*> \brief \b ZLANHT 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 tridiagonal matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLANHT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E ) * * .. Scalar Arguments .. * CHARACTER NORM * INTEGER N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ) * COMPLEX*16 E( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLANHT 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 tridiagonal matrix A. *> \endverbatim *> *> \return ZLANHT *> \verbatim *> *> ZLANHT = ( 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 ZLANHT as described *> above. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, ZLANHT is *> set to zero. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of A. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is COMPLEX*16 array, dimension (N-1) *> The (n-1) sub-diagonal or super-diagonal elements of A. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E ) * * -- 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 INTEGER N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ) COMPLEX*16 E( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I DOUBLE PRECISION ANORM, SCALE, SUM * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL DLASSQ, ZLASSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * IF( N.LE.0 ) THEN ANORM = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * ANORM = ABS( D( N ) ) DO 10 I = 1, N - 1 SUM = ABS( D( I ) ) IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM SUM = ABS( E( I ) ) IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 10 CONTINUE ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. \$ LSAME( NORM, 'I' ) ) THEN * * Find norm1(A). * IF( N.EQ.1 ) THEN ANORM = ABS( D( 1 ) ) ELSE ANORM = ABS( D( 1 ) )+ABS( E( 1 ) ) SUM = ABS( E( N-1 ) )+ABS( D( N ) ) IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM DO 20 I = 2, N - 1 SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) ) IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 20 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SCALE = ZERO SUM = ONE IF( N.GT.1 ) THEN CALL ZLASSQ( N-1, E, 1, SCALE, SUM ) SUM = 2*SUM END IF CALL DLASSQ( N, D, 1, SCALE, SUM ) ANORM = SCALE*SQRT( SUM ) END IF * ZLANHT = ANORM RETURN * * End of ZLANHT * END