# uu[:n] = u[:-1]; uu[n:2*n] = u[:-1]; uu[2*n:] = u
# du[:,istage] = -(uu[n+1:2*n+2] - uu[n-1:2*n]) / (2.0*dx)
# u[:] = u0
# for jstage in range(istage + 1):
# u += du[:,jstage] * dt * stages.beta[istage][jstage]
# os.system('mencoder mf://central_*.png -mf type=png:fps=10 -ovc lavc ' + \
# '-lavcopts vcodec=mpeg4:mbd=2:trell -oac copy -o central.avi')
# os.system('rm -rf central_*.png')
# interpolation based derivative
gamma = 2.0 / dx
xx = numpy.zeros(2*n+1)
xx[:n] = x[:-1]
xx[n:] = x + x[-1] - x[0]
da = interp_1d_grad_coef(n,xx,gamma)
u = numpy.exp(-25*x**2)
u = numpy.cos(-25*x)
u0 = numpy.zeros(n+1)
uu = numpy.zeros(3*n+1)
du = numpy.zeros([n+1, nstage])
for i in range(1001):
if i % 20 == 0:
print '%d / %d' % (i, 20000)
pylab.cla()
pylab.plot(x,u,'+-')
pylab.ylim([-0.5,1.0])
pylab.title('t = %f' % (i * dt))
pylab.savefig('periodic_interp_%04d.png' % int(i*dt*10/2))
u0[:] = u
# du[:,1,istage] = (uu[2:,0] - uu[:-2,0]) / (2.0*dx)
# u[:,:] = u0
# for jstage in range(istage + 1):
# u += du[:,:,jstage] * dt * stages.beta[istage][jstage]
# u[0,0] = 0.0; u[-1,0] = 0.0
# # u[0,1] = u[1,1]; u[-1,1] = u[-2,1]
# os.system('mencoder mf://wave_central_*.png -mf type=png:fps=10 -ovc lavc ' + \
# '-lavcopts vcodec=mpeg4:mbd=2:trell -oac copy -o wave_central.avi')
# os.system('rm -rf wave_central_*.png')
# interpolation based derivative
gamma = 2.0 / dx
da = numpy.zeros([n+1, n+1])
for i in range(n+1):
da[:,i] = interp_1d_grad_coef(i,x,gamma)
u = numpy.zeros([n+1, 2])
u[:,0] = numpy.exp(-25*x**2)
u[:,1] = u[:,0]
u0 = numpy.zeros([n+1, 2])
du = numpy.zeros([n+1, 2, nstage])
for i in range(1001):
if i % 20 == 0:
print '%d / %d' % (i, 20000)
pylab.cla()
pylab.plot(x,u,'+-')
pylab.ylim([-2.0,2.0])
pylab.title('t = %f' % (i * dt))
pylab.savefig('wave_interp_%04d.png' % int(i*dt*10/2))
u0[:,:] = u
# pylab.matplotlib.interactive(True)
n = 50
s = numpy.linspace(-1, 1, n+1)
dx = s[1] - s[0]
gamma = 2.0 / dx
dt = 0.005
stages = rungekutta.runge6
nstage = len(stages.alpha)
# interpolation based derivative
# x = numpy.sin(s * numpy.pi / 2)
x = s
da = numpy.zeros([n+1, n+1])
for i in range(1,n):
if i < n - i:
da[:2*i+1,i] = interp_1d_grad_coef(i,s[:2*i+1],gamma)
else:
# da[2*i-n:,i] = interp_1d_grad_coef(n-i,s[2*i-n:],gamma)
da[:,i] = interp_1d_grad_coef(i,s,gamma)
# da[:,i] /= numpy.cos(s[i] * numpy.pi / 2)
pylab.plot(x, da, '+-')
# pylab.show()
# stop
u = numpy.exp(-x**2*10)
u = numpy.cos(-(x+1)*10)
u0 = numpy.zeros(n+1)
du = numpy.zeros([n+1, nstage])
for i in range(1001):
if i % 20 == 0:
print '%d / %d' % (i, 20000)
# for jstage in range(istage + 1):
# u += du[:,:,jstage] * dt * stages.beta[istage][jstage]
# u[0,0] = 0.0; u[-1,0] = 0.0
# # u[0,1] = u[1,1]; u[-1,1] = u[-2,1]
# os.system('mencoder mf://wave_central_*.png -mf type=png:fps=10 -ovc lavc ' + \
# '-lavcopts vcodec=mpeg4:mbd=2:trell -oac copy -o wave_central.avi')
# os.system('rm -rf wave_central_*.png')
# interpolation based derivative
gamma = 2.0 / dx
da1 = numpy.zeros([n+1, n+1])
da2 = numpy.zeros([n+1, n+1])
for i in range(n+1):
if i < n - i:
da1[:2*i+1,i] = interp_1d_grad_coef(i,x[:2*i+1],gamma)
da2[:,i] = interp_1d_grad_coef(i,x,gamma)
else:
da1[:,i] = interp_1d_grad_coef(i,x,gamma)
da2[2*i-n:,i] = interp_1d_grad_coef(n-i,x[2*i-n:],gamma)
#pylab.plot(da[:,0], '+-')
#pylab.plot(da[:,n/2], '+-')
#stop
u = numpy.zeros([n+1, 2])
u[:,0] = numpy.exp(-25*x**2)
u0 = numpy.zeros([n+1, 2])
du = numpy.zeros([n+1, 2, nstage])
for i in range(1001):
if i % 10 == 0:
print '%d / %d' % (i, 20000)