How do i find the row echelon form (REF)-CodePudding

import numpy as np
import sympy as sp

Vec = np.matrix([[1,1,1,5],[1,2,0,3],[2,1,3,12]]) 
Vec_rref = sp.Matrix(Vec).rref()
print(Vec_rref) ##<--  this code prints the RREF, but i am looking for the code for REF (See below)

I have found plenty of codes which solves the RREF but not codes for REF, if **it makes sense. The code i have developed gives the following:

(Matrix([
[1, 0,  2,  7],
[0, 1, -1, -2],
[0, 0,  0,  0]]), (0, 1))

I am looking for a code which should solve the following:

      1XXX
REF = 01XX
      001X

and not

       100X
RREF = 010X
       001X

New here so bare with me guys. Thanks in advance :-)

CodePudding user response：

You are using the function of sympy: rref wich is associated to "reduced row-echelon form". You might want to use .echelon_form() instead

import numpy as np
import sympy as sp
from scipy import linalg

Vec = np.matrix([[1,1,1,5],
                 [1,2,0,3],
                 [2,1,3,12]]) 

Vec_rref =sp.Matrix(Vec).echelon_form()

print(Vec_rref)

wich outputs:

Matrix([[1, 1, 1, 5], [0, 1, -1, -2], [0, 0, 0, 0]])