de/d73/zlanhe_8f_source.html

 *> \brief \b ZLANHE 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/

 *

 *> \htmlonly

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 *> [TXT]</a>

 *> \endhtmlonly

 *

 *  Definition:

 *  ===========

 *

 *       DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK )

 *

 *       .. Scalar Arguments ..

 *       CHARACTER          NORM, UPLO

 *       INTEGER            LDA, N

 *       ..

 *       .. Array Arguments ..

 *       DOUBLE PRECISION   WORK( * )

 *       COMPLEX*16         A( LDA, * )

 *       ..

 *

 *

 *> \par Purpose:

 *  =============

 *>

 *> \verbatim

 *>

 *> ZLANHE  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 ZLANHE

 *> \verbatim

 *>

 *>    ZLANHE = ( 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 ZLANHE 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, ZLANHE is

 *>          set to zero.

 *> \endverbatim

 *>

 *> \param[in] A

 *> \verbatim

 *>          A is COMPLEX*16 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 DOUBLE PRECISION 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 complex16HEauxiliary

 *

 *  =====================================================================

       DOUBLE PRECISION FUNCTION zlanhe( 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..--

 *

       IMPLICIT NONE

 *     .. Scalar Arguments ..

       CHARACTER          norm, uplo

       INTEGER            lda, n

 *     ..

 *     .. Array Arguments ..

       DOUBLE PRECISION   work( * )

       COMPLEX*16         a( lda, * )

 *     ..

 *

 * =====================================================================

 *

 *     .. Parameters ..

       DOUBLE PRECISION   one, zero

       parameter( one = 1.0d+0, zero = 0.0d+0 )

 *     ..

 *     .. Local Scalars ..

       INTEGER            i, j

       DOUBLE PRECISION   absa, sum, value

 *     ..

 *     .. Local Arrays ..

       DOUBLE PRECISION   ssq( 2 ), colssq( 2 )

 *     ..

 *     .. External Functions ..

       LOGICAL            lsame, disnan

       EXTERNAL           lsame, disnan

 *     ..

 *     .. External Subroutines ..

       EXTERNAL           zlassq, dcombssq

 *     ..

 *     .. Intrinsic Functions ..

       INTRINSIC          abs, dble, 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 ) )

                   IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum

    10          CONTINUE

                sum = abs( dble( a( j, j ) ) )

                IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum

    20       CONTINUE

          ELSE

             DO 40 j = 1, n

                sum = abs( dble( a( j, j ) ) )

                IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum

                DO 30 i = j + 1, n

                   sum = abs( a( i, j ) )

                   IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum

    30          CONTINUE

    40       CONTINUE

          END IF

       ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.

      $         ( norm.EQ.'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( dble( a( j, j ) ) )

    60       CONTINUE

             DO 70 i = 1, n

                sum = work( i )

                IF( VALUE .LT. sum .OR. disnan( 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( dble( a( j, j ) ) )

                DO 90 i = j + 1, n

                   absa = abs( a( i, j ) )

                   sum = sum + absa

                   work( i ) = work( i ) + absa

    90          CONTINUE

                IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum

   100       CONTINUE

          END IF

       ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN

 *

 *        Find normF(A).

 *        SSQ(1) is scale

 *        SSQ(2) is sum-of-squares

 *        For better accuracy, sum each column separately.

 *

          ssq( 1 ) = zero

          ssq( 2 ) = one

 *

 *        Sum off-diagonals

 *

          IF( lsame( uplo, 'U' ) ) THEN

             DO 110 j = 2, n

                colssq( 1 ) = zero

                colssq( 2 ) = one

                CALL zlassq( j-1, a( 1, j ), 1,

      $                      colssq( 1 ), colssq( 2 ) )

                CALL dcombssq( ssq, colssq )

   110       CONTINUE

          ELSE

             DO 120 j = 1, n - 1

                colssq( 1 ) = zero

                colssq( 2 ) = one

                CALL zlassq( n-j, a( j+1, j ), 1,

      $                      colssq( 1 ), colssq( 2 ) )

                CALL dcombssq( ssq, colssq )

   120       CONTINUE

          END IF

          ssq( 2 ) = 2*ssq( 2 )

 *

 *        Sum diagonal

 *

          DO 130 i = 1, n

             IF( dble( a( i, i ) ).NE.zero ) THEN

                absa = abs( dble( a( i, i ) ) )

                IF( ssq( 1 ).LT.absa ) THEN

                   ssq( 2 ) = one + ssq( 2 )*( ssq( 1 ) / absa )**2

                   ssq( 1 ) = absa

                ELSE

                   ssq( 2 ) = ssq( 2 ) + ( absa / ssq( 1 ) )**2

                END IF

             END IF

   130    CONTINUE

          VALUE = ssq( 1 )*sqrt( ssq( 2 ) )

       END IF

 *

       zlanhe = VALUE

       RETURN

 *

 *     End of ZLANHE

 *

       END

disnan
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59

dcombssq
subroutine dcombssq(V1, V2)
DCOMBSSQ adds two scaled sum of squares quantities.
Definition: dcombssq.f:60

lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53

zlanhe
double precision function zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhe.f:124

zlassq
subroutine zlassq(N, X, INCX, SCALE, SUMSQ)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f:106