [ \
[ 0.0, 1.0 ], \
[ 3.0, 2.0 ], \
[ 4.0, 5.0 ], \
[ 1.0, 3.0 ] ] )
r8mat_print(4, 2, xv, ' Quadrilateral vertices:')
xg = square_grid_points(ns, xv, ng)
r82col_print_part(ng, xg, 20, ' Part of the grid point array:')
#
# Write the data to a file.
#
filename = 'square_grid_points.xy'
r8mat_write(filename, ng, 2, xg)
print ''
print ' Data written to the file "%s".' % (filename)
#
# Plot the data.
#
filename = 'square_grid_points.png'
square_grid_display(xv, ng, xg, filename)
#
# Terminate.
#
print ''
print 'SQUARE_GRID_POINTS_TEST:'
print ' Normal end of execution.'
return
def ball_grid_points_test ( ): #*****************************************************************************80 # #% BALL_GRID_POINTS_TEST tests BALL_GRID_POINTS. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 11 April 2015 # # Author: # # John Burkardt # import numpy as np from ball_grid_count import ball_grid_count from ball_grid_display import ball_grid_display from r83col_print_part import r83col_print_part from r8mat_write import r8mat_write print '' print 'BALL_GRID_POINTS_TEST:' print ' BALL_GRID_POINTS can define a grid of points' print ' with N+1 points on a horizontal or vertical radius,' print ' based on any ball.' n = 4 r = 2.0 c = np.array ( [ 1.0, 5.0, 2.0 ] ) print '' print ' We use N = %d' % ( n ) print ' Radius R = %g' % ( r ) print ' Center C = (%g,%g,%g)' % ( c[0], c[1], c[2] ) ng = ball_grid_count ( n, r, c ) print '' print ' Number of grid points will be %d' % ( ng ) xg = ball_grid_points ( n, r, c, ng ) r83col_print_part ( ng, xg, 20, ' Part of the grid point array:' ) filename = 'ball_grid_points.xyz' r8mat_write ( filename, ng, 3, xg ) print '' print ' Data written to the file "%s".' % ( filename ) # # Plot the grid. # filename = 'ball_grid_points.png' ball_grid_display ( r, c, ng, xg, filename ) print '' print ' Plot written to the file "%s".' % ( filename ) # # Terminate. # print '' print 'BALL_GRID_POINTS_TEST:' print ' Normal end of execution.' return
def circle_arc_grid_points_test():
#*****************************************************************************80
#
## CIRCLE_ARC_GRID_POINTS_TEST demonstrates the use of CIRCLE_ARC_GRID.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 17 April 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from circle_arc_grid_display import circle_arc_grid_display
from r82col_print_part import r82col_print_part
from r8mat_write import r8mat_write
print ''
print 'CIRCLE_ARC_GRID_POINTS_TEST'
print ' CIRCLE_ARC_GRID_POINTS returns points along a circular arc.'
print ' In this example, we compute points on a 90 degree arc.'
r = 2.0
c = np.array([5.0, 5.0])
a = np.array([0.0, 90.0])
n = 20
#
# Echo the input.
#
print ''
print ' Radius = %g' % (r)
print ' Center = %g %g\n' % (c[0], c[1])
print ' Angle 1 = %g' % (a[0])
print ' Angle 2 = %g' % (a[1])
print ' Number of points = %d' % (n)
#
# Compute the data.
#
xy = circle_arc_grid_points(r, c, a, n)
#
# Print a little of the data.
#
r82col_print_part(n, xy, 10, ' Some points on the arc:')
#
# Write the data.
#
filename = 'circle_arc_grid_points.xy'
r8mat_write(filename, n, 2, xy)
print ''
print ' Data written to "%s"' % (filename)
#
# Plot the data.
#
filename = 'circle_arc_grid_points.png'
circle_arc_grid_display(r, c, a, n, xy, filename)
print ''
print ' Plot saved in file "%s"' % (filename)
#
# Terminate.
#
print ''
print 'CIRCLE_ARC_GRID_POINTS_TEST:'
print ' Normal end of execution.'
return
def fd1d_heat_explicit_test01():
# *****************************************************************************80
#
## FD1D_HEAT_EXPLICIT_TEST01 does a simple test problem
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 06 November 2014
#
# Author:
#
# John Burkardt
#
from fd1d_heat_explicit import fd1d_heat_explicit
from fd1d_heat_explicit_cfl import fd1d_heat_explicit_cfl
from r8mat_write import r8mat_write
from r8vec_write import r8vec_write
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import matplotlib.pyplot as plt
import numpy as np
print ""
print "FD1D_HEAT_EXPLICIT_TEST01:"
print " Compute an approximate solution to the time-dependent"
print " one dimensional heat equation:"
print ""
print " dH/dt - K * d2H/dx2 = f(x,t)"
print ""
print " Run a simple test case."
#
# Heat coefficient.
#
k = k_test01()
#
# X_NUM is the number of equally spaced nodes to use between 0 and 1.
#
x_num = 21
x_min = 0.0
x_max = 1.0
dx = (x_max - x_min) / (x_num - 1)
x = np.linspace(x_min, x_max, x_num)
#
# T_NUM is the number of equally spaced time points between 0 and 10.0.
#
t_num = 201
t_min = 0.0
t_max = 80.0
dt = (t_max - t_min) / (t_num - 1)
t = np.linspace(t_min, t_max, t_num)
#
# Get the CFL coefficient.
#
cfl = fd1d_heat_explicit_cfl(k, t_num, t_min, t_max, x_num, x_min, x_max)
print ""
print " Number of X nodes = %d" % (x_num)
print " X interval is [%f,%f]" % (x_min, x_max)
print " X spacing is %f" % (dx)
print " Number of T values = %d" % (t_num)
print " T interval is [%f,%f]" % (t_min, t_max)
print " T spacing is %f" % (dt)
print " Constant K = %g" % (k)
print " CFL coefficient = %g" % (cfl)
#
# Running the code produces an array H of temperatures H(t,x),
# and vectors x and t.
#
hmat = np.zeros((x_num, t_num))
for j in range(0, t_num):
if j == 0:
h = ic_test01(x_num, x, t[j])
h = bc_test01(x_num, x, t[j], h)
else:
h = fd1d_heat_explicit(x_num, x, t[j - 1], dt, cfl, rhs_test01, bc_test01, h)
for i in range(0, x_num):
hmat[i, j] = h[i]
#
# Plot the data.
#
tmat, xmat = np.meshgrid(t, x)
fig = plt.figure()
# ax = fig.add_subplot ( 111, projection = '3d' )
ax = Axes3D(fig)
surf = ax.plot_surface(xmat, tmat, hmat)
plt.xlabel("<---X--->")
plt.ylabel("<---T--->")
plt.title("U(X,T)")
plt.savefig("plot_test01.png")
plt.show()
#
# Write the data to files.
#
r8mat_write("h_test01.txt", x_num, t_num, hmat)
r8vec_write("t_test01.txt", t_num, t)
r8vec_write("x_test01.txt", x_num, x)
print ""
print ' H(X,T) written to "h_test01.txt"'
print ' T values written to "t_test01.txt"'
print ' X values written to "x_test01.txt"'
#
# Terminate.
#
print ""
print "FD1D_HEAT_EXPLICIT_TEST01:"
print " Normal end of execution."
return
def circle_arc_grid_points_test ( ): #*****************************************************************************80 # ## CIRCLE_ARC_GRID_POINTS_TEST demonstrates the use of CIRCLE_ARC_GRID. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 17 April 2015 # # Author: # # John Burkardt # import numpy as np from circle_arc_grid_display import circle_arc_grid_display from r82col_print_part import r82col_print_part from r8mat_write import r8mat_write print '' print 'CIRCLE_ARC_GRID_POINTS_TEST' print ' CIRCLE_ARC_GRID_POINTS returns points along a circular arc.' print ' In this example, we compute points on a 90 degree arc.' r = 2.0 c = np.array ( [ 5.0, 5.0 ] ) a = np.array ( [ 0.0, 90.0 ] ) n = 20; # # Echo the input. # print '' print ' Radius = %g' % ( r ) print ' Center = %g %g\n' % ( c[0], c[1] ) print ' Angle 1 = %g' % ( a[0] ) print ' Angle 2 = %g' % ( a[1] ) print ' Number of points = %d' % ( n ) # # Compute the data. # xy = circle_arc_grid_points ( r, c, a, n ) # # Print a little of the data. # r82col_print_part ( n, xy, 10, ' Some points on the arc:' ) # # Write the data. # filename = 'circle_arc_grid_points.xy' r8mat_write ( filename, n, 2, xy ) print '' print ' Data written to "%s"' % ( filename ) # # Plot the data. # filename = 'circle_arc_grid_points.png' circle_arc_grid_display ( r, c, a, n, xy, filename ) print '' print ' Plot saved in file "%s"' % ( filename ) # # Terminate. # print '' print 'CIRCLE_ARC_GRID_POINTS_TEST:' print ' Normal end of execution.' return
def triangle_grid_points_test(n):
#*****************************************************************************80
#
## TRIANGLE_GRID_POINTS_TEST tests TRIANGLE_GRID_POINTS.
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 09 April 2015
#
# Author:
#
# John Burkardt
#
import numpy as np
from r82col_print_part import r82col_print_part
from r8mat_print import r8mat_print
from r8mat_write import r8mat_write
from triangle_grid_count import triangle_grid_count
from triangle_grid_display import triangle_grid_display
print ''
print 'TRIANGLE_GRID_POINTS_TEST:'
print ' TRIANGLE_GRID_POINTS defines a triangular grid'
print ' with N+1 points on a side, based on any triangle.'
print ''
print ' Input value of N is %d' % (n)
ng = triangle_grid_count(n)
print ' Number of grid points will be %d' % (ng)
t = np.array ( [ \
[ 0.0, 0.0 ], \
[ 1.0, 0.0 ], \
[ 0.5, 0.86602540378443860 ] ] )
r8mat_print(3, 2, t, ' Triangle vertices:')
tg = triangle_grid_points(n, t)
r82col_print_part(ng, tg, 20, ' Part of the grid point array:')
#
# Write the data to a file.
#
filename = 'triangle_grid_points.xy'
r8mat_write(filename, ng, 2, tg)
#
# Plot the data.
#
print ''
print ' Data written to the file "%s".' % (filename)
filename = 'triangle_grid_points.png'
triangle_grid_display(t, ng, tg, filename)
print ''
print 'TRIANGLE_GRID_POINTS_TEST:'
print ' Normal end of execution.'
return
