# Get grid points and steps
x = []
dx = np.empty((dim,))
nx = np.ones((dim,), dtype=int) * nx0
for d in np.arange(dim):
x.append(np.linspace(-xlim[d], xlim[d], nx[d]))
dx[d] = x[d][1] - x[d][0]
N = np.prod(nx)
idx = np.indices(nx).reshape(dim, -1)
X, Y = np.meshgrid(*x, indexing='xy') # ! Different that for numerical
# -> Need transpose vectors !
# Read eigenvalues
print 'Reading backward eigenvalues'
eigValBackward = np.empty((nev,), dtype=complex)
ergoPlot.loadtxt_complex('%s/eigValBackward%s.txt' \
% (resDir, postfix), eigValBackward)
isortBackward = np.argsort(-eigValBackward.real)
eigValBackward = eigValBackward[isortBackward]
# Read eigenvectors
print 'Reading backward eigenvectors'
eigVecBackward = np.empty((nx0**2, nev), dtype=complex)
ergoPlot.loadtxt_complex('%s/eigVecBackward%s.txt' % (resDir, postfix),
eigVecBackward)
eigVecBackward = eigVecBackward[:, isortBackward]
# Convert second eigenvectors to phase and amplitude
if eigValBackward[1].imag > 0:
eigVec2 = eigVecBackward[:, 1]
else:
eigVec2 = eigVecBackward[:, 2]
meanPoints = (points * rho0_tile).sum(1)
stdPoints = np.sqrt(((points - np.tile(meanPoints, (N, 1)).T)**2 * rho0_tile).sum(1))
#print 'Mean points = ', meanPoints
#print 'Std points = ', stdPoints
print 'Saving eigenvalues'
np.savetxt('../results/numericalFP/w_hopf%s.txt' % postfix, w)
np.savetxt('../results/numericalFP/ev_hopf%s.txt' % postfix, v)
np.savetxt('../results/numericalFP/statDist_hopf%s.txt' % postfix, rho0)
else:
print 'Reading eigenvalues'
srcFileEigVal = '../results/numericalFP/w_hopf%s.txt' % postfix
w = np.empty((nev,), dtype=complex)
ergoPlot.loadtxt_complex(srcFileEigVal, w)
srcFileEigVec = '../results/numericalFP/ev_hopf%s.txt' % postfix
print 'Reading eigenvectors'
v = np.empty((N, nev), dtype=complex)
ergoPlot.loadtxt_complex(srcFileEigVec, v)
rho0 = np.loadtxt('../results/numericalFP/statDist_hopf%s.txt' % postfix)
print 'Plotting'
fig = plt.figure()
#fig.set_visible(False)
ax = fig.add_subplot(111)
ax.scatter(w.real, w.imag, c='b', edgecolors='face')
ax.set_xlim(-30, 0.1)
ax.set_ylim(-10, 10)
ax.set_xlabel(r'$\Re(\lambda_1)$', fontsize=ergoPlot.fs_latex)
ax.set_ylabel(r'$\Im(\lambda_1)$', fontsize=ergoPlot.fs_latex)
mu = muRng[imu]
mu += 1.e-8
if mu < 0:
signMu = 'm'
else:
signMu = 'p'
for ieps in np.arange(epsRng.shape[0]):
eps = epsRng[ieps]
postfix = '_%s_mu%s%02d_beta%s%03d_eps%03d_nx%d_nSTD%d_nev%d' \
% (model, signMu, int(round(np.abs(mu) * 10)),
signBeta, int(round(np.abs(beta) * 100)), int(round(eps * 100)),
nx0, nSTD, nev)
# Read eigenvalues
eigValii = np.empty((nev,), dtype=complex)
ergoPlot.loadtxt_complex('%s/eigValForward%s.txt' \
% (resDir, postfix), eigValii)
isort = np.argsort(-eigValii.real)
eigValii = eigValii[isort]
eigVal[ieps, imu] = eigValii
# Comparison with analytics of real part of the second eigenvalue versus the noise
fig = plt.figure()
ax = fig.add_subplot(111)
xplot = np.linspace(0., epsRng[-1], 1000)
XP = np.matrix(xplot).T
evMin = []
muLineStyle = ['-', '--']
muMarker = ['x', '+']
muMarkerSize = [6, 9]
lw = 2
colors = rcParams['axes.prop_cycle'].by_key()['color']
yticks = np.concatenate((yticksNeg, yticksPos))
zticks = np.logspace(np.log10(zlimEig[0]), np.log10(zlimEig[1]),
int(np.round(np.log10(zlimEig[1]/zlimEig[0]) + 1)))
zticks = np.logspace(np.log10(zlimEig[0]), np.log10(zlimEig[1]),
int(np.round(np.log10(zlimEig[1]/zlimEig[0])/2 + 1)))
maxCondition = 10
# maxCondition = 10
Analytical eigenvalues
if cfg.model.delaysDays[1] == 90:
eigAna = []
eigDrift = np.empty((2,), dtype=complex)
stabFile = '../../Transfer/transferSDDE/results/stability/stabilitySpectrum_Battisti1989_Zero_tau1%d.txt' \
% (int(cfg.model.delaysDays[1] * 1. / 365 * 1000),)
ergoPlot.loadtxt_complex(stabFile, eigDrift)
for ii in np.arange(20):
for jj in np.arange(20):
eigAna.append(eigDrift[0] * ii + eigDrift[1] * jj)
eigAna = np.array(eigAna, dtype=complex)
eigAna = eigAna[np.argsort(-np.abs(eigAna))]
# # Read grid
coord = ergoPlot.readGrid(gridFile, dimObs)
if dimObs == 1:
X = coord[0]
elif dimObs == 2:
X, Y = np.meshgrid(coord[0], coord[1])
coord = (X.flatten(), Y.flatten())
elif dimObs == 3:
X, Y, Z = np.meshgrid(coord[0], coord[1], coord[2], indexing='ij')
