dlangb.f

          DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
         $                 WORK )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          NORM
          INTEGER            KL, KU, LDAB, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DLANGB  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.
    *
    *  Description
    *  ===========
    *
    *  DLANGB returns the value
    *
    *     DLANGB = ( 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.
    *
    *  Arguments
    *  =========
    *
    *  NORM    (input) CHARACTER*1
    *          Specifies the value to be returned in DLANGB as described
    *          above.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.  When N = 0, DLANGB is
    *          set to zero.
    *
    *  KL      (input) INTEGER
    *          The number of sub-diagonals of the matrix A.  KL >= 0.
    *
    *  KU      (input) INTEGER
    *          The number of super-diagonals of the matrix A.  KU >= 0.
    *
    *  AB      (input) DOUBLE PRECISION 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).
    *
    *  LDAB    (input) INTEGER
    *          The leading dimension of the array AB.  LDAB >= KL+KU+1.
    *
    *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
    *          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
    *          referenced.
    *
    * =====================================================================
    *
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, J, K, L
          DOUBLE PRECISION   SCALE, SUM, VALUE
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DLASSQ
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. 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 )
                   VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
       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
                VALUE = MAX( 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
                VALUE = MAX( VALUE, WORK( I ) )
       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 DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
       90    CONTINUE
             VALUE = SCALE*SQRT( SUM )
          END IF
    *
          DLANGB = VALUE
          RETURN
    *
    *     End of DLANGB
    *
          END