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    1: *> \brief \b ZLANGB
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download ZLANGB + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlangb.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlangb.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlangb.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
   22: *                        WORK )
   23: * 
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          NORM
   26: *       INTEGER            KL, KU, LDAB, N
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   WORK( * )
   30: *       COMPLEX*16         AB( LDAB, * )
   31: *       ..
   32: *  
   33: *
   34: *> \par Purpose:
   35: *  =============
   36: *>
   37: *> \verbatim
   38: *>
   39: *> ZLANGB  returns the value of the one norm,  or the Frobenius norm, or
   40: *> the  infinity norm,  or the element of  largest absolute value  of an
   41: *> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
   42: *> \endverbatim
   43: *>
   44: *> \return ZLANGB
   45: *> \verbatim
   46: *>
   47: *>    ZLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
   48: *>             (
   49: *>             ( norm1(A),         NORM = '1', 'O' or 'o'
   50: *>             (
   51: *>             ( normI(A),         NORM = 'I' or 'i'
   52: *>             (
   53: *>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
   54: *>
   55: *> where  norm1  denotes the  one norm of a matrix (maximum column sum),
   56: *> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
   57: *> normF  denotes the  Frobenius norm of a matrix (square root of sum of
   58: *> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
   59: *> \endverbatim
   60: *
   61: *  Arguments:
   62: *  ==========
   63: *
   64: *> \param[in] NORM
   65: *> \verbatim
   66: *>          NORM is CHARACTER*1
   67: *>          Specifies the value to be returned in ZLANGB as described
   68: *>          above.
   69: *> \endverbatim
   70: *>
   71: *> \param[in] N
   72: *> \verbatim
   73: *>          N is INTEGER
   74: *>          The order of the matrix A.  N >= 0.  When N = 0, ZLANGB is
   75: *>          set to zero.
   76: *> \endverbatim
   77: *>
   78: *> \param[in] KL
   79: *> \verbatim
   80: *>          KL is INTEGER
   81: *>          The number of sub-diagonals of the matrix A.  KL >= 0.
   82: *> \endverbatim
   83: *>
   84: *> \param[in] KU
   85: *> \verbatim
   86: *>          KU is INTEGER
   87: *>          The number of super-diagonals of the matrix A.  KU >= 0.
   88: *> \endverbatim
   89: *>
   90: *> \param[in] AB
   91: *> \verbatim
   92: *>          AB is COMPLEX*16 array, dimension (LDAB,N)
   93: *>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
   94: *>          column of A is stored in the j-th column of the array AB as
   95: *>          follows:
   96: *>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
   97: *> \endverbatim
   98: *>
   99: *> \param[in] LDAB
  100: *> \verbatim
  101: *>          LDAB is INTEGER
  102: *>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
  103: *> \endverbatim
  104: *>
  105: *> \param[out] WORK
  106: *> \verbatim
  107: *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
  108: *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
  109: *>          referenced.
  110: *> \endverbatim
  111: *
  112: *  Authors:
  113: *  ========
  114: *
  115: *> \author Univ. of Tennessee 
  116: *> \author Univ. of California Berkeley 
  117: *> \author Univ. of Colorado Denver 
  118: *> \author NAG Ltd. 
  119: *
  120: *> \date November 2011
  121: *
  122: *> \ingroup complex16GBauxiliary
  123: *
  124: *  =====================================================================
  125:       DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
  126:      $                 WORK )
  127: *
  128: *  -- LAPACK auxiliary routine (version 3.4.0) --
  129: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  130: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  131: *     November 2011
  132: *
  133: *     .. Scalar Arguments ..
  134:       CHARACTER          NORM
  135:       INTEGER            KL, KU, LDAB, N
  136: *     ..
  137: *     .. Array Arguments ..
  138:       DOUBLE PRECISION   WORK( * )
  139:       COMPLEX*16         AB( LDAB, * )
  140: *     ..
  141: *
  142: * =====================================================================
  143: *
  144: *     .. Parameters ..
  145:       DOUBLE PRECISION   ONE, ZERO
  146:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
  147: *     ..
  148: *     .. Local Scalars ..
  149:       INTEGER            I, J, K, L
  150:       DOUBLE PRECISION   SCALE, SUM, VALUE
  151: *     ..
  152: *     .. External Functions ..
  153:       LOGICAL            LSAME
  154:       EXTERNAL           LSAME
  155: *     ..
  156: *     .. External Subroutines ..
  157:       EXTERNAL           ZLASSQ
  158: *     ..
  159: *     .. Intrinsic Functions ..
  160:       INTRINSIC          ABS, MAX, MIN, SQRT
  161: *     ..
  162: *     .. Executable Statements ..
  163: *
  164:       IF( N.EQ.0 ) THEN
  165:          VALUE = ZERO
  166:       ELSE IF( LSAME( NORM, 'M' ) ) THEN
  167: *
  168: *        Find max(abs(A(i,j))).
  169: *
  170:          VALUE = ZERO
  171:          DO 20 J = 1, N
  172:             DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
  173:                VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
  174:    10       CONTINUE
  175:    20    CONTINUE
  176:       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
  177: *
  178: *        Find norm1(A).
  179: *
  180:          VALUE = ZERO
  181:          DO 40 J = 1, N
  182:             SUM = ZERO
  183:             DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
  184:                SUM = SUM + ABS( AB( I, J ) )
  185:    30       CONTINUE
  186:             VALUE = MAX( VALUE, SUM )
  187:    40    CONTINUE
  188:       ELSE IF( LSAME( NORM, 'I' ) ) THEN
  189: *
  190: *        Find normI(A).
  191: *
  192:          DO 50 I = 1, N
  193:             WORK( I ) = ZERO
  194:    50    CONTINUE
  195:          DO 70 J = 1, N
  196:             K = KU + 1 - J
  197:             DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
  198:                WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
  199:    60       CONTINUE
  200:    70    CONTINUE
  201:          VALUE = ZERO
  202:          DO 80 I = 1, N
  203:             VALUE = MAX( VALUE, WORK( I ) )
  204:    80    CONTINUE
  205:       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
  206: *
  207: *        Find normF(A).
  208: *
  209:          SCALE = ZERO
  210:          SUM = ONE
  211:          DO 90 J = 1, N
  212:             L = MAX( 1, J-KU )
  213:             K = KU + 1 - J + L
  214:             CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
  215:    90    CONTINUE
  216:          VALUE = SCALE*SQRT( SUM )
  217:       END IF
  218: *
  219:       ZLANGB = VALUE
  220:       RETURN
  221: *
  222: *     End of ZLANGB
  223: *
  224:       END