STPRFS(l) ) STPRFS(l)
STPRFS - provide error bounds and backward error estimates for the solution to a system of
linear equations with a triangular packed coefficient matrix
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, * )
STPRFS provides error bounds and backward error estimates for the solution to a system of
linear equations with a triangular 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.
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 = Transpose)
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)*(2*n-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 bound for each solution vector X(j) (the j-th column
of the solution matrix X). If XTRUE is the true solution corresponding to X(j),
FERR(j) is an estimated upper bound for the magnitude of the largest element in
(X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The esti-
mate is as reliable as the estimate for RCOND, and is almost always a slight over-
estimate of the true error.
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 element of A or B that makes X(j) an exact solu-
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
LAPACK version 3.0 15 June 2000 STPRFS(l)