图上马蒂厄特征交叉

Question

我需要绘制各种q的mathieu特征参数。这个图应该显示“长笛”形状，从左边的宽到右边的很窄。下面的代码可以做到这一点，但是它也引入了一些带间跳变(从图中可以明显看出)。我怎么才能解决这个问题？

谢谢!

上午

import numpy as np
import scipy as sp
import scipy.special as spfun
from matplotlib import pyplot as plt

uplim =120#E_rec
Npts =1000 
Nstates =8 
q = np.linspace(0, uplim/4.0, Npts)
EA = np.zeros([Npts,Nstates])
EB = np.zeros([Npts,Nstates])
U = 4*q 

print np.shape(EA)    #plt.fill_between(U, EA[:,i], EB[:,i]) #plt.plot(U,Ea,U,Eb) 
for i in range(Nstates):
    a = spfun.mathieu_a(i,q)
    b = spfun.mathieu_b(i+1,q)
    EA[:,i] = a + 2*q
    EB[:,i] = b + 2*q 
    plt.fill_between(U, EA[:,i], EB[:,i]) #plt.plot(U,Ea,U,Eb) 

print np.shape(EA)    #plt.fill_between(U, EA[:,i], EB[:,i]) #plt.plot(U,Ea,U,Eb) 
plt.show()

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正如DSM和pv所指出的那样，这是一个令人垂涎的错误。你走得越远，故障就越严重。最后我做的是导出我想从Mathematica导出的值表，并将它们导入python并进行内插。不太好，但很管用。

Answer 1

我尝试用用于Python的NAG库的最新版本计算这个值，其中包括一个新的Mathieu函数例程。我更加努力--更多的州和更高的提升价值。

%matplotlib inline
import numpy as np
import scipy as sp
import scipy.special as spfun
from naginterfaces.library import specfun
from matplotlib import pyplot as plt

uplim =150#E_rec
Npts = 4000 
Nstates = 10
q = np.linspace(0, uplim/4.0, Npts)
EA = np.zeros([Npts,Nstates])
EB = np.zeros([Npts,Nstates])
U = 4*q 

plt.figure(figsize=(15,8))
plt.subplot(1,2,1)
plt.title('Using SciPy')

for i in range(Nstates):
    a = spfun.mathieu_a(i,q)
    b = spfun.mathieu_b(i+1,q)
    EA[:,i] = a + 2*q
    EB[:,i] = b + 2*q 
    plt.fill_between(U, EA[:,i], EB[:,i]) #plt.plot(U,Ea,U,Eb) 


plt.subplot(1,2,2)
plt.title('Using NAG')

for i in range(Nstates):
    a = [specfun.mathieu_ang_periodic_real(ordval=i, q=qi, parity=0, mode=3)[2] for qi in q]
    b = [specfun.mathieu_ang_periodic_real(ordval=i+1, q=qi, parity=1, mode=3)[2] for qi in q]
    EA[:,i] = a + 2*q
    EB[:,i] = b + 2*q 
    plt.fill_between(U, EA[:,i], EB[:,i]) 

plt.show()

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这使用的Mark27和ScipPy的1.2.1版本