da/d61/slansp_8f_source.html

 *> \brief \b SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.

 *

 *  =========== DOCUMENTATION ===========

 *

 * Online html documentation available at

 *            http://www.netlib.org/lapack/explore-html/

 *

 *> \htmlonly

 *> Download SLANSP + dependencies

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 *> [TGZ]</a>

 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slansp.f">

 *> [ZIP]</a>

 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slansp.f">

 *> [TXT]</a>

 *> \endhtmlonly

 *

 *  Definition:

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

 *

 *       REAL             FUNCTION SLANSP( NORM, UPLO, N, AP, WORK )

 *

 *       .. Scalar Arguments ..

 *       CHARACTER          NORM, UPLO

 *       INTEGER            N

 *       ..

 *       .. Array Arguments ..

 *       REAL               AP( * ), WORK( * )

 *       ..

 *

 *

 *> \par Purpose:

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

 *>

 *> \verbatim

 *>

 *> SLANSP  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,  supplied in packed form.

 *> \endverbatim

 *>

 *> \return SLANSP

 *> \verbatim

 *>

 *>    SLANSP = ( 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 SLANSP 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 supplied.

 *>          = 'U':  Upper triangular part of A is supplied

 *>          = 'L':  Lower triangular part of A is supplied

 *> \endverbatim

 *>

 *> \param[in] N

 *> \verbatim

 *>          N is INTEGER

 *>          The order of the matrix A.  N >= 0.  When N = 0, SLANSP is

 *>          set to zero.

 *> \endverbatim

 *>

 *> \param[in] AP

 *> \verbatim

 *>          AP is REAL array, dimension (N*(N+1)/2)

 *>          The upper or lower triangle of the symmetric matrix A, packed

 *>          columnwise in a linear array.  The j-th column of A is stored

 *>          in the array AP as follows:

 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;

 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

 *> \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 realOTHERauxiliary

 *

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

       REAL             function slansp( norm, uplo, n, ap, 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..--

 *

       IMPLICIT NONE

 *     .. Scalar Arguments ..

       CHARACTER          norm, uplo

       INTEGER            n

 *     ..

 *     .. Array Arguments ..

       REAL               ap( * ), work( * )

 *     ..

 *

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

 *

 *     .. Parameters ..

       REAL               one, zero

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

 *     ..

 *     .. Local Scalars ..

       INTEGER            i, j, k

       REAL               absa, sum, value

 *     ..

 *     .. Local Arrays ..

       REAL               ssq( 2 ), colssq( 2 )

 *     ..

 *     .. External Functions ..

       LOGICAL            lsame, sisnan

       EXTERNAL           lsame, sisnan

 *     ..

 *     .. External Subroutines ..

       EXTERNAL           slassq, scombssq

 *     ..

 *     .. 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

             k = 1

             DO 20 j = 1, n

                DO 10 i = k, k + j - 1

                   sum = abs( ap( i ) )

                   IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum

    10          CONTINUE

                k = k + j

    20       CONTINUE

          ELSE

             k = 1

             DO 40 j = 1, n

                DO 30 i = k, k + n - j

                   sum = abs( ap( i ) )

                   IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum

    30          CONTINUE

                k = k + n - j + 1

    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

          k = 1

          IF( lsame( uplo, 'U' ) ) THEN

             DO 60 j = 1, n

                sum = zero

                DO 50 i = 1, j - 1

                   absa = abs( ap( k ) )

                   sum = sum + absa

                   work( i ) = work( i ) + absa

                   k = k + 1

    50          CONTINUE

                work( j ) = sum + abs( ap( k ) )

                k = k + 1

    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( ap( k ) )

                k = k + 1

                DO 90 i = j + 1, n

                   absa = abs( ap( k ) )

                   sum = sum + absa

                   work( i ) = work( i ) + absa

                   k = k + 1

    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).

 *        SSQ(1) is scale

 *        SSQ(2) is sum-of-squares

 *        For better accuracy, sum each column separately.

 *

          ssq( 1 ) = zero

          ssq( 2 ) = one

 *

 *        Sum off-diagonals

 *

          k = 2

          IF( lsame( uplo, 'U' ) ) THEN

             DO 110 j = 2, n

                colssq( 1 ) = zero

                colssq( 2 ) = one

                CALL slassq( j-1, ap( k ), 1, colssq( 1 ), colssq( 2 ) )

                CALL scombssq( ssq, colssq )

                k = k + j

   110       CONTINUE

          ELSE

             DO 120 j = 1, n - 1

                colssq( 1 ) = zero

                colssq( 2 ) = one

                CALL slassq( n-j, ap( k ), 1, colssq( 1 ), colssq( 2 ) )

                CALL scombssq( ssq, colssq )

                k = k + n - j + 1

   120       CONTINUE

          END IF

          ssq( 2 ) = 2*ssq( 2 )

 *

 *        Sum diagonal

 *

          k = 1

          colssq( 1 ) = zero

          colssq( 2 ) = one

          DO 130 i = 1, n

             IF( ap( k ).NE.zero ) THEN

                absa = abs( ap( k ) )

                IF( colssq( 1 ).LT.absa ) THEN

                   colssq( 2 ) = one + colssq(2)*( colssq(1) / absa )**2

                   colssq( 1 ) = absa

                ELSE

                   colssq( 2 ) = colssq( 2 ) + ( absa / colssq( 1 ) )**2

                END IF

             END IF

             IF( lsame( uplo, 'U' ) ) THEN

                k = k + i + 1

             ELSE

                k = k + n - i + 1

             END IF

   130    CONTINUE

          CALL scombssq( ssq, colssq )

          VALUE = ssq( 1 )*sqrt( ssq( 2 ) )

       END IF

 *

       slansp = VALUE

       RETURN

 *

 *     End of SLANSP

 *

       END

scombssq
subroutine scombssq(V1, V2)
SCOMBSSQ adds two scaled sum of squares quantities
Definition: scombssq.f:60

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

slassq
subroutine slassq(N, X, INCX, SCALE, SUMSQ)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f:103

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

slansp
real function slansp(NORM, UPLO, N, AP, WORK)
SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansp.f:114