217 lines
5.7 KiB
Fortran
217 lines
5.7 KiB
Fortran
*> \brief \b DTPT01
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, UPLO
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* INTEGER N
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* DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DTPT01 computes the residual for a triangular matrix A times its
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*> inverse when A is stored in packed format:
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*> RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
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*> where EPS is the machine epsilon.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the matrix A is upper or lower triangular.
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> Specifies whether or not the matrix A is unit triangular.
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*> = 'N': Non-unit triangular
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*> = 'U': Unit triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] AP
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*> \verbatim
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*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
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*> The original upper or lower triangular matrix A, packed
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*> columnwise in a linear array. The j-th column of A is stored
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*> in the array AP as follows:
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*> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
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*> if UPLO = 'L',
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*> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
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*> \endverbatim
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*>
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*> \param[in,out] AINVP
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*> \verbatim
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*> AINVP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
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*> On entry, the (triangular) inverse of the matrix A, packed
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*> columnwise in a linear array as in AP.
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*> On exit, the contents of AINVP are destroyed.
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*> \endverbatim
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*>
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*> \param[out] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> The reciprocal condition number of A, computed as
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*> 1/(norm(A) * norm(AINV)).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is DOUBLE PRECISION
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*> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup double_lin
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*
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* =====================================================================
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SUBROUTINE DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, UPLO
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INTEGER N
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DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL UNITD
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INTEGER J, JC
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DOUBLE PRECISION AINVNM, ANORM, EPS
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, DLANTP
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EXTERNAL LSAME, DLAMCH, DLANTP
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* ..
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* .. External Subroutines ..
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EXTERNAL DTPMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0.
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*
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IF( N.LE.0 ) THEN
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RCOND = ONE
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
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*
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EPS = DLAMCH( 'Epsilon' )
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ANORM = DLANTP( '1', UPLO, DIAG, N, AP, WORK )
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AINVNM = DLANTP( '1', UPLO, DIAG, N, AINVP, WORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCOND = ZERO
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RESID = ONE / EPS
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RETURN
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END IF
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RCOND = ( ONE / ANORM ) / AINVNM
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*
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* Compute A * AINV, overwriting AINV.
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*
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UNITD = LSAME( DIAG, 'U' )
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IF( LSAME( UPLO, 'U' ) ) THEN
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JC = 1
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DO 10 J = 1, N
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IF( UNITD )
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$ AINVP( JC+J-1 ) = ONE
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*
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* Form the j-th column of A*AINV
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*
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CALL DTPMV( 'Upper', 'No transpose', DIAG, J, AP,
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$ AINVP( JC ), 1 )
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*
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* Subtract 1 from the diagonal
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*
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AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE
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JC = JC + J
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10 CONTINUE
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ELSE
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JC = 1
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DO 20 J = 1, N
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IF( UNITD )
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$ AINVP( JC ) = ONE
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*
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* Form the j-th column of A*AINV
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*
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CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ),
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$ AINVP( JC ), 1 )
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*
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* Subtract 1 from the diagonal
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*
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AINVP( JC ) = AINVP( JC ) - ONE
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JC = JC + N - J + 1
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20 CONTINUE
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END IF
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*
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* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
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*
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RESID = DLANTP( '1', UPLO, 'Non-unit', N, AINVP, WORK )
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*
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RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
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*
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RETURN
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*
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* End of DTPT01
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*
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END
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