def copy_installed_scripts():
"""
Copy installed executable scripts to the scitools++/bin directory.
"""
print '********* copy installed executable scripts **************'
scripts = SCRIPTS # see top of this file
print scripts
for script in scripts:
system("cp `which %s` %s" % (script, bindir))
# fix headers (replace user-specific install path):
for f in scripts:
system(r'subst.py "#!.+" "#!/usr/bin/env python" %s' % \
join(bindir, f))
for f in glob.glob(join(bindir, '*.old~')):
os.remove(f)
def copy_installed_scripts():
"""
Copy installed executable scripts to the scitools++/bin directory.
"""
print '********* copy installed executable scripts **************'
scripts = SCRIPTS # see top of this file
print scripts
for script in scripts:
system("cp `which %s` %s" % (script, bindir))
# fix headers (replace user-specific install path):
for f in scripts:
system(r'subst.py "#!.+" "#!/usr/bin/env python" %s' % \
join(bindir, f))
for f in glob.glob(join(bindir, '*.old~')):
os.remove(f)
def copy_installed_modules():
"""
Copy installed modules to scitools++.
An alternative is to copy the source of these modules and
run multiple setup.py in scitools++ to install each dir in scitools++.
The set-up now is that scitools++ should just be in PYTHONPATH and
then everything is correctly installed.
"""
print '********* copy installed modules to scitools++ **************'
path = join(sys.prefix, 'lib', 'python' + sys.version[:3], 'site-packages')
files = MODULES # see top of this file
print files
files = [join(path, file) for file in files]
pmw = join(py_package_src, 'Pmw_1_3', 'Pmw')
files.append(pmw)
# copy files to libdir:
# (shutil.copytree does not work properly for this type of copy)
cmd = 'cp -r ' + ' '.join(files) + ' ' + libdir
print cmd
system(cmd)
def copy_installed_modules():
"""
Copy installed modules to scitools++.
An alternative is to copy the source of these modules and
run multiple setup.py in scitools++ to install each dir in scitools++.
The set-up now is that scitools++ should just be in PYTHONPATH and
then everything is correctly installed.
"""
print '********* copy installed modules to scitools++ **************'
path = join(sys.prefix, 'lib', 'python' + sys.version[:3], 'site-packages')
files = MODULES # see top of this file
print files
files = [join(path, file) for file in files]
pmw = join(py_package_src, 'Pmw_1_3', 'Pmw')
files.append(pmw)
# copy files to libdir:
# (shutil.copytree does not work properly for this type of copy)
cmd = 'cp -r ' + ' '.join(files) + ' ' + libdir
print cmd
system(cmd)
def make_f77(f, bc, I):
code = """
subroutine scheme_f77(up, u, um, x, y, t, nx, ny, Cx2, Cy2,
& dt2, t_old)
integer nx, ny
real*8 up(0:nx, 0:ny), u(0:nx, 0:ny), um(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 Cx2, Cy2, dt2, t, t_old
Cf2py intent(in, out) up
real*8 f
external f
do j = 1, ny-1
do i = 1, nx-1
up(i,j) = - um(i,j) + 2*u(i,j) +
& Cx2*(u(i-1,j) - 2*u(i,j) + u(i+1,j)) +
& Cy2*(u(i,j-1) - 2*u(i,j) + u(i,j+1)) +
& dt2*f(x(i),y(j),t_old)
end do
end do
return
end
subroutine ic_f77(u, um, x, y, nx, ny, Cx2, Cy2, dt)
integer nx, ny
real*8 u(0:nx, 0:ny), um(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 Cx2, Cy2, dt, dt2
Cf2py intent(in, out) u, um
real*8 f, ic
external f, ic
dt2 = dt*dt
do j = 0, ny
do i = 0, nx
u(i,j) = ic(x(i),y(j))
end do
end do
do j = 1, ny-1
do i = 1, nx-1
um(i,j) = u(i,j) +
& 0.5*Cx2*(u(i-1,j) - 2*u(i,j) + u(i+1,j)) +
& 0.5*Cy2*(u(i,j-1) - 2*u(i,j) + u(i,j+1)) +
& dt2*f(x(i),y(j),0.0D0)
end do
end do
C boundary values:
call bc_f77(um, x, y, nx, ny, dt)
return
end
subroutine bc_f77(up, x, y, nx, ny, t)
integer nx, ny
real*8 up(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 t
Cf2py intent(in, out) up
real*8 bc
external bc
i = 0
do j = 0, ny
up(i,j) = bc(x(i),y(j),t)
end do
j = 0
do i = 0, nx
up(i,j) = bc(x(i),y(j),t)
end do
i = nx
do j = 0, ny
up(i,j) = bc(x(i),y(j),t)
end do
j = ny
do i = 0, nx
up(i,j) = bc(x(i),y(j),t)
end do
return
end
%s
%s
%s
%s
""" % (f.F77_code('f'), bc.F77_code('bc'), I.F77_code('ic'), I.F77_pow())
f = open('_tmp.f', 'w')
f.write(code)
f.close()
cmd = "f2py -m f77 -c --fcompiler='gfortran' --build-dir tmp2"\
" -DF2PY_REPORT_ON_ARRAY_COPY=1 _tmp.f"
print cmd
os.system('rm -rf tmp2')
failure, output = system(cmd)
if failure:
print 'unsuccessful F77 extension module compilation'
print output
sys.exit(1)
def solver(
I,
f,
c,
bc,
Lx,
Ly,
nx,
ny,
dt,
tstop,
user_action=None,
implementation={
'ic': 'vectorized', # or 'scalar'
'inner': 'vectorized',
'bc': 'vectorized',
'storage': 'f77'
},
verbose=True):
"""
Solve the 2D wave equation u_tt = u_xx + u_yy + f(x,t) on (0,L) with
u = bc(x,y, t) on the boundary and initial condition du/dt = 0.
nx and ny are the total number of grid cells in the x and y
directions. The grid points are numbered as (0,0), (1,0), (2,0),
..., (nx,0), (0,1), (1,1), ..., (nx, ny).
dt is the time step. If dt<=0, an optimal time step is used.
tstop is the stop time for the simulation.
I, f, bc are functions: I(x,y), f(x,y,t), bc(x,y,t)
user_action: function of (u, x, y, t) called at each time
level (x and y are one-dimensional coordinate vectors).
This function allows the calling code to plot the solution,
compute errors, etc.
implementation: a dictionary specifying how the initial
condition ('ic'), the scheme over inner points ('inner'),
and the boundary conditions ('bc') are to be implemented.
Two values are legal: 'scalar' or 'vectorized'.
'scalar' means straight loops over grid points, while
'vectorized' means special NumPy vectorized operations.
If a key in the implementation dictionary is missing, it
defaults in this function to 'scalar' (the safest strategy).
Note that if 'vectorized' is specified, the functions I, f,
and bc must work in vectorized mode. It is always recommended
to first run the 'scalar' mode and then compare 'vectorized'
results with the 'scalar' results to check that I, f, and bc
work.
verbose: true if a message at each time step is written,
false implies no output during the simulation.
"""
dx = Lx / float(nx)
dy = Ly / float(ny)
x = linspace(0, Lx, nx + 1) # grid points in x dir
y = linspace(0, Ly, ny + 1) # grid points in y dir
xv = x[:, newaxis] # for vectorized function evaluations
yv = y[newaxis, :]
if dt <= 0: # max time step?
dt = (1 / float(c)) * (1 / sqrt(1 / dx**2 + 1 / dy**2))
Cx2 = (c * dt / dx)**2
Cy2 = (c * dt / dy)**2 # help variables
dt2 = dt**2
up = zeros((nx + 1, ny + 1)) # solution array
u = up.copy() # solution at t-dt
um = up.copy() # solution at t-2*dt
# use scalar implementation mode if no info from user:
if 'ic' not in implementation:
implementation['ic'] = 'scalar'
if 'bc' not in implementation:
implementation['bc'] = 'scalar'
if 'inner' not in implementation:
implementation['inner'] = 'scalar'
if 'f77' in implementation.itervalues():
# import F77 extension module, or build it if necessary
try:
import wave2D_func1_loop as f77
except:
print 'Make the F77 extension module on the fly...'
cmd = 'f2py -m wave2D_func1_loop -c --build-dir tmp1 '\
'-DF2PY_REPORT_ON_ARRAY_COPY=1 wave2D_func1_loop_0.f'
failure, output = system(cmd)
try:
import wave2D_func1_loop as f77
except:
print 'Something went wrong with f2py - '\
'try manual executition of\n ', cmd
print output
sys.exit(1)
# turn arrays to column major storage after the init. cond.
# set initial condition:
t = 0.0
if implementation['ic'] == 'scalar':
for i in iseq(0, nx):
for j in iseq(0, ny):
u[i, j] = I(x[i], y[j])
for i in iseq(1, nx - 1):
for j in iseq(1, ny - 1):
um[i,j] = u[i,j] + \
0.5*Cx2*(u[i-1,j] - 2*u[i,j] + u[i+1,j]) + \
0.5*Cy2*(u[i,j-1] - 2*u[i,j] + u[i,j+1]) + \
dt2*f(x[i], y[j], t)
# boundary values of um (equals t=dt when du/dt=0)
i = 0
for j in iseq(0, ny):
um[i, j] = bc(x[i], y[j], t + dt)
j = 0
for i in iseq(0, nx):
um[i, j] = bc(x[i], y[j], t + dt)
i = nx
for j in iseq(0, ny):
um[i, j] = bc(x[i], y[j], t + dt)
j = ny
for i in iseq(0, nx):
um[i, j] = bc(x[i], y[j], t + dt)
elif implementation['ic'] == 'vectorized' or \
implementation['ic'] == 'f77': # not impl. in F77
# vectorized version:
u = I(xv, yv)
um[1:nx,1:ny] = u[1:nx,1:ny] + \
0.5*Cx2*(u[0:nx-1,1:ny] - 2*u[1:nx,1:ny] + u[2:nx+1,1:ny]) + \
0.5*Cy2*(u[1:nx,0:ny-1] - 2*u[1:nx,1:ny] + u[1:nx,2:ny+1]) + \
dt2*f(xv[1:nx,:], yv[:,1:ny], 0.0)
# boundary values (t=dt):
i = 0
um[i, :] = bc(x[i], y, t + dt)
j = 0
um[:, j] = bc(x, y[j], t + dt)
i = nx
um[i, :] = bc(x[i], y, t + dt)
j = ny
um[:, j] = bc(x, y[j], t + dt)
if user_action is not None:
user_action(u, x, y, t) # allow user to plot etc.
while t <= tstop:
t_old = t
t += dt
if verbose:
print 'solving (%s version) at t=%g' % \
(implementation['inner'], t)
# update all inner points:
if implementation['inner'] == 'scalar':
for i in iseq(start=1, stop=nx - 1):
for j in iseq(start=1, stop=ny - 1):
up[i,j] = - um[i,j] + 2*u[i,j] + \
Cx2*(u[i-1,j] - 2*u[i,j] + u[i+1,j]) + \
Cy2*(u[i,j-1] - 2*u[i,j] + u[i,j+1]) + \
dt2*f(x[i], y[j], t_old)
elif implementation['inner'] == 'vectorized':
up[1:nx,1:ny] = - um[1:nx,1:ny] + 2*u[1:nx,1:ny] + \
Cx2*(u[0:nx-1,1:ny] - 2*u[1:nx,1:ny] + u[2:nx+1,1:ny]) + \
Cy2*(u[1:nx,0:ny-1] - 2*u[1:nx,1:ny] + u[1:nx,2:ny+1]) + \
dt2*f(xv[1:nx,:], yv[:,1:ny], t_old)
elif implementation['inner'] == 'f77':
f_array = f(xv, yv, t_old)
if isinstance(f_array, (float, int)):
# f was not properly vectorized, turn const into array:
f_array = zeros((x.size, y.size)) + f_array
up = f77.loop(u, um, f_array, Cx2, Cy2, dt2)
#id_u = id(u); id_um = id(um)
#up,u,um = f77.loop(up, u, um, f_array, Cx2, Cy2, dt2)
#print 'u changed:', id_u!=id(u),
#print 'um changed:', id_um!=id(um),
else:
raise ValueError, 'version=%s' % implementation['inner']
# insert boundary conditions:
if implementation['bc'] == 'scalar':
i = 0
for j in iseq(0, ny):
up[i, j] = bc(x[i], y[j], t)
j = 0
for i in iseq(0, nx):
up[i, j] = bc(x[i], y[j], t)
i = nx
for j in iseq(0, ny):
up[i, j] = bc(x[i], y[j], t)
j = ny
for i in iseq(0, nx):
up[i, j] = bc(x[i], y[j], t)
elif implementation['bc'] == 'vectorized' or \
implementation['ic'] == 'f77': # not impl. in F77
i = 0
up[i, :] = bc(x[i], y, t)
j = 0
up[:, j] = bc(x, y[j], t)
i = nx
up[i, :] = bc(x[i], y, t)
j = ny
up[:, j] = bc(x, y[j], t)
if user_action is not None:
user_action(up, x, y, t)
# update data structures for next step:
um, u, up = u, up, um
#tmp = um; um = u; u = up; up = tmp
# safer and slower: um = u.copy(); u = up.copy()
return dt # dt might be computed in this function
def solver(I, f, c, bc, Lx, Ly, nx, ny, dt, tstop,
user_action=None,
implementation={'ic': 'vectorized', # or 'scalar'
'inner': 'vectorized',
'bc': 'vectorized',
'storage': 'f77'},
verbose=True):
"""
Solve the 2D wave equation u_tt = u_xx + u_yy + f(x,t) on (0,L) with
u = bc(x,y, t) on the boundary and initial condition du/dt = 0.
nx and ny are the total number of grid cells in the x and y
directions. The grid points are numbered as (0,0), (1,0), (2,0),
..., (nx,0), (0,1), (1,1), ..., (nx, ny).
dt is the time step. If dt<=0, an optimal time step is used.
tstop is the stop time for the simulation.
I, f, bc are functions: I(x,y), f(x,y,t), bc(x,y,t)
user_action: function of (u, x, y, t) called at each time
level (x and y are one-dimensional coordinate vectors).
This function allows the calling code to plot the solution,
compute errors, etc.
implementation: a dictionary specifying how the initial
condition ('ic'), the scheme over inner points ('inner'),
and the boundary conditions ('bc') are to be implemented.
Two values are legal: 'scalar' or 'vectorized'.
'scalar' means straight loops over grid points, while
'vectorized' means special NumPy vectorized operations.
If a key in the implementation dictionary is missing, it
defaults in this function to 'scalar' (the safest strategy).
Note that if 'vectorized' is specified, the functions I, f,
and bc must work in vectorized mode. It is always recommended
to first run the 'scalar' mode and then compare 'vectorized'
results with the 'scalar' results to check that I, f, and bc
work.
verbose: true if a message at each time step is written,
false implies no output during the simulation.
"""
dx = Lx/float(nx)
dy = Ly/float(ny)
x = linspace(0, Lx, nx+1) # grid points in x dir
y = linspace(0, Ly, ny+1) # grid points in y dir
xv = x[:,newaxis] # for vectorized function evaluations
yv = y[newaxis,:]
if dt <= 0: # max time step?
dt = (1/float(c))*(1/sqrt(1/dx**2 + 1/dy**2))
Cx2 = (c*dt/dx)**2; Cy2 = (c*dt/dy)**2 # help variables
dt2 = dt**2
up = zeros((nx+1,ny+1)) # solution array
u = up.copy() # solution at t-dt
um = up.copy() # solution at t-2*dt
# use scalar implementation mode if no info from user:
if 'ic' not in implementation:
implementation['ic'] = 'scalar'
if 'bc' not in implementation:
implementation['bc'] = 'scalar'
if 'inner' not in implementation:
implementation['inner'] = 'scalar'
if 'f77' in implementation.itervalues():
# import F77 extension module, or build it if necessary
try:
import wave2D_func1_loop as f77
except:
print 'Make the F77 extension module on the fly...'
cmd = 'f2py -m wave2D_func1_loop -c --build-dir tmp1 '\
'-DF2PY_REPORT_ON_ARRAY_COPY=1 wave2D_func1_loop_0.f'
failure, output = system(cmd)
try:
import wave2D_func1_loop as f77
except:
print 'Something went wrong with f2py - '\
'try manual executition of\n ', cmd
print output
sys.exit(1)
# turn arrays to column major storage after the init. cond.
# set initial condition:
t = 0.0
if implementation['ic'] == 'scalar':
for i in iseq(0,nx):
for j in iseq(0,ny):
u[i,j] = I(x[i], y[j])
for i in iseq(1,nx-1):
for j in iseq(1,ny-1):
um[i,j] = u[i,j] + \
0.5*Cx2*(u[i-1,j] - 2*u[i,j] + u[i+1,j]) + \
0.5*Cy2*(u[i,j-1] - 2*u[i,j] + u[i,j+1]) + \
dt2*f(x[i], y[j], t)
# boundary values of um (equals t=dt when du/dt=0)
i = 0
for j in iseq(0,ny): um[i,j] = bc(x[i], y[j], t+dt)
j = 0
for i in iseq(0,nx): um[i,j] = bc(x[i], y[j], t+dt)
i = nx
for j in iseq(0,ny): um[i,j] = bc(x[i], y[j], t+dt)
j = ny
for i in iseq(0,nx): um[i,j] = bc(x[i], y[j], t+dt)
elif implementation['ic'] == 'vectorized' or \
implementation['ic'] == 'f77': # not impl. in F77
# vectorized version:
u = I(xv,yv)
um[1:nx,1:ny] = u[1:nx,1:ny] + \
0.5*Cx2*(u[0:nx-1,1:ny] - 2*u[1:nx,1:ny] + u[2:nx+1,1:ny]) + \
0.5*Cy2*(u[1:nx,0:ny-1] - 2*u[1:nx,1:ny] + u[1:nx,2:ny+1]) + \
dt2*f(xv[1:nx,:], yv[:,1:ny], 0.0)
# boundary values (t=dt):
i = 0; um[i,:] = bc(x[i], y, t+dt)
j = 0; um[:,j] = bc(x, y[j], t+dt)
i = nx; um[i,:] = bc(x[i], y, t+dt)
j = ny; um[:,j] = bc(x, y[j], t+dt)
if user_action is not None:
user_action(u, x, y, t) # allow user to plot etc.
while t <= tstop:
t_old = t; t += dt
if verbose:
print 'solving (%s version) at t=%g' % \
(implementation['inner'], t)
# update all inner points:
if implementation['inner'] == 'scalar':
for i in iseq(start=1, stop=nx-1):
for j in iseq(start=1, stop=ny-1):
up[i,j] = - um[i,j] + 2*u[i,j] + \
Cx2*(u[i-1,j] - 2*u[i,j] + u[i+1,j]) + \
Cy2*(u[i,j-1] - 2*u[i,j] + u[i,j+1]) + \
dt2*f(x[i], y[j], t_old)
elif implementation['inner'] == 'vectorized':
up[1:nx,1:ny] = - um[1:nx,1:ny] + 2*u[1:nx,1:ny] + \
Cx2*(u[0:nx-1,1:ny] - 2*u[1:nx,1:ny] + u[2:nx+1,1:ny]) + \
Cy2*(u[1:nx,0:ny-1] - 2*u[1:nx,1:ny] + u[1:nx,2:ny+1]) + \
dt2*f(xv[1:nx,:], yv[:,1:ny], t_old)
elif implementation['inner'] == 'f77':
f_array = f(xv, yv, t_old)
if isinstance(f_array, (float,int)):
# f was not properly vectorized, turn const into array:
f_array = zeros((x.size,y.size)) + f_array
up = f77.loop(u, um, f_array, Cx2, Cy2, dt2)
#id_u = id(u); id_um = id(um)
#up,u,um = f77.loop(up, u, um, f_array, Cx2, Cy2, dt2)
#print 'u changed:', id_u!=id(u),
#print 'um changed:', id_um!=id(um),
else:
raise ValueError, 'version=%s' % implementation['inner']
# insert boundary conditions:
if implementation['bc'] == 'scalar':
i = 0
for j in iseq(0,ny): up[i,j] = bc(x[i], y[j], t)
j = 0
for i in iseq(0,nx): up[i,j] = bc(x[i], y[j], t)
i = nx
for j in iseq(0,ny): up[i,j] = bc(x[i], y[j], t)
j = ny
for i in iseq(0,nx): up[i,j] = bc(x[i], y[j], t)
elif implementation['bc'] == 'vectorized' or \
implementation['ic'] == 'f77': # not impl. in F77
i = 0; up[i,:] = bc(x[i], y, t)
j = 0; up[:,j] = bc(x, y[j], t)
i = nx; up[i,:] = bc(x[i], y, t)
j = ny; up[:,j] = bc(x, y[j], t)
if user_action is not None:
user_action(up, x, y, t)
# update data structures for next step:
um, u, up = u, up, um
#tmp = um; um = u; u = up; up = tmp
# safer and slower: um = u.copy(); u = up.copy()
return dt # dt might be computed in this function
def solver(I, f, c, bc, Lx, Ly, nx, ny, dt, tstop,
user_action=None,
implementation={'ic': 'vectorized', # or 'scalar' or 'weave'
'inner': 'vectorized',
'bc': 'vectorized',
'storage': 'f77'},
verbose=True):
"""
Solve the 2D wave equation u_tt = u_xx + u_yy + f(x,t) on (0,L) with
u = bc(x,y, t) on the boundary and initial condition du/dt = 0.
nx and ny are the total number of grid cells in the x and y
directions. The grid points are numbered as (0,0), (1,0), (2,0),
..., (nx,0), (0,1), (1,1), ..., (nx, ny).
dt is the time step. If dt<=0, an optimal time step is used.
tstop is the stop time for the simulation.
I, f, bc are functions: I(x,y), f(x,y,t), bc(x,y,t)
user_action: function of (u, x, y, t) called at each time
level (x and y are one-dimensional coordinate vectors).
This function allows the calling code to plot the solution,
compute errors, etc.
implementation: a dictionary specifying how the initial
condition ('ic'), the scheme over inner points ('inner'),
and the boundary conditions ('bc') are to be implemented.
Two values are legal: 'scalar' or 'vectorized'.
'scalar' means straight loops over grid points, while
'vectorized' means special NumPy vectorized operations.
If a key in the implementation dictionary is missing, it
defaults in this function to 'scalar' (the safest strategy).
Note that if 'vectorized' is specified, the functions I, f,
and bc must work in vectorized mode. It is always recommended
to first run the 'scalar' mode and then compare 'vectorized'
results with the 'scalar' results to check that I, f, and bc
work.
verbose: true if a message at each time step is written,
false implies no output during the simulation.
"""
dx = Lx/float(nx)
dy = Ly/float(ny)
x = linspace(0, Lx, nx+1) # grid points in x dir
y = linspace(0, Ly, ny+1) # grid points in y dir
xv = x[:,newaxis] # for vectorized function evaluations
yv = y[newaxis,:]
if dt <= 0: # max time step?
dt = (1/float(c))*(1/sqrt(1/dx**2 + 1/dy**2))
Cx2 = (c*dt/dx)**2; Cy2 = (c*dt/dy)**2 # help variables
dt2 = dt**2
up = zeros((nx+1,ny+1)) # solution array
u = up.copy() # solution at t-dt
um = up.copy() # solution at t-2*dt
# use scalar implementation mode if no info from user:
if 'ic' not in implementation:
implementation['ic'] = 'scalar'
if 'bc' not in implementation:
implementation['bc'] = 'scalar'
if 'inner' not in implementation:
implementation['inner'] = 'scalar'
if 'weave' in implementation.itervalues() or \
'f77' in implementation.itervalues():
# we avoid callback to Python and require f, bc, and I to be
# string formulas:
if not isinstance(f, StringFunction) or \
not isinstance(bc, StringFunction) or \
not isinstance(I, StringFunction):
raise TypeError, \
'with Weave or F77, f, bc, and I must be StringFunction'
if 'f77' in implementation.itervalues():
# build F77 module:
code = """
subroutine scheme(up, u, um, x, y, nx, ny, Cx2, Cy2, dt2,
& t_old)
integer nx, ny
real*8 up(0:nx, 0:ny), u(0:nx, 0:ny), um(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 Cx2, Cy2, dt2, t_old
Cf2py intent(in, out) up
real*8 f
external f
do j = 1, ny-1
do i = 1, nx-1
up(i,j) = - um(i,j) + 2*u(i,j) +
& Cx2*(u(i-1,j) - 2*u(i,j) + u(i+1,j)) +
& Cy2*(u(i,j-1) - 2*u(i,j) + u(i,j+1)) +
& dt2*f(x(i),y(j),t_old)
end do
end do
return
end
subroutine initcond(u, um, x, y, nx, ny, Cx2, Cy2, dt2)
integer nx, ny
real*8 u(0:nx, 0:ny), um(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 Cx2, Cy2, dt2, dt
Cf2py intent(in, out) u, um
real*8 f, bc, ic
external f, bc, ic
do j = 0, ny
do i = 0, nx
u(i,j) = ic(x(i),y(j))
end do
end do
do j = 1, ny-1
do i = 1, nx-1
um(i,j) = u(i,j) +
& 0.5*Cx2*(u(i-1,j) - 2*u(i,j) + u(i+1,j)) +
& 0.5*Cy2*(u(i,j-1) - 2*u(i,j) + u(i,j+1)) +
& dt2*f(x(i),y(j),0.0D0)
end do
end do
C boundary values:
dt = sqrt(dt2)
i = 0
do j = 0, ny
um(i,j) = bc(x(i),y(j),dt)
end do
j = 0
do i = 0, nx
um(i,j) = bc(x(i),y(j),dt)
end do
i = nx
do j = 0, ny
um(i,j) = bc(x(i),y(j),dt)
end do
j = ny
do i = 0, nx
um(i,j) = bc(x(i),y(j),dt)
end do
return
end
subroutine bcond(up, x, y, nx, ny, t)
integer nx, ny
real*8 up(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 t
Cf2py intent(in, out) up
real*8 bc
external bc
i = 0
do j = 0, ny
up(i,j) = bc(x(i),y(j),t)
end do
j = 0
do i = 0, nx
up(i,j) = bc(x(i),y(j),t)
end do
i = nx
do j = 0, ny
up(i,j) = bc(x(i),y(j),t)
end do
j = ny
do i = 0, nx
up(i,j) = bc(x(i),y(j),t)
end do
return
end
%s
%s
%s
%s
""" % (f.F77_code('f'), bc.F77_code('bc'), I.F77_code('ic'), I.F77_pow())
f = open('_tmp.f', 'w')
f.write(code)
f.close()
# use old F2PY, installed as F2PY by hpl:
cmd = "F2PY -m f77 -c --fcompiler='Gnu' --build-dir tmp2"\
" -DF2PY_REPORT_ON_ARRAY_COPY=1 _tmp.f"
print cmd
shutil.rmtree('tmp2')
failure, output = system(cmd)
if failure:
print 'unsuccessful F77 extension module compilation'
print output
sys.exit(1)
import f77
# turn arrays to column major storage after the init. cond.
if 'weave' in implementation.itervalues():
# additional code with f, bc, and I functions:
extra_code = f.C_code('_f', inline=True) + \
bc.C_code('_bc', inline=True) + \
I.C_code('_I', inline=True)
# set initial condition:
t0 = time.clock()
t = 0.0
if implementation['ic'] == 'scalar':
for i in iseq(0,nx):
for j in iseq(0,ny):
u[i,j] = I(x[i], y[j])
for i in iseq(1,nx-1):
for j in iseq(1,ny-1):
um[i,j] = u[i,j] + \
0.5*Cx2*(u[i-1,j] - 2*u[i,j] + u[i+1,j]) + \
0.5*Cy2*(u[i,j-1] - 2*u[i,j] + u[i,j+1]) + \
dt2*f(x[i], y[j], t)
# boundary values of um (equals t=dt when du/dt=0)
i = 0
for j in iseq(0,ny): um[i,j] = bc(x[i], y[j], t+dt)
j = 0
for i in iseq(0,nx): um[i,j] = bc(x[i], y[j], t+dt)
i = nx
for j in iseq(0,ny): um[i,j] = bc(x[i], y[j], t+dt)
j = ny
for i in iseq(0,nx): um[i,j] = bc(x[i], y[j], t+dt)
elif implementation['ic'] == 'vectorized':
# vectorized version:
# not sure why we need f.vectorize when globals() is
# supplied in the constructor:
if isinstance(f, StringFunction):
f.vectorize(globals())
u[:,:] = I(xv,yv) # works for scalar I too...
um[1:nx,1:ny] = u[1:nx,1:ny] + \
0.5*Cx2*(u[0:nx-1,1:ny] - 2*u[1:nx,1:ny] + u[2:nx+1,1:ny]) + \
0.5*Cy2*(u[1:nx,0:ny-1] - 2*u[1:nx,1:ny] + u[1:nx,2:ny+1]) + \
dt2*f(xv[1:nx,:], yv[:,1:ny], 0.0)
# scalar f should be ok in all vectorized expressions
# boundary values (evaluate at t=dt since du/dt=0 at t=0):
i = 0; um[i,:] = bc(x[i], y, t+dt) # works for scalar bc too...
j = 0; um[:,j] = bc(x, y[j], t+dt)
i = nx; um[i,:] = bc(x[i], y, t+dt)
j = ny; um[:,j] = bc(x, y[j], t+dt)
elif implementation['ic'] == 'f77':
u, um = f77.initcond(u, um, x, y, Cx2, Cy2, dt2)
elif implementation['ic'] == 'weave':
code = """
int i,j;
for (i=0; i<=nx; i++) {
for (j=0; j<=ny; j++) {
u(i,j) = _I(x(i), y(j));
}
}
for (i=1; i<=nx-1; i++) {
for (j=1; j<=ny-1; j++) {
um(i,j) = u(i,j) + \
0.5*Cx2*(u(i-1,j) - 2*u(i,j) + u(i+1,j)) + \
0.5*Cy2*(u(i,j-1) - 2*u(i,j) + u(i,j+1)) + \
dt2*_f(x(i), y(j), t);
}
}
// boundary values of um (equals t=dt when du/dt=0)
double xv, yv;
i = 0; xv = x(i);
for (j=0; j<=ny; j++) { um(i,j) = _bc(xv, y(j), t+dt); }
j = 0; yv = y(j);
for (i=0; i<=nx; i++) { um(i,j) = _bc(x(i), yv, t+dt); }
i = nx; xv = x(i);
for (j=0; j<=ny; j++) { um(i,j) = _bc(xv, y(j), t+dt); }
j = ny; yv = y(j);
for (i=0; i<=nx; i++) { um(i,j) = _bc(x(i), yv, t+dt); }
"""
args = ['u', 'um', 'nx', 'ny', 'x', 'y',
'Cx2', 'Cy2', 'dt2', 'dt', 't']
err = weave.inline(code, args,
type_converters=weave.converters.blitz,
support_code=extra_code, compiler='gcc')
t_ic = time.clock() - t0
if implementation['inner'] == 'f77':
# turn input arrays to Fortran storage for all arrays
# that are input arrays in loop subroutine
# (actually not necessary as up, u, and um are all fed
# through the f77.loop routine and brought to column
# major storage in turn - recall um=u, u=up, up=um)
if implementation.get('storage', 'f77') == 'f77':
up = asarray(up, order='Fortran')
u = asarray(u, order='Fortran')
um = asarray(um, order='Fortran')
if user_action is not None:
user_action(u, xv, yv, t) # allow user to plot etc.
t_inner = 0 # CPU time inner loops
t_bc = 0 # CPU time boundary update
while t <= tstop:
t_old = t; t += dt
if verbose:
print 'solving (%s version) at t=%g' % \
(implementation['inner'], t)
t0 = time.clock()
# update all inner points:
if implementation['inner'] == 'scalar':
for i in iseq(start=1, stop=nx-1):
for j in iseq(start=1, stop=ny-1):
up[i,j] = - um[i,j] + 2*u[i,j] + \
Cx2*(u[i-1,j] - 2*u[i,j] + u[i+1,j]) + \
Cy2*(u[i,j-1] - 2*u[i,j] + u[i,j+1]) + \
dt2*f(x[i], y[j], t_old)
elif implementation['inner'] == 'vectorized':
up[1:nx,1:ny] = - um[1:nx,1:ny] + 2*u[1:nx,1:ny] + \
Cx2*(u[0:nx-1,1:ny] - 2*u[1:nx,1:ny] + u[2:nx+1,1:ny]) + \
Cy2*(u[1:nx,0:ny-1] - 2*u[1:nx,1:ny] + u[1:nx,2:ny+1]) + \
dt2*f(xv[1:nx,:], yv[:,1:ny], t_old)
elif implementation['inner'] == 'f77':
up = f77.scheme(up, u, um, x, y, Cx2, Cy2, dt2, t_old)
elif implementation['inner'] == 'weave':
code = """
int i,j;
for (i=1; i<=nx-1; i++) {
for (j=1; j<=ny-1; j++) {
up(i,j) = -um(i,j) + 2*u(i,j) + \
Cx2*(u(i-1,j) - 2*u(i,j) + u(i+1,j)) + \
Cy2*(u(i,j-1) - 2*u(i,j) + u(i,j+1)) + \
dt2*_f(x(i), y(j), t_old);
}
}
"""
args = ['up', 'u', 'um', 'nx', 'ny', 'x', 'y',
'Cx2', 'Cy2', 'dt2', 't_old']
err = weave.inline(code, args,
type_converters=weave.converters.blitz,
support_code=extra_code, compiler='gcc')
#id_u = id(u); id_um = id(um)
#up,u,um = f77.loop(up, u, um, f_array, Cx2, Cy2, dt2)
#print 'u changed:', id_u!=id(u),
#print 'um changed:', id_um!=id(um),
else:
raise ValueError, 'version=%s' % implementation['inner']
t_inner += time.clock() - t0
t0 = time.clock()
# insert boundary conditions:
if implementation['bc'] == 'scalar':
i = 0
for j in iseq(0,ny): up[i,j] = bc(x[i], y[j], t)
j = 0
for i in iseq(0,nx): up[i,j] = bc(x[i], y[j], t)
i = nx
for j in iseq(0,ny): up[i,j] = bc(x[i], y[j], t)
j = ny
for i in iseq(0,nx): up[i,j] = bc(x[i], y[j], t)
elif implementation['bc'] == 'vectorized':
i = 0; up[i,:] = bc(x[i], y, t)
j = 0; up[:,j] = bc(x, y[j], t)
i = nx; up[i,:] = bc(x[i], y, t)
j = ny; up[:,j] = bc(x, y[j], t)
elif implementation['ic'] == 'f77':
up = f77.bcond(up, x, y, t)
elif implementation['bc'] == 'weave':
code = """
// boundary values of u
double xv, yv; int i, j;
i = 0; xv = x(i);
for (j=0; j<=ny; j++) { up(i,j) = _bc(xv, y(j), t); }
j = 0; yv = y(j);
for (i=0; i<=nx; i++) { up(i,j) = _bc(x(i), yv, t); }
i = nx; xv = x(i);
for (j=0; j<=ny; j++) { up(i,j) = _bc(xv, y(j), t); }
j = ny; yv = y(j);
for (i=0; i<=nx; i++) { up(i,j) = _bc(x(i), yv, t); }
"""
args = ['up', 'nx', 'ny', 'x', 'y', 't']
err = weave.inline(code, args,
type_converters=weave.converters.blitz,
support_code=extra_code, compiler='gcc')
t_bc += time.clock() - t0
if user_action is not None:
user_action(up, xv, yv, t)
# update data structures for next step:
um, u, up = u, up, um
#tmp = um; um = u; u = up; up = tmp
# safer and slower: um = u.copy(); u = up.copy()
# dt might be computed in this function
return dt, t_ic, t_inner, t_bc
def make_f77(f, bc, I):
code = """
subroutine scheme_f77(up, u, um, x, y, t, nx, ny, Cx2, Cy2,
& dt2, t_old)
integer nx, ny
real*8 up(0:nx, 0:ny), u(0:nx, 0:ny), um(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 Cx2, Cy2, dt2, t, t_old
Cf2py intent(in, out) up
real*8 f
external f
do j = 1, ny-1
do i = 1, nx-1
up(i,j) = - um(i,j) + 2*u(i,j) +
& Cx2*(u(i-1,j) - 2*u(i,j) + u(i+1,j)) +
& Cy2*(u(i,j-1) - 2*u(i,j) + u(i,j+1)) +
& dt2*f(x(i),y(j),t_old)
end do
end do
return
end
subroutine ic_f77(u, um, x, y, nx, ny, Cx2, Cy2, dt)
integer nx, ny
real*8 u(0:nx, 0:ny), um(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 Cx2, Cy2, dt, dt2
Cf2py intent(in, out) u, um
real*8 f, ic
external f, ic
dt2 = dt*dt
do j = 0, ny
do i = 0, nx
u(i,j) = ic(x(i),y(j))
end do
end do
do j = 1, ny-1
do i = 1, nx-1
um(i,j) = u(i,j) +
& 0.5*Cx2*(u(i-1,j) - 2*u(i,j) + u(i+1,j)) +
& 0.5*Cy2*(u(i,j-1) - 2*u(i,j) + u(i,j+1)) +
& dt2*f(x(i),y(j),0.0D0)
end do
end do
C boundary values:
call bc_f77(um, x, y, nx, ny, dt)
return
end
subroutine bc_f77(up, x, y, nx, ny, t)
integer nx, ny
real*8 up(0:nx, 0:ny)
real*8 x(0:nx), y(0:ny)
real*8 t
Cf2py intent(in, out) up
real*8 bc
external bc
i = 0
do j = 0, ny
up(i,j) = bc(x(i),y(j),t)
end do
j = 0
do i = 0, nx
up(i,j) = bc(x(i),y(j),t)
end do
i = nx
do j = 0, ny
up(i,j) = bc(x(i),y(j),t)
end do
j = ny
do i = 0, nx
up(i,j) = bc(x(i),y(j),t)
end do
return
end
%s
%s
%s
%s
""" % (f.F77_code('f'), bc.F77_code('bc'), I.F77_code('ic'), I.F77_pow())
f = open('_tmp.f', 'w')
f.write(code)
f.close()
cmd = "f2py -m f77 -c --fcompiler='gfortran' --build-dir tmp2"\
" -DF2PY_REPORT_ON_ARRAY_COPY=1 _tmp.f"
print cmd
os.system('rm -rf tmp2')
failure, output = system(cmd)
if failure:
print 'unsuccessful F77 extension module compilation'
print output
sys.exit(1)
os.mkdir('tmp')
filelist = glob.glob('*.py')
for file in filelist: shutil.copy(file,'tmp')
shutil.rmtree('tmp')
# redirect output from a command into a variable:
cmd = "perl -pe '' hw.py"
resfile = os.popen(cmd)
res = resfile.readlines()
print "Output of the command " + cmd + " was\n"
for line in res:
print line, # the comma prevents extra newline
import commands
from scitools.misc import system
failure, res = system(cmd)
print res
#----------------------------------------------------------------------------
name = "/usr/home/hpl/scripting/perl/intro/hw.pl"
[head,tail] = os.path.split(name)
print "file=",name
print "head=",head
print "tail=",tail
basename = os.path.basename(name)
dirname = os.path.dirname(name)
print "dirname =",dirname
print "basename=",basename