added visualization of minimizer

Author: pancetta

projects/parallelSDC/minimization.py

@@ -0,0 +1,72 @@
+import numpy as np
+import scipy.optimize as opt
+import matplotlib.pylab as plt
+
+from pySDC.implementations.collocation_classes.gauss_radau_right import CollGaussRadau_Right
+
+
+def main():
+    def rho(x):
+        return max(abs(np.linalg.eigvals(np.eye(M) - np.diag([x[i] for i in range(M)]).dot(coll.Qmat[1:, 1:]))))
+
+    M = 2
+
+    coll = CollGaussRadau_Right(M, 0, 1)
+
+    x0 = np.ones(M)
+    d = opt.minimize(rho, x0, method='Nelder-Mead')
+
+    print(d)
+    numsteps = 800
+    xdim = np.linspace(0, 8, numsteps)
+    ydim = np.linspace(0, 13, numsteps)
+
+    minfield = np.zeros((len(xdim), len(ydim)))
+
+    for idx, x in enumerate(xdim):
+        for idy, y in enumerate(ydim):
+            minfield[idx, idy] = max(abs(np.linalg.eigvals(np.eye(M) - np.diag([x, y]).dot(coll.Qmat[1:, 1:]))))
+
+    # Set up plotting parameters
+    params = {'legend.fontsize': 20,
+              'figure.figsize': (12, 8),
+              'axes.labelsize': 20,
+              'axes.titlesize': 20,
+              'xtick.labelsize': 16,
+              'ytick.labelsize': 16,
+              'lines.linewidth': 3
+              }
+    plt.rcParams.update(params)
+
+    plt.figure()
+    plt.pcolor(xdim, ydim, minfield.T, cmap='Reds', vmin=0, vmax=1)
+    plt.text(d.x[0], d.x[1], 'X', horizontalalignment='center', verticalalignment='center')
+    plt.xlim((min(xdim), max(xdim)))
+    plt.ylim((min(ydim), max(ydim)))
+    plt.xlabel('component 1')
+    plt.ylabel('component 2')
+    cbar = plt.colorbar()
+    cbar.set_label('spectral radius')
+
+    fname = 'data/parallelSDC_minimizer_full.png'
+    plt.savefig(fname, rasterized=True, bbox_inches='tight')
+
+    plt.figure()
+    xdim_part = xdim[int(0.25*numsteps):int(0.75*numsteps)+1]
+    ydim_part = ydim[0:int(0.25*numsteps)]
+    minfield_part = minfield[int(0.25*numsteps):int(0.75*numsteps)+1, 0:int(0.25*numsteps)]
+    plt.pcolor(xdim_part, ydim_part, minfield_part.T, cmap='Reds', vmin=0, vmax=1)
+    plt.text(d.x[0], d.x[1], 'X', horizontalalignment='center', verticalalignment='center')
+    plt.xlim((min(xdim_part), max(xdim_part)))
+    plt.ylim((min(ydim_part), max(ydim_part)))
+    plt.xlabel('component 1')
+    plt.ylabel('component 2')
+    cbar = plt.colorbar()
+    cbar.set_label('spectral radius')
+
+    fname = 'data/parallelSDC_minimizer_zoom.png'
+    plt.savefig(fname, rasterized=True, bbox_inches='tight')
+
+
+if __name__ == "__main__":
+    main()