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以前に私が回答したこの質問と全く同じなので、参考にしてください。
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[【python】numpyとscipyで変数を含んだ行列式を計算したい](https://teratail.com/questions/275887#reply-393270)
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[【python】numpyとscipyで変数を含んだ行列式を計算したい](https://teratail.com/questions/275887#reply-393270)
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# 複素数でとく場合
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ある複素数をZとすると、Z=0⇔|Z|=0なので、今回は|Z|を最小化するという問題になります。
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``minimize``を使います。
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```python
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import cmath
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import numpy as np
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import scipy
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from scipy.integrate import quad
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import numpy.linalg as LA
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from scipy import optimize
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#積分1
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def M(func, a, b, **kwargs):
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def real_func(r):
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return scipy.real(func(r))
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def imag_func(r):
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return scipy.imag(func(r))
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real_integral = quad(real_func, a, b, **kwargs)
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imag_integral = quad(imag_func, a, b, **kwargs)
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return (real_integral[0] + 1j*imag_integral[0], real_integral[1:], imag_integral[1:])
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#複素積分計算1
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def F_r2(func, a, b, **kwargs):
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def real_func(r):
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return scipy.real(func(r))
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def imag_func(r):
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return scipy.imag(func(r))
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real_integral = quad(real_func, a, b, **kwargs)
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imag_integral = quad(imag_func, a, b, **kwargs)
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return (real_integral[0] + 1j*imag_integral[0], real_integral[1:], imag_integral[1:])
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#複素積分計算2
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def F_r3(func, a, b, **kwargs):
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def real_func(r):
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return scipy.real(func(r))
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def imag_func(r):
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return scipy.imag(func(r))
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real_integral = quad(real_func, a, b, **kwargs)
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imag_integral = quad(imag_func, a, b, **kwargs)
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return (real_integral[0] + 1j*imag_integral[0], real_integral[1:], imag_integral[1:])
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#複素積分計算3
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def G_r2(func, a, b, **kwargs):
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def real_func(r):
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return scipy.real(func(r))
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def imag_func(r):
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return scipy.imag(func(r))
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real_integral = quad(real_func, a, b, **kwargs)
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imag_integral = quad(imag_func, a, b, **kwargs)
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return (real_integral[0] + 1j*imag_integral[0], real_integral[1:], imag_integral[1:])
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#複素積分計算4
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def G_r3(func, a, b, **kwargs):
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def real_func(r):
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return scipy.real(func(r))
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def imag_func(r):
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return scipy.imag(func(r))
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real_integral = quad(real_func, a, b, **kwargs)
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imag_integral = quad(imag_func, a, b, **kwargs)
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return (real_integral[0] + 1j*imag_integral[0], real_integral[1:], imag_integral[1:])
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def A(x):
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#数値は仮
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r0 = 1
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r1 = 1
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r2 = 1
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r3 = 1
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vr2 = 1
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beta2 = 1
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n = 1
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Q = 1
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ganma = - Q / cmath.tan(beta2)
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omega = x[0]+x[1]*1j
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A_M = M(lambda r: r2 / (r * cmath.sin(beta2)), r2, r1)
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A_F_r2 = F_r2(lambda r: cmath.exp((-1j* (omega * cmath.pi * (r**2 - r2**2) / Q - n * ganma * cmath.log(r / r2) / Q ))) * (r / r2)**(n + 1), r3, r2)
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A_F_r3 = F_r3(lambda r: cmath.exp((-1j* (omega * cmath.pi * (r**2 - r2**2) / Q - n * ganma * cmath.log(r / r2) / Q ))) * (r / r3)**(n + 1), r3, r3)
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A_G_r2 = G_r2(lambda r: cmath.exp((-1j* (omega * cmath.pi * (r**2 - r2**2) / Q - n * ganma * cmath.log(r / r2) / Q ))) * (r2 / r)**(n - 1), r2, r2)
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A_G_r3 = G_r3(lambda r: cmath.exp((-1j* (omega * cmath.pi * (r**2 - r2**2) / Q - n * ganma * cmath.log(r / r2) / Q ))) * (r3 / r)**(n - 1), r3, r2)
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#raund_theta算出
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raund_theta = cmath.exp(-1j *(omega * cmath.pi * (r3**2 - r2**2) / Q - n * ganma * cmath.log(r3 / r2) / Q)) - ((n - 1) / r3 ) * 0.5 * A_G_r3[0]
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#各種値計算
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a11 = r2 * vr2
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a12 = (1 - cmath.exp(-2* beta2 * 1j)) * ( 1j * r2 * omega / cmath.tan(beta2) - 0.5 * A_M[0] * n * omega )
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a13 = r1**n * omega
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a14 = omega / r1**n
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a22 = 1 - cmath.exp(-2* 1j * beta2)
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a23 = r1**(n -1)
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a24 = 1 / r1**(n + 1)
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a31 = (1j * omega - ganma /(2 * cmath.pi * r3**2) * 1j * n + Q/(2 * cmath.pi * r3**2)) * (0.5 * A_F_r3[0] - 0.5 * A_G_r3[0] - 1j * (r2 / r3)**(n + 1) * cmath.exp(-2 * 1j * beta2) * (-1j *((0.5 * A_F_r2[0]) + (0.5 * A_G_r2[0])))) + Q/(2 * cmath.pi * r3**2) * (raund_theta + 1j * (n + 1) * r2**(n + 1) / r3**(n + 2) * cmath.exp(-2 * 1j * beta2) * (-1j * ((0.5 * A_F_r2[0]) + (0.5 * A_G_r2[0]))))
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a32 = (1j * omega - ganma /(2 * cmath.pi * r3**2) * 1j * n + Q/(2 * cmath.pi * r3**2)) * (-1j * (r3 / r2)**(n - 1) - 1j * (r2 / r3)**(n + 1) * cmath.exp(-2 * 1j * beta2)) + (Q/(2 * cmath.pi * r3)) * (-1j * (n - 1) * r3**(n - 2) / r2**(n - 1) + 1j * (n + 1) * r2**(n + 1) / r3**(n + 2) * cmath.exp(-2 * 1j * beta2))
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a43 = omega * r0**(n - 1)
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a44 = -omega / r0**(n + 1)
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#行列計算
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A = np.matrix([
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[a11, a12, a13, a14],
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[ 0, a22, a23, a24],
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[a31, a32, 0, 0],
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[ 0, 0, a43, a44]
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])
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return np.abs(LA.det(A))
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optimize.minimize(A, [0,1], method='Nelder-Mead')
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```
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# 結果
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どういう計算をしているかわからないので、計算結果があっているかどうかはわかりません。
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結果としてはomega = -1e-5 - 1.67e-5iとなります。
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```text
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final_simplex: (array([[-1.00106837e-05, -1.67414895e-05],
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[-1.63706702e-05, 4.94895503e-05],
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[-5.72935526e-05, -4.18866985e-06]]), array([1.47572037e-05, 3.94333956e-05, 4.34533398e-05]))
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fun: 1.475720371432839e-05
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message: 'Optimization terminated successfully.'
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nfev: 76
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nit: 41
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status: 0
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success: True
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x: array([-1.00106837e-05, -1.67414895e-05])
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```
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