Fix: remove hold calls; minor other mods

roryyorke · roryyorke · commit 9e41ae73946e · 2019-01-01T14:47:36.000+02:00
Added titles, removed all show calls except last.
diff --git a/examples/phaseplots.py b/examples/phaseplots.py
@@ -23,7 +23,7 @@ def invpend_ode(x, t, m=1., l=1., b=0.2, g=1):
 # Set up the figure the way we want it to look
 mpl.figure(); mpl.clf(); 
 mpl.axis([-2*pi, 2*pi, -2.1, 2.1]);
-mpl.title('Inverted pendlum')
+mpl.title('Inverted pendulum')
 
 # Outer trajectories
 phase_plot(invpend_ode,
@@ -35,9 +35,7 @@ def invpend_ode(x, t, m=1., l=1., b=0.2, g=1):
     logtime = (3, 0.7) )
 
 # Separatrices
-mpl.hold(True);
 phase_plot(invpend_ode, X0 = [[-2.3056, 2.1], [2.3056, -2.1]], T=6, lingrid=0)
-mpl.show();
 
 #
 # Systems of ODEs: damped oscillator example (simulation + phase portrait)
@@ -49,9 +47,10 @@ def oscillator_ode(x, t, m=1., b=1, k=1):
 # Generate a vector plot for the damped oscillator
 mpl.figure(); mpl.clf();
 phase_plot(oscillator_ode, [-1, 1, 10], [-1, 1, 10], 0.15);
-mpl.hold(True); mpl.plot([0], [0], '.');
+#mpl.plot([0], [0], '.');
 # a=gca; set(a,'FontSize',20); set(a,'DataAspectRatio',[1,1,1]);
-mpl.xlabel('x1'); mpl.ylabel('x2');
+mpl.xlabel('$x_1$'); mpl.ylabel('$x_2$');
+mpl.title('Damped oscillator, vector field')
 
 # Generate a phase plot for the damped oscillator
 mpl.figure(); mpl.clf(); 
@@ -61,11 +60,10 @@ def oscillator_ode(x, t, m=1., b=1, k=1):
     [-1, 1], [-0.3, 1], [0, 1], [0.25, 1], [0.5, 1], [0.75, 1], [1, 1],
     [1, -1], [0.3, -1], [0, -1], [-0.25, -1], [-0.5, -1], [-0.75, -1], [-1, -1]
   ], T = np.linspace(0, 8, 80), timepts = [0.25, 0.8, 2, 3])
-mpl.hold(True); mpl.plot([0], [0], 'k.'); # 'MarkerSize', AM_data_markersize*3);
+mpl.plot([0], [0], 'k.'); # 'MarkerSize', AM_data_markersize*3);
 # set(gca,'DataAspectRatio',[1,1,1]);
-mpl.xlabel('x1'); mpl.ylabel('x2');
-
-mpl.show()
+mpl.xlabel('$x_1$'); mpl.ylabel('$x_2$');
+mpl.title('Damped oscillator, vector field and stream lines')
 
 #
 # Stability definitions
@@ -88,9 +86,10 @@ def saddle_ode(x, t):
     [-1.3,-1]
   ], T = np.linspace(0, 10, 100), 
   timepts = [0.3, 1, 2, 3], parms = (m, b, k));
-mpl.hold(True); mpl.plot([0], [0], 'k.'); # 'MarkerSize', AM_data_markersize*3);
+mpl.plot([0], [0], 'k.'); # 'MarkerSize', AM_data_markersize*3);
 # set(gca,'FontSize', 16); 
-mpl.xlabel('{\itx}_1'); mpl.ylabel('{\itx}_2');
+mpl.xlabel('$x_1$'); mpl.ylabel('$x_2$');
+mpl.title('Asymptotically stable point')
 
 # Saddle
 mpl.figure(); mpl.clf();
@@ -103,9 +102,10 @@ def saddle_ode(x, t):
     [0.95, 1], [0.9, 1], [0.8, 1], [0.6, 1], [0.4, 1], [0.2, 1],
     [-0.5, -0.45], [-0.45, -0.5], [0.5, 0.45], [0.45, 0.5],
     [-0.04, 0.04], [0.04, -0.04] ], T = np.linspace(0, 2, 20));
-mpl.hold(True); mpl.plot([0], [0], 'k.'); # 'MarkerSize', AM_data_markersize*3);
+mpl.plot([0], [0], 'k.'); # 'MarkerSize', AM_data_markersize*3);
 # set(gca,'FontSize', 16); 
-mpl.xlabel('{\itx}_1'); mpl.ylabel('{\itx}_2');
+mpl.xlabel('$x_1$'); mpl.ylabel('$x_2$');
+mpl.title('Saddle point')
 
 # Stable isL
 m = 1; b = 0; k = 1;			# zero damping
@@ -115,8 +115,9 @@ def saddle_ode(x, t):
   [pi/6, pi/3, pi/2, 2*pi/3, 5*pi/6, pi, 7*pi/6, 4*pi/3, 9*pi/6, 5*pi/3, 11*pi/6, 2*pi], 
   X0 = [ [0.2,0], [0.4,0], [0.6,0], [0.8,0], [1,0], [1.2,0], [1.4,0] ],
   T = np.linspace(0, 20, 200), parms = (m, b, k));
-mpl.hold(True); mpl.plot([0], [0], 'k.') # 'MarkerSize', AM_data_markersize*3);
+mpl.plot([0], [0], 'k.') # 'MarkerSize', AM_data_markersize*3);
 # set(gca,'FontSize', 16); 
-mpl.xlabel('{\itx}_1'); mpl.ylabel('{\itx}_2');
+mpl.xlabel('$x_1$'); mpl.ylabel('$x_2$');
+mpl.title('Undamped system\nLyapunov stable, not asympt. stable')
 
 mpl.show()
