ssprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, provide error bounds and backward error estimates for the solution
SUBROUTINE SSPRFS(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(*) REAL AP(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE SSPRFS_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(*) REAL 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, DIMENSION(:) :: AP, AF, FERR, BERR, WORK REAL, 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, DIMENSION(:) :: AP, AF, FERR, BERR, WORK REAL, DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void ssprfs(char uplo, int n, int nrhs, float *ap, float *af, int *ipivot, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info); void ssprfs_64(char uplo, long n, long nrhs, float *ap, float *af, long *ipivot, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, float *work, long *iwork, long *info);
Oracle Solaris Studio Performance Library ssprfs(3P)
NAME
ssprfs - improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric indefinite and packed, provide
error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE SSPRFS(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(*)
REAL AP(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE SSPRFS_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(*)
REAL 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, DIMENSION(:) :: AP, AF, FERR, BERR, WORK
REAL, 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, DIMENSION(:) :: AP, AF, FERR, BERR, WORK
REAL, DIMENSION(:,:) :: B, X
C INTERFACE
#include <sunperf.h>
void ssprfs(char uplo, int n, int nrhs, float *ap, float *af, int
*ipivot, float *b, int ldb, float *x, int ldx, float *ferr,
float *berr, int *info);
void ssprfs_64(char uplo, long n, long nrhs, float *ap, float *af, long
*ipivot, float *b, long ldb, float *x, long ldx, float *ferr,
float *berr, float *work, long *iwork, long *info);
PURPOSE
ssprfs 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)
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 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.
AF (input)
Real 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 factor-
ization A = U*D*U**T or A = L*D*L**T as computed by SSPTRF,
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 SSPTRF.
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 SSPTRS. On exit, the improved solu-
tion 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 solution vector X(j) (the j-th column of the
solution matrix X). If XTRUE is the true solution corre-
sponding 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)
Real array, dimension (NRHS) The componentwise relative back-
ward 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) Integer
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
7 Nov 2015 ssprfs(3P)