TRISOLV Function
solves linear systems with triangular matrices
- TRISOLV( code,
,
, piv>)
The TRISOLV function returns the following value:
![x](images/langref_langrefeq78.gif)
- is the
matrix
containing
solutions of
the
linear systems specified by code,
, and
.
The inputs to the TRISOLV function are as follows:
- code
- specifies which of the following forms of
triangular linear system has to be solved:
- code=1
- solve
,
upper triangular
- code=2
- solve
,
upper triangular
- code=3
- solve
,
lower triangular
- code=4
- solve
,
lower triangular
![r](images/langref_langrefeq50.gif)
- specifies the
nonsingular upper (code=1,2)
or lower (code=3,4) triangular coefficient matrix
.
Only the upper or lower triangle of argument matrix
is used; the other triangle can contain any information.
![b](images/langref_langrefeq43.gif)
- specifies the
matrix,
, of
right-hand sides
.
- piv
- specifies an optional
vector that relates the
order of the columns of matrix
to the order of
the columns of an original coefficient matrix
for which matrix
has been computed as a factor.
For example, the vector piv can be the result of
the QR decomposition of a matrix
whose columns were
permuted in the order
.
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.
If TRISOLV recognizes the upper or lower triangular matrix
as a singular matrix (that is, one that contains at least
one zero diagonal element), it exits with an error message.
Consider the following example:
R = { 1 0 0 0,
3 2 0 0,
1 -3 5 0,
2 7 9 -1 };
b = {1, 1, 4, -6 };
x = trisolv(4, R, b);
print x;
X
1
-1
0
1
Also see the example in the QR call section.
Copyright © 2009 by SAS Institute Inc., Cary, NC, USA. All rights reserved.