Python script to calculate row echelon matrices from non-row echelon matrices (for Gaussian elimination, say)

echelon.py

#!/usr/bin/env python3
# encoding: utf-8
# Row Echelon Calculator
# (for Gaussian Elimination)

# INPUT:
# Matrix of any dimensions in the following form:
# input := { row, "\n" }, ".\n"
# row   := { num, " "  }
# num   := <float>
# (or, to be short, just separate numbers with spaces, use periods (.) for 
# decimal separators, press enter for a new matrix row and type a . to stop)

# OUTPUT:
# New matrix in row-echelon form

# Example
# > 3   4.5 2.0e3 -5
# > 1.3 3.4 5.6   29.71
# > 2.5 3.5 4.5   5.5 
# > 3.5 2.1 3.4   9.955
# > .
# Outputs:
# 3.00 4.50 2000.00 -5.00
# 0.00 1.45 -861.07 31.88
# 0.00 0.00 -1810.63 15.16
# 0.00 0.00 0.00 49.86

# row_mult :: [a], Multiplier -> [a]
# multiply a list by a number
def row_mult(row, num):
  return [x * num for x in row]

# row_sub :: [a], [a] -> [a]
# subtract one row from another
def row_sub(row_left, row_right):
  return [a - b for (a, b) in zip(row_left, row_right)]

# row_echelon :: Matrix -> Matrix
# calculate the row echelon form of the matrix
def row_echelon(mtx): 
  temp_mtx = list(mtx)

  def echelonify(rw, col):
    for i, row in enumerate(temp_mtx[(col+1):]):
      i += 1
      if rw[col] == 0: continue
      temp_mtx[i+col] = row_sub(row, row_mult(rw, row[col] / rw[col]))      

  for i in range(len(mtx)):
    # print("d: echelonifying row #"+str(i))
    active_row = temp_mtx[i]
    echelonify(active_row, i)

  # flatten out values very close to zero
  temp_mtx = [
    [(0 if (0.0000000001 > x > -0.0000000001) else x) 
      for x in row] 
    for row in temp_mtx
  ]

  return temp_mtx

if __name__=='__main__':
  print ("[ Row Echelon Calculator ] ")
  print ("Type any number of rows of whitespace-separated floating numbers to \nmake a matrix.")
  print ("Type a . to stop entering a matrix.")
  mtx = []

  # always limit yo' whiles
  n_tries = 1000
  while n_tries > 0:
    n_tries -= 1
    try: 
      inp = input("> ").strip()
    except KeyboardInterrupt:
      print("interrupted - exiting")
      exit(0)
    
    # we're done here, the matrix has been collected
    if inp == '.':
      break

    elif inp == '':
      print("empty line - try again!")
      continue

    try:
      row = list(map(float, inp.split()))
      mtx.append(row)
    except Exception as e:
      print("exception while reading this row:" + str(e))
      print("try again!")

  # print("d: collected all rows! now beginning calculation")

  try:
    mtx_result = row_echelon(mtx)
    # print("d: done calculating! printing output mtx")
    # simple matrix printy thing
    for row in mtx_result:
      print (' '.join(("{0:.2f}".format(x) for x in row)))
    # print("d: eof")
  except Exception as e:
    print("exception while calculating row echelon form: " + str(e))
    exit(1)