LAPACK 3.3.1 Linear Algebra PACKage

# dlaqsp.f

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```00001       SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          EQUED, UPLO
00010       INTEGER            N
00011       DOUBLE PRECISION   AMAX, SCOND
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   AP( * ), S( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  DLAQSP equilibrates a symmetric matrix A using the scaling factors
00021 *  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 *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
00036 *          On entry, the upper or lower triangle of the symmetric matrix
00037 *          A, packed columnwise in a linear array.  The j-th column of A
00038 *          is stored in the array AP as follows:
00039 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00040 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
00041 *
00042 *          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
00043 *          the same storage format as A.
00044 *
00045 *  S       (input) DOUBLE PRECISION array, dimension (N)
00046 *          The scale factors for A.
00047 *
00048 *  SCOND   (input) DOUBLE PRECISION
00049 *          Ratio of the smallest S(i) to the largest S(i).
00050 *
00051 *  AMAX    (input) DOUBLE PRECISION
00052 *          Absolute value of largest matrix entry.
00053 *
00054 *  EQUED   (output) CHARACTER*1
00055 *          Specifies whether or not equilibration was done.
00056 *          = 'N':  No equilibration.
00057 *          = 'Y':  Equilibration was done, i.e., A has been replaced by
00058 *                  diag(S) * A * diag(S).
00059 *
00060 *  Internal Parameters
00061 *  ===================
00062 *
00063 *  THRESH is a threshold value used to decide if scaling should be done
00064 *  based on the ratio of the scaling factors.  If SCOND < THRESH,
00065 *  scaling is done.
00066 *
00067 *  LARGE and SMALL are threshold values used to decide if scaling should
00068 *  be done based on the absolute size of the largest matrix element.
00069 *  If AMAX > LARGE or AMAX < SMALL, scaling is done.
00070 *
00071 *  =====================================================================
00072 *
00073 *     .. Parameters ..
00074       DOUBLE PRECISION   ONE, THRESH
00075       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
00076 *     ..
00077 *     .. Local Scalars ..
00078       INTEGER            I, J, JC
00079       DOUBLE PRECISION   CJ, LARGE, SMALL
00080 *     ..
00081 *     .. External Functions ..
00082       LOGICAL            LSAME
00083       DOUBLE PRECISION   DLAMCH
00084       EXTERNAL           LSAME, DLAMCH
00085 *     ..
00086 *     .. Executable Statements ..
00087 *
00088 *     Quick return if possible
00089 *
00090       IF( N.LE.0 ) THEN
00091          EQUED = 'N'
00092          RETURN
00093       END IF
00094 *
00095 *     Initialize LARGE and SMALL.
00096 *
00097       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
00098       LARGE = ONE / SMALL
00099 *
00100       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
00101 *
00102 *        No equilibration
00103 *
00104          EQUED = 'N'
00105       ELSE
00106 *
00107 *        Replace A by diag(S) * A * diag(S).
00108 *
00109          IF( LSAME( UPLO, 'U' ) ) THEN
00110 *
00111 *           Upper triangle of A is stored.
00112 *
00113             JC = 1
00114             DO 20 J = 1, N
00115                CJ = S( J )
00116                DO 10 I = 1, J
00117                   AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
00118    10          CONTINUE
00119                JC = JC + J
00120    20       CONTINUE
00121          ELSE
00122 *
00123 *           Lower triangle of A is stored.
00124 *
00125             JC = 1
00126             DO 40 J = 1, N
00127                CJ = S( J )
00128                DO 30 I = J, N
00129                   AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
00130    30          CONTINUE
00131                JC = JC + N - J + 1
00132    40       CONTINUE
00133          END IF
00134          EQUED = 'Y'
00135       END IF
00136 *
00137       RETURN
00138 *
00139 *     End of DLAQSP
00140 *
00141       END
```