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

NAME

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

SYNOPSIS

  SUBROUTINE SGTRFS( TRANSA, N, NRHS, LOW, DIAG, UP, LOWF, DIAGF, 
 *      UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, 
 *      INFO)
  CHARACTER * 1 TRANSA
  INTEGER N, NRHS, LDB, LDX, INFO
  INTEGER IPIVOT(*), WORK2(*)
  REAL LOW(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

  SUBROUTINE SGTRFS_64( TRANSA, N, NRHS, LOW, DIAG, UP, LOWF, DIAGF, 
 *      UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, 
 *      INFO)
  CHARACTER * 1 TRANSA
  INTEGER*8 N, NRHS, LDB, LDX, INFO
  INTEGER*8 IPIVOT(*), WORK2(*)
  REAL LOW(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

F95 INTERFACE

  SUBROUTINE GTRFS( [TRANSA], [N], [NRHS], LOW, DIAG, UP, LOWF, DIAGF, 
 *       UPF1, UPF2, IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  INTEGER :: N, NRHS, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: IPIVOT, WORK2
  REAL, DIMENSION(:) :: LOW, DIAG, UP, LOWF, DIAGF, UPF1, UPF2, FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: B, X

  SUBROUTINE GTRFS_64( [TRANSA], [N], [NRHS], LOW, DIAG, UP, LOWF, 
 *       DIAGF, UPF1, UPF2, IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  INTEGER(8) :: N, NRHS, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
  REAL, DIMENSION(:) :: LOW, DIAG, UP, LOWF, DIAGF, UPF1, UPF2, FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: B, X

C INTERFACE

#include <sunperf.h>

void sgtrfs(char transa, int n, int nrhs, float *low, float *diag, float *up, float *lowf, float *diagf, float *upf1, float *upf2, int *ipivot, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info);

void sgtrfs_64(char transa, long n, long nrhs, float *low, float *diag, float *up, float *lowf, float *diagf, float *upf1, float *upf2, long *ipivot, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);

PURPOSE

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

ARGUMENTS

• TRANSA (input)
  Specifies the form of the system of equations:

   = 'N':  A * X  = B     (No transpose)

   = 'T':  A**T * X  = B  (Transpose)

   = 'C':  A**H * X  = B  (Conjugate transpose  = Transpose)

• 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.

• LOW (input)
  The (n-1) subdiagonal elements of A.

• DIAG (input)
  The diagonal elements of A.

• UP (input)
  The (n-1) superdiagonal elements of A.

• LOWF (input)
  The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.

• DIAGF (input)
  The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

• UPF1 (input)
  The (n-1) elements of the first superdiagonal of U.

• UPF2 (input)
  The (n-2) elements of the second superdiagonal of U.

• IPIVOT (input)
  The pivot indices; for 1 < = i < = n, row i of the matrix was interchanged with row IPIVOT(i). IPIVOT(i) will always be either i or i+1; IPIVOT(i) = i indicates a row interchange was not required.

• 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 SGTTRS. 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(3*N)

• WORK2 (workspace)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

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