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Code/getPowers.py

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+import numpy as np
+import pandas as pd
+from scipy.sparse.linalg import lsqr
+from scipy.linalg import *
+from sympy import Matrix
+from sympy import symbols, Add, Mul, S
+from numpy.linalg import matrix_rank
+from itertools import combinations
+
+
+N = np.array([[ 0,  1,  1],
+              [ 0, -1, -1],
+              [ 1,  0, 0],
+              [ 0,  0,  0],
+              [ 0,  0,  0],
+              [ 0,  0, 0],])
+
+N = np.array([[ 0,  0,  3,  1,  1,  1,  1,  1,  1],
+              [ 0,  0, -2,  0,  0,  0,  0,  0,  0],
+              [ 1,  1, -1,  0,  0,  0,  0,  0,  0],
+              [ 0,  0,  0,  0,  0,  0,  0,  0,  0],
+              [ 0,  0,  0,  0,  0,  0,  0,  0,  0],
+              [ 0,  0,  0,  0,  0,  0,  0,  0,  0]])
+
+a = np.array([ 1, -2,  1,  0,  0,  0])
+
+def getPowers(N,a):
+    rand_drop_cols = np.arange(0,len(N[0]),1)
+    rand_drop_rows = np.arange(0,len(N),1)
+    rand_drop_rows = np.flip(rand_drop_rows)
+    rank = matrix_rank(N)
+    d_cols = list(combinations(rand_drop_cols,len(N[0])-rank))
+    d_rows = list(combinations(rand_drop_rows,len(N)-rank))
+    for i in d_cols:
+        M = N
+        M = np.delete(M,i,1)
+        M = np.transpose(M)
+        for j in d_rows:
+            P = M
+            P = np.delete(P,j,1)
+            if np.linalg.det(P)!=0:
+                solved_M = np.transpose(P)
+                indices_sol = j
+                indices_powers = i
+                break
+
+    b = np.delete(a,indices_sol)
+    params = np.linalg.solve(solved_M,b)
+
+    sol = []
+    for i in range(len(N[0])):
+        if i in indices_powers:
+            sol = sol + [0]
+        else:
+            sol = sol + [params[0]]
+            params = np.delete(params,0)
+
+    # this is the solution:
+    sol = np.array(sol)
+    return(sol)
+
+