zpbrfs

NAME

zpbrfs - improve 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 solution

SYNOPSIS

  SUBROUTINE ZPBRFS( UPLO, N, NDIAG, 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, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
 
  SUBROUTINE ZPBRFS_64( UPLO, N, NDIAG, 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, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE PBRFS( UPLO, [N], NDIAG, [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, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
 
  SUBROUTINE PBRFS_64( UPLO, [N], NDIAG, [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, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK2

C INTERFACE

#include <sunperf.h>

void zpbrfs(char uplo, int n, int ndiag, 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 ndiag, 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 solution.

ARGUMENTS

* UPLO (input)
* N (input): The order of the matrix A. N >= 0.
* NDIAG (input): The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. NDIAG >= 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 NDIAG+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 >= NDIAG+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 CPBTRF, in the same storage format as A (see A).
* LDAF (input): The leading dimension of the array AF. LDAF >= NDIAG+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 CPBTRS. 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 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): 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): dimension(2*N)
* WORK2 (workspace)
* INFO (output)