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D.3.2.12 gaussred_pivot
Procedure from library linalg.lib (see linalg_lib).
- Usage:
- gaussred_pivot(A); A any constant matrix
- Return:
- list Z: Z[1]=P , Z[2]=U , Z[3]=S , Z[4]=rank(A)
gives a row reduced matrix S, a permutation matrix P and a
normalized lower triangular matrix U, with P*A=U*S
- Note:
- with row pivoting
Example:
| | LIB "linalg.lib";
ring r=0,(x),dp;
matrix A[5][4] = 1, 3,-1,4,
2, 5,-1,3,
1, 3,-1,4,
0, 4,-3,1,
-3,1,-5,-2;
list Z=gaussred_pivot(A); //construct P,U,S s.t. P*A=U*S
print(Z[1]); //P
==> 0,0,0,0,1,
==> 0,1,0,0,0,
==> 0,0,1,0,0,
==> 0,0,0,1,0,
==> 1,0,0,0,0
print(Z[2]); //U
==> 1, 0, 0, 0,0,
==> -2/3,1, 0, 0,0,
==> -1/3,10/17,1, 0,0,
==> 0, 12/17,-1/2,1,0,
==> -1/3,10/17,1, 0,1
print(Z[3]); //S
==> -3,1, -5, -2,
==> 0, 17/3,-13/3,5/3,
==> 0, 0, -2/17,40/17,
==> 0, 0, 0, 1,
==> 0, 0, 0, 0
print(Z[4]); //rank
==> 4
print(Z[1]*A); //P*A
==> -3,1,-5,-2,
==> 2, 5,-1,3,
==> 1, 3,-1,4,
==> 0, 4,-3,1,
==> 1, 3,-1,4
print(Z[2]*Z[3]); //U*S
==> -3,1,-5,-2,
==> 2, 5,-1,3,
==> 1, 3,-1,4,
==> 0, 4,-3,1,
==> 1, 3,-1,4
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