#!/usr/bin/env python
#
# file: $ENGR_2011/lecture_08.py
#
# A simple Python program that demonstrates basic vectors and matrices
#

# import system modules
#
import os
import sys
import numpy as np
from numpy.linalg import matrix_rank
from scipy.linalg import solve

# function: myloadtxt
#
# arguments:
#  fname: a filename containing a matrix
#
# return: a numpy float array
#
# Note: we use our own loader because numpy's loadtxt does not handle
# single line matrices properly - it converts them to vectors
#
def myloadtxt(fname):

    # open the file
    #
    fp = open(fname)
    if fp is None:
        print("Error: error opening file (%s)" % (fname))
        return None

    # read the lines into a list
    #
    lines = []
    for l in fp:
        lines.append(l.rstrip('\n'))

    # create a numpy array
    #
    nrows = len(lines)
    ncols = len(lines[0].split())
    A = np.zeros((nrows, ncols))
    
    # loop over the list and parse the entries
    #
    for i in range(0, nrows):
        vals = lines[i].split()
        for j in range(0, ncols):
            A[i][j] = float(vals[j])

    # exit gracefully
    #
    return(A)

    # end of function
    #

# function: main
#
def main(argv):

    # read a matrix from a file specified at the command line
    #
    A = myloadtxt(argv[1])

    # print the matrices
    #
    print("A:\n", A)

    # invert the matrix
    #
    B = np.linalg.inv(A)

    # display the result
    #
    print("B = A_inv\n", B)
    
    # verify the result
    #
    C = B @ A
    print("C = A_inv * A\n", C)

    # exit gracefully
    #
    return True

# begin gracefully
#
if __name__ == '__main__':
    main(sys.argv[0:])

#
# end of file