dsprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, pro- vides error bounds and backward error estimates for the solution
SUBROUTINE DSPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*), WORK2(*) DOUBLE PRECISION AP(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DSPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*), WORK2(*) DOUBLE PRECISION AP(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE SPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT, WORK2 REAL(8), DIMENSION(:) :: AP, AF, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X SUBROUTINE SPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2 REAL(8), DIMENSION(:) :: AP, AF, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void dsprfs(char uplo, int n, int nrhs, double *ap, double *af, int *ipivot, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dsprfs_64(char uplo, long n, long nrhs, double *ap, double *af, long *ipivot, double *b, long ldb, double *x, long ldx, dou- ble *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library dsprfs(3P)
NAME
dsprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and packed, pro-
vides error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE DSPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*), WORK2(*)
DOUBLE PRECISION AP(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
SUBROUTINE DSPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*), WORK2(*)
DOUBLE PRECISION AP(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*),
WORK(*)
F95 INTERFACE
SUBROUTINE SPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT, WORK2
REAL(8), DIMENSION(:) :: AP, AF, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
SUBROUTINE SPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
REAL(8), DIMENSION(:) :: AP, AF, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
C INTERFACE
#include <sunperf.h>
void dsprfs(char uplo, int n, int nrhs, double *ap, double *af, int
*ipivot, double *b, int ldb, double *x, int ldx, double
*ferr, double *berr, int *info);
void dsprfs_64(char uplo, long n, long nrhs, double *ap, double *af,
long *ipivot, double *b, long ldb, double *x, long ldx, dou-
ble *ferr, double *berr, long *info);
PURPOSE
dsprfs improves the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and packed, and
provides error bounds and backward error estimates for the solution.
ARGUMENTS
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.
AP (input)
Double precsion 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', 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.
AF (input)
Double precsion array, dimension (N*(N+1)/2) The factored
form of the matrix A. AF contains the block diagonal matrix
D and the multipliers used to obtain the factor U or L from
the factorization A = U*D*U**T or A = L*D*L**T as computed by
DSPTRF, stored as a packed triangular matrix.
IPIVOT (input)
Integer array, dimension (N) Details of the interchanges and
the block structure of D as determined by DSPTRF.
B (input) Double precision 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)
Double precision array, dimension (LDX,NRHS) On entry, the
solution matrix X, as computed by DSPTRS. On exit, the
improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output)
Double precision array, dimension (NRHS) The estimated for-
ward error bound for each solution vector X(j) (the j-th col-
umn 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
estimate is as reliable as the estimate for RCOND, and is
almost always a slight overestimate of the true error.
BERR (output)
Double precision 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)
Double precision 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 illegal value
7 Nov 2015 dsprfs(3P)