LAPACK 3.3.1 Linear Algebra PACKage

# claqsb.f

Go to the documentation of this file.
```00001       SUBROUTINE CLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.3.1) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *  -- April 2011                                                      --
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          EQUED, UPLO
00010       INTEGER            KD, LDAB, N
00011       REAL               AMAX, SCOND
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               S( * )
00015       COMPLEX            AB( LDAB, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  CLAQSB equilibrates a symmetric band matrix A using the scaling
00022 *  factors in the vector S.
00023 *
00024 *  Arguments
00025 *  =========
00026 *
00027 *  UPLO    (input) CHARACTER*1
00028 *          Specifies whether the upper or lower triangular part of the
00029 *          symmetric matrix A is stored.
00030 *          = 'U':  Upper triangular
00031 *          = 'L':  Lower triangular
00032 *
00033 *  N       (input) INTEGER
00034 *          The order of the matrix A.  N >= 0.
00035 *
00036 *  KD      (input) INTEGER
00037 *          The number of super-diagonals of the matrix A if UPLO = 'U',
00038 *          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
00039 *
00040 *  AB      (input/output) COMPLEX array, dimension (LDAB,N)
00041 *          On entry, the upper or lower triangle of the symmetric band
00042 *          matrix A, stored in the first KD+1 rows of the array.  The
00043 *          j-th column of A is stored in the j-th column of the array AB
00044 *          as follows:
00045 *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
00046 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
00047 *
00048 *          On exit, if INFO = 0, the triangular factor U or L from the
00049 *          Cholesky factorization A = U**T *U or A = L*L**T of the band
00050 *          matrix A, in the same storage format as A.
00051 *
00052 *  LDAB    (input) INTEGER
00053 *          The leading dimension of the array AB.  LDAB >= KD+1.
00054 *
00055 *  S       (input) REAL array, dimension (N)
00056 *          The scale factors for A.
00057 *
00058 *  SCOND   (input) REAL
00059 *          Ratio of the smallest S(i) to the largest S(i).
00060 *
00061 *  AMAX    (input) REAL
00062 *          Absolute value of largest matrix entry.
00063 *
00064 *  EQUED   (output) CHARACTER*1
00065 *          Specifies whether or not equilibration was done.
00066 *          = 'N':  No equilibration.
00067 *          = 'Y':  Equilibration was done, i.e., A has been replaced by
00068 *                  diag(S) * A * diag(S).
00069 *
00070 *  Internal Parameters
00071 *  ===================
00072 *
00073 *  THRESH is a threshold value used to decide if scaling should be done
00074 *  based on the ratio of the scaling factors.  If SCOND < THRESH,
00075 *  scaling is done.
00076 *
00077 *  LARGE and SMALL are threshold values used to decide if scaling should
00078 *  be done based on the absolute size of the largest matrix element.
00079 *  If AMAX > LARGE or AMAX < SMALL, scaling is done.
00080 *
00081 *  =====================================================================
00082 *
00083 *     .. Parameters ..
00084       REAL               ONE, THRESH
00085       PARAMETER          ( ONE = 1.0E+0, THRESH = 0.1E+0 )
00086 *     ..
00087 *     .. Local Scalars ..
00088       INTEGER            I, J
00089       REAL               CJ, LARGE, SMALL
00090 *     ..
00091 *     .. External Functions ..
00092       LOGICAL            LSAME
00093       REAL               SLAMCH
00094       EXTERNAL           LSAME, SLAMCH
00095 *     ..
00096 *     .. Intrinsic Functions ..
00097       INTRINSIC          MAX, MIN
00098 *     ..
00099 *     .. Executable Statements ..
00100 *
00101 *     Quick return if possible
00102 *
00103       IF( N.LE.0 ) THEN
00104          EQUED = 'N'
00105          RETURN
00106       END IF
00107 *
00108 *     Initialize LARGE and SMALL.
00109 *
00110       SMALL = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Precision' )
00111       LARGE = ONE / SMALL
00112 *
00113       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
00114 *
00115 *        No equilibration
00116 *
00117          EQUED = 'N'
00118       ELSE
00119 *
00120 *        Replace A by diag(S) * A * diag(S).
00121 *
00122          IF( LSAME( UPLO, 'U' ) ) THEN
00123 *
00124 *           Upper triangle of A is stored in band format.
00125 *
00126             DO 20 J = 1, N
00127                CJ = S( J )
00128                DO 10 I = MAX( 1, J-KD ), J
00129                   AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
00130    10          CONTINUE
00131    20       CONTINUE
00132          ELSE
00133 *
00134 *           Lower triangle of A is stored.
00135 *
00136             DO 40 J = 1, N
00137                CJ = S( J )
00138                DO 30 I = J, MIN( N, J+KD )
00139                   AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
00140    30          CONTINUE
00141    40       CONTINUE
00142          END IF
00143          EQUED = 'Y'
00144       END IF
00145 *
00146       RETURN
00147 *
00148 *     End of CLAQSB
00149 *
00150       END
```