csprfs - 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 CSPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CSPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*) REAL FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE SPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: AP, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE SPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: AP, AF, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void csprfs(char uplo, int n, int nrhs, complex *ap, complex *af, int *ipivot, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void csprfs_64(char uplo, long n, long nrhs, complex *ap, complex *af, long *ipivot, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);
Oracle Solaris Studio Performance Library csprfs(3P)
NAME
csprfs - 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 CSPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX, FERR,
BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CSPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
COMPLEX AP(*), AF(*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE SPRFS(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X, LDX,
FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: AP, AF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE SPRFS_64(UPLO, N, NRHS, AP, AF, IPIVOT, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: AP, AF, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void csprfs(char uplo, int n, int nrhs, complex *ap, complex *af, int
*ipivot, complex *b, int ldb, complex *x, int ldx, float
*ferr, float *berr, int *info);
void csprfs_64(char uplo, long n, long nrhs, complex *ap, complex *af,
long *ipivot, complex *b, long ldb, complex *x, long ldx,
float *ferr, float *berr, long *info);
PURPOSE
csprfs 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)
Complex array, dimension (N*(N+1)/2) The upper or lower tri-
angle of the symmetric matrix A, packed columnwise in a lin-
ear 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)
Complex 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 CSPTRF,
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 CSPTRF.
B (input) Complex 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)
Complex array, dimension (LDX,NRHS) On entry, the solution
matrix X, as computed by CSPTRS. 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)
Complex array, dimension(2*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 csprfs(3P)