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    1: *> \brief \b DLAQGB
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DLAQGB + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqgb.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqgb.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqgb.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
   22: *                          AMAX, EQUED )
   23: * 
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          EQUED
   26: *       INTEGER            KL, KU, LDAB, M, N
   27: *       DOUBLE PRECISION   AMAX, COLCND, ROWCND
   28: *       ..
   29: *       .. Array Arguments ..
   30: *       DOUBLE PRECISION   AB( LDAB, * ), C( * ), R( * )
   31: *       ..
   32: *  
   33: *
   34: *> \par Purpose:
   35: *  =============
   36: *>
   37: *> \verbatim
   38: *>
   39: *> DLAQGB equilibrates a general M by N band matrix A with KL
   40: *> subdiagonals and KU superdiagonals using the row and scaling factors
   41: *> in the vectors R and C.
   42: *> \endverbatim
   43: *
   44: *  Arguments:
   45: *  ==========
   46: *
   47: *> \param[in] M
   48: *> \verbatim
   49: *>          M is INTEGER
   50: *>          The number of rows of the matrix A.  M >= 0.
   51: *> \endverbatim
   52: *>
   53: *> \param[in] N
   54: *> \verbatim
   55: *>          N is INTEGER
   56: *>          The number of columns of the matrix A.  N >= 0.
   57: *> \endverbatim
   58: *>
   59: *> \param[in] KL
   60: *> \verbatim
   61: *>          KL is INTEGER
   62: *>          The number of subdiagonals within the band of A.  KL >= 0.
   63: *> \endverbatim
   64: *>
   65: *> \param[in] KU
   66: *> \verbatim
   67: *>          KU is INTEGER
   68: *>          The number of superdiagonals within the band of A.  KU >= 0.
   69: *> \endverbatim
   70: *>
   71: *> \param[in,out] AB
   72: *> \verbatim
   73: *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
   74: *>          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
   75: *>          The j-th column of A is stored in the j-th column of the
   76: *>          array AB as follows:
   77: *>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
   78: *>
   79: *>          On exit, the equilibrated matrix, in the same storage format
   80: *>          as A.  See EQUED for the form of the equilibrated matrix.
   81: *> \endverbatim
   82: *>
   83: *> \param[in] LDAB
   84: *> \verbatim
   85: *>          LDAB is INTEGER
   86: *>          The leading dimension of the array AB.  LDA >= KL+KU+1.
   87: *> \endverbatim
   88: *>
   89: *> \param[in] R
   90: *> \verbatim
   91: *>          R is DOUBLE PRECISION array, dimension (M)
   92: *>          The row scale factors for A.
   93: *> \endverbatim
   94: *>
   95: *> \param[in] C
   96: *> \verbatim
   97: *>          C is DOUBLE PRECISION array, dimension (N)
   98: *>          The column scale factors for A.
   99: *> \endverbatim
  100: *>
  101: *> \param[in] ROWCND
  102: *> \verbatim
  103: *>          ROWCND is DOUBLE PRECISION
  104: *>          Ratio of the smallest R(i) to the largest R(i).
  105: *> \endverbatim
  106: *>
  107: *> \param[in] COLCND
  108: *> \verbatim
  109: *>          COLCND is DOUBLE PRECISION
  110: *>          Ratio of the smallest C(i) to the largest C(i).
  111: *> \endverbatim
  112: *>
  113: *> \param[in] AMAX
  114: *> \verbatim
  115: *>          AMAX is DOUBLE PRECISION
  116: *>          Absolute value of largest matrix entry.
  117: *> \endverbatim
  118: *>
  119: *> \param[out] EQUED
  120: *> \verbatim
  121: *>          EQUED is CHARACTER*1
  122: *>          Specifies the form of equilibration that was done.
  123: *>          = 'N':  No equilibration
  124: *>          = 'R':  Row equilibration, i.e., A has been premultiplied by
  125: *>                  diag(R).
  126: *>          = 'C':  Column equilibration, i.e., A has been postmultiplied
  127: *>                  by diag(C).
  128: *>          = 'B':  Both row and column equilibration, i.e., A has been
  129: *>                  replaced by diag(R) * A * diag(C).
  130: *> \endverbatim
  131: *
  132: *> \par Internal Parameters:
  133: *  =========================
  134: *>
  135: *> \verbatim
  136: *>  THRESH is a threshold value used to decide if row or column scaling
  137: *>  should be done based on the ratio of the row or column scaling
  138: *>  factors.  If ROWCND < THRESH, row scaling is done, and if
  139: *>  COLCND < THRESH, column scaling is done.
  140: *>
  141: *>  LARGE and SMALL are threshold values used to decide if row scaling
  142: *>  should be done based on the absolute size of the largest matrix
  143: *>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
  144: *> \endverbatim
  145: *
  146: *  Authors:
  147: *  ========
  148: *
  149: *> \author Univ. of Tennessee 
  150: *> \author Univ. of California Berkeley 
  151: *> \author Univ. of Colorado Denver 
  152: *> \author NAG Ltd. 
  153: *
  154: *> \date November 2011
  155: *
  156: *> \ingroup doubleGBauxiliary
  157: *
  158: *  =====================================================================
  159:       SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
  160:      $                   AMAX, EQUED )
  161: *
  162: *  -- LAPACK auxiliary routine (version 3.4.0) --
  163: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  164: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  165: *     November 2011
  166: *
  167: *     .. Scalar Arguments ..
  168:       CHARACTER          EQUED
  169:       INTEGER            KL, KU, LDAB, M, N
  170:       DOUBLE PRECISION   AMAX, COLCND, ROWCND
  171: *     ..
  172: *     .. Array Arguments ..
  173:       DOUBLE PRECISION   AB( LDAB, * ), C( * ), R( * )
  174: *     ..
  175: *
  176: *  =====================================================================
  177: *
  178: *     .. Parameters ..
  179:       DOUBLE PRECISION   ONE, THRESH
  180:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
  181: *     ..
  182: *     .. Local Scalars ..
  183:       INTEGER            I, J
  184:       DOUBLE PRECISION   CJ, LARGE, SMALL
  185: *     ..
  186: *     .. External Functions ..
  187:       DOUBLE PRECISION   DLAMCH
  188:       EXTERNAL           DLAMCH
  189: *     ..
  190: *     .. Intrinsic Functions ..
  191:       INTRINSIC          MAX, MIN
  192: *     ..
  193: *     .. Executable Statements ..
  194: *
  195: *     Quick return if possible
  196: *
  197:       IF( M.LE.0 .OR. N.LE.0 ) THEN
  198:          EQUED = 'N'
  199:          RETURN
  200:       END IF
  201: *
  202: *     Initialize LARGE and SMALL.
  203: *
  204:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
  205:       LARGE = ONE / SMALL
  206: *
  207:       IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
  208:      $     THEN
  209: *
  210: *        No row scaling
  211: *
  212:          IF( COLCND.GE.THRESH ) THEN
  213: *
  214: *           No column scaling
  215: *
  216:             EQUED = 'N'
  217:          ELSE
  218: *
  219: *           Column scaling
  220: *
  221:             DO 20 J = 1, N
  222:                CJ = C( J )
  223:                DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
  224:                   AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
  225:    10          CONTINUE
  226:    20       CONTINUE
  227:             EQUED = 'C'
  228:          END IF
  229:       ELSE IF( COLCND.GE.THRESH ) THEN
  230: *
  231: *        Row scaling, no column scaling
  232: *
  233:          DO 40 J = 1, N
  234:             DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
  235:                AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
  236:    30       CONTINUE
  237:    40    CONTINUE
  238:          EQUED = 'R'
  239:       ELSE
  240: *
  241: *        Row and column scaling
  242: *
  243:          DO 60 J = 1, N
  244:             CJ = C( J )
  245:             DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
  246:                AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
  247:    50       CONTINUE
  248:    60    CONTINUE
  249:          EQUED = 'B'
  250:       END IF
  251: *
  252:       RETURN
  253: *
  254: *     End of DLAQGB
  255: *
  256:       END