clanhe.f

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*> \brief \b CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       REAL             FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK )
*
*       .. Scalar Arguments ..
*       CHARACTER          NORM, UPLO
*       INTEGER            LDA, N
*       ..
*       .. Array Arguments ..
*       REAL               WORK( * )
*       COMPLEX            A( LDA, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CLANHE  returns the value of the one norm,  or the Frobenius norm, or
*> the  infinity norm,  or the  element of  largest absolute value  of a
*> complex hermitian matrix A.
*> \endverbatim
*>
*> \return CLANHE
*> \verbatim
*>
*>    CLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*>             (
*>             ( norm1(A),         NORM = '1', 'O' or 'o'
*>             (
*>             ( normI(A),         NORM = 'I' or 'i'
*>             (
*>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
*>
*> where  norm1  denotes the  one norm of a matrix (maximum column sum),
*> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
*> normF  denotes the  Frobenius norm of a matrix (square root of sum of
*> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NORM
*> \verbatim
*>          NORM is CHARACTER*1
*>          Specifies the value to be returned in CLANHE as described
*>          above.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          hermitian matrix A is to be referenced.
*>          = 'U':  Upper triangular part of A is referenced
*>          = 'L':  Lower triangular part of A is referenced
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.  When N = 0, CLANHE is
*>          set to zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX array, dimension (LDA,N)
*>          The hermitian matrix A.  If UPLO = 'U', the leading n by n
*>          upper triangular part of A contains the upper triangular part
*>          of the matrix A, and the strictly lower triangular part of A
*>          is not referenced.  If UPLO = 'L', the leading n by n lower
*>          triangular part of A contains the lower triangular part of
*>          the matrix A, and the strictly upper triangular part of A is
*>          not referenced. Note that the imaginary parts of the diagonal
*>          elements need not be set and are assumed to be zero.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(N,1).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (MAX(1,LWORK)),
*>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
*>          WORK is not referenced.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexHEauxiliary
*
*  =====================================================================
      REAL             function clanhe( norm, uplo, n, a, lda, work )
*
*  -- LAPACK auxiliary 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          norm, uplo
      INTEGER            lda, n
*     ..
*     .. Array Arguments ..
      REAL               work( * )
      COMPLEX            a( lda, * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      REAL               one, zero
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            i, j
      REAL               absa, SCALE, sum, value
*     ..
*     .. External Functions ..
      LOGICAL            lsame, sisnan
      EXTERNAL           lsame, sisnan
*     ..
*     .. External Subroutines ..
      EXTERNAL           classq
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, real, sqrt
*     ..
*     .. Executable Statements ..
*
      IF( n.EQ.0 ) THEN
         VALUE = zero
      ELSE IF( lsame( norm, 'm' ) ) THEN
*
*        Find max(abs(A(i,j))).
*
         VALUE = ZERO
         IF( LSAME( UPLO, 'u' ) ) THEN
            DO 20 J = 1, N
               DO 10 I = 1, J - 1
                  SUM = ABS( A( I, J ) )
.LT..OR.                  IF( VALUE  SUM  SISNAN( SUM ) ) VALUE = SUM
   10          CONTINUE
               SUM = ABS( REAL( A( J, J ) ) )
.LT..OR.               IF( VALUE  SUM  SISNAN( SUM ) ) VALUE = SUM
   20       CONTINUE
         ELSE
            DO 40 J = 1, N
               SUM = ABS( REAL( A( J, J ) ) )
.LT..OR.               IF( VALUE  SUM  SISNAN( SUM ) ) VALUE = SUM
               DO 30 I = J + 1, N
                  SUM = ABS( A( I, J ) )
.LT..OR.                  IF( VALUE  SUM  SISNAN( SUM ) ) VALUE = SUM
   30          CONTINUE
   40       CONTINUE
         END IF
      ELSE IF( ( LSAME( NORM, 'i.OR.' ) )  ( LSAME( NORM, 'o.OR.' ) ) 
.EQ.     $         ( NORM'1' ) ) THEN
*
*        Find normI(A) ( = norm1(A), since A is hermitian).
*
         VALUE = ZERO
         IF( LSAME( UPLO, 'u' ) ) THEN
            DO 60 J = 1, N
               SUM = ZERO
               DO 50 I = 1, J - 1
                  ABSA = ABS( A( I, J ) )
                  SUM = SUM + ABSA
                  WORK( I ) = WORK( I ) + ABSA
   50          CONTINUE
               WORK( J ) = SUM + ABS( REAL( A( J, J ) ) )
   60       CONTINUE
            DO 70 I = 1, N
               SUM = WORK( I )
.LT..OR.               IF( VALUE  SUM  SISNAN( SUM ) ) VALUE = SUM
   70       CONTINUE
         ELSE
            DO 80 I = 1, N
               WORK( I ) = ZERO
   80       CONTINUE
            DO 100 J = 1, N
               SUM = WORK( J ) + ABS( REAL( A( J, J ) ) )
               DO 90 I = J + 1, N
                  ABSA = ABS( A( I, J ) )
                  SUM = SUM + ABSA
                  WORK( I ) = WORK( I ) + ABSA
   90          CONTINUE
.LT..OR.               IF( VALUE  SUM  SISNAN( SUM ) ) VALUE = SUM
  100       CONTINUE
         END IF
      ELSE IF( ( LSAME( NORM, 'f.OR.' ) )  ( LSAME( NORM, 'e' ) ) ) THEN
*
*        Find normF(A).
*
         SCALE = ZERO
         SUM = ONE
         IF( LSAME( UPLO, 'u' ) ) THEN
            DO 110 J = 2, N
               CALL CLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
  110       CONTINUE
         ELSE
            DO 120 J = 1, N - 1
               CALL CLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
  120       CONTINUE
         END IF
         SUM = 2*SUM
         DO 130 I = 1, N
.NE.            IF( REAL( A( I, I ) )ZERO ) THEN
               ABSA = ABS( REAL( A( I, I ) ) )
.LT.               IF( SCALEABSA ) THEN
                  SUM = ONE + SUM*( SCALE / ABSA )**2
                  SCALE = ABSA
               ELSE
                  SUM = SUM + ( ABSA / SCALE )**2
               END IF
            END IF
  130    CONTINUE
         VALUE = SCALE*SQRT( SUM )
      END IF
*
      CLANHE = VALUE
      RETURN
*
*     End of CLANHE
*
      END