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D.3.2.15 U_D_O
Procedure from library linalg.lib (see linalg_lib).
- Usage:
U_D_O(A); constant invertible matrix A
- Return:
list Z: Z[1]=P , Z[2]=U , Z[3]=D , Z[4]=O
gives a permutation matrix P,
a normalized lower triangular matrix U ,
a diagonal matrix D, and
a normalized upper triangular matrix O
with P*A=U*D*O- Note:
Z[1]=-1 means that A is not regular (proc uses gaussred)
Example:
LIB "linalg.lib"; ring r = 0,(x),dp; matrix A[5][5] = 10, 4, 0, -9, 8, -3, 6, -6, -4, 9, 0, 3, -1, -9, -8, -4,-2, -6, -10,10, -9, 5, -1, -6, 5; list Z = U_D_O(A); //construct P,U,D,O s.t. P*A=U*D*O print(Z[1]); //P print(Z[2]); //U print(Z[3]); //D print(Z[4]); //O print(Z[1]*A); //P*A print(Z[2]*Z[3]*Z[4]); //U*D*O |