def test_radial_waves(plot=1, version='scalar'):
L = 1
c = 1
def I(r):
return 0
def f(r, t):
return 8 * exp(-100 * r) * sin(100 * t)
def U_L_func(t):
return 0
n = 500
dr = L / float(n)
dt = 0.5 * dr
tstop = 2
if plot:
g = graph(program='Gnuplot')
g.configure(ymin=-0.055, ymax=0.055)
else:
g = None
dt, r, v, cpu = solver_r(I,
f,
c,
U_L_func,
L,
n,
dt,
tstop,
g,
user_action=None,
version=version)
print 'CPU time', version, 'version:', cpu
print 'v[0] final time:', v[-1][0]
def test_solver2(N, plot=True, version='scalar'):
s = StoreSolution()
s.main(N, version)
print 'CPU time:', s.cpu
if len(s.x) < 10: print s.solutions
if plot:
from CurveViz import graph
g = graph(program='Gnuplot', coor=s.x, ymax=1, ymin=-1)
for s in s.solutions:
g.plotcurve(s)
def test_solver2(N, plot=True, version='scalar'):
s = StoreSolution()
s.main(N, version)
print 'CPU time:', s.cpu
if len(s.x) < 10: print s.solutions
if plot:
from CurveViz import graph
g = graph(program='Gnuplot', coor=s.x, ymax=1, ymin=-1)
for s in s.solutions:
g.plotcurve(s)
def test_solver_plug(plot=1, version='scalar', n=50):
L = 1
c = 1
tstop = 2
def I(x):
"""Plug profile as initial condition."""
if abs(x - L / 2.0) > 0.1:
return 0
else:
return 1
def f(x, t):
return 0
def U_0(t):
return 0
def U_L(t):
return 0
def action(u, x, t):
pass
#print t, u
if plot:
g = graph(program='Gnuplot')
g.configure(ymin=-1.1, ymax=1.1)
else:
g = None
import time
t0 = time.clock()
solutions, x, dt, cpu = visualizer(I,
f,
c,
U_0,
U_L,
L,
n,
0,
tstop,
user_action=None,
version=version,
graphics=g)
print 'CPU time: %s version =' % version, cpu
# check that first and last (if tstop=2) are equal:
if not allclose(solutions[0], solutions[-1], atol=1.0E-10, rtol=1.0E-12):
print 'error in computations'
else:
print 'correct solution'
def __init__(self, solver, plot=0, **graphics_kwargs):
"""Store solver instance. Initialize graphics tool."""
self.s = solver
self.solutions = [] # store self.up at each time level
if not 'program' in graphics_kwargs:
graphics_kwargs['program'] = 'Gnuplot'
self._plot = plot
if self._plot:
self.g = graph(**graphics_kwargs)
# could use scitools.easyviz.blt_ instead...
else:
self.g = None
def __init__(self, solver, plot=0, **graphics_kwargs):
"""Store solver instance. Initialize graphics tool."""
self.s = solver
self.solutions = [] # store self.up at each time level
if not 'program' in graphics_kwargs:
graphics_kwargs['program'] = 'Gnuplot'
self._plot = plot
if self._plot:
self.g = graph(**graphics_kwargs)
# could use scitools.easyviz.blt_ instead...
else:
self.g = None
def test2(program, parent=None):
from CurveViz import graph
t = linspace(-4, 4, 81)
g = graph(coor=t, ymin=-1.2, ymax=1.2, xlabel='t',
program=program, parent_frame=parent)
# make animations:
for p in linspace(0, 3, 13):
u = exp(-p*p)*(sin(t) + 0.2*sin(5*t))
g.plotcurve((t,u), legend='u(t); p=%4.2f' % p)
# plot several curves in one plot:
t = linspace(0, 10, 101)
g.configure(coor=t) # change coordinate vector
g.configure(ymin=-4, ymax=4, ylabel='u')
u1 = sin(t)*t; u2 = sin(t)*sqrt(t)
g.plotcurves([((t,u1),'t ampl.'),((t,u2),'sqrt(t) ampl.')], ps=1)
def test2(program, parent=None):
from CurveViz import graph
t = linspace(-4, 4, 81)
g = graph(coor=t, ymin=-1.2, ymax=1.2, xlabel='t',
program=program, parent_frame=parent)
# make animations:
for p in linspace(0, 3, 13):
u = exp(-p*p)*(sin(t) + 0.2*sin(5*t))
g.plotcurve((t,u), legend='u(t); p=%4.2f' % p)
# plot several curves in one plot:
t = linspace(0, 10, 101)
g.configure(coor=t) # change coordinate vector
g.configure(ymin=-4, ymax=4, ylabel='u')
u1 = sin(t)*t; u2 = sin(t)*sqrt(t)
g.plotcurves([((t,u1),'t ampl.'),((t,u2),'sqrt(t) ampl.')], ps=1)
def test_solver_plug(plot=1, version='scalar', n=50):
L = 1
c = 1
tstop = 2
def I(x):
"""Plug profile as initial condition."""
if abs(x-L/2.0) > 0.1:
return 0
else:
return 1
def f(x,t):
return 0
def U_0(t):
return 0
def U_L(t):
return 0
def action(u, x, t):
pass
#print t, u
if plot:
g = graph(program='Gnuplot')
g.configure(ymin=-1.1, ymax=1.1)
else:
g = None
import time
t0 = time.clock()
solutions, x, dt, cpu = visualizer(I, f, c, U_0, U_L, L,
n, 0, tstop, user_action=None, version=version, graphics=g)
print 'CPU time: %s version =' % version, cpu
# check that first and last (if tstop=2) are equal:
if not allclose(solutions[0], solutions[-1],
atol=1.0E-10, rtol=1.0E-12):
print 'error in computations'
else:
print 'correct solution'
def test_radial_waves(plot=1, version='scalar'):
L = 1
c = 1
def I(r): return 0
def f(r,t):
return 8*exp(-100*r)*sin(100*t)
def U_L_func(t):
return 0
n = 500
dr = L/float(n)
dt = 0.5*dr
tstop = 2
if plot:
g = graph(program='Gnuplot')
g.configure(ymin=-0.055, ymax=0.055)
else:
g = None
dt, r, v, cpu = solver_r(I, f, c, U_L_func, L, n, dt, tstop,
g, user_action=None, version=version)
print 'CPU time', version, 'version:', cpu
print 'v[0] final time:', v[-1][0]
def solver_r_v1(I, f, c, U_L, L, n, dt, tstop,
version='scalar', plot=True, umin=0, umax=1):
"""
1D wave equation as in wave1D_func1.solver, but the present
function models spherical waves. The physical solution is v=u/r.
The boundary condition at r=0 is u=0 because of symmetry
so u(L)=U_L is the only free boundary condition.
This version winds numerical solution and visualization
together. An alternative is the solver_r function.
"""
import time
t0 = time.clock()
dr = L/float(n)
r = linspace(0, L, n+1) # grid points in r dir
if dt <= 0: dt = dr/float(c) # max time step? stability limit
C2 = (c*dt/dr)**2 # help variable in the scheme
dt2 = dt*dt
up = zeros(n+1) # solution array
u = up.copy() # solution at t-dt
um = up.copy() # solution at t-2*dt
v = up.copy() # physical solution (up/r)
# set initial condition (pointwise - allows straight if-tests):
for i in iseq(0,n):
u[i] = I(r[i])
for i in iseq(1,n-1):
um[i] = u[i] + 0.5*C2*(u[i-1] - 2*u[i] + u[i+1]) + \
dt2*f(x[i], t)
um[0] = 0; um[n] = U_L(t+dt)
if plot:
g = graph(program='Gnuplot')
g.configure(ymin=umin, ymax=umax, coor=r)
v[1:] = u[1:]/r[1:]
v[0] = v[1] # from the b.c. dv/dr=0 at r=0
g.plotcurve(v, legend='u(r,t=0)')
solutions = [u.copy()] # hold all u arrays, start with init cond.
t = 0.0
while t <= tstop:
t_old = t; t += dt
# update all inner points:
if version == 'scalar':
for i in iseq(start=1, stop=n-1):
up[i] = - um[i] + 2*u[i] + \
C2*(u[i-1] - 2*u[i] + u[i+1]) + \
dt2*f(r[i], t_old)
elif version == 'vectorized':
up[1:n] = - um[1:n] + 2*u[1:n] + \
C2*(u[0:n-1] - 2*u[1:n] + u[2:n+1]) + \
dt2*f(r[1:n], t_old)
# insert boundary conditions:
up[0] = 0; up[n] = U_L(t)
# physical solution:
v[1:] = up[1:]/r[1:]; v[0] = v[1]
# update data structures for next step
um = u.copy(); u = up.copy()
# efficiency improvement of the update:
# tmp = um; um = u; u = up; up = tmp
if plot: g.plotcurve(v, legend='v(r,t=%9.4E)' % t)
solutions.append(v.copy()) # save a copy!
t1 = time.clock()
return dt, r, solutions, t1-t0
def solver_r_v1(I,
f,
c,
U_L,
L,
n,
dt,
tstop,
version='scalar',
plot=True,
umin=0,
umax=1):
"""
1D wave equation as in wave1D_func1.solver, but the present
function models spherical waves. The physical solution is v=u/r.
The boundary condition at r=0 is u=0 because of symmetry
so u(L)=U_L is the only free boundary condition.
This version winds numerical solution and visualization
together. An alternative is the solver_r function.
"""
import time
t0 = time.clock()
dr = L / float(n)
r = linspace(0, L, n + 1) # grid points in r dir
if dt <= 0: dt = dr / float(c) # max time step? stability limit
C2 = (c * dt / dr)**2 # help variable in the scheme
dt2 = dt * dt
up = zeros(n + 1) # solution array
u = up.copy() # solution at t-dt
um = up.copy() # solution at t-2*dt
v = up.copy() # physical solution (up/r)
# set initial condition (pointwise - allows straight if-tests):
for i in iseq(0, n):
u[i] = I(r[i])
for i in iseq(1, n - 1):
um[i] = u[i] + 0.5*C2*(u[i-1] - 2*u[i] + u[i+1]) + \
dt2*f(x[i], t)
um[0] = 0
um[n] = U_L(t + dt)
if plot:
g = graph(program='Gnuplot')
g.configure(ymin=umin, ymax=umax, coor=r)
v[1:] = u[1:] / r[1:]
v[0] = v[1] # from the b.c. dv/dr=0 at r=0
g.plotcurve(v, legend='u(r,t=0)')
solutions = [u.copy()] # hold all u arrays, start with init cond.
t = 0.0
while t <= tstop:
t_old = t
t += dt
# update all inner points:
if version == 'scalar':
for i in iseq(start=1, stop=n - 1):
up[i] = - um[i] + 2*u[i] + \
C2*(u[i-1] - 2*u[i] + u[i+1]) + \
dt2*f(r[i], t_old)
elif version == 'vectorized':
up[1:n] = - um[1:n] + 2*u[1:n] + \
C2*(u[0:n-1] - 2*u[1:n] + u[2:n+1]) + \
dt2*f(r[1:n], t_old)
# insert boundary conditions:
up[0] = 0
up[n] = U_L(t)
# physical solution:
v[1:] = up[1:] / r[1:]
v[0] = v[1]
# update data structures for next step
um = u.copy()
u = up.copy()
# efficiency improvement of the update:
# tmp = um; um = u; u = up; up = tmp
if plot: g.plotcurve(v, legend='v(r,t=%9.4E)' % t)
solutions.append(v.copy()) # save a copy!
t1 = time.clock()
return dt, r, solutions, t1 - t0