# simeq.py   solve simultaneous equations AX=Y and invert
# solve real linear equations for X where Y = A * X
# usage:  X = simeq(A,Y)    X = simeqb(B)   B = invert(A)
# for user using [[ ]] matrix rather than numpy array

from numpy import array
from numpy.linalg import solve
from numpy.linalg import inv
from numpy.linalg import det

def simeq(A,Y):
  n = len(Y)
  a = array([[A[i][j] for j in range(n)]for i in range(n)])
  y = array([Y[j] for j in range(n)])
  x=solve(a,y)
  X = [x[j] for j in range(n)]
  return X;

def simeqb(B):
  n = len(B)
  a = array([[B[i][j] for j in range(n)]for i in range(n)])
  y = array([B[i][n] for i in range(n)])
  x=solve(a,y)
  X = [x[j] for j in range(n)]
  return X;

def invert(A):
  n = len(A)
  b = array([[A[i][j] for j in range(n)]for i in range(n)])
  b = inv(b)
  B = [[b[i][j] for j in range(n)] for i in range(n)]
  return B

def determ(A):
  n = len(A)
  b = array([[A[i][j] for j in range(n)]for i in range(n)])
  B = det(b)
  return B