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TRISOLV Function

solves linear systems with triangular matrices

TRISOLV( code, r, b<, piv>)

The TRISOLV function returns the following value:
x
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:
code
specifies which of the following forms of triangular linear system has to be solved:
code=1
solve Rx = b, R upper triangular

code=2
solve R' x = b, R upper triangular

code=3
solve R' x = b, R lower triangular

code=4
solve Rx = b, R lower triangular

r
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.

b
specifies the n ×p matrix, B, of p right-hand sides bk.

piv
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[1], ... , Apiv[n].
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 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.

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