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*> \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 ===========
*
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* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
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*
*> \htmlonly
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*> Download DLANSY + dependencies
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*> [TGZ]</a>
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*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansy.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
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*
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* .. Scalar Arguments ..
* CHARACTER NORM, UPLO
* INTEGER LDA, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
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*
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*
*> \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:
* ========
*
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*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
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*
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*> \date December 2016
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*
*> \ingroup doubleSYauxiliary
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLANSY ( NORM , UPLO , N , A , LDA , WORK )
*
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* -- LAPACK auxiliary routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
* .. 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
