zpbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, provide error bounds and backward error estimates for the solution
SUBROUTINE ZPBRFS(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZPBRFS_64(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE PBRFS(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE PBRFS_64(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER(8) :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zpbrfs(char uplo, int n, int kd, int nrhs, doublecomplex *a, int lda, doublecomplex *af, int ldaf, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info); void zpbrfs_64(char uplo, long n, long kd, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library zpbrfs(3P)
NAME
zpbrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and banded,
provide error bounds and backward error estimates for the solution
SYNOPSIS
SUBROUTINE ZPBRFS(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB, X,
LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
SUBROUTINE ZPBRFS_64(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO
DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
F95 INTERFACE
SUBROUTINE PBRFS(UPLO, N, KD, NRHS, A, LDA, AF, LDAF, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
SUBROUTINE PBRFS_64(UPLO, N, KD, NRHS, A, LDA, AF, LDAF,
B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
INTEGER(8) :: N, KD, NRHS, LDA, LDAF, LDB, LDX, INFO
REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void zpbrfs(char uplo, int n, int kd, int nrhs, doublecomplex *a, int
lda, doublecomplex *af, int ldaf, doublecomplex *b, int ldb,
doublecomplex *x, int ldx, double *ferr, double *berr, int
*info);
void zpbrfs_64(char uplo, long n, long kd, long nrhs, doublecomplex *a,
long lda, doublecomplex *af, long ldaf, doublecomplex *b,
long ldb, doublecomplex *x, long ldx, double *ferr, double
*berr, long *info);
PURPOSE
zpbrfs improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite and banded,
and provides error bounds and backward error estimates for the solu-
tion.
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.
KD (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 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) The upper or lower triangle of the Hermitian band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array A as follows:
if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDA (input)
The leading dimension of the array A. LDA >= KD+1.
AF (input)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A as computed by
ZPBTRF, in the same storage format as A (see A).
LDAF (input)
The leading dimension of the array AF. LDAF >= KD+1.
B (input) The right hand side matrix B.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
X (input/output)
On entry, the solution matrix X, as computed by ZPBTRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output)
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 esti-
mated upper bound for the magnitude of the largest element in
(X(j) - XTRUE) divided by the magnitude of the largest ele-
ment 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)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in any ele-
ment of A or B that makes X(j) an exact solution).
WORK (workspace)
dimension(2*N)
WORK2 (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
7 Nov 2015 zpbrfs(3P)