solves linear systems with triangular matrices
- TRISOLV( code, r, b<, piv>)
The TRISOLV function returns the following value:
- is the n ×p matrix X containing p solutions of
the p linear systems specified by code, r, and b.
The inputs to the TRISOLV function are as follows:
For code=1 and code=3, the
solution is obtained by backward elimination.
For code=2 and code=4, the
solution is obtained by forward substitution.
- specifies which of the following forms of
triangular linear system has to be solved:
- solve Rx = b, R upper triangular
- solve R' x = b, R upper triangular
- solve R' x = b, R lower triangular
- solve Rx = b, R lower triangular
- specifies the n ×n nonsingular upper (code=1,2)
or lower (code=3,4) triangular coefficient matrix R.
Only the upper or lower triangle of argument matrix r
is used; the other triangle can contain any information.
- specifies the n ×p matrix,
B, of p right-hand sides bk.
- specifies an optional n vector that relates the
order of the columns of matrix R to the order of
the columns of an original coefficient matrix A
for which matrix R has been computed as a factor.
For example, the vector piv can be the result of
the QR decomposition of a matrix A whose columns were
permuted in the order Apiv, ... , Apiv[n].
If TRISOLV recognizes the upper or lower triangular matrix
R as a singular matrix (that is, one that contains at least
one zero diagonal element), it exits with an error message.
See the example in the QR call section.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.