OpenBLAS/lapack-netlib/SRC/cla_syrcond_x.f

*> \brief \b CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       REAL FUNCTION CLA_SYRCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X,
*                                    INFO, WORK, RWORK )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            N, LDA, LDAF, INFO
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
*       REAL               RWORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>    CLA_SYRCOND_X Computes the infinity norm condition number of
*>    op(A) * diag(X) where X is a COMPLEX vector.
*> \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 number of linear equations, i.e., the order of the
*>     matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX array, dimension (LDA,N)
*>     On entry, the N-by-N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>     The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*>          AF is COMPLEX array, dimension (LDAF,N)
*>     The block diagonal matrix D and the multipliers used to
*>     obtain the factor U or L as computed by CSYTRF.
*> \endverbatim
*>
*> \param[in] LDAF
*> \verbatim
*>          LDAF is INTEGER
*>     The leading dimension of the array AF.  LDAF >= 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 CSYTRF.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is COMPLEX array, dimension (N)
*>     The vector X in the formula op(A) * diag(X).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>       = 0:  Successful exit.
*>     i > 0:  The ith argument is invalid.
*> \endverbatim
*>
*> \param[in] WORK
*> \verbatim
*>          WORK is COMPLEX array, dimension (2*N).
*>     Workspace.
*> \endverbatim
*>
*> \param[in] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (N).
*>     Workspace.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexSYcomputational
*
*  =====================================================================
      REAL FUNCTION CLA_SYRCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X,
     $                             INFO, WORK, RWORK )
*
*  -- LAPACK computational 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          UPLO
      INTEGER            N, LDA, LDAF, INFO
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * )
      REAL               RWORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            KASE
      REAL               AINVNM, ANORM, TMP
      INTEGER            I, J
      LOGICAL            UP, UPPER
      COMPLEX            ZDUM
*     ..
*     .. Local Arrays ..
      INTEGER            ISAVE( 3 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CLACN2, CSYTRS, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX
*     ..
*     .. Statement Functions ..
      REAL               CABS1
*     ..
*     .. Statement Function Definitions ..
      CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
*     ..
*     .. Executable Statements ..
*
      CLA_SYRCOND_X = 0.0E+0
*
      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( LDAF.LT.MAX( 1, N ) ) THEN
         INFO = -6
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'CLA_SYRCOND_X', -INFO )
         RETURN
      END IF
      UP = .FALSE.
      IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
*
*     Compute norm of op(A)*op2(C).
*
      ANORM = 0.0
      IF ( UP ) THEN
         DO I = 1, N
            TMP = 0.0E+0
            DO J = 1, I
               TMP = TMP + CABS1( A( J, I ) * X( J ) )
            END DO
            DO J = I+1, N
               TMP = TMP + CABS1( A( I, J ) * X( J ) )
            END DO
            RWORK( I ) = TMP
            ANORM = MAX( ANORM, TMP )
         END DO
      ELSE
         DO I = 1, N
            TMP = 0.0E+0
            DO J = 1, I
               TMP = TMP + CABS1( A( I, J ) * X( J ) )
            END DO
            DO J = I+1, N
               TMP = TMP + CABS1( A( J, I ) * X( J ) )
            END DO
            RWORK( I ) = TMP
            ANORM = MAX( ANORM, TMP )
         END DO
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 ) THEN
         CLA_SYRCOND_X = 1.0E+0
         RETURN
      ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
         RETURN
      END IF
*
*     Estimate the norm of inv(op(A)).
*
      AINVNM = 0.0E+0
*
      KASE = 0
   10 CONTINUE
      CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
      IF( KASE.NE.0 ) THEN
         IF( KASE.EQ.2 ) THEN
*
*           Multiply by R.
*
            DO I = 1, N
               WORK( I ) = WORK( I ) * RWORK( I )
            END DO
*
            IF ( UP ) THEN
               CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV,
     $            WORK, N, INFO )
            ELSE
               CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV,
     $            WORK, N, INFO )
            ENDIF
*
*           Multiply by inv(X).
*
            DO I = 1, N
               WORK( I ) = WORK( I ) / X( I )
            END DO
         ELSE
*
*           Multiply by inv(X**T).
*
            DO I = 1, N
               WORK( I ) = WORK( I ) / X( I )
            END DO
*
            IF ( UP ) THEN
               CALL CSYTRS( 'U', N, 1, AF, LDAF, IPIV,
     $            WORK, N, INFO )
            ELSE
               CALL CSYTRS( 'L', N, 1, AF, LDAF, IPIV,
     $            WORK, N, INFO )
            END IF
*
*           Multiply by R.
*
            DO I = 1, N
               WORK( I ) = WORK( I ) * RWORK( I )
            END DO
         END IF
         GO TO 10
      END IF
*
*     Compute the estimate of the reciprocal condition number.
*
      IF( AINVNM .NE. 0.0E+0 )
     $   CLA_SYRCOND_X = 1.0E+0 / AINVNM
*
      RETURN
*
      END