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dlansy
C DLANSY    SOURCE    BP208322  22/09/16    21:15:03     11454          *> \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*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansy.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansy.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansy.f">*> [TXT]&lt;/a>*> \endhtmlonly**  Definition:*  ===========**       REAL*8 FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )**       .. Scalar Arguments ..*       CHARACTER          NORM, UPLO*       INTEGER            LDA, N*       ..*       .. Array Arguments ..*       REAL*8   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 REAL*8 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 REAL*8 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 doubleSYauxiliary**  =====================================================================      FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )      REAL*8 DLANSY**  -- LAPACK auxiliary routine --*  -- LAPACK is a software package provided by Univ. of Tennessee,    --*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--**     .. Scalar Arguments ..      CHARACTER          NORM, UPLO      INTEGER            LDA, N*     ..*     .. Array Arguments ..      REAL*8   A( LDA, * ), WORK( * )*     ..** =====================================================================**     .. Parameters ..      REAL*8   ONE, ZERO      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )*     ..*     .. Local Scalars ..      INTEGER            I, J      REAL*8   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  

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