Contents
spprfs - improve the computed solution to a system of linear
equations when the coefficient matrix is symmetric positive
definite and packed, and provides error bounds and backward
error estimates for the solution
SUBROUTINE SPPRFS(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR,
WORK, WORK2, INFO)
CHARACTER * 1 UPLO
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER WORK2(*)
REAL A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
SUBROUTINE SPPRFS_64(UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 WORK2(*)
REAL A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
F95 INTERFACE
SUBROUTINE PPRFS(UPLO, [N], [NRHS], A, AF, B, [LDB], X, [LDX], FERR,
BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL, DIMENSION(:) :: A, AF, FERR, BERR, WORK
REAL, DIMENSION(:,:) :: B, X
SUBROUTINE PPRFS_64(UPLO, [N], [NRHS], A, AF, B, [LDB], X, [LDX], FERR,
BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: WORK2
REAL, DIMENSION(:) :: A, AF, FERR, BERR, WORK
REAL, DIMENSION(:,:) :: B, X
C INTERFACE
#include <sunperf.h>
void spprfs(char uplo, int n, int nrhs, float *a, float *af,
float *b, int ldb, float *x, int ldx, float *ferr,
float *berr, int *info);
void spprfs_64(char uplo, long n, long nrhs, float *a, float
*af, float *b, long ldb, float *x, long ldx, float
*ferr, float *berr, long *info);
spprfs improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric positive
definite and packed, and provides error bounds and backward
error estimates for the solution.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
NRHS (input)
The number of right hand sides, i.e., the number
of columns of the matrices B and X. NRHS >= 0.
A (input) REAL array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric
matrix A, packed columnwise in a linear array.
The j-th column of A is stored in the array A as
follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j)
for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2)
= A(i,j) for j<=i<=n.
AF (input) REAL array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, as com-
puted by SPPTRF/CPPTRF, packed columnwise in a
linear array in the same format as A (see A).
B (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,N).
X (input/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by
SPPTRS. On exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >=
max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solu-
tion 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 ele-
ment in (X(j) - XTRUE) divided by the magnitude of
the largest element in X(j). The estimate is as
reliable as the estimate for RCOND, and is almost
always a slight overestimate 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 solution).
WORK (workspace)
REAL array, dimension(3*N)
WORK2 (workspace)
INTEGER array, dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value