LAPACK 3.3.1 Linear Algebra PACKage

# zlaqgb.f

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```00001       SUBROUTINE ZLAQGB( 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   C( * ), R( * )
00016       COMPLEX*16         AB( LDAB, * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  ZLAQGB equilibrates a general M by N band matrix A with KL
00023 *  subdiagonals and KU superdiagonals using the row and scaling factors
00024 *  in the vectors R and C.
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  M       (input) INTEGER
00030 *          The number of rows of the matrix A.  M >= 0.
00031 *
00032 *  N       (input) INTEGER
00033 *          The number of columns of the matrix A.  N >= 0.
00034 *
00035 *  KL      (input) INTEGER
00036 *          The number of subdiagonals within the band of A.  KL >= 0.
00037 *
00038 *  KU      (input) INTEGER
00039 *          The number of superdiagonals within the band of A.  KU >= 0.
00040 *
00041 *  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
00042 *          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
00043 *          The j-th column of A is stored in the j-th column of the
00044 *          array AB as follows:
00045 *          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
00046 *
00047 *          On exit, the equilibrated matrix, in the same storage format
00048 *          as A.  See EQUED for the form of the equilibrated matrix.
00049 *
00050 *  LDAB    (input) INTEGER
00051 *          The leading dimension of the array AB.  LDA >= KL+KU+1.
00052 *
00053 *  R       (input) DOUBLE PRECISION array, dimension (M)
00054 *          The row scale factors for A.
00055 *
00056 *  C       (input) DOUBLE PRECISION array, dimension (N)
00057 *          The column scale factors for A.
00058 *
00059 *  ROWCND  (input) DOUBLE PRECISION
00060 *          Ratio of the smallest R(i) to the largest R(i).
00061 *
00062 *  COLCND  (input) DOUBLE PRECISION
00063 *          Ratio of the smallest C(i) to the largest C(i).
00064 *
00065 *  AMAX    (input) DOUBLE PRECISION
00066 *          Absolute value of largest matrix entry.
00067 *
00068 *  EQUED   (output) CHARACTER*1
00069 *          Specifies the form of equilibration that was done.
00070 *          = 'N':  No equilibration
00071 *          = 'R':  Row equilibration, i.e., A has been premultiplied by
00072 *                  diag(R).
00073 *          = 'C':  Column equilibration, i.e., A has been postmultiplied
00074 *                  by diag(C).
00075 *          = 'B':  Both row and column equilibration, i.e., A has been
00076 *                  replaced by diag(R) * A * diag(C).
00077 *
00078 *  Internal Parameters
00079 *  ===================
00080 *
00081 *  THRESH is a threshold value used to decide if row or column scaling
00082 *  should be done based on the ratio of the row or column scaling
00083 *  factors.  If ROWCND < THRESH, row scaling is done, and if
00084 *  COLCND < THRESH, column scaling is done.
00085 *
00086 *  LARGE and SMALL are threshold values used to decide if row scaling
00087 *  should be done based on the absolute size of the largest matrix
00088 *  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
00089 *
00090 *  =====================================================================
00091 *
00092 *     .. Parameters ..
00093       DOUBLE PRECISION   ONE, THRESH
00094       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
00095 *     ..
00096 *     .. Local Scalars ..
00097       INTEGER            I, J
00098       DOUBLE PRECISION   CJ, LARGE, SMALL
00099 *     ..
00100 *     .. External Functions ..
00101       DOUBLE PRECISION   DLAMCH
00102       EXTERNAL           DLAMCH
00103 *     ..
00104 *     .. Intrinsic Functions ..
00105       INTRINSIC          MAX, MIN
00106 *     ..
00107 *     .. Executable Statements ..
00108 *
00109 *     Quick return if possible
00110 *
00111       IF( M.LE.0 .OR. N.LE.0 ) THEN
00112          EQUED = 'N'
00113          RETURN
00114       END IF
00115 *
00116 *     Initialize LARGE and SMALL.
00117 *
00118       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
00119       LARGE = ONE / SMALL
00120 *
00121       IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
00122      \$     THEN
00123 *
00124 *        No row scaling
00125 *
00126          IF( COLCND.GE.THRESH ) THEN
00127 *
00128 *           No column scaling
00129 *
00130             EQUED = 'N'
00131          ELSE
00132 *
00133 *           Column scaling
00134 *
00135             DO 20 J = 1, N
00136                CJ = C( J )
00137                DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
00138                   AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
00139    10          CONTINUE
00140    20       CONTINUE
00141             EQUED = 'C'
00142          END IF
00143       ELSE IF( COLCND.GE.THRESH ) THEN
00144 *
00145 *        Row scaling, no column scaling
00146 *
00147          DO 40 J = 1, N
00148             DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
00149                AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
00150    30       CONTINUE
00151    40    CONTINUE
00152          EQUED = 'R'
00153       ELSE
00154 *
00155 *        Row and column scaling
00156 *
00157          DO 60 J = 1, N
00158             CJ = C( J )
00159             DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
00160                AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
00161    50       CONTINUE
00162    60    CONTINUE
00163          EQUED = 'B'
00164       END IF
00165 *
00166       RETURN
00167 *
00168 *     End of ZLAQGB
00169 *
00170       END
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