LAPACK 3.3.1
Linear Algebra PACKage

dlaqgb.f

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00001       SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
00002      $                   AMAX, EQUED )
00003 *
00004 *  -- LAPACK auxiliary routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          EQUED
00011       INTEGER            KL, KU, LDAB, M, N
00012       DOUBLE PRECISION   AMAX, COLCND, ROWCND
00013 *     ..
00014 *     .. Array Arguments ..
00015       DOUBLE PRECISION   AB( LDAB, * ), C( * ), R( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  DLAQGB equilibrates a general M by N band matrix A with KL
00022 *  subdiagonals and KU superdiagonals using the row and scaling factors
00023 *  in the vectors R and C.
00024 *
00025 *  Arguments
00026 *  =========
00027 *
00028 *  M       (input) INTEGER
00029 *          The number of rows of the matrix A.  M >= 0.
00030 *
00031 *  N       (input) INTEGER
00032 *          The number of columns of the matrix A.  N >= 0.
00033 *
00034 *  KL      (input) INTEGER
00035 *          The number of subdiagonals within the band of A.  KL >= 0.
00036 *
00037 *  KU      (input) INTEGER
00038 *          The number of superdiagonals within the band of A.  KU >= 0.
00039 *
00040 *  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
00041 *          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
00042 *          The j-th column of A is stored in the j-th column of the
00043 *          array AB as follows:
00044 *          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
00045 *
00046 *          On exit, the equilibrated matrix, in the same storage format
00047 *          as A.  See EQUED for the form of the equilibrated matrix.
00048 *
00049 *  LDAB    (input) INTEGER
00050 *          The leading dimension of the array AB.  LDA >= KL+KU+1.
00051 *
00052 *  R       (input) DOUBLE PRECISION array, dimension (M)
00053 *          The row scale factors for A.
00054 *
00055 *  C       (input) DOUBLE PRECISION array, dimension (N)
00056 *          The column scale factors for A.
00057 *
00058 *  ROWCND  (input) DOUBLE PRECISION
00059 *          Ratio of the smallest R(i) to the largest R(i).
00060 *
00061 *  COLCND  (input) DOUBLE PRECISION
00062 *          Ratio of the smallest C(i) to the largest C(i).
00063 *
00064 *  AMAX    (input) DOUBLE PRECISION
00065 *          Absolute value of largest matrix entry.
00066 *
00067 *  EQUED   (output) CHARACTER*1
00068 *          Specifies the form of equilibration that was done.
00069 *          = 'N':  No equilibration
00070 *          = 'R':  Row equilibration, i.e., A has been premultiplied by
00071 *                  diag(R).
00072 *          = 'C':  Column equilibration, i.e., A has been postmultiplied
00073 *                  by diag(C).
00074 *          = 'B':  Both row and column equilibration, i.e., A has been
00075 *                  replaced by diag(R) * A * diag(C).
00076 *
00077 *  Internal Parameters
00078 *  ===================
00079 *
00080 *  THRESH is a threshold value used to decide if row or column scaling
00081 *  should be done based on the ratio of the row or column scaling
00082 *  factors.  If ROWCND < THRESH, row scaling is done, and if
00083 *  COLCND < THRESH, column scaling is done.
00084 *
00085 *  LARGE and SMALL are threshold values used to decide if row scaling
00086 *  should be done based on the absolute size of the largest matrix
00087 *  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
00088 *
00089 *  =====================================================================
00090 *
00091 *     .. Parameters ..
00092       DOUBLE PRECISION   ONE, THRESH
00093       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
00094 *     ..
00095 *     .. Local Scalars ..
00096       INTEGER            I, J
00097       DOUBLE PRECISION   CJ, LARGE, SMALL
00098 *     ..
00099 *     .. External Functions ..
00100       DOUBLE PRECISION   DLAMCH
00101       EXTERNAL           DLAMCH
00102 *     ..
00103 *     .. Intrinsic Functions ..
00104       INTRINSIC          MAX, MIN
00105 *     ..
00106 *     .. Executable Statements ..
00107 *
00108 *     Quick return if possible
00109 *
00110       IF( M.LE.0 .OR. N.LE.0 ) THEN
00111          EQUED = 'N'
00112          RETURN
00113       END IF
00114 *
00115 *     Initialize LARGE and SMALL.
00116 *
00117       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
00118       LARGE = ONE / SMALL
00119 *
00120       IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
00121      $     THEN
00122 *
00123 *        No row scaling
00124 *
00125          IF( COLCND.GE.THRESH ) THEN
00126 *
00127 *           No column scaling
00128 *
00129             EQUED = 'N'
00130          ELSE
00131 *
00132 *           Column scaling
00133 *
00134             DO 20 J = 1, N
00135                CJ = C( J )
00136                DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
00137                   AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
00138    10          CONTINUE
00139    20       CONTINUE
00140             EQUED = 'C'
00141          END IF
00142       ELSE IF( COLCND.GE.THRESH ) THEN
00143 *
00144 *        Row scaling, no column scaling
00145 *
00146          DO 40 J = 1, N
00147             DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
00148                AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
00149    30       CONTINUE
00150    40    CONTINUE
00151          EQUED = 'R'
00152       ELSE
00153 *
00154 *        Row and column scaling
00155 *
00156          DO 60 J = 1, N
00157             CJ = C( J )
00158             DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
00159                AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
00160    50       CONTINUE
00161    60    CONTINUE
00162          EQUED = 'B'
00163       END IF
00164 *
00165       RETURN
00166 *
00167 *     End of DLAQGB
00168 *
00169       END
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