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static_plots.py
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import numpy as np
import matplotlib.pyplot as plt
from numpy import sin, cos, exp, pi
def mystery_harmonics():
'''
problem for students
'''
nx=1000
L=1
x=np.linspace(0,L,nx)
k=2*pi/L
n=[2,5,7]
labels=["A", "B", "C"]
fig=plt.figure(figsize=(14,6))
ax=fig.add_subplot(111)
ax.set_xlim(0,L)
for i in range(3):
label=labels[i]
ax.plot(x,sin(k*n[i]*x),lw=4, alpha=.5, label=label)
ax.legend(fontsize="xx-large",loc=3)
ax.grid()
plt.close()
return fig
def periodic_sawtooth():
'''
plot sawtooth function
'''
nx=100
L=1
A=1
x=np.linspace(0,L,nx)
y=A*x
fig=plt.figure(figsize=(14,6))
ax=fig.add_subplot(111)
ax.set_xlim(-3*L/2,3*L/2)
ax.set_title("periodic sawtooth function",size=20)
ax.set_xlabel("x", size=20)
ax.plot(x-L,y,lw=4, color="blue")
ax.plot(x,y,lw=4, color="blue")
ax.plot([0,0],[A,0], lw=4, color="black",alpha=.5)
ax.plot(x+L,y,lw=4, color="blue")
ax.plot([L,L],[A,0], lw=4, color="black",alpha=.5)
ax.plot([-L,-L],[A,0], lw=4, color="black",alpha=.5)
ax.plot([2*L,2*L],[A,0], lw=4, color="black",alpha=.5)
ax.plot(x[int(nx/2):]-2*L,y[int(nx/2):],lw=4, color="blue")
ax.plot(x[:int(nx/2)] +2*L,y[:int(nx/2)],lw=4, color="blue")
ax.grid()
plt.close()
return fig
def sawtooth_static_plot():
'''
plot sawtooth function
'''
nx=1000
L=1
A=1
x=np.linspace(-L/2,L/2,nx)
y=A*x
n_h=50
harmonics=np.zeros((n_h,x.size))
for i in range(n_h):
n=i + 1
bn=(-1)**(n+1)*A/pi/n
kn=2*n*pi/L
harmonics[i,:]=bn*sin(kn*x)
fig=plt.figure(figsize=(14,6))
ax=fig.add_subplot(221)
ax.set_xlim(-3*L/2,3*L/2)
ax.set_title(r"$n=1$",size=20)
h=harmonics[0,:]
ax.plot(x,y,color="blue")
ax.plot(x-L,y,color="blue")
ax.plot(x+L,y,color="blue")
ax.axvline(-L/2,color="black",alpha=.5)
ax.axvline(L/2,color="black",alpha=.5)
ax.plot(x,h,color="orange")
ax.plot(x-L,h,color="orange")
ax.plot(x+L,h,color="orange")
ax.grid()
ax=fig.add_subplot(222)
ax.set_xlim(-3*L/2,3*L/2)
ax.set_title(r"$n=5$",size=20)
h=np.sum(harmonics[:5,:],axis=0)
ax.plot(x,y,color="blue")
ax.plot(x-L,y,color="blue")
ax.plot(x+L,y,color="blue")
ax.axvline(-L/2,color="black",alpha=.5)
ax.axvline(L/2,color="black",alpha=.5)
ax.plot(x,h,color="orange")
ax.plot(x-L,h,color="orange")
ax.plot(x+L,h,color="orange")
ax.grid()
ax=fig.add_subplot(223)
ax.set_xlim(-3*L/2,3*L/2)
ax.set_title(r"$n=20$",size=20)
ax.set_xlabel("x", size=20)
h=np.sum(harmonics[:20,:],axis=0)
ax.plot(x,y,color="blue")
ax.plot(x-L,y,color="blue")
ax.plot(x+L,y,color="blue")
ax.axvline(-L/2,color="black",alpha=.5)
ax.axvline(L/2,color="black",alpha=.5)
ax.plot(x,h,color="orange")
ax.plot(x-L,h,color="orange")
ax.plot(x+L,h,color="orange")
ax.grid()
ax=fig.add_subplot(224)
ax.set_xlim(-3*L/2,3*L/2)
ax.set_title(r"$n=50$",size=20)
ax.set_xlabel("x", size=20)
h=np.sum(harmonics,axis=0)
ax.plot(x,y,color="blue")
ax.plot(x-L,y,color="blue")
ax.plot(x+L,y,color="blue")
ax.axvline(-L/2,color="black",alpha=.5)
ax.axvline(L/2,color="black",alpha=.5)
ax.plot(x,h,color="orange")
ax.plot(x-L,h,color="orange")
ax.plot(x+L,h,color="orange")
ax.grid()
plt.tight_layout()
plt.close()
return fig