stbt02.f

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*> \brief \b STBT02
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE STBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
*                          LDX, B, LDB, WORK, RESID )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, TRANS, UPLO
*       INTEGER            KD, LDAB, LDB, LDX, N, NRHS
*       REAL               RESID
*       ..
*       .. Array Arguments ..
*       REAL               AB( LDAB, * ), B( LDB, * ), WORK( * ),
*      $                   X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> STBT02 computes the residual for the computed solution to a
*> triangular system of linear equations  A*x = b  or  A' *x = b when
*> A is a triangular band matrix.  Here A' is the transpose of A and
*> x and b are N by NRHS matrices.  The test ratio is the maximum over
*> the number of right hand sides of
*>    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A or A' and EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the matrix A is upper or lower triangular.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          Specifies the operation applied to A.
*>          = 'N':  A *x = b  (No transpose)
*>          = 'T':  A'*x = b  (Transpose)
*>          = 'C':  A'*x = b  (Conjugate transpose = Transpose)
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>          Specifies whether or not the matrix A is unit triangular.
*>          = 'N':  Non-unit triangular
*>          = 'U':  Unit triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] KD
*> \verbatim
*>          KD is INTEGER
*>          The number of superdiagonals or subdiagonals of the
*>          triangular band matrix A.  KD >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of right hand sides, i.e., the number of columns
*>          of the matrices X and B.  NRHS >= 0.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*>          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).
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*>          LDAB is INTEGER
*>          The leading dimension of the array AB.  LDAB >= KD+1.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is REAL array, dimension (LDX,NRHS)
*>          The computed solution vectors for the system of linear
*>          equations.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the array X.  LDX >= max(1,N).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*>          B is REAL array, dimension (LDB,NRHS)
*>          The right hand side vectors for the system of linear
*>          equations.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is REAL
*>          The maximum over the number of right hand sides of
*>          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup single_lin
*
*  =====================================================================
      SUBROUTINE stbt02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
     $                   LDX, B, LDB, WORK, RESID )
*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, TRANS, UPLO
      INTEGER            KD, LDAB, LDB, LDX, N, NRHS
      REAL               RESID
*     ..
*     .. Array Arguments ..
      REAL               AB( ldab, * ), B( ldb, * ), WORK( * ),
     $                   x( ldx, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      REAL               ANORM, BNORM, EPS, XNORM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SASUM, SLAMCH, SLANTB
      EXTERNAL           lsame, sasum, slamch, slantb
*     ..
*     .. External Subroutines ..
      EXTERNAL           saxpy, scopy, stbmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0 or NRHS = 0
*
      IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
         resid = zero
         RETURN
      END IF
*
*     Compute the 1-norm of A or A'.
*
      IF( lsame( trans, 'N' ) ) THEN
         anorm = slantb( '1', uplo, diag, n, kd, ab, ldab, work )
      ELSE
         anorm = slantb( 'I', uplo, diag, n, kd, ab, ldab, work )
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = slamch( 'Epsilon' )
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         RETURN
      END IF
*
*     Compute the maximum over the number of right hand sides of
*        norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*
      resid = zero
      DO 10 j = 1, nrhs
         CALL scopy( n, x( 1, j ), 1, work, 1 )
         CALL stbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
         CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
         bnorm = sasum( n, work, 1 )
         xnorm = sasum( n, x( 1, j ), 1 )
         IF( xnorm.LE.zero ) THEN
            resid = one / eps
         ELSE
            resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
         END IF
   10 CONTINUE
*
      RETURN
*
*     End of STBT02
*
      END