script to plot maximum singular value versus wave number kappa

Author: Daniel Ruprecht

scripts/plot_svd_vs_waveno.py

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+import sys
+sys.path.append('../src')
+
+from parareal import parareal
+from impeuler import impeuler
+from intexact import intexact
+from trapezoidal import trapezoidal
+from special_integrator import special_integrator
+from solution_linear import solution_linear
+import numpy as np
+import scipy.sparse as sparse
+import math
+
+from pylab import rcParams
+import matplotlib.pyplot as plt
+from matplotlib.patches import Polygon
+from subprocess import call
+import sympy
+from pylab import rcParams
+
+if __name__ == "__main__":
+
+    Tend     = 16.0
+    nslices  = int(Tend) # Make sure each time slice has length 1
+    U_speed  = 1.0
+    nu_v     = [0.0, 1e-1, 0.5]
+    ncoarse  = 1
+    nfine    = 10
+    dx       = 1.0
+    Nsamples = 80
+    u0_val   = np.array([[1.0]], dtype='complex')
+
+    k_vec = np.linspace(0.0, np.pi, Nsamples+1, endpoint=False)
+
+    svds = np.zeros((np.size(nu_v),np.size(k_vec)))
+
+    for j in range(0,np.size(nu_v)):
+      nu = nu_v[j]
+      for i in range(0,np.size(k_vec)):
+        waveno = k_vec[i]
+        symb = -(1j*U_speed*waveno + nu*waveno**2)
+        symb_coarse = symb
+#    symb_coarse = -(1.0/dx)*(1.0 - np.exp(-1j*waveno*dx))
+
+        # Solution objects define the problem
+        u0      = solution_linear(u0_val, np.array([[symb]],dtype='complex'))
+        ucoarse = solution_linear(u0_val, np.array([[symb_coarse]],dtype='complex'))
+
+        para = parareal(0.0, Tend, nslices, intexact, impeuler, nfine, ncoarse, 0.0, 0, u0)
+        svds[j,i]         = para.get_max_svd(ucoarse=ucoarse)        
+
+    rcParams['figure.figsize'] = 2.5, 2.5
+    fs = 8
+    fig  = plt.figure()
+    plt.plot(k_vec, svds[0,:], label=(r'$\nu$=%3.2f' % nu_v[0]))
+    plt.plot(k_vec, svds[1,:], label=(r'$\nu$=%3.2f' % nu_v[1]))
+    plt.plot(k_vec, svds[2,:], label=(r'$\nu$=%3.2f' % nu_v[2]))
+    plt.gca().tick_params(axis='both', which='major', labelsize=fs-2)
+    plt.gca().tick_params(axis='x', which='minor', bottom='off')
+    plt.xlabel(r'Wave number $\kappa$', fontsize=fs, labelpad=1)
+    plt.xlim([k_vec[0], k_vec[-1]])
+    plt.ylabel(r'Maximum singular value $\sigma$', fontsize=fs, labelpad=0)
+    plt.legend(loc='upper left', fontsize=fs, prop={'size':fs-2})
+    filename='svd_vs_waveno.pdf'
+    fig.savefig(filename, bbox_inches='tight')
+    call(["pdfcrop", filename, filename])
+#    plt.show()