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*> \brief \b DTPT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, UPLO
* INTEGER N
* DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTPT01 computes the residual for a triangular matrix A times its
*> inverse when A is stored in packed format:
*> RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
*> where 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] 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] AP
*> \verbatim
*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
*> The original 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,out] AINVP
*> \verbatim
*> AINVP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
*> On entry, the (triangular) inverse of the matrix A, packed
*> columnwise in a linear array as in AP.
*> On exit, the contents of AINVP are destroyed.
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*> RCOND is DOUBLE PRECISION
*> The reciprocal condition number of A, computed as
*> 1/(norm(A) * norm(AINV)).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, 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, UPLO
INTEGER N
DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UNITD
INTEGER J, JC
DOUBLE PRECISION AINVNM, ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, DLANTP
EXTERNAL LSAME, DLAMCH, DLANTP
* ..
* .. External Subroutines ..
EXTERNAL DTPMV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RCOND = ONE
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = DLANTP( '1', UPLO, DIAG, N, AP, WORK )
AINVNM = DLANTP( '1', UPLO, DIAG, N, AINVP, WORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCOND = ZERO
RESID = ONE / EPS
RETURN
END IF
RCOND = ( ONE / ANORM ) / AINVNM
*
* Compute A * AINV, overwriting AINV.
*
UNITD = LSAME( DIAG, 'U' )
IF( LSAME( UPLO, 'U' ) ) THEN
JC = 1
DO 10 J = 1, N
IF( UNITD )
$ AINVP( JC+J-1 ) = ONE
*
* Form the j-th column of A*AINV
*
CALL DTPMV( 'Upper', 'No transpose', DIAG, J, AP,
$ AINVP( JC ), 1 )
*
* Subtract 1 from the diagonal
*
AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE
JC = JC + J
10 CONTINUE
ELSE
JC = 1
DO 20 J = 1, N
IF( UNITD )
$ AINVP( JC ) = ONE
*
* Form the j-th column of A*AINV
*
CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ),
$ AINVP( JC ), 1 )
*
* Subtract 1 from the diagonal
*
AINVP( JC ) = AINVP( JC ) - ONE
JC = JC + N - J + 1
20 CONTINUE
END IF
*
* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
*
RESID = DLANTP( '1', UPLO, 'Non-unit', N, AINVP, WORK )
*
RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
*
RETURN
*
* End of DTPT01
*
END
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