*> \brief \b SPOCON
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*
* Definition:
* ===========
*
* SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, N
* REAL ANORM, RCOND
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* REAL A( LDA, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SPOCON 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 SPOTRF.
*>
*> 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 REAL 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 SPOTRF.
*> \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 REAL
*> The 1-norm (or infinity-norm) of the symmetric matrix A.
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*> RCOND is REAL
*> 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 REAL 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 realPOcomputational
*
* =====================================================================
SUBROUTINE SPOCON( 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
REAL ANORM, RCOND
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
REAL A( LDA, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
CHARACTER NORMIN
INTEGER IX, KASE
REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ISAMAX
REAL SLAMCH
EXTERNAL LSAME, ISAMAX, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL SLACN2, SLATRS, SRSCL, 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( 'SPOCON', -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 = SLAMCH( 'Safe minimum' )
*
* Estimate the 1-norm of inv(A).
*
KASE = 0
NORMIN = 'N'
10 CONTINUE
CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( UPPER ) THEN
*
* Multiply by inv(U**T).
*
CALL SLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
$ LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
NORMIN = 'Y'
*
* Multiply by inv(U).
*
CALL SLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
$ A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
ELSE
*
* Multiply by inv(L).
*
CALL SLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
$ A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
NORMIN = 'Y'
*
* Multiply by inv(L**T).
*
CALL SLATRS( '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 = ISAMAX( N, WORK, 1 )
IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 20
CALL SRSCL( 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 SPOCON
*
END