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    1:       DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
    2:      $                 WORK )
    3: *
    4: *  -- LAPACK auxiliary routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          NORM
   11:       INTEGER            KL, KU, LDAB, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   WORK( * )
   15:       COMPLEX*16         AB( LDAB, * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  ZLANGB  returns the value of the one norm,  or the Frobenius norm, or
   22: *  the  infinity norm,  or the element of  largest absolute value  of an
   23: *  n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
   24: *
   25: *  Description
   26: *  ===========
   27: *
   28: *  ZLANGB returns the value
   29: *
   30: *     ZLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
   31: *              (
   32: *              ( norm1(A),         NORM = '1', 'O' or 'o'
   33: *              (
   34: *              ( normI(A),         NORM = 'I' or 'i'
   35: *              (
   36: *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
   37: *
   38: *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
   39: *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
   40: *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
   41: *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
   42: *
   43: *  Arguments
   44: *  =========
   45: *
   46: *  NORM    (input) CHARACTER*1
   47: *          Specifies the value to be returned in ZLANGB as described
   48: *          above.
   49: *
   50: *  N       (input) INTEGER
   51: *          The order of the matrix A.  N >= 0.  When N = 0, ZLANGB is
   52: *          set to zero.
   53: *
   54: *  KL      (input) INTEGER
   55: *          The number of sub-diagonals of the matrix A.  KL >= 0.
   56: *
   57: *  KU      (input) INTEGER
   58: *          The number of super-diagonals of the matrix A.  KU >= 0.
   59: *
   60: *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)
   61: *          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
   62: *          column of A is stored in the j-th column of the array AB as
   63: *          follows:
   64: *          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
   65: *
   66: *  LDAB    (input) INTEGER
   67: *          The leading dimension of the array AB.  LDAB >= KL+KU+1.
   68: *
   69: *  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
   70: *          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
   71: *          referenced.
   72: *
   73: * =====================================================================
   74: *
   75: *     .. Parameters ..
   76:       DOUBLE PRECISION   ONE, ZERO
   77:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   78: *     ..
   79: *     .. Local Scalars ..
   80:       INTEGER            I, J, K, L
   81:       DOUBLE PRECISION   SCALE, SUM, VALUE
   82: *     ..
   83: *     .. External Functions ..
   84:       LOGICAL            LSAME
   85:       EXTERNAL           LSAME
   86: *     ..
   87: *     .. External Subroutines ..
   88:       EXTERNAL           ZLASSQ
   89: *     ..
   90: *     .. Intrinsic Functions ..
   91:       INTRINSIC          ABS, MAX, MIN, SQRT
   92: *     ..
   93: *     .. Executable Statements ..
   94: *
   95:       IF( N.EQ.0 ) THEN
   96:          VALUE = ZERO
   97:       ELSE IF( LSAME( NORM, 'M' ) ) THEN
   98: *
   99: *        Find max(abs(A(i,j))).
  100: *
  101:          VALUE = ZERO
  102:          DO 20 J = 1, N
  103:             DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
  104:                VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
  105:    10       CONTINUE
  106:    20    CONTINUE
  107:       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
  108: *
  109: *        Find norm1(A).
  110: *
  111:          VALUE = ZERO
  112:          DO 40 J = 1, N
  113:             SUM = ZERO
  114:             DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
  115:                SUM = SUM + ABS( AB( I, J ) )
  116:    30       CONTINUE
  117:             VALUE = MAX( VALUE, SUM )
  118:    40    CONTINUE
  119:       ELSE IF( LSAME( NORM, 'I' ) ) THEN
  120: *
  121: *        Find normI(A).
  122: *
  123:          DO 50 I = 1, N
  124:             WORK( I ) = ZERO
  125:    50    CONTINUE
  126:          DO 70 J = 1, N
  127:             K = KU + 1 - J
  128:             DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
  129:                WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
  130:    60       CONTINUE
  131:    70    CONTINUE
  132:          VALUE = ZERO
  133:          DO 80 I = 1, N
  134:             VALUE = MAX( VALUE, WORK( I ) )
  135:    80    CONTINUE
  136:       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
  137: *
  138: *        Find normF(A).
  139: *
  140:          SCALE = ZERO
  141:          SUM = ONE
  142:          DO 90 J = 1, N
  143:             L = MAX( 1, J-KU )
  144:             K = KU + 1 - J + L
  145:             CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
  146:    90    CONTINUE
  147:          VALUE = SCALE*SQRT( SUM )
  148:       END IF
  149: *
  150:       ZLANGB = VALUE
  151:       RETURN
  152: *
  153: *     End of ZLANGB
  154: *
  155:       END