dd/d66/dlantb_8f_source.html

 *> \brief \b DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
 *
 *  =========== DOCUMENTATION ===========
 *
 * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
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 *> [TXT]</a>
 *> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB,
 *                        LDAB, WORK )
 *
 *       .. Scalar Arguments ..
 *       CHARACTER          DIAG, NORM, UPLO
 *       INTEGER            K, LDAB, N
 *       ..
 *       .. Array Arguments ..
 *       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
 *       ..
 *
 *
 *> \par Purpose:
 *  =============
 *>
 *> \verbatim
 *>
 *> DLANTB  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 triangular band matrix A,  with ( k + 1 ) diagonals.
 *> \endverbatim
 *>
 *> \return DLANTB
 *> \verbatim
 *>
 *>    DLANTB = ( 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 DLANTB as described
 *>          above.
 *> \endverbatim
 *>
 *> \param[in] UPLO
 *> \verbatim
 *>          UPLO is CHARACTER*1
 *>          Specifies whether the matrix A is upper or lower triangular.
 *>          = 'U':  Upper triangular
 *>          = 'L':  Lower triangular
 *> \endverbatim
 *>
 *> \param[in] DIAG
 *> \verbatim
 *>          DIAG is CHARACTER*1
 *>          Specifies whether or not the matrix A is unit triangular.
 *>          = 'N':  Non-unit triangular
 *>          = 'U':  Unit triangular
 *> \endverbatim
 *>
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
 *>          The order of the matrix A.  N >= 0.  When N = 0, DLANTB is
 *>          set to zero.
 *> \endverbatim
 *>
 *> \param[in] K
 *> \verbatim
 *>          K is INTEGER
 *>          The number of super-diagonals of the matrix A if UPLO = 'U',
 *>          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
 *>          K >= 0.
 *> \endverbatim
 *>
 *> \param[in] AB
 *> \verbatim
 *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
 *>          The upper or lower triangular 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).
 *>          Note that when DIAG = 'U', the elements of the array AB
 *>          corresponding to the diagonal elements of the matrix A are
 *>          not referenced, but are assumed to be one.
 *> \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'; 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 lantb
 *
 *  =====================================================================
       DOUBLE PRECISION FUNCTION dlantb( NORM, UPLO, DIAG, 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..--
 *
 *     .. Scalar Arguments ..
       CHARACTER          DIAG, 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 ..
       LOGICAL            UDIAG
       INTEGER            I, J, L
       DOUBLE PRECISION   SCALE, SUM, VALUE
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           dlassq
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, DISNAN
       EXTERNAL           lsame, disnan
 *     ..
 *     .. 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))).
 *
          IF( lsame( diag, 'U' ) ) THEN
             VALUE = one
             IF( lsame( uplo, 'U' ) ) THEN
                DO 20 j = 1, n
                   DO 10 i = max( k+2-j, 1 ), k
                      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 = 2, 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
             VALUE = zero
             IF( lsame( uplo, 'U' ) ) THEN
                DO 60 j = 1, n
                   DO 50 i = max( k+2-j, 1 ), k + 1
                      sum = abs( ab( i, j ) )
                      IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
    50             CONTINUE
    60          CONTINUE
             ELSE
                DO 80 j = 1, n
                   DO 70 i = 1, min( n+1-j, k+1 )
                      sum = abs( ab( i, j ) )
                      IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
    70             CONTINUE
    80          CONTINUE
             END IF
          END IF
       ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
 *
 *        Find norm1(A).
 *
          VALUE = zero
          udiag = lsame( diag, 'U' )
          IF( lsame( uplo, 'U' ) ) THEN
             DO 110 j = 1, n
                IF( udiag ) THEN
                   sum = one
                   DO 90 i = max( k+2-j, 1 ), k
                      sum = sum + abs( ab( i, j ) )
    90             CONTINUE
                ELSE
                   sum = zero
                   DO 100 i = max( k+2-j, 1 ), k + 1
                      sum = sum + abs( ab( i, j ) )
   100             CONTINUE
                END IF
                IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
   110       CONTINUE
          ELSE
             DO 140 j = 1, n
                IF( udiag ) THEN
                   sum = one
                   DO 120 i = 2, min( n+1-j, k+1 )
                      sum = sum + abs( ab( i, j ) )
   120             CONTINUE
                ELSE
                   sum = zero
                   DO 130 i = 1, min( n+1-j, k+1 )
                      sum = sum + abs( ab( i, j ) )
   130             CONTINUE
                END IF
                IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
   140       CONTINUE
          END IF
       ELSE IF( lsame( norm, 'I' ) ) THEN
 *
 *        Find normI(A).
 *
          VALUE = zero
          IF( lsame( uplo, 'U' ) ) THEN
             IF( lsame( diag, 'U' ) ) THEN
                DO 150 i = 1, n
                   work( i ) = one
   150          CONTINUE
                DO 170 j = 1, n
                   l = k + 1 - j
                   DO 160 i = max( 1, j-k ), j - 1
                      work( i ) = work( i ) + abs( ab( l+i, j ) )
   160             CONTINUE
   170          CONTINUE
             ELSE
                DO 180 i = 1, n
                   work( i ) = zero
   180          CONTINUE
                DO 200 j = 1, n
                   l = k + 1 - j
                   DO 190 i = max( 1, j-k ), j
                      work( i ) = work( i ) + abs( ab( l+i, j ) )
   190             CONTINUE
   200          CONTINUE
             END IF
          ELSE
             IF( lsame( diag, 'U' ) ) THEN
                DO 210 i = 1, n
                   work( i ) = one
   210          CONTINUE
                DO 230 j = 1, n
                   l = 1 - j
                   DO 220 i = j + 1, min( n, j+k )
                      work( i ) = work( i ) + abs( ab( l+i, j ) )
   220             CONTINUE
   230          CONTINUE
             ELSE
                DO 240 i = 1, n
                   work( i ) = zero
   240          CONTINUE
                DO 260 j = 1, n
                   l = 1 - j
                   DO 250 i = j, min( n, j+k )
                      work( i ) = work( i ) + abs( ab( l+i, j ) )
   250             CONTINUE
   260          CONTINUE
             END IF
          END IF
          DO 270 i = 1, n
             sum = work( i )
             IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
   270    CONTINUE
       ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
 *
 *        Find normF(A).
 *
          IF( lsame( uplo, 'U' ) ) THEN
             IF( lsame( diag, 'U' ) ) THEN
                scale = one
                sum = n
                IF( k.GT.0 ) THEN
                   DO 280 j = 2, n
                      CALL dlassq( min( j-1, k ),
      $                            ab( max( k+2-j, 1 ), j ), 1, scale,
      $                            sum )
   280             CONTINUE
                END IF
             ELSE
                scale = zero
                sum = one
                DO 290 j = 1, n
                   CALL dlassq( min( j, k+1 ), ab( max( k+2-j, 1 ), j ),
      $                         1, scale, sum )
   290          CONTINUE
             END IF
          ELSE
             IF( lsame( diag, 'U' ) ) THEN
                scale = one
                sum = n
                IF( k.GT.0 ) THEN
                   DO 300 j = 1, n - 1
                      CALL dlassq( min( n-j, k ), ab( 2, j ), 1, scale,
      $                            sum )
   300             CONTINUE
                END IF
             ELSE
                scale = zero
                sum = one
                DO 310 j = 1, n
                   CALL dlassq( min( n-j+1, k+1 ), ab( 1, j ), 1, scale,
      $                         sum )
   310          CONTINUE
             END IF
          END IF
          VALUE = scale*sqrt( sum )
       END IF
 *
       dlantb = VALUE
       RETURN
 *
 *     End of DLANTB
 *
       END
dlantb
double precision function dlantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
Definition: dlantb.f:140