#------------------------------------------------------------------------------
#  Matrix.py
#------------------------------------------------------------------------------
"""
This module provides functions for performing some standard matrix operations.
Matrices are represented as nested lists, i.e. lists of lists of numbers (float
or int.)  Functions that take two matrix arguments will raise a ValueError()
if the matrices are not compatible, i.e. the same number of rows and columns.
"""
#------------------------------------------------------------------------------
# import statements
#------------------------------------------------------------------------------
import random

#------------------------------------------------------------------------------
# function definitions
#------------------------------------------------------------------------------


# compatible() ----------------------------------------------------------------
def compatible(A, B):
   """
   Returns True if A and B have the same number of rows and columns, and
   False otherwise.
   """
   result = (len(A)==len(B)) # True or False
   i = 0
   while result and i<len(A):
      result = (len(A[i])==len(B[i])) # True or False
      i += 1
   # end while
   return result
# end compatible() ------------------------------------------------------------


# add() -----------------------------------------------------------------------
def add(A, B):
   """ 
   Return a matrix that is the sum A+B of matrices A and B.
   """
   if not compatible(A, B):
      raise ValueError('add(): incompatible matrices:\n'+str(A)+'\n'+str(B))
   # end if

   C = []
   for i in range(len(A)):
      R = []
      for j in range(len(A[i])):
         R.append(A[i][j]+B[i][j])
      # end inner for
      C.append(R)
   # end outer for
   return C
# end add() -------------------------------------------------------------------


# negate() --------------------------------------------------------------------
def negate(A):
   """
   Return the negative -A of matrix A.
   """
   negativeA = []
   for row in A:
      negativeRow = []
      for x in row:
         negativeRow.append(-x)
      # end inner for
      negativeA.append(negativeRow)
   #end outer for
   return negativeA
# end negate() ----------------------------------------------------------------


# sub() -----------------------------------------------------------------------
def sub(A, B):
   """ 
   Return a matrix that is the difference A-B of matrices A and B.
   """
   if not compatible(A, B):
      raise ValueError('sub(): incompatible matrices:\n'+str(A)+'\n'+str(B))
   # end if 

   return add(A, negate(B))
# end sub() -------------------------------------------------------------------


# scalarMult() ----------------------------------------------------------------
def scalarMult(c, A):
   """
   Return a matrix that is the scalar multiple of matrix A by the number c.
   """
   M = []
   for row in A:
      newRow = []
      for x in row:
         newRow.append(c*x)
      # end for
      M.append(newRow)
   # end for
   return M
# end scalarMult() ------------------------------------------------------------


# randomMatrix() --------------------------------------------------------------
def randomMatrix(n, m, a, b):
   """
   Return square matrix of size n by m whose entries are random floats in
   the range [a, b).
   """
   M = []
   for i in range(n):
      newRow = []
      for j in range(m):
         newRow.append(random.uniform(a, b))
      # end for 
      M.append(newRow)
   # end for
   return M
# end randomMatrix() ----------------------------------------------------------


# printMatrix() ---------------------------------------------------------------
def printMatrix(M):
   """
   Print in nice format.
   """
   print('[')
   for row in M:
      print('  ',row)
   # end for
   print(']')
# end printMatrix() -----------------------------------------------------------