• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

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

SYNOPSIS

  SUBROUTINE CPTRFS( UPLO, N, NRHS, DIAG, OFFD, DIAGF, OFFDF, B, LDB, 
 *      X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  COMPLEX OFFD(*), OFFDF(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NRHS, LDB, LDX, INFO
  REAL DIAG(*), DIAGF(*), FERR(*), BERR(*), WORK2(*)

  SUBROUTINE CPTRFS_64( UPLO, N, NRHS, DIAG, OFFD, DIAGF, OFFDF, B, 
 *      LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  COMPLEX OFFD(*), OFFDF(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NRHS, LDB, LDX, INFO
  REAL DIAG(*), DIAGF(*), FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE PTRFS( UPLO, [N], [NRHS], DIAG, OFFD, DIAGF, OFFDF, B, 
 *       [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: OFFD, OFFDF, WORK
  COMPLEX, DIMENSION(:,:) :: B, X
  INTEGER :: N, NRHS, LDB, LDX, INFO
  REAL, DIMENSION(:) :: DIAG, DIAGF, FERR, BERR, WORK2

  SUBROUTINE PTRFS_64( UPLO, [N], [NRHS], DIAG, OFFD, DIAGF, OFFDF, B, 
 *       [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: OFFD, OFFDF, WORK
  COMPLEX, DIMENSION(:,:) :: B, X
  INTEGER(8) :: N, NRHS, LDB, LDX, INFO
  REAL, DIMENSION(:) :: DIAG, DIAGF, FERR, BERR, WORK2

C INTERFACE

#include <sunperf.h>

void cptrfs(char uplo, int n, int nrhs, float *diag, complex *offd, float *diagf, complex *offdf, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info);

void cptrfs_64(char uplo, long n, long nrhs, float *diag, complex *offd, float *diagf, complex *offdf, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);

PURPOSE

cptrfs improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution.

ARGUMENTS

• UPLO (input)
  Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization:

   = 'U':  OFFD is the superdiagonal of A, and A  = U**H*DIAG*U;

   = 'L':  OFFD is the subdiagonal of A, and A  = L*DIAG*L**H.
  (The two forms are equivalent if A is real.)

• 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 matrix B. NRHS > = 0.

• DIAG (input)
  The n real diagonal elements of the tridiagonal matrix A.

• OFFD (input)
  The (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).

• DIAGF (input)
  The n diagonal elements of the diagonal matrix DIAG from the factorization computed by CPTTRF.

• OFFDF (input)
  The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by CPTTRF (see UPLO).

• 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 CPTTRS. On exit, the improved solution matrix X.

• LDX (input)
  The leading dimension of the array X. LDX > = max(1,N).

• FERR (output)
  The 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).

• 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(N)

• WORK2 (workspace)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value