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# stprfs

```
NAME
STPRFS - provide error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular packed coefficient matrix

SYNOPSIS
SUBROUTINE STPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB,
X, LDX, FERR, BERR, WORK, IWORK, INFO )

CHARACTER      DIAG, TRANS, UPLO

INTEGER        INFO, LDB, LDX, N, NRHS

INTEGER        IWORK( * )

REAL           AP( * ), B( LDB, * ), BERR( * ), FERR( *
), WORK( * ), X( LDX, * )

PURPOSE
STPRFS provides error bounds and backward error estimates
for the solution to a system of linear equations with a tri-
angular packed coefficient matrix.

The solution matrix X must be computed by STPTRS or some
other means before entering this routine.  STPRFS does not
do iterative refinement because doing so cannot improve the
backward error.

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.

TRANS   (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N':  A * X = B  (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate transpose = Tran-
spose)

DIAG    (input) CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of
columns of the matrices B and X.  NRHS >= 0.

AP      (input) REAL array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed
columnwise in a linear array.  The j-th column of A
is stored in the array AP as follows: if UPLO = 'U',
AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO =
'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = 'U', the diagonal elements of A are not
referenced and are assumed to be 1.

B       (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >=
max(1,N).

X       (input) REAL array, dimension (LDX,NRHS)
The solution matrix X.

LDX     (input) INTEGER
The leading dimension of the array X.  LDX >=
max(1,N).

FERR    (output) REAL array, dimension (NRHS)
The estimated forward error bounds for each solution
vector X(j) (the j-th column of the solution matrix
X).  If XTRUE is the true solution, FERR(j) bounds
the magnitude of the largest entry in (X(j) - XTRUE)
divided by the magnitude of the largest entry in
X(j).  The quality of the error bound depends on the
quality of the estimate of norm(inv(A)) computed in
the code; if the estimate of norm(inv(A)) is accu-
rate, the error bound is guaranteed.

BERR    (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each
solution vector X(j) (i.e., the smallest relative
change in any entry of A or B that makes X(j) an
exact solution).

WORK    (workspace) REAL array, dimension (3*N)

IWORK   (workspace) INTEGER array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
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