def plotEvolution():
#ky_list = linspace(0.3, pi, 17)
ky_list = logspace(-1, log10(pi), 3)
results = []
"""
for w0 in [ -0.4 + 0.05j , -0.2 + 0.01j, - 0.8 - 0.01j, - 1.2 - 0.04j ]:
res = []
for n in range(len(ky_list)):
w0 = solveDispersion(ky_list[n], (w0, w0+0.01, w0+0.001j), doPlots=False)
res.append(w0)
results.append(res)
"""
w0 = -0.4 + 0.05j
for w0_init in [ -0.25 + 0.05j, -0.5 + 0.01j, -0.4 + 0.02 ]:
res = []
idx_l = where(ky_list < 2.55)
idx_u = where(ky_list >= 2.55)
idx = append(idx_u, idx_l[0][::-1])
ky_list_mod = ky_list[idx]
for n in range(len(ky_list)):
print " ky ---> " , ky_list[idx][n]
if (abs(ky_list[idx][n] - 2.55) < 0.1) : w0 = w0_init
w0 = solveDispersion(ky_list[idx][n], (w0, w0+0.01, w0+0.001j), doPlots=False)
res.append(w0)
res = array(res)
results.append(res[idx])
results = array(results)
#fig = gkcStyle.newFigure(ratio='1.41:1', basesize=9)
fig = gkcStyle.newFigure(ratio='1.41:1', basesize=18)
subplot(121)
for res in results:
semilogx(ky_list, imag(res), '-', label='imag')
gkcStyle.plotZeroLine(min(ky_list), max(ky_list))
xlim((min(ky_list), max(ky_list)))
xlabel("$k_y$")
ylabel("Growthrates $\\gamma$")
#savefig("Growthrate.pdf", bbox_inches='tight')
subplot(122)
#clf()
for res in results:
semilogx(ky_list, real(res), '-', label='imag')
gkcStyle.plotZeroLine(min(ky_list), max(ky_list))
xlim((min(ky_list), max(ky_list)))
xlabel("$k_y$")
ylabel("Frequency $\\gamma$")
savefig("Frequency.pdf", bbox_inches='tight')
# Save max tendency
savetxt("Tendency.txt", array([ky_list, real(results), imag(results)]).T)
def solveDispersion(ky):
L = zeros((Nx,Nx), dtype=complex)
def setup_L(w):
L[:,:] = 0.
iCode.setupMatrixPy(species, w, ky, X, kx_list, Ls, Ln, Nx, L, dk*dx, lambda_D2)
return L
def solveEquation(w):
w = complex(w)
L = setup_L(w)
# Get Minium absolute eigenvalue.
#
# The non-linear eigenvalue problem obeys
# det(L) = 0. This requirement is equal
# to an eigenvalue 0 for the linear eigenvalue
# problem det(L'- lambda I) = 0, which is identical
# to the non-linear requirenement once lambda = 0.
#
# [ This is less sensitive (and thus numerically less demanding)
# than caluculating directly the determinant
val = getMinEigenvalue(L)
#val = det(A)
#(sign, logdet) = np.linalg.slogdet(L)
#val = sign * logdet
print ky, " w : %.8f+%.8f j" % (real(complex(w)), imag(complex(w))) , " Determinant : %.2e " % abs(val)
return val
try :
#omega = complex(mp.findroot(solveEquation, (w0, w0+0.05, w0-0.005j), solver='muller', tol=1.e-15, ftol=1.e-15, maxsteps=5000))
omega = complex(mp.findroot(solveEquation, (w0, w0-0.01, w0+0.001j), solver='muller', tol=1.e-15, ftol=1.e-15, maxsteps=5000))
except:
return float('nan') + 1.j * float('nan')
#traceback.print_exc(file=sys.stdout)
try:
# n = 0
# solution found for w0, get solution vector
werr = solveEquation(omega)
L = setup_L(omega)
# We found our eigenvalue omega, now we use the
# inverse iteration to find the closest eigenvector
# to the eigenvalue
L__lambda_I = L - omega * eye(Nx)
# Start with random inital eigenvector
b = 1. * rand(Nx) + 1.j * rand(Nx)
# Convergence is fast thus large iteration number not required
# However, how to best check the error ?
# e.g. A dot phi
# Tested also, Rayleigh-Quotient Iteration but less successfull.
for n in range(128):
# rescale b
b = b/real(sqrt(vdot(b,b)))
# inverse iteration
b = solve(L__lambda_I, b)
# calculate error
r = dot(L,b)
residual = real(sqrt(vdot(r,r)))
print("I-I Residual : %.2e " % residual )
if (residual < 1.e-9) : break
clf()
fig = gkcStyle.newFigure(ratio='1.41:1', basesize=9)
fig.suptitle("$\omega_0$ = %.4f %.4fi $\pm$ %.2e %.2e i" % (real(omega), imag(omega), real(werr), imag(werr)))
###################### Plot Fourier Modes ##########3
plot(kx_list, real(b), 'r.-', label="real")
plot(kx_list, imag(b), '.-', label="imag", color=gkcStyle.color_indigo)
xlim((min(kx_list), max(kx_list)))
xlabel("$k_x$")
ylabel("$\phi(k_x)$")
legend(ncol=2).draw_frame(0)
savefig(str(ky) + "_Plot1.pdf", bbox_inches='tight')
################### Plot real modes ########3
clf()
# We have to transform to FFTW format, which has
# form of [ k=0, k=1, ..., k = N/2, k = -(N/2-1), ..., k=-1 ]
F = append(append(b[Nx/2], b[Nx/2+1:]), b[:Nx/2])
K = np.fft.ifft(F)
K = append(append(K[Nx/2], K[Nx/2+1:]), K[:Nx/2])
# Correct for phase
K = K * exp(-1.j*arctan2(imag(sum(K)),real(sum(K))))
#print " Phase : " , arctan2(imag(sum(K)),real(sum(K)))
#F_list = append(append(kx_list[Nx/2], kx_list[Nx/2+1:]), kx_list[:Nx/2])
#print "fft kx_list -----------> " , F_list
plot(X, real(K), 'r.-', label='real')
plot(X, imag(K), '.-', label='imag', color=gkcStyle.color_indigo)
plot(X, abs(K), 'g-', label='abs', linewidth=5., alpha=0.5)
xlim((min(X), max(X)))
xlabel("$x$")
ylabel("$\phi(x)$")
legend(ncol=2).draw_frame(0)
savefig(str(ky) + "_Plot2.pdf", bbox_inches='tight')
################ Plot Contour
clf()
y = linspace(0., Ly, 512)
KxKy = zeros((Nx, 65), dtype=complex)
nky = ky * Ly / (2.*pi)
KxKy[:,nky] = K
#np.fft.ifft(F)
XY = np.fft.irfft(KxKy, axis=1, n=512)
xlabel("$x$")
ylabel("$y$")
contourf(X, y, XY.T, 20, vmin=-abs(XY).max(), vmax=abs(XY).max())
#contourf(X, y, XY.T, 20, vmin=-abs(XY).max(), vmax=abs(XY).max())
colorbar()
savefig(str(ky) + "_Plot3.pdf", bbox_inches='tight')
# append and normalize
sol.append(np.fft.ifft(b/abs(b).max()))
except:
traceback.print_exc(file=sys.stdout)
return omega
def solveDispersion(ky):
A = zeros((Nx,Nx), dtype=complex)
def setupA(w):
A[:,:] = 0.
iCode.setupMatrixPy(species, w, ky, X, kx_list, Ls, Ln, Nx, A, dk*dx, lambda_D2)
return A
def solveEquation(w):
global D_min, w_min
A = setupA(complex(w))
#print A
#val = SlepcDet.getMinAbsEigenvalue(A)
val = SlepcDet.getMinAbsEigenvaluLA(A)
#val = det(A)
#(sign, logdet) = np.linalg.slogdet(A)
#val = sign * logdet
if abs(val) < abs(D_min) : w_min = complex(w)
print ky, " w : %.3f+%.3f j" % (real(complex(w)), imag(complex(w))) , " Determinant : %.2e " % abs(val)
if val != val: return 0. + 0.j
return val
try :
w0= -0.01 + 0.02j
w_damp = complex(mp.findroot(solveEquation, (w0, w0-0.005j, w0+0.005), solver='muller', tol=1.e-8, ftol=1.e-8, maxsteps=5000))
#w_damp = PyPPL.getZero(solveEquation, init=(w0, w0+0.01j, w0+0.02), solver='muller', tol=1.e-9, ftol=1.e-6, maxsteps=5000)
except:
traceback.print_exc(file=sys.stdout)
try:
#for n in range(Nx):
n = 0
global w_min
print "-----------------> ", w_min
# solution found for w0, get solution vector
werr = solveEquation(w_min)
A = setupA(w_min)
#print A
#S = solve(A, append(1.+0.j,zeros(Nx-1, dtype=complex)))
#S = solve(A, append(1.+0.j, append(zeros(Nx-2, dtype=complex), 1.+0.j)))
#b = append(0., append(1.+0., zeros(Nx-2, dtype=complex)))
#b = zeros(Nx, dtype=complex)
#b = ones(Nx, dtype=complex)
#b[:] = 0. ;
#b[0] = 1.
#S, err = solve(A, b), 0.
#S, err = sla.lgmres(A,b, tol=1.e-9)
# We found our eigenvalue w_min, now we use the
# inverse iteration to find the closest eigenvector
I = (1.+0.j) * eye(Nx)
b = (1.+1.j) * ones(Nx, dtype=complex)
for n in range(4096):
b_prev = b
b = solve(A - w_min * I, b)
# RESCALE
b = b / sum(abs(b))
if (abs(sum( sqrt(sum(b**2)/sum(b_prev**2)) * b_prev - b )) < 1.e-10) : break
#print("Eigv Error : %.2e Abs : %.2e " % (abs(sum( sqrt(sum(b**2)/sum(b_prev**2)) * b_prev - b )), sum(abs(b))) )
#print "Sol : " , b
clf()
gkcStyle.newFigure(ratio='2.33:1', basesize=12)
subplot(131)
fig.suptitle("$\omega_0$ = %.4f %.4fi $\pm$ %.2e %.2e i" % (real(w_min), imag(w_min), real(werr), imag(werr)))
###################### Plot Fourier Modes ##########3
b = -real(b) + 1.j * imag(b)
plot(kx_list, real(b), 'r.-', label="real")
plot(kx_list, imag(b), '.-', label="imag", color=gkcStyle.color_indigo)
xlim((min(kx_list), max(kx_list)))
xlabel("$k_x$")
ylabel("$\phi(k_x)$")
legend(ncol=2).draw_frame(0)
################### Plot real modes ########3
subplot(132)
# Remove High frequency modes
#b[:3] = 0.;
#b[-4:] = 0.;
# We have to transform to FFTW format
F = append(append(b[Nx/2], b[Nx/2+1:]), b[:Nx/2])
print "F--------------->", F
plot(X,real(np.fft.ifft(F)), 'r.-', label='real')
plot(X,imag(np.fft.ifft(F)), '.-', label='imag', color=gkcStyle.color_indigo)
xlim((min(X), max(X)))
xlabel("$x$")
ylabel("$\phi(x)$")
legend(ncol=2).draw_frame(0)
################ Plot Contour
subplot(133)
y = linspace(0., Ly, 128)
KxKy = zeros((Nx, 65), dtype=complex)
nky = ky * Ly / (2.*pi)
KxKy[:,nky] = np.fft.ifft(F)
XY = np.fft.irfft(KxKy, axis=1)
xlabel("$x$")
ylabel("$y$")
contourf(X, y, XY.T, 20, vmin=-abs(XY).max(), vmax=abs(XY).max())
colorbar()
savefig("Plot2_" + str(ky) + ".png", bbox_inches='tight')
# append and normalize
sol.append(np.fft.ifft(b/abs(b).max()))
except:
#species = [ Species(name= "Adiab"), Species(m=1.,q=1.,T=1.,n=1.,eta=5., name="Ion"), Species(m=0.0025,q=-1.,T=1.,n=1., eta=0., name="Electron") ]
traceback.print_exc(file=sys.stdout)
return w_min, abs(solveEquation(w_min))
# std-ITG (1)
w_0, kx, phi_k, x, phi_0 = disp.solveEquation((w0, w0+0.0005, w0+0.0002j), 0.49, stdSetup_swITG)
# sw-ITG (1)
w_1, kx, phi_k, x, phi_1 = disp.solveEquation((w0, w0+0.0005, w0+0.0002j), 2.5, stdSetup_swITG)
# sw-ITG (2)
w_2, kx, phi_k, x, phi_2 = disp.solveEquation((w0, w0+0.0005, w0+0.0002j), 9., stdSetup_swITG)
"""
# sw-ITG (2)
w_2, kx, phi_k, x, phi_2 = disp.solveEquation((w0, w0+0.0005, w0+0.0002j), 0.5, stdSetup_swITG)
########### Plotting #######333
gkcStyle.newFigure(ratio="2.33:1", basesize=10.)
subplot(121)
plot(x, real(phi_0), label="%.3f %.3f" % (real(w_0), imag(w_0)))
plot(x, real(phi_1), label="%.3f %.3f" % (real(w_1), imag(w_1)))
plot(x, real(phi_2), label="%.3f %.3f" % (real(w_2), imag(w_2)))
gkcStyle.plotZeroLine(min(kx), max(kx))
xlim((-5, 5.))
xlabel("$X$")
ylabel("$\phi(x)$")
####
subplot(122)
plot(x, imag(phi_0), label="%.3f %.3f" % (real(w_0), imag(w_0)))
plot(x, imag(phi_1), label="%.3f %.3f" % (real(w_1), imag(w_1)))
from pylab import *
import gkcStyle
fig = gkcStyle.newFigure(ratio="2.33:1", basesize=12)
Nx = array([ 33., 65., 127., 197., 257., 369., 513., 713.])
omega = [ -0.260 - 0.004j , - 0.218 + 0.061j, -0.229 + 0.082j, -0.233 + 0.0882j, - 0.235 + 0.0905j, -0.237 + 0.09267j, -0.238 + 0.094j, -0.239 + 0.0949j]
# Frequency
subplot(211)
plot(1./Nx, real(omega), 'o-')
xticks([0., 0.005, 0.01, 0.02, 0.04], [" \n$\\infty$", "200", "100", "50", "25"])
xlabel("Nx")
ylabel("Frequency")
subplot(212)
plot(1./Nx, imag(omega), 'o-')
xticks([0., 0.005, 0.01, 0.02, 0.04], [" \n$\\infty$", "200", "100", "50", "25"])
xlabel("Nx")
ylabel("Frequency")
savefig("Convergence.pdf", bbox_inches='tight')
param = { 'disp' : 'GyroSlab', 'mode' : mode, 'beta' : 1.0e-5, 'tau' : 1., 'lambdaD' : 1.e-5, 'rhoLn' : rhoLn, \
'rhoLT' : rhoLT, 'kx' : np.sqrt(2.) * 1.e-1 , 'kp' : 2. * np.sqrt(2.) * 1.e-3, 'm_ie' : m_ie, 'adiab' : lambda x : 1 }
omega_th = []
for ky in ky_list:
omega_th.append(getDispersion(ky, param))
#omega_th.append(getDispersion(sqrt(1837.) * ky, param))
omega_th = np.array(omega_th) * param['kp'] #/sqrt(1837.)
fileh5.close()
############################## Plot Figure ###################
gkcStyle.newFigure(ratio="1:1.33", basesize=12)
# Plot Growthrates
pylab.subplot(
211,
title="Benchmark of Smolykov et al. (PRL, 2002) using gkc++ (rev. 173)")
pylab.semilogx(D['ky'][1:-1],
2. * np.imag(omega_sim[1:-1]),
'^',
label='gkc++')
pylab.semilogx(ky_list,
np.imag(omega_th),
'-',
color='#FF4444',
alpha=0.8,
def solveDispersion(ky):
L = zeros((Nx, Nx), dtype=complex)
def setup_L(w):
L[:, :] = 0.
iCode.setupMatrixPy(species, w, ky, X, kx_list, Ls, Ln, Nx, L, dk * dx,
lambda_D2)
return L
def solveEquation(w):
w = complex(w)
L = setup_L(w)
# Get Minium absolute eigenvalue.
#
# The non-linear eigenvalue problem obeys
# det(L) = 0. This requirement is equal
# to an eigenvalue 0 for the linear eigenvalue
# problem det(L'- lambda I) = 0, which is identical
# to the non-linear requirenement once lambda = 0.
#
# [ This is less sensitive (and thus numerically less demanding)
# than caluculating directly the determinant
val = getMinEigenvalue(L)
#val = det(A)
#(sign, logdet) = np.linalg.slogdet(L)
#val = sign * logdet
print ky, " w : %.8f+%.8f j" % (real(complex(w)), imag(
complex(w))), " Determinant : %.2e " % abs(val)
return val
try:
#omega = complex(mp.findroot(solveEquation, (w0, w0+0.05, w0-0.005j), solver='muller', tol=1.e-15, ftol=1.e-15, maxsteps=5000))
omega = complex(
mp.findroot(solveEquation, (w0, w0 - 0.01, w0 + 0.001j),
solver='muller',
tol=1.e-15,
ftol=1.e-15,
maxsteps=5000))
except:
return float('nan') + 1.j * float('nan')
#traceback.print_exc(file=sys.stdout)
try:
# n = 0
# solution found for w0, get solution vector
werr = solveEquation(omega)
L = setup_L(omega)
# We found our eigenvalue omega, now we use the
# inverse iteration to find the closest eigenvector
# to the eigenvalue
L__lambda_I = L - omega * eye(Nx)
# Start with random inital eigenvector
b = 1. * rand(Nx) + 1.j * rand(Nx)
# Convergence is fast thus large iteration number not required
# However, how to best check the error ?
# e.g. A dot phi
# Tested also, Rayleigh-Quotient Iteration but less successfull.
for n in range(128):
# rescale b
b = b / real(sqrt(vdot(b, b)))
# inverse iteration
b = solve(L__lambda_I, b)
# calculate error
r = dot(L, b)
residual = real(sqrt(vdot(r, r)))
print("I-I Residual : %.2e " % residual)
if (residual < 1.e-9): break
clf()
fig = gkcStyle.newFigure(ratio='1.41:1', basesize=9)
fig.suptitle("$\omega_0$ = %.4f %.4fi $\pm$ %.2e %.2e i" %
(real(omega), imag(omega), real(werr), imag(werr)))
###################### Plot Fourier Modes ##########3
plot(kx_list, real(b), 'r.-', label="real")
plot(kx_list, imag(b), '.-', label="imag", color=gkcStyle.color_indigo)
xlim((min(kx_list), max(kx_list)))
xlabel("$k_x$")
ylabel("$\phi(k_x)$")
legend(ncol=2).draw_frame(0)
savefig(str(ky) + "_Plot1.pdf", bbox_inches='tight')
################### Plot real modes ########3
clf()
# We have to transform to FFTW format, which has
# form of [ k=0, k=1, ..., k = N/2, k = -(N/2-1), ..., k=-1 ]
F = append(append(b[Nx / 2], b[Nx / 2 + 1:]), b[:Nx / 2])
K = np.fft.ifft(F)
K = append(append(K[Nx / 2], K[Nx / 2 + 1:]), K[:Nx / 2])
# Correct for phase
K = K * exp(-1.j * arctan2(imag(sum(K)), real(sum(K))))
#print " Phase : " , arctan2(imag(sum(K)),real(sum(K)))
#F_list = append(append(kx_list[Nx/2], kx_list[Nx/2+1:]), kx_list[:Nx/2])
#print "fft kx_list -----------> " , F_list
plot(X, real(K), 'r.-', label='real')
plot(X, imag(K), '.-', label='imag', color=gkcStyle.color_indigo)
plot(X, abs(K), 'g-', label='abs', linewidth=5., alpha=0.5)
xlim((min(X), max(X)))
xlabel("$x$")
ylabel("$\phi(x)$")
legend(ncol=2).draw_frame(0)
savefig(str(ky) + "_Plot2.pdf", bbox_inches='tight')
################ Plot Contour
clf()
y = linspace(0., Ly, 512)
KxKy = zeros((Nx, 65), dtype=complex)
nky = ky * Ly / (2. * pi)
KxKy[:, nky] = K
#np.fft.ifft(F)
XY = np.fft.irfft(KxKy, axis=1, n=512)
xlabel("$x$")
ylabel("$y$")
contourf(X, y, XY.T, 20, vmin=-abs(XY).max(), vmax=abs(XY).max())
#contourf(X, y, XY.T, 20, vmin=-abs(XY).max(), vmax=abs(XY).max())
colorbar()
savefig(str(ky) + "_Plot3.pdf", bbox_inches='tight')
# append and normalize
sol.append(np.fft.ifft(b / abs(b).max()))
except:
traceback.print_exc(file=sys.stdout)
return omega
def solveMode(ky_list, w_init_list, Nx, Setup):
print "Nx"
disp = solveDispersion(Nx)
for (ky, w_init) in zip(ky_list, w_init_list) :
w0, kx_list, K, X, R = disp.solveEquation(w_init, ky, Setup)
clf()
fig = gkcStyle.newFigure(ratio='1.41:1', basesize=9)
fig.suptitle("$w0$ = %.4f %.4fi $\pm$ %.2e %.2e i" % (real(w0), imag(w0), 0., 0.))
###################### Plot Fourier Modes ##########
plot(kx_list, real(K), 'r.-', label="real")
plot(kx_list, imag(K), '.-', label="imag", color=gkcStyle.color_indigo)
xlim((min(kx_list), max(kx_list)))
xlabel("$k_x$")
ylabel("$\phi(k_x)$")
legend(ncol=2).draw_frame(0)
savefig(str(ky) + "_Plot1.pdf", bbox_inches='tight')
################### Plot real modes ########3
clf()
plot(X, real(R), 'r.-', label='real')
plot(X, imag(R), '.-', label='imag', color=gkcStyle.color_indigo)
xlim((min(X), max(X)))
xlabel("$x$")
ylabel("$\phi(x)$")
legend(ncol=2).draw_frame(0)
savefig(str(ky) + "_Plot2.pdf", bbox_inches='tight')
################ Plot Contour ###############
clf()
Ly = 2.*pi/ky
y = linspace(0., Ly, 256)
KxKy = zeros((Nx, 65), dtype=complex)
KxKy[:,1] = R
XY = np.fft.irfft(KxKy, axis=1, n=256)
xlabel("$x$")
ylabel("$y$")
contourf(X, y, XY.T, 20, vmin=-abs(XY).max(), vmax=abs(XY).max())
colorbar()
savefig(str(ky) + "_Plot3.pdf", bbox_inches='tight')
# append and normalize
#sol.append(np.fft.ifft(b/abs(b).max()))
# Write out real mode structure
savetxt("IntegralCode_ky_" + str(ky) + ".txt", array([X, real(K), imag(K)]).T )
param = { 'disp' : 'GyroSlab', 'mode' : mode, 'beta' : 1.0e-5, 'tau' : 1., 'lambdaD' : 1.e-5, 'rhoLn' : rhoLn, \
'rhoLT' : rhoLT, 'kx' : np.sqrt(2.) * 1.e-1 , 'kp' : 2. * np.sqrt(2.) * 1.e-3, 'm_ie' : m_ie, 'adiab' : lambda x : 1 }
omega_th = []
for ky in ky_list :
omega_th.append(getDispersion(ky, param))
#omega_th.append(getDispersion(sqrt(1837.) * ky, param))
omega_th = np.array(omega_th) * param['kp']#/sqrt(1837.)
fileh5.close()
############################## Plot Figure ###################
gkcStyle.newFigure(ratio="1:1.33", basesize=12)
# Plot Growthrates
pylab.subplot(211, title="Benchmark of Smolykov et al. (PRL, 2002) using gkc++ (rev. 173)")
pylab.semilogx(D['ky'][1:-1], 2. * np.imag(omega_sim[1:-1]), '^', label='gkc++')
pylab.semilogx(ky_list, np.imag(omega_th), '-', color='#FF4444', alpha=0.8, linewidth=5., label='Theory')
gkcStyle.plotZeroLine(D['ky'][1], D['ky'][-1], direction='horizontal', color="#666666", lw=1.5)
pylab.xlim((D['ky'][1], D['ky'][-1]))
if (isKinetic) : pylab.ylim((-0.005, 0.015))
else : pylab.ylim((-0.002, 0.005))
