LAPACK 3.3.1 Linear Algebra PACKage

slaqsb.f

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00066 *          = 'Y':  Equilibration was done, i.e., A has been replaced by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