SRC/dpbrfs.f(3)

NAME
SRC/dpbrfs.f

SYNOPSIS

  Functions/Subroutines
subroutine dpbrfs (uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DPBRFS

Function/Subroutine Documentation

  subroutine dpbrfs (character uplo, integer n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb, 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)

DPBRFS

Purpose:

    !>
    !> DPBRFS improves the computed solution to a system of linear
    !> equations when the coefficient matrix is symmetric positive definite
    !> and banded, and provides error bounds and backward error estimates
    !> for the solution.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

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

    KD

    !>          KD is INTEGER
    !>          The number of superdiagonals of the matrix A if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
    !>

    NRHS

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

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          The upper or lower triangle of the symmetric band matrix A,
    !>          stored in the first KD+1 rows of the array.  The j-th column
    !>          of A is stored in the j-th column of the array AB as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD+1.
    !>

    AFB

    !>          AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**T*U or A = L*L**T of the band matrix A as computed by
    !>          DPBTRF, in the same storage format as A (see AB).
    !>

    LDAFB

    !>          LDAFB is INTEGER
    !>          The leading dimension of the array AFB.  LDAFB >= KD+1.
    !>

    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 DPBTRS.
    !>          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 187 of file dpbrfs.f.

Author

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