cla_porcond_c.f

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*> \brief \b CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       REAL FUNCTION CLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, C, CAPPLY,
*                                    INFO, WORK, RWORK )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       LOGICAL            CAPPLY
*       INTEGER            N, LDA, LDAF, INFO
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
*       REAL               C( * ), RWORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>    CLA_PORCOND_C Computes the infinity norm condition number of
*>    op(A) * inv(diag(C)) where C is a REAL 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 triangular factor U or L from the Cholesky factorization
*>     A = U**H*U or A = L*L**H, as computed by CPOTRF.
*> \endverbatim
*>
*> \param[in] LDAF
*> \verbatim
*>          LDAF is INTEGER
*>     The leading dimension of the array AF.  LDAF >= max(1,N).
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*>          C is REAL array, dimension (N)
*>     The vector C in the formula op(A) * inv(diag(C)).
*> \endverbatim
*>
*> \param[in] CAPPLY
*> \verbatim
*>          CAPPLY is LOGICAL
*>     If .TRUE. then access the vector C in the formula above.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>       = 0:  Successful exit.
*>     i > 0:  The ith argument is invalid.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX array, dimension (2*N).
*>     Workspace.
*> \endverbatim
*>
*> \param[out] 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.
*
*> \ingroup la_porcond
*
*  =====================================================================
      REAL function cla_porcond_c( uplo, n, a, lda, af, ldaf, c,
     $                             capply,
     $                             info, work, rwork )
*
*  -- 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
      LOGICAL            capply
      INTEGER            n, lda, ldaf, info
*     ..
*     .. Array Arguments ..
      COMPLEX            a( lda, * ), af( ldaf, * ), work( * )
      REAL               c( * ), 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, cpotrs, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, real, aimag
*     ..
*     .. Statement Functions ..
      REAL cabs1
*     ..
*     .. Statement Function Definitions ..
      cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
*     ..
*     .. Executable Statements ..
*
      cla_porcond_c = 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_PORCOND_C', -info )
         RETURN
      END IF
      up = .false.
      IF ( lsame( uplo, 'U' ) ) up = .true.
*
*     Compute norm of op(A)*op2(C).
*
      anorm = 0.0e+0
      IF ( up ) THEN
         DO i = 1, n
            tmp = 0.0e+0
            IF ( capply ) THEN
               DO j = 1, i
                  tmp = tmp + cabs1( a( j, i ) ) / c( j )
               END DO
               DO j = i+1, n
                  tmp = tmp + cabs1( a( i, j ) ) / c( j )
               END DO
            ELSE
               DO j = 1, i
                  tmp = tmp + cabs1( a( j, i ) )
               END DO
               DO j = i+1, n
                  tmp = tmp + cabs1( a( i, j ) )
               END DO
            END IF
            rwork( i ) = tmp
            anorm = max( anorm, tmp )
         END DO
      ELSE
         DO i = 1, n
            tmp = 0.0e+0
            IF ( capply ) THEN
               DO j = 1, i
                  tmp = tmp + cabs1( a( i, j ) ) / c( j )
               END DO
               DO j = i+1, n
                  tmp = tmp + cabs1( a( j, i ) ) / c( j )
               END DO
            ELSE
               DO j = 1, i
                  tmp = tmp + cabs1( a( i, j ) )
               END DO
               DO j = i+1, n
                  tmp = tmp + cabs1( a( j, i ) )
               END DO
            END IF
            rwork( i ) = tmp
            anorm = max( anorm, tmp )
         END DO
      END IF
*
*     Quick return if possible.
*
      IF( n.EQ.0 ) THEN
         cla_porcond_c = 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 cpotrs( 'U', n, 1, af, ldaf,
     $            work, n, info )
            ELSE
               CALL cpotrs( 'L', n, 1, af, ldaf,
     $            work, n, info )
            ENDIF
*
*           Multiply by inv(C).
*
            IF ( capply ) THEN
               DO i = 1, n
                  work( i ) = work( i ) * c( i )
               END DO
            END IF
         ELSE
*
*           Multiply by inv(C**H).
*
            IF ( capply ) THEN
               DO i = 1, n
                  work( i ) = work( i ) * c( i )
               END DO
            END IF
*
            IF ( up ) THEN
               CALL cpotrs( 'U', n, 1, af, ldaf,
     $            work, n, info )
            ELSE
               CALL cpotrs( 'L', n, 1, af, ldaf,
     $            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_porcond_c = 1.0e+0 / ainvnm
*
      RETURN
*
*     End of CLA_PORCOND_C
*
      REAL function cla_porcond_c( uplo, n, a, lda, af, ldaf, c, …
      END