dtpt02.f

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*> \brief \b DTPT02
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
*                          WORK, RESID )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, TRANS, UPLO
*       INTEGER            LDB, LDX, N, NRHS
*       DOUBLE PRECISION   RESID
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DTPT02 computes the residual for the computed solution to a
*> triangular system of linear equations op(A)*X = B, when the
*> triangular matrix A is stored in packed format. The test ratio is
*> the maximum over
*>    norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
*> where op(A) = A or A**T, b is the column of B, x is the solution
*> vector, and EPS is the machine epsilon.
*> The norm used is the 1-norm.
*> \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**T * X = B  (Transpose)
*>          = 'C':  A**H * 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] 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] AP
*> \verbatim
*>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
*>          The upper or lower triangular matrix A, packed columnwise in
*>          a linear array.  The j-th column of A is stored in the array
*>          AP as follows:
*>          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
*>          if UPLO = 'L',
*>             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          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.
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE dtpt02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
     $                   WORK, RESID )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, TRANS, UPLO
      INTEGER            LDB, LDX, N, NRHS
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DASUM, DLAMCH, DLANTP
      EXTERNAL           lsame, dasum, dlamch, dlantp
*     ..
*     .. External Subroutines ..
      EXTERNAL           daxpy, dcopy, dtpmv
*     ..
*     .. 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 op(A).
*
      IF( lsame( trans, 'N' ) ) THEN
         anorm = dlantp( '1', uplo, diag, n, ap, work )
      ELSE
         anorm = dlantp( 'I', uplo, diag, n, ap, work )
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = dlamch( '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 dcopy( n, x( 1, j ), 1, work, 1 )
         CALL dtpmv( uplo, trans, diag, n, ap, work, 1 )
         CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
         bnorm = dasum( n, work, 1 )
         xnorm = dasum( 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 DTPT02
*
      END