SRC/dgtrfs.f(3)

NAME
SRC/dgtrfs.f

SYNOPSIS

  Functions/Subroutines
subroutine dgtrfs (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DGTRFS

Function/Subroutine Documentation

  subroutine dgtrfs (character trans, integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) dlf, double precision, dimension( * ) df, double precision, dimension( * ) duf, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DGTRFS

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.
    !>

Parameters
    TRANS

    !>          TRANS is 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

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 0.
    !>

    DL

    !>          DL is DOUBLE PRECISION array, dimension (N-1)
    !>          The (n-1) subdiagonal elements of A.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          The diagonal elements of A.
    !>

    DU

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

    DLF

    !>          DLF is 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

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

    DUF

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

    DU2

    !>          DU2 is DOUBLE PRECISION array, dimension (N-2)
    !>          The (n-2) elements of the second superdiagonal of U.
    !>

    IPIV

    !>          IPIV is 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

    !>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
    !>          The right hand side matrix B.
    !>

    LDB

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

    X

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

    LDX

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

    FERR

    !>          FERR is 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

    !>          BERR is 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

    !>          WORK is DOUBLE PRECISION array, dimension (3*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Internal Parameters:

    !>  ITMAX is the maximum number of steps of iterative refinement.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 206 of file dgtrfs.f.

Author

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