dgtrfs(3S)

NAME
     DGTRFS - 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 DGTRFS( 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( * )

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     DGTRFS 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) DOUBLE PRECISION array, dimension (N-1)
             The (n-1) subdiagonal elements of A.

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

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

     DLF     (input) DOUBLE PRECISION array, dimension (N-1)
             The (n-1) multipliers that define the matrix L from the LU
             factorization of A as computed by DGTTRF.

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

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

     DU2     (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
             On entry, the solution matrix X, as computed by DGTTRS.  On exit,
             the improved solution matrix X.

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

     FERR    (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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