db/dea/slansy_8f_source.html

*> \brief \b SLANSY 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/

*

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*> \endhtmlonly

*

*  Definition:

*  ===========

*

*       REAL             FUNCTION SLANSY( NORM, UPLO, N, A, LDA, WORK )

*

*       .. Scalar Arguments ..

*       CHARACTER          NORM, UPLO

*       INTEGER            LDA, N

*       ..

*       .. Array Arguments ..

*       REAL               A( LDA, * ), WORK( * )

*       ..

*

*

*> \par Purpose:

*  =============

*>

*> \verbatim

*>

*> SLANSY  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 SLANSY

*> \verbatim

*>

*>    SLANSY = ( 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 SLANSY 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, SLANSY is

*>          set to zero.

*> \endverbatim

*>

*> \param[in] A

*> \verbatim

*>          A is REAL 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 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 realSYauxiliary

*

*  =====================================================================

      REAL             function slansy( norm, uplo, n, a, lda, work )

*

*  -- 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               a( lda, * ), work( * )

*     ..

*

* =====================================================================

*

*     .. Parameters ..

      REAL               one, zero

      parameter( one = 1.0e+0, zero = 0.0e+0 )

*     ..

*     .. Local Scalars ..

      INTEGER            i, j

      REAL               absa, scale, sum, value

*     ..

*     .. External Subroutines ..

      EXTERNAL           slassq

*     ..

*     .. External Functions ..

      LOGICAL            lsame, sisnan

      EXTERNAL           lsame, sisnan

*     ..

*     .. 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. sisnan( 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. 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 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. 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( 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 slassq( j-1, a( 1, j ), 1, scale, sum )

  110       CONTINUE

         ELSE

            DO 120 j = 1, n - 1

               CALL slassq( n-j, a( j+1, j ), 1, scale, sum )

  120       CONTINUE

         END IF

         sum = 2*sum

         CALL slassq( n, a, lda+1, scale, sum )

         VALUE = scale*sqrt( sum )

      END IF

*

      slansy = VALUE

      RETURN

*

*     End of SLANSY

*

      END

slassq
subroutine slassq(n, x, incx, scl, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f90:137

sisnan
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59

lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53

slansy
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansy.f:122