Created
December 20, 2019 14:41
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| import numpy as np | |
| def M_matrix_element(A,j): | |
| M = np.delete(A, j, 0) | |
| M = np.delete(M, j, 1) | |
| return M | |
| def M_matrix(A): | |
| n = np.shape(A)[0] | |
| return np.array([np.linalg.eig(M_matrix_element(A,j))[0] for j in range(n)]).T | |
| def mho(a,i): | |
| index = [k for k in range(len(a))] | |
| index.remove(index[i]) | |
| return np.prod([a[i]-a[k] for k in index]) | |
| def mho_red(a, m, i, j): | |
| index = range(len(a)-1) | |
| return np.prod([a[i]-m[k,j] for k in index]) | |
| def eig_DPTZ(a, m): | |
| n = len(a) | |
| v = [[np.sqrt(mho_red(a,m,i,j)/mho(a,i)) for i in range(n)] for j in range(n)] | |
| return np.array(v) | |
| # Example of usage | |
| a1 = 1; a2 = 2; a3 = 3 | |
| a4 = -1; a5 = 1; a6 = -1 | |
| A = [[a1,a4,a5], | |
| [a4,a2,a6], | |
| [a5,a6,a3]] | |
| # Obtaining the eigenvalues | |
| a,V = np.linalg.eig(A) | |
| m = M_matrix(A) | |
| # Calculating eigenvectors elements (without signs) | |
| V2 = eig_DPTZ(a, m) | |
| # Comparing the results | |
| print('Eigenvectors', V) | |
| print('DPTZ eigenvectors elements (magnitude)', V2) |
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