*> \brief \b DPOCON * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DPOCON + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, * INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. * INTEGER IWORK( * ) * DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DPOCON estimates the reciprocal of the condition number (in the *> 1-norm) of a real symmetric positive definite matrix using the *> Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF. *> *> An estimate is obtained for norm(inv(A)), and the reciprocal of the *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The triangular factor U or L from the Cholesky factorization *> A = U**T*U or A = L*L**T, as computed by DPOTRF. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] ANORM *> \verbatim *> ANORM is DOUBLE PRECISION *> The 1-norm (or infinity-norm) of the symmetric matrix A. *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is DOUBLE PRECISION *> The reciprocal of the condition number of the matrix A, *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an *> estimate of the 1-norm of inv(A) computed in this routine. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (3*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup doublePOcomputational * * ===================================================================== SUBROUTINE DPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, \$ INFO ) * * -- LAPACK computational 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 UPLO INTEGER INFO, LDA, N DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPPER CHARACTER NORMIN INTEGER IX, KASE DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX DOUBLE PRECISION DLAMCH EXTERNAL LSAME, IDAMAX, DLAMCH * .. * .. External Subroutines .. EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( ANORM.LT.ZERO ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DPOCON', -INFO ) RETURN END IF * * Quick return if possible * RCOND = ZERO IF( N.EQ.0 ) THEN RCOND = ONE RETURN ELSE IF( ANORM.EQ.ZERO ) THEN RETURN END IF * SMLNUM = DLAMCH( 'Safe minimum' ) * * Estimate the 1-norm of inv(A). * KASE = 0 NORMIN = 'N' 10 CONTINUE CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( UPPER ) THEN * * Multiply by inv(U**T). * CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A, \$ LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO ) NORMIN = 'Y' * * Multiply by inv(U). * CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, \$ A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO ) ELSE * * Multiply by inv(L). * CALL DLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N, \$ A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO ) NORMIN = 'Y' * * Multiply by inv(L**T). * CALL DLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A, \$ LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO ) END IF * * Multiply by 1/SCALE if doing so will not cause overflow. * SCALE = SCALEL*SCALEU IF( SCALE.NE.ONE ) THEN IX = IDAMAX( N, WORK, 1 ) IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) \$ GO TO 20 CALL DRSCL( N, SCALE, WORK, 1 ) END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) \$ RCOND = ( ONE / AINVNM ) / ANORM * 20 CONTINUE RETURN * * End of DPOCON * END