sgbt02.f3

Usage

Functions/Subroutines

subroutine sgbt02 (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)
SGBT02

Function/Subroutine Documentation

subroutine sgbt02 (character trans, integer m, integer n, integer kl, integer ku, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real resid)

SGBT02

Purpose:

!>
!> SGBT02 computes the residual for a solution of a banded system of
!> equations op(A)*X = B:
!>    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
!> where op(A) = A or A**T, depending on TRANS, and EPS is the
!> machine epsilon.
!> The norm used is the 1-norm.
!>

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)
!>

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

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

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

!>          KU is INTEGER
!>          The number of superdiagonals within the band of A.  KU >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of columns of B.  NRHS >= 0.
!>

!>          A is REAL array, dimension (LDA,N)
!>          The original matrix A in band storage, stored in rows 1 to
!>          KL+KU+1.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,KL+KU+1).
!>

!>          X is REAL array, dimension (LDX,NRHS)
!>          The computed solution vectors for the system of linear
!>          equations.
!>

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  If TRANS = 'N',
!>          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
!>

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the right hand side vectors for the system of
!>          linear equations.
!>          On exit, B is overwritten with the difference B - A*X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  IF TRANS = 'N',
!>          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
!>

RWORK

!>          RWORK is REAL array, dimension (MAX(1,LRWORK)),
!>          where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK
!>          is not referenced.
!>

RESID

!>          RESID is REAL
!>          The maximum over the number of right hand sides of
!>          norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 147 of file sgbt02.f.