def solver_scaled(T, dt, theta):
"""
Solve u'=-u, u(0)=1 for (0,T] with step dt and theta method.
"""
# Is the scaled problem already solved and dimensionless
# curve available from file?
# See if u_scaled.dat has the right parameters.
already_computed = False
datafile = 'u_scaled.dat'
if os.path.isfile(datafile): # does u_scaled.dat exist?
infile = open(datafile, 'r')
infoline = infile.readline() # read the first line
words = infoline.split() # split line into words
T_, dt_, theta_ = [float(w) for w in words]
if T_ == T and dt_ == dt and theta_ == theta:
# The file was computed with the desired data, load
# the solution into arrays
data = np.loadtxt(infile)
u_scaled = data[1,:]
t_scaled = data[0,:]
print 'Read scaled solution from file'
already_computed = True
infile.close()
if not already_computed:
# T, dt or theta is different from u_scaled.dat
u_scaled, t_scaled = \
solver_unscaled(I=1, a=1, T=T, dt=dt, theta=theta)
outfile = open(datafile, 'w')
outfile.write('%f %f %.1f\n' % (T, dt, theta))
# np.savetxt saves a two-dim array (table) to file
np.savetxt(outfile, np.array([t_scaled, u_scaled]))
outfile.close()
print 'Computed scaled solution'
return u_scaled, t_scaled
def solver_scaled(T, dt, theta):
"""
Solve u'=-u, u(0)=1 for (0,T] with step dt and theta method.
"""
# Is the scaled problem already solved and dimensionless
# curve available from file?
# See if u_scaled.dat has the right parameters.
already_computed = False
datafile = 'u_scaled.dat'
if os.path.isfile(datafile): # does u_scaled.dat exist?
infile = open(datafile, 'r')
infoline = infile.readline() # read the first line
words = infoline.split() # split line into words
T_, dt_, theta_ = [float(w) for w in words]
if T_ == T and dt_ == dt and theta_ == theta:
# The file was computed with the desired data, load
# the solution into arrays
data = np.loadtxt(infile)
u_scaled = data[1, :]
t_scaled = data[0, :]
print 'Read scaled solution from file'
already_computed = True
infile.close()
if not already_computed:
# T, dt or theta is different from u_scaled.dat
u_scaled, t_scaled = \
solver_unscaled(I=1, a=1, T=T, dt=dt, theta=theta)
outfile = open(datafile, 'w')
outfile.write('%f %f %.1f\n' % (T, dt, theta))
# np.savetxt saves a two-dim array (table) to file
np.savetxt(outfile, np.array([t_scaled, u_scaled]))
outfile.close()
print 'Computed scaled solution'
return u_scaled, t_scaled
def solver_scaled(T, dt, theta):
"""
Solve u'=-u, u(0)=1 for (0,T] with step dt and theta method.
"""
print 'Computing the numerical solution'
return solver_unscaled(I=1, a=1, T=T, dt=dt, theta=theta)