/
gauss_jordan (2).py
42 lines (39 loc) · 1.21 KB
/
gauss_jordan (2).py
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def gauss_jordan(m, eps = 1.0/(10**10)):
"""Puts given matrix (2D array) into the Reduced Row Echelon Form.
Returns True if successful, False if 'm' is singular.
NOTE: make sure all the matrix items support fractions! Int matrix will NOT work!
Written by Jarno Elonen in April 2005, released into Public Domain"""
(h, w) = (len(m), len(m[0]))
for y in range(0,h):
maxrow = y
for y2 in range(y+1, h): # Find max pivot
if abs(m[y2][y]) > abs(m[maxrow][y]):
maxrow = y2
(m[y], m[maxrow]) = (m[maxrow], m[y])
if abs(m[y][y]) <= eps: # Singular?
return False
for y2 in range(y+1, h): # Eliminate column y
c = m[y2][y] / m[y][y]
for x in range(y, w):
m[y2][x] -= m[y][x] * c
for y in range(h-1, 0-1, -1): # Backsubstitute
c = m[y][y]
for y2 in range(0,y):
for x in range(w-1, y-1, -1):
m[y2][x] -= m[y][x] * m[y2][y] / c
m[y][y] /= c
for x in range(h, w): # Normalize row y
m[y][x] /= c
return True
'''
Example:
x + y + z = 2
2x + y + z = 3
x + 2y + z = 4
=> (x,y,z)=(1,2,-1)
'''
mtx = [[1.0, 1.0, 1.0, 2.0],
[2.0, 1.0, 1.0, 3.0],
[1.0, 2.0, 1.0, 4.0]]
gauss_jordan(mtx)
print mtx