SRC/stbrfs.f(3)

NAME
SRC/stbrfs.f

SYNOPSIS

  Functions/Subroutines
subroutine stbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info)
STBRFS

Function/Subroutine Documentation

  subroutine stbrfs (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

STBRFS

Purpose:

    !>
    !> STBRFS provides error bounds and backward error estimates for the
    !> solution to a system of linear equations with a triangular band
    !> coefficient matrix.
    !>
    !> The solution matrix X must be computed by STBTRS or some other
    !> means before entering this routine.  STBRFS does not do iterative
    !> refinement because doing so cannot improve the backward error.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  A is upper triangular;
    !>          = 'L':  A is lower triangular.
    !>

    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)
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          = 'N':  A is non-unit triangular;
    !>          = 'U':  A is unit triangular.
    !>

    N

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

    KD

    !>          KD is INTEGER
    !>          The number of superdiagonals or subdiagonals of the
    !>          triangular band matrix A.  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 REAL array, dimension (LDAB,N)
    !>          The upper or lower triangular 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).
    !>          If DIAG = 'U', the diagonal elements of A are not referenced
    !>          and are assumed to be 1.
    !>

    LDAB

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

    B

    !>          B is REAL 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 REAL array, dimension (LDX,NRHS)
    !>          The solution matrix X.
    !>

    LDX

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

    FERR

    !>          FERR is 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

    !>          BERR is 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

    !>          WORK is REAL 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 186 of file stbrfs.f.

Author

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