#include "ESMF_LapackBlas.inc" !> \brief \b DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix. ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DLANSY + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansy.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansy.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansy.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) ! ! .. Scalar Arguments .. ! CHARACTER NORM, UPLO ! INTEGER LDA, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DLANSY returns the value of the one norm, or the Frobenius norm, or !> the infinity norm, or the element of largest absolute value of a !> real symmetric matrix A. !> \endverbatim !> !> \return DLANSY !> \verbatim !> !> DLANSY = ( 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 DLANSY as described !> above. !> \endverbatim !> !> \param[in] UPLO !> \verbatim !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> symmetric 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, DLANSY is !> set to zero. !> \endverbatim !> !> \param[in] A !> \verbatim !> A is DOUBLE PRECISION array, dimension (LDA,N) !> The symmetric 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. !> \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. ! !> \date December 2016 ! !> \ingroup doubleSYauxiliary ! ! ===================================================================== DOUBLE PRECISION FUNCTION DLANSY( 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 .. DOUBLE PRECISION A( LDA, * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) ! .. ! .. Local Scalars .. INTEGER I, J DOUBLE PRECISION ABSA, SCALE, SUM, VALUE ! .. ! .. External Subroutines .. EXTERNAL DLASSQ ! .. ! .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN ! .. ! .. Intrinsic Functions .. INTRINSIC ABS, 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 SUM = ABS( A( I, J ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J, 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 symmetric). ! 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( 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( 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). ! SCALE = ZERO SUM = ONE IF( LSAME( UPLO, 'U' ) ) THEN DO 110 J = 2, N CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) 110 CONTINUE ELSE DO 120 J = 1, N - 1 CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) 120 CONTINUE END IF SUM = 2*SUM CALL DLASSQ( N, A, LDA+1, SCALE, SUM ) VALUE = SCALE*SQRT( SUM ) END IF ! DLANSY = VALUE RETURN ! ! End of DLANSY ! END