def row_echelon(matlist, K):
"""
Returns the row echelon form of a matrix with diagonal elements
reduced to 1.
Examples
========
>>> from sympy.matrices.densesolve import row_echelon
>>> from sympy import QQ
>>> a = [
... [QQ(3), QQ(7), QQ(4)],
... [QQ(2), QQ(4), QQ(5)],
... [QQ(6), QQ(2), QQ(3)]]
>>> row_echelon(a, QQ)
[[1, 7/3, 4/3], [0, 1, -7/2], [0, 0, 1]]
See Also
========
rref
"""
result_matlist = copy.deepcopy(matlist)
nrow = len(result_matlist)
for i in range(nrow):
if result_matlist[i][i] != 1 and result_matlist[i][i] != 0:
rowmul(result_matlist, i, 1 / result_matlist[i][i], K)
for j in range(i + 1, nrow):
if result_matlist[j][i] != 0:
rowadd(result_matlist, j, i, -result_matlist[j][i], K)
return result_matlist
def row_echelon(matlist, K):
"""
Returns the row echelon form of a matrix with diagonal elements
reduced to 1.
Examples
========
>>> from sympy.matrices.densesolve import row_echelon
>>> from sympy import QQ
>>> a = [
... [QQ(3), QQ(7), QQ(4)],
... [QQ(2), QQ(4), QQ(5)],
... [QQ(6), QQ(2), QQ(3)]]
>>> row_echelon(a, QQ)
[[1, 7/3, 4/3], [0, 1, -7/2], [0, 0, 1]]
See Also
========
rref
"""
result_matlist = copy.deepcopy(matlist)
nrow = len(result_matlist)
for i in range(nrow):
if (result_matlist[i][i] != 1 and result_matlist[i][i] != 0):
rowmul(result_matlist, i, 1/result_matlist[i][i], K)
for j in range(i + 1, nrow):
if (result_matlist[j][i] != 0):
rowadd(result_matlist, j, i, -result_matlist[j][i], K)
return result_matlist