spbrfs

NAME

spbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution

SYNOPSIS

  SUBROUTINE SPBRFS( UPLO, N, NDIAG, NRHS, A, LDA, AF, LDAF, B, LDB, 
 *      X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER WORK2(*)
  REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
 
  SUBROUTINE SPBRFS_64( UPLO, N, NDIAG, NRHS, A, LDA, AF, LDAF, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER*8 WORK2(*)
  REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

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
  INTEGER :: N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: WORK2
  REAL, DIMENSION(:) :: FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: A, AF, B, X
 
  SUBROUTINE PBRFS_64( UPLO, [N], NDIAG, [NRHS], A, [LDA], AF, [LDAF], 
 *       B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, NDIAG, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: WORK2
  REAL, DIMENSION(:) :: FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: A, AF, B, X

C INTERFACE

#include <sunperf.h>

void spbrfs(char uplo, int n, int ndiag, int nrhs, float *a, int lda, float *af, int ldaf, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info);

void spbrfs_64(char uplo, long n, long ndiag, long nrhs, float *a, long lda, float *af, long ldaf, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);

PURPOSE

spbrfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric 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 symmetric 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**T*U or A = L*L**T of the band matrix A as computed by SPBTRF, 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 SPBTRS. 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)