I have a sage script that generates 12 plots with functions, and of course so far all the y-axis are scaled separately. In order to make the plots easier to compare i would like to have the same ymin and ymax across all the plots. How can i do that?
The script is not beautiful, and I am not proud of it. actually I would be happy to get suggestions how to structure it better, so here it goes... there are some not-so-easy-to-automate differences about the (very similar in structure) parts which could be put into functions, with very long function calls.
dU,a, x, d_e, epsilon_m, epsilon_s, v_ges, U =var('dU a x d_e epsilon_m epsilon_s v_ges U')
d_k = var('d_k')
d_m = var('d_m')
#========= dielectric constants ==================================
epsilon_0 = var('epsilon_0', latex_name=r'\varepsilon_0')
#sediment
epsilon_s = var('epsilon_s', latex_name=r'\varepsilon_s')
# seawater
epsilon_m = var('epsilon_m', latex_name=r'\varepsilon_m')
epsilon_Ersatz = var('epsilon_Ersatz', latex_name=r'\varepsilon_{Ersatz}')
epsilon_Ersatz = d_k * ( (epsilon_m/d_m) + (epsilon_s/(d_k-d_m) ) )
#===========================================
#============ electric potential field ===============================
v(epsilon,Q,r) = Q/(4*pi*epsilon*r)
p_1 = v(epsilon_0*epsilon_m, 1, abs(a))
p_2 = v(epsilon_0*epsilon_m, -1, abs(d_e-a))
p_3 = v(epsilon_0*epsilon_Ersatz, -1, sqrt((2*d_k)^2+a^2))
p_4 = v(epsilon_0*epsilon_Ersatz, 1, sqrt((2*d_k)^2+(d_e -a)^2))
p_fix_rhs = p_1 + p_2 + p_3 + p_4
d = var ('d')
d = (U/p_fix_rhs).subs({
d_e : 1,
x : -.25,
d_m : .075,
epsilon_m : 76,
epsilon_0 : 8.854187817e-12,
epsilon_s : RIF(3.5,40).n(),
a : 0.01
})
v_1 = v(epsilon_0*epsilon_m, 1, abs(x))
v_2 = v(epsilon_0*epsilon_m, -1, abs(d_e-x))
v_3 = v(epsilon_0*epsilon_Ersatz, -1, sqrt((2*d_k)^2+x^2))
v_4 = v(epsilon_0*epsilon_Ersatz, 1, sqrt((2*d_k)^2+(d_e -x)^2))
v_ges_rhs = dU + d*( v_1 + v_2 + v_3 + v_4)
show(v_ges_rhs)
#==================================================
#==================================================
# one boundary condition is that the electric potential is U at a given point x = r_0. (radius of the electrode)
# I need to scale the electric charge Q accordingly.
print "d_m without error"
tiefe = v_ges_rhs.subs({
dU : RIF(-0.01,0.01),
U : RIF(9.99,10.01),
d_e : RIF(.999,1.001),
x : -.25,
d_m : 0.075,
epsilon_m : RIF(75,77),
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='Distance to seabed without error', title_pos=(0.5,1.1)).save('d_m-noerror.png')
print "epsilon_m without error"
tiefe = v_ges_rhs.subs({
dU : RIF(-0.01,0.01),
U : RIF(9.99,10.01),
d_e : RIF(.999,1.001),
x : -.25,
d_m : RIF(.05,.1),
epsilon_m : 76,
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='$\epsilon_m$ without error', title_pos=(0.5,1.1)).save('epsilon_m-noerror.png')
print "epsilon_s without error"
tiefe = v_ges_rhs.subs({
dU : RIF(-0.01,0.01),
U : RIF(9.99,10.01),
d_e : RIF(.999,1.001),
x : -.25,
d_m : RIF(.05,.1),
epsilon_m : RIF(75,77),
epsilon_s : 21.75,
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='$\epsilon_s$ without error', title_pos=(0.5,1.1)).save('epsilon_s-noerror.png')
print "d_e without error"
tiefe = v_ges_rhs.subs({
dU : RIF(-0.01,0.01),
U : RIF(9.99,10.01),
d_e : 1,
x : -.25,
d_m : RIF(.05,.1),
epsilon_m : RIF(75,77),
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='Distance of elektrodes witout error', title_pos=(0.5,1.1)).save('d_e-noerror.png')
print "only error is d_m"
tiefe = v_ges_rhs.subs({
dU : 0,
U : 10,
d_e : 1,
x : -.25,
d_m : RIF(.05,.1),
epsilon_m : 76,
epsilon_s : 21.75,
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='Only Error is distance to seabed', title_pos=(0.5,1.1)).save('d_m-error.png')
print "only error is d_e"
tiefe = v_ges_rhs.subs({
dU : 0,
U : 10,
d_e : RIF(.999,1.001),
x : -.25,
d_m : .075,
epsilon_m : 76,
epsilon_s : 21.75,
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='Distance of electrodes with error', title_pos=(0.5,1.1)).save('d_e-error.png')
print "only error is epsilon_m"
tiefe = v_ges_rhs.subs({
dU : 0,
U : 10,
d_e : 1,
x : -.25,
d_m : .075,
epsilon_m : RIF(75,77),
epsilon_s : 21.75,
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='$\epsilon_m$ with error', title_pos=(0.5,1.1)).save('epsilon_m-error.png')
print "only error is epsilon_s"
tiefe = v_ges_rhs.subs({
dU : 0,
U : 10,
d_e : 1,
x : -.25,
d_m : .075,
epsilon_m : 76,
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='$\epsilon_s$ with error', title_pos=(0.5,1.1)).save('epsilon_s-error.png')
print "only error is dU"
tiefe = v_ges_rhs.subs({
dU : RIF(-0.01,0.01),
U : 10,
d_e : 1,
x : -.25,
d_m : .075,
epsilon_m : 76,
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='$\Delta U$ with error', title_pos=(0.5,1.1)).save('dU-error.png')
print "only error is U"
tiefe = v_ges_rhs.subs({
dU : 0,
U : RIF(9.99,10.01),
d_e : 1,
x : -.25,
d_m : .075,
epsilon_m : 76,
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='$U$ with error', title_pos=(0.5,1.1)).save('U-error.png')
print "all values have errors"
tiefe = v_ges_rhs.subs({
dU : RIF(-0.01,0.01),
U : RIF(9.99,10.01),
d_e : RIF(.999,1.001),
x : -.25,
d_m : RIF(.05,.1),
epsilon_m : RIF(75,77),
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='All values have errors', title_pos=(0.5,1.1)).save('all-error.png')
print "dU is without error"
tiefe = v_ges_rhs.subs({
dU : 0,
U : RIF(9.99,10.01),
d_e : RIF(.999,1.001),
x : -.25,
d_m : RIF(.05,.1),
epsilon_m : RIF(75,77),
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='$\Delta U$ without error', title_pos=(0.5,1.1)).save('dU-noerror.png')
print "U is without error"
tiefe = v_ges_rhs.subs({
dU : RIF(-0.01,0.01),
U : 10,
d_e : RIF(.999,1.001),
x : -.25,
d_m : RIF(.05,.1),
epsilon_m : RIF(75,77),
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='$U$ is without error', title_pos=(0.5,1.1)).save('U-noerror.png')
print "all values have errors. but this is without seawater, just sediment"
tiefe = v_ges_rhs.subs({
dU : RIF(-0.01,0.01),
U : RIF(9.99,10.01),
d_e : RIF(.999,1.001),
x : -.25,
d_m : 0.0001,
epsilon_m : 75,
epsilon_s : RIF(3.5,40),
epsilon_0 : 8.854187817e-12
})
f = lambda x: tiefe.subs({d_k: x})
f_lower = lambda x: RIF(tiefe.subs({d_k : x})).lower()
f_upper = lambda x: RIF(tiefe.subs({d_k : x})).upper()
plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'red', 'green'], legend_label=['without error', 'lower margin of error', 'upper margin of error'], axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], figsize=8, axes_labels_size=1, title='all values have errors. but this is without seawater, just sediment', title_pos=(0.5,1.1)).save('JustSediment.png')
