db/d45/slangb_8f_source.html

 *> \brief \b SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
 *
 *  =========== DOCUMENTATION ===========
 *
 * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
 *> Download SLANGB + dependencies
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 *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slangb.f">
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 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slangb.f">
 *> [TXT]</a>
 *> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       REAL             FUNCTION SLANGB( NORM, N, KL, KU, AB, LDAB,
 *                        WORK )
 *
 *       .. Scalar Arguments ..
 *       CHARACTER          NORM
 *       INTEGER            KL, KU, LDAB, N
 *       ..
 *       .. Array Arguments ..
 *       REAL               AB( LDAB, * ), WORK( * )
 *       ..
 *
 *
 *> \par Purpose:
 *  =============
 *>
 *> \verbatim
 *>
 *> SLANGB  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 band matrix  A,  with kl sub-diagonals and ku super-diagonals.
 *> \endverbatim
 *>
 *> \return SLANGB
 *> \verbatim
 *>
 *>    SLANGB = ( 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 SLANGB as described
 *>          above.
 *> \endverbatim
 *>
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
 *>          The order of the matrix A.  N >= 0.  When N = 0, SLANGB is
 *>          set to zero.
 *> \endverbatim
 *>
 *> \param[in] KL
 *> \verbatim
 *>          KL is INTEGER
 *>          The number of sub-diagonals of the matrix A.  KL >= 0.
 *> \endverbatim
 *>
 *> \param[in] KU
 *> \verbatim
 *>          KU is INTEGER
 *>          The number of super-diagonals of the matrix A.  KU >= 0.
 *> \endverbatim
 *>
 *> \param[in] AB
 *> \verbatim
 *>          AB is REAL array, dimension (LDAB,N)
 *>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
 *>          column of A is stored in the j-th column of the array AB as
 *>          follows:
 *>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
 *> \endverbatim
 *>
 *> \param[in] LDAB
 *> \verbatim
 *>          LDAB is INTEGER
 *>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
 *> \endverbatim
 *>
 *> \param[out] WORK
 *> \verbatim
 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
 *>          where LWORK >= N when NORM = 'I'; 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 langb
 *
 *  =====================================================================
       REAL             FUNCTION slangb( NORM, N, KL, KU, 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..--
 *
 *     .. Scalar Arguments ..
       CHARACTER          NORM
       INTEGER            KL, KU, LDAB, N
 *     ..
 *     .. Array Arguments ..
       REAL               AB( ldab, * ), WORK( * )
 *     ..
 *
 * =====================================================================
 *
 *
 *     .. Parameters ..
       REAL               ONE, ZERO
       parameter( one = 1.0e+0, zero = 0.0e+0 )
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J, K, L
       REAL               SCALE, SUM, VALUE, TEMP
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           slassq
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, SISNAN
       EXTERNAL           lsame, sisnan
 *     ..
 *     .. 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
          DO 20 j = 1, n
             DO 10 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
                temp = abs( ab( i, j ) )
                IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
    10       CONTINUE
    20    CONTINUE
       ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
 *
 *        Find norm1(A).
 *
          VALUE = zero
          DO 40 j = 1, n
             sum = zero
             DO 30 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
                sum = sum + abs( ab( i, j ) )
    30       CONTINUE
             IF( VALUE.LT.sum .OR. sisnan( sum ) ) VALUE = sum
    40    CONTINUE
       ELSE IF( lsame( norm, 'I' ) ) THEN
 *
 *        Find normI(A).
 *
          DO 50 i = 1, n
             work( i ) = zero
    50    CONTINUE
          DO 70 j = 1, n
             k = ku + 1 - j
             DO 60 i = max( 1, j-ku ), min( n, j+kl )
                work( i ) = work( i ) + abs( ab( k+i, j ) )
    60       CONTINUE
    70    CONTINUE
          VALUE = zero
          DO 80 i = 1, n
             temp = work( i )
             IF( VALUE.LT.temp .OR. sisnan( temp ) ) VALUE = temp
    80    CONTINUE
       ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
 *
 *        Find normF(A).
 *
          scale = zero
          sum = one
          DO 90 j = 1, n
             l = max( 1, j-ku )
             k = ku + 1 - j + l
             CALL slassq( min( n, j+kl )-l+1, ab( k, j ), 1, scale, sum )
    90    CONTINUE
          VALUE = scale*sqrt( sum )
       END IF
 *
       slangb = VALUE
       RETURN
 *
 *     End of SLANGB
 *
       END
slangb
real function slangb(NORM, N, KL, KU, AB, LDAB, WORK)
SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slangb.f:124