lapack/SRC/dsycon.f

*> \brief \b DSYCON
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
*                          IWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, LDA, N
*       DOUBLE PRECISION   ANORM, RCOND
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * ), IWORK( * )
*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DSYCON estimates the reciprocal of the condition number (in the
*> 1-norm) of a real symmetric matrix A using the factorization
*> A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
*>
*> 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
*>          Specifies whether the details of the factorization are stored
*>          as an upper or lower triangular matrix.
*>          = 'U':  Upper triangular, form is A = U*D*U**T;
*>          = 'L':  Lower triangular, form is A = L*D*L**T.
*> \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 block diagonal matrix D and the multipliers used to
*>          obtain the factor U or L as computed by DSYTRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          Details of the interchanges and the block structure of D
*>          as determined by DSYTRF.
*> \endverbatim
*>
*> \param[in] ANORM
*> \verbatim
*>          ANORM is DOUBLE PRECISION
*>          The 1-norm of the original 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 (2*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 doubleSYcomputational
*
*  =====================================================================
      SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, 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            IPIV( * ), IWORK( * )
      DOUBLE PRECISION   A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, KASE
      DOUBLE PRECISION   AINVNM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLACN2, DSYTRS, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          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 = -6
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DSYCON', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      RCOND = ZERO
      IF( N.EQ.0 ) THEN
         RCOND = ONE
         RETURN
      ELSE IF( ANORM.LE.ZERO ) THEN
         RETURN
      END IF
*
*     Check that the diagonal matrix D is nonsingular.
*
      IF( UPPER ) THEN
*
*        Upper triangular storage: examine D from bottom to top
*
         DO 10 I = N, 1, -1
            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
     $         RETURN
   10    CONTINUE
      ELSE
*
*        Lower triangular storage: examine D from top to bottom.
*
         DO 20 I = 1, N
            IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
     $         RETURN
   20    CONTINUE
      END IF
*
*     Estimate the 1-norm of the inverse.
*
      KASE = 0
   30 CONTINUE
      CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
      IF( KASE.NE.0 ) THEN
*
*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
*
         CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
         GO TO 30
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
      IF( AINVNM.NE.ZERO )
     $   RCOND = ( ONE / AINVNM ) / ANORM
*
      RETURN
*
*     End of DSYCON
*
      END