SGTRFS(3)                  MathKeisan LAPACK routine                 SGTRFS(3)



NAME
       SGTRFS - the computed solution to a system of linear equations when the
       coefficient matrix is tridiagonal, and provides error bounds and  back-
       ward error estimates for the solution

SYNOPSIS
       SUBROUTINE SGTRFS( TRANS,  N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV,
                          B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

           CHARACTER      TRANS

           INTEGER        INFO, LDB, LDX, N, NRHS

           INTEGER        IPIV( * ), IWORK( * )

           REAL           B( LDB, * ), BERR( * ), D( * ), DF( * ),  DL(  *  ),
                          DLF(  *  ),  DU( * ), DU2( * ), DUF( * ), FERR( * ),
                          WORK( * ), X( LDX, * )

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
       TRANS   (input) CHARACTER*1
               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) INTEGER
               The order of the matrix A.  N >= 0.

       NRHS    (input) INTEGER
               The number of right hand sides, i.e., the number of columns  of
               the matrix B.  NRHS >= 0.

       DL      (input) REAL array, dimension (N-1)
               The (n-1) subdiagonal elements of A.

       D       (input) REAL array, dimension (N)
               The diagonal elements of A.

       DU      (input) REAL array, dimension (N-1)
               The (n-1) superdiagonal elements of A.

       DLF     (input) REAL array, dimension (N-1)
               The (n-1) multipliers that define the matrix L from the LU fac-
               torization of A as computed by SGTTRF.

       DF      (input) REAL array, dimension (N)
               The n diagonal elements of the upper triangular matrix  U  from
               the LU factorization of A.

       DUF     (input) REAL array, dimension (N-1)
               The (n-1) elements of the first superdiagonal of U.

       DU2     (input) REAL array, dimension (N-2)
               The (n-2) elements of the second superdiagonal of U.

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

       B       (input) REAL array, dimension (LDB,NRHS)
               The right hand side matrix B.

       LDB     (input) INTEGER
               The leading dimension of the array B.  LDB >= max(1,N).

       X       (input/output) REAL array, dimension (LDX,NRHS)
               On entry, the solution matrix X, as  computed  by  SGTTRS.   On
               exit, the improved solution matrix X.

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

       FERR    (output) REAL array, dimension (NRHS)
               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) REAL array, dimension (NRHS)
               The componentwise relative backward error of each solution vec-
               tor X(j) (i.e., the smallest relative change in any element  of
               A or B that makes X(j) an exact solution).

       WORK    (workspace) REAL array, dimension (3*N)

       IWORK   (workspace) INTEGER array, dimension (N)

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS
       ITMAX is the maximum number of steps of iterative refinement.



 LAPACK routine (version 3.1)    November 2006                       SGTRFS(3)