Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  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

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 factorization 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
                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) 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 3.2)               April 2011                            SGTRFS(3lapack)