sgbrfs.f(3)

NAME
sgbrfs.f -

SYNOPSIS

  Functions/Subroutines
subroutine sgbrfs (TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SGBRFS

Function/Subroutine Documentation

  subroutine sgbrfs (characterTRANS, integerN, integerKL, integerKU, integerNRHS, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, real, dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

SGBRFS

Purpose:

     SGBRFS improves the computed solution to a system of linear
     equations when the coefficient matrix is banded, 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.

    KL

              KL is INTEGER
              The number of subdiagonals within the band of A.  KL >= 0.

    KU

              KU is INTEGER
              The number of superdiagonals within the band of A.  KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.
              The j-th column of A is stored in the j-th column of the
              array AB as follows:
              AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KL+KU+1.

    AFB

              AFB is REAL array, dimension (LDAFB,N)
              Details of the LU factorization of the band matrix A, as
              computed by SGBTRF.  U is stored as an upper triangular band
              matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
              the multipliers used during the factorization are stored in
              rows KL+KU+2 to 2*KL+KU+1.

    LDAFB

              LDAFB is INTEGER
              The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.

    IPIV

              IPIV is INTEGER array, dimension (N)
              The pivot indices from SGBTRF; for 1<=i<=N, row i of the
              matrix was interchanged with row IPIV(i).

    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)
              On entry, the solution matrix X, as computed by SGBTRS.
              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 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

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.

Date:
    November 2011

Definition at line 204 of file sgbrfs.f.

Author

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