db/dad/dlansb_8f_source.html

 *> \brief \b DLANSB 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 band matrix.

 *

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

 *

 * Online html documentation available at

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

 *

 *> \htmlonly

 *> Download DLANSB + dependencies

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 *> [TGZ]</a>

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

 *> [ZIP]</a>

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

 *> [TXT]</a>

 *> \endhtmlonly

 *

 *  Definition:

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

 *

 *       DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB,

 *                        WORK )

 *

 *       .. Scalar Arguments ..

 *       CHARACTER          NORM, UPLO

 *       INTEGER            K, LDAB, N

 *       ..

 *       .. Array Arguments ..

 *       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )

 *       ..

 *

 *

 *> \par Purpose:

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

 *>

 *> \verbatim

 *>

 *> DLANSB  returns the value of the one norm,  or the Frobenius norm, or

 *> the  infinity norm,  or the element of  largest absolute value  of an

 *> n by n symmetric band matrix A,  with k super-diagonals.

 *> \endverbatim

 *>

 *> \return DLANSB

 *> \verbatim

 *>

 *>    DLANSB = ( 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 DLANSB as described

 *>          above.

 *> \endverbatim

 *>

 *> \param[in] UPLO

 *> \verbatim

 *>          UPLO is CHARACTER*1

 *>          Specifies whether the upper or lower triangular part of the

 *>          band matrix A is supplied.

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

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

 *> \endverbatim

 *>

 *> \param[in] N

 *> \verbatim

 *>          N is INTEGER

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

 *>          set to zero.

 *> \endverbatim

 *>

 *> \param[in] K

 *> \verbatim

 *>          K is INTEGER

 *>          The number of super-diagonals or sub-diagonals of the

 *>          band matrix A.  K >= 0.

 *> \endverbatim

 *>

 *> \param[in] AB

 *> \verbatim

 *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)

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

 *>          stored in the first K+1 rows of AB.  The j-th column of A is

 *>          stored in the j-th column of the array AB as follows:

 *>          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;

 *>          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).

 *> \endverbatim

 *>

 *> \param[in] LDAB

 *> \verbatim

 *>          LDAB is INTEGER

 *>          The leading dimension of the array AB.  LDAB >= K+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.

 *

 *> \ingroup doubleOTHERauxiliary

 *

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

       DOUBLE PRECISION FUNCTION dlansb( NORM, UPLO, N, K, AB, LDAB,

      $                 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            k, ldab, n

 *     ..

 *     .. Array Arguments ..

       DOUBLE PRECISION   ab( ldab, * ), work( * )

 *     ..

 *

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

 *

 *     .. Parameters ..

       DOUBLE PRECISION   one, zero

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

 *     ..

 *     .. Local Scalars ..

       INTEGER            i, j, l

       DOUBLE PRECISION   absa, sum, value

 *     ..

 *     .. Local Arrays ..

       DOUBLE PRECISION   ssq( 2 ), colssq( 2 )

 *     ..

 *     .. External Functions ..

       LOGICAL            lsame, disnan

       EXTERNAL           lsame, disnan

 *     ..

 *     .. External Subroutines ..

       EXTERNAL           dlassq, dcombssq

 *     ..

 *     .. Intrinsic Functions ..

       INTRINSIC          abs, max, min, 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 = max( k+2-j, 1 ), k + 1

                   sum = abs( ab( i, j ) )

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

    10          CONTINUE

    20       CONTINUE

          ELSE

             DO 40 j = 1, n

                DO 30 i = 1, min( n+1-j, k+1 )

                   sum = abs( ab( 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

                l = k + 1 - j

                DO 50 i = max( 1, j-k ), j - 1

                   absa = abs( ab( l+i, j ) )

                   sum = sum + absa

                   work( i ) = work( i ) + absa

    50          CONTINUE

                work( j ) = sum + abs( ab( k+1, 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( ab( 1, j ) )

                l = 1 - j

                DO 90 i = j + 1, min( n, j+k )

                   absa = abs( ab( l+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).

 *        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

 *

          IF( k.GT.0 ) THEN

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

                DO 110 j = 2, n

                   colssq( 1 ) = zero

                   colssq( 2 ) = one

                   CALL dlassq( min( j-1, k ), ab( max( k+2-j, 1 ), j ),

      $                         1, colssq( 1 ), colssq( 2 ) )

                   CALL dcombssq( ssq, colssq )

   110          CONTINUE

                l = k + 1

             ELSE

                DO 120 j = 1, n - 1

                   colssq( 1 ) = zero

                   colssq( 2 ) = one

                   CALL dlassq( min( n-j, k ), ab( 2, j ), 1,

      $                         colssq( 1 ), colssq( 2 ) )

                   CALL dcombssq( ssq, colssq )

   120          CONTINUE

                l = 1

             END IF

             ssq( 2 ) = 2*ssq( 2 )

          ELSE

             l = 1

          END IF

 *

 *        Sum diagonal

 *

          colssq( 1 ) = zero

          colssq( 2 ) = one

          CALL dlassq( n, ab( l, 1 ), ldab, colssq( 1 ), colssq( 2 ) )

          CALL dcombssq( ssq, colssq )

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

       END IF

 *

       dlansb = VALUE

       RETURN

 *

 *     End of DLANSB

 *

       END

disnan
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59

dlassq
subroutine dlassq(n, x, incx, scl, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f90:126

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

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

dlansb
double precision function dlansb(NORM, UPLO, N, K, AB, LDAB, WORK)
DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansb.f:129