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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/
*
*> \htmlonly
*> Download CLANHE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clanhe.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clanhe.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhe.f">
*> [TXT]</a>
*> \endhtmlonly
*
* 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.
*
*> \date December 2016
*
*> \ingroup complexHEauxiliary
*
* =====================================================================
REAL FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK )
*
* -- LAPACK auxiliary 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 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 ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
10 CONTINUE
SUM = ABS( REAL( A( J, J ) ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
20 CONTINUE
ELSE
DO 40 J = 1, N
SUM = ABS( REAL( A( J, J ) ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
DO 30 I = J + 1, N
SUM = ABS( A( I, J ) )
IF( VALUE .LT. SUM .OR. SISNAN( 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( REAL( A( J, J ) ) )
60 CONTINUE
DO 70 I = 1, N
SUM = WORK( I )
IF( VALUE .LT. SUM .OR. 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
IF( VALUE .LT. SUM .OR. 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
IF( REAL( A( I, I ) ).NE.ZERO ) THEN
ABSA = ABS( REAL( A( I, I ) ) )
IF( SCALE.LT.ABSA ) 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
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