Improved visual quality of kernel function plots

theory/SPH/Kernels/kernels.py

@@ -26,31 +26,53 @@ from scipy.optimize import fsolve
 from matplotlib.font_manager import FontProperties
 import numpy
 
-params = {
-    'axes.labelsize': 10,
-    'axes.titlesize': 8,
-    'font.size': 10,
-    'legend.fontsize': 9,
-    'xtick.labelsize': 10,
-    'ytick.labelsize': 10,
-    'xtick.major.pad': 2.5,
-    'ytick.major.pad': 2.5,
-    'text.usetex': True,
-'figure.figsize' : (4.15,4.15),
-'figure.subplot.left'    : 0.14,
-'figure.subplot.right'   : 0.99,
-'figure.subplot.bottom'  : 0.06,
-'figure.subplot.top'     : 0.99,
+params = {'axes.labelsize': 9,
+'axes.titlesize': 10,
+'font.size': 12,
+'legend.fontsize': 12,
+'xtick.labelsize': 9,
+'ytick.labelsize': 9,
+'text.usetex': True,
+'figure.figsize' : (3.15,3.15),
+'figure.subplot.left'    : 0.17,
+'figure.subplot.right'   : 0.99  ,
+'figure.subplot.bottom'  : 0.08  ,
+'figure.subplot.top'     : 0.99  ,
 'figure.subplot.wspace'  : 0.  ,
 'figure.subplot.hspace'  : 0.  ,
 'lines.markersize' : 6,
-'lines.linewidth' : 1.5,
+'lines.linewidth' : 3.,
 'text.latex.unicode': True
 }
 rcParams.update(params)
 rc('font',**{'family':'sans-serif','sans-serif':['Times']})
 
 
+# params = {
+#     'axes.labelsize': 10,
+#     'axes.titlesize': 8,
+#     'font.size': 10,
+#     'legend.fontsize': 9,
+#     'xtick.labelsize': 10,
+#     'ytick.labelsize': 10,
+#     'xtick.major.pad': 2.5,
+#     'ytick.major.pad': 2.5,
+#     'text.usetex': True,
+# 'figure.figsize' : (4.15,4.15),
+# 'figure.subplot.left'    : 0.14,
+# 'figure.subplot.right'   : 0.99,
+# 'figure.subplot.bottom'  : 0.06,
+# 'figure.subplot.top'     : 0.99,
+# 'figure.subplot.wspace'  : 0.  ,
+# 'figure.subplot.hspace'  : 0.  ,
+# 'lines.markersize' : 6,
+# 'lines.linewidth' : 1.5,
+# 'text.latex.unicode': True
+# }
+# rcParams.update(params)
+# rc('font',**{'family':'sans-serif','sans-serif':['Times']})
+
+
 #Parameters
 eta = 1.2348422195325 # Resolution (Gives 48 neighbours for a cubic spline kernel)
 dx  = 1.5#4 #2.7162  # Mean inter-particle separation
@@ -135,13 +157,13 @@ xx = linspace(0., 5*h, 1000)
 maxY = 1.2*Gaussian(0, h)
 
 # Plot the kernels
-plot(xx, Gaussian(xx, h), 'k-', linewidth=0.7, label="${\\rm %14s\\quad H=\\infty}$"%("Gaussian~~~~~~"))
-plot(xx, W_cubic_spline(xx), 'b-', label="${\\rm %14s\\quad H=%4.3f}$"%("Cubic~spline~~", H_cubic))
-plot(xx, W_quartic_spline(xx), 'c-', label="${\\rm %14s\\quad H=%4.3f}$"%("Quartic~spline", H_quartic))
-plot(xx, W_quintic_spline(xx), 'g-', label="${\\rm %14s\\quad H=%4.3f}$"%("Quintic~spline", H_quintic))
-plot(xx, W_WendlandC2(xx), 'r-', label="${\\rm %14s\\quad H=%4.3f}$"%("Wendland~C2~", H_WendlandC2))
-plot(xx, W_WendlandC4(xx), 'm-', label="${\\rm %14s\\quad H=%4.3f}$"%("Wendland~C4~", H_WendlandC4))
-plot(xx, W_WendlandC6(xx), 'y-', label="${\\rm %14s\\quad H=%4.3f}$"%("Wendland~C6~", H_WendlandC6))
+plot(xx, Gaussian(xx, h), 'k-', linewidth=0.7, label="${\\rm %14s~ H=\\infty}$"%("Gaussian~~~~~~"))
+plot(xx, W_cubic_spline(xx), 'b-', label="${\\rm %14s~ H=%4.3f}$"%("Cubic~spline~~", H_cubic), lw=1.5)
+plot(xx, W_quartic_spline(xx), 'c-', label="${\\rm %14s~ H=%4.3f}$"%("Quartic~spline", H_quartic), lw=1.5)
+plot(xx, W_quintic_spline(xx), 'g-', label="${\\rm %14s~ H=%4.3f}$"%("Quintic~spline", H_quintic), lw=1.5)
+plot(xx, W_WendlandC2(xx), 'r-', label="${\\rm %14s~ H=%4.3f}$"%("Wendland~C2~", H_WendlandC2), lw=1.5)
+plot(xx, W_WendlandC4(xx), 'm-', label="${\\rm %14s~ H=%4.3f}$"%("Wendland~C4~", H_WendlandC4), lw=1.5)
+plot(xx, W_WendlandC6(xx), 'y-', label="${\\rm %14s~ H=%4.3f}$"%("Wendland~C6~", H_WendlandC6), lw=1.5)
 
 # Indicate the position of H
 arrow(H_cubic, 0.12*maxY , 0., -0.12*maxY*0.9, fc='b', ec='b', length_includes_head=True, head_width=0.03, head_length=0.12*maxY*0.3)
@@ -152,33 +174,33 @@ arrow(H_WendlandC4, 0.12*maxY , 0., -0.12*maxY*0.9, fc='m', ec='m', length_inclu
 arrow(H_WendlandC6, 0.12*maxY , 0., -0.12*maxY*0.9, fc='y', ec='y', length_includes_head=True, head_width=0.03, head_length=0.12*maxY*0.3)
 
 # Show h
-plot([h, h], [0., maxY], 'k:', linewidth=0.5)
-text(h, maxY*0.35, "$h\\equiv\\eta\\langle x\\rangle = %.4f$"%h, rotation=90, backgroundcolor='w', ha='center', va='bottom')
+plot([h, h], [0., 0.63*maxY], 'k:', linewidth=0.5)
+text(h, maxY*0.65, "$h\\equiv\\eta\\langle x\\rangle$", rotation=90,  ha='center', va='bottom', fontsize=9)
 
 # Show sigma
-plot([h/2, h/2], [0., maxY], 'k:', linewidth=0.5)
-text(h/2, maxY*0.05, "$\\sigma\\equiv h/2$", rotation=90, backgroundcolor='w', ha='center', va='bottom')
+plot([h/2, h/2], [0., 0.63*maxY], 'k:', linewidth=0.5)
+text(h/2, maxY*0.65, "$\\sigma\\equiv h/2$", rotation=90,  ha='center', va='bottom', fontsize=9)
 
 # Show <x>
-plot([dx, dx], [0., maxY], 'k:', linewidth=0.5)
-text(dx, maxY*0.35, "$\\langle x\\rangle = %.1f$"%dx, rotation=90, backgroundcolor='w', ha='center', va='bottom')
+plot([dx, dx], [0., 0.63*maxY], 'k:', linewidth=0.5)
+text(dx, maxY*0.65, "$\\langle x\\rangle = %.1f$"%dx, rotation=90,  ha='center', va='bottom', fontsize=9)
 
 xlim(0., 2.5*h)
 ylim(0., maxY)
 gca().xaxis.set_ticklabels([])
 ylabel("$W(r,h)$", labelpad=1.5)
-legend(loc="upper right", handlelength=1.2, handletextpad=0.2)
+legend(loc="upper right", frameon=False, handletextpad=0.1, handlelength=1.2, fontsize=8)
 
 
 # Same but now in log space
 subplot(212, yscale="log")
-plot(xx, Gaussian(xx, h), 'k-', linewidth=0.7, label="${\\rm Gaussian}$")
-plot(xx, W_cubic_spline(xx), 'b-', label="${\\rm Cubic~spline}$")
-plot(xx, W_quartic_spline(xx), 'c-', label="${\\rm Quartic~spline}$")
-plot(xx, W_quintic_spline(xx), 'g-', label="${\\rm Quintic~spline}$")
-plot(xx, W_WendlandC2(xx), 'r-', label="${\\rm Wendland~C2}$")
-plot(xx, W_WendlandC4(xx), 'm-', label="${\\rm Wendland~C4}$")
-plot(xx, W_WendlandC6(xx), 'y-', label="${\\rm Wendland~C6}$")
+plot(xx, Gaussian(xx, h), 'k-', linewidth=0.7, label="${\\rm Gaussian}$", lw=1.5)
+plot(xx, W_cubic_spline(xx), 'b-', label="${\\rm Cubic~spline}$", lw=1.5)
+plot(xx, W_quartic_spline(xx), 'c-', label="${\\rm Quartic~spline}$", lw=1.5)
+plot(xx, W_quintic_spline(xx), 'g-', label="${\\rm Quintic~spline}$", lw=1.5)
+plot(xx, W_WendlandC2(xx), 'r-', label="${\\rm Wendland~C2}$", lw=1.5)
+plot(xx, W_WendlandC4(xx), 'm-', label="${\\rm Wendland~C4}$", lw=1.5)
+plot(xx, W_WendlandC6(xx), 'y-', label="${\\rm Wendland~C6}$", lw=1.5)
 
 # Show h
 plot([h, h], [0., 1.], 'k:', linewidth=0.5)
@@ -191,21 +213,22 @@ plot([dx, dx], [0., 1.], 'k:', linewidth=0.5)
 
 
 # Show plot properties
-text(h/5., 1e-3, "$\\langle x \\rangle = %3.1f$"%(dx), va="top", backgroundcolor='w')
-text(h/5.+0.06, 3e-4, "$\\eta = %5.4f$"%(eta), va="top", backgroundcolor='w')
+text(h/5., 2e-3, "$\\langle x \\rangle = %3.1f$"%(dx), va="top", backgroundcolor='w', fontsize=9)
+text(h/5.+0.06, 4e-4, "$\\eta = %5.4f$"%(eta), va="top", backgroundcolor='w', fontsize=9)
+text(h/5.+0.06, 8e-5, "$h = \\eta\\langle x \\rangle = %5.4f$"%(h), va="top", backgroundcolor='w', fontsize=9)
 
 # Show number of neighbours
-text(1.9*h, 2e-1/2.9**0, "$N_{\\rm ngb}=\\infty$", fontsize=10)
-text(1.9*h, 2e-1/2.9**1, "$N_{\\rm ngb}=%3.1f$"%(N_H_cubic), color='b', fontsize=9)
-text(1.9*h, 2e-1/2.9**2, "$N_{\\rm ngb}=%3.1f$"%(N_H_quartic), color='c', fontsize=9)
-text(1.9*h, 2e-1/2.9**3, "$N_{\\rm ngb}=%3.1f$"%(N_H_quintic), color='g', fontsize=9)
-text(1.9*h, 2e-1/2.9**4, "$N_{\\rm ngb}=%3.1f$"%(N_H_WendlandC2), color='r', fontsize=9)
-text(1.9*h, 2e-1/2.9**5, "$N_{\\rm ngb}=%3.1f$"%(N_H_WendlandC4), color='m', fontsize=9)
-text(1.9*h, 2e-1/2.9**6, "$N_{\\rm ngb}=%3.0f$"%(N_H_WendlandC6), color='y', fontsize=9)
+text(1.75*h, 2e-1/2.9**0, "$N_{\\rm ngb}=\\infty$", fontsize=10)
+text(1.75*h, 2e-1/2.9**1, "$N_{\\rm ngb}=%3.1f$"%(N_H_cubic), color='b', fontsize=9)
+text(1.75*h, 2e-1/2.9**2, "$N_{\\rm ngb}=%3.1f$"%(N_H_quartic), color='c', fontsize=9)
+text(1.75*h, 2e-1/2.9**3, "$N_{\\rm ngb}=%3.1f$"%(N_H_quintic), color='g', fontsize=9)
+text(1.75*h, 2e-1/2.9**4, "$N_{\\rm ngb}=%3.1f$"%(N_H_WendlandC2), color='r', fontsize=9)
+text(1.75*h, 2e-1/2.9**5, "$N_{\\rm ngb}=%3.1f$"%(N_H_WendlandC4), color='m', fontsize=9)
+text(1.75*h, 2e-1/2.9**6, "$N_{\\rm ngb}=%3.0f$"%(N_H_WendlandC6), color='y', fontsize=9)
 
 xlim(0., 2.5*h)
 ylim(1e-5, 0.7)
-xlabel("$r$", labelpad=0)
+xlabel("$r$", labelpad=-1)
 ylabel("$W(r,h)$", labelpad=0.5)
 
 savefig("kernels.pdf")
@@ -282,13 +305,13 @@ figure()
 subplot(211)
 
 plot([0, 2.5*h], [0., 0.], 'k--', linewidth=0.7)
-plot(xx, d_Gaussian(xx, h), 'k-', linewidth=0.7, label="${\\rm Gaussian}$")
-plot(xx, dW_cubic_spline(xx), 'b-', label="${\\rm Cubic~spline}$")
-plot(xx, dW_quartic_spline(xx), 'c-', label="${\\rm Quartic~spline}$")
-plot(xx, dW_quintic_spline(xx), 'g-', label="${\\rm Quintic~spline}$")
-plot(xx, dW_WendlandC2(xx), 'r-', label="${\\rm Wendland~C2}$")
-plot(xx, dW_WendlandC4(xx), 'm-', label="${\\rm Wendland~C4}$")
-plot(xx, dW_WendlandC6(xx), 'y-', label="${\\rm Wendland~C6}$")
+plot(xx, d_Gaussian(xx, h), 'k-', linewidth=0.7, label="${\\rm Gaussian}$", lw=1.5)
+plot(xx, dW_cubic_spline(xx), 'b-', label="${\\rm Cubic~spline}$", lw=1.5)
+plot(xx, dW_quartic_spline(xx), 'c-', label="${\\rm Quartic~spline}$", lw=1.5)
+plot(xx, dW_quintic_spline(xx), 'g-', label="${\\rm Quintic~spline}$", lw=1.5)
+plot(xx, dW_WendlandC2(xx), 'r-', label="${\\rm Wendland~C2}$", lw=1.5)
+plot(xx, dW_WendlandC4(xx), 'm-', label="${\\rm Wendland~C4}$", lw=1.5)
+plot(xx, dW_WendlandC6(xx), 'y-', label="${\\rm Wendland~C6}$", lw=1.5)
 
 maxY = d_Gaussian(h/2, h)
 
@@ -307,7 +330,7 @@ gca().xaxis.set_ticklabels([])
 ylim(1.1*maxY, -0.1*maxY)
 xlabel("$r$", labelpad=0)
 ylabel("$\\partial W(r,h)/\\partial r$", labelpad=0.5)
-legend(loc="lower right")
+legend(loc="lower right", frameon=False, handletextpad=0.1, handlelength=1.2, fontsize=8)
 
 
 
@@ -317,23 +340,23 @@ maxY = d2_Gaussian(h,h)
 plot([h/2, h/2], [-4*maxY, 1.4*maxY], 'k:', linewidth=0.5)
 plot([h, h], [-4*maxY, 1.4*maxY], 'k:', linewidth=0.5)
 plot([dx, dx], [-4*maxY, 1.4*maxY], 'k:', linewidth=0.5)
-text(h/2, -3.*maxY, "$\\sigma\\equiv h/2$", rotation=90, backgroundcolor='w', ha='center', va='bottom')
-text(h, -3.*maxY, "$h\\equiv\\eta\\langle x\\rangle = %.4f$"%h, rotation=90, backgroundcolor='w', ha='center', va='bottom')
-text(dx, -3.*maxY, "$\\langle x\\rangle = %.1f$"%dx, rotation=90, backgroundcolor='w', ha='center', va='bottom')
+text(h/2, -2.9*maxY, "$\\sigma\\equiv h/2$", rotation=90, backgroundcolor='w', ha='center', va='bottom', fontsize=9)
+text(h, -2.9*maxY, "$h\\equiv\\eta\\langle x\\rangle$", rotation=90, backgroundcolor='w', ha='center', va='bottom', fontsize=9)
+text(dx, -2.9*maxY, "$\\langle x\\rangle = %.1f$"%dx, rotation=90, backgroundcolor='w', ha='center', va='bottom', fontsize=9)
 
 
 plot([0, 2.5*h], [0., 0.], 'k--', linewidth=0.7)
 plot(xx, d2_Gaussian(xx, h), 'k-', linewidth=0.7, label="${\\rm Gaussian}$")
-plot(xx, d2W_cubic_spline(xx), 'b-', label="${\\rm Cubic~spline}$")
-plot(xx, d2W_quartic_spline(xx), 'c-', label="${\\rm Quartic~spline}$")
-plot(xx, d2W_quintic_spline(xx), 'g-', label="${\\rm Quintic~spline}$")
-plot(xx, d2W_WendlandC2(xx), 'r-', label="${\\rm Wendland~C2}$")
-plot(xx, d2W_WendlandC4(xx), 'm-', label="${\\rm Wendland~C4}$")
-plot(xx, d2W_WendlandC6(xx), 'y-', label="${\\rm Wendland~C6}$")
+plot(xx, d2W_cubic_spline(xx), 'b-', label="${\\rm Cubic~spline}$", lw=1.5)
+plot(xx, d2W_quartic_spline(xx), 'c-', label="${\\rm Quartic~spline}$", lw=1.5)
+plot(xx, d2W_quintic_spline(xx), 'g-', label="${\\rm Quintic~spline}$", lw=1.5)
+plot(xx, d2W_WendlandC2(xx), 'r-', label="${\\rm Wendland~C2}$", lw=1.5)
+plot(xx, d2W_WendlandC4(xx), 'm-', label="${\\rm Wendland~C4}$", lw=1.5)
+plot(xx, d2W_WendlandC6(xx), 'y-', label="${\\rm Wendland~C6}$", lw=1.5)
 
 xlim(0., 2.5*h)
 ylim(-3.2*maxY, 1.3*maxY)
-xlabel("$r$", labelpad=0)
+xlabel("$r$", labelpad=-1)
 ylabel("$\\partial^2 W(r,h)/\\partial r^2$", labelpad=0.5)