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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DLAQSP 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DLAQSP + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsp.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsp.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsp.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER EQUED, UPLO 00025 * INTEGER N 00026 * DOUBLE PRECISION AMAX, SCOND 00027 * .. 00028 * .. Array Arguments .. 00029 * DOUBLE PRECISION AP( * ), S( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> DLAQSP equilibrates a symmetric matrix A using the scaling factors 00039 *> in the vector S. 00040 *> \endverbatim 00041 * 00042 * Arguments: 00043 * ========== 00044 * 00045 *> \param[in] UPLO 00046 *> \verbatim 00047 *> UPLO is CHARACTER*1 00048 *> Specifies whether the upper or lower triangular part of the 00049 *> symmetric matrix A is stored. 00050 *> = 'U': Upper triangular 00051 *> = 'L': Lower triangular 00052 *> \endverbatim 00053 *> 00054 *> \param[in] N 00055 *> \verbatim 00056 *> N is INTEGER 00057 *> The order of the matrix A. N >= 0. 00058 *> \endverbatim 00059 *> 00060 *> \param[in,out] AP 00061 *> \verbatim 00062 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00063 *> On entry, the upper or lower triangle of the symmetric matrix 00064 *> A, packed columnwise in a linear array. The j-th column of A 00065 *> is stored in the array AP as follows: 00066 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00067 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00068 *> 00069 *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in 00070 *> the same storage format as A. 00071 *> \endverbatim 00072 *> 00073 *> \param[in] S 00074 *> \verbatim 00075 *> S is DOUBLE PRECISION array, dimension (N) 00076 *> The scale factors for A. 00077 *> \endverbatim 00078 *> 00079 *> \param[in] SCOND 00080 *> \verbatim 00081 *> SCOND is DOUBLE PRECISION 00082 *> Ratio of the smallest S(i) to the largest S(i). 00083 *> \endverbatim 00084 *> 00085 *> \param[in] AMAX 00086 *> \verbatim 00087 *> AMAX is DOUBLE PRECISION 00088 *> Absolute value of largest matrix entry. 00089 *> \endverbatim 00090 *> 00091 *> \param[out] EQUED 00092 *> \verbatim 00093 *> EQUED is CHARACTER*1 00094 *> Specifies whether or not equilibration was done. 00095 *> = 'N': No equilibration. 00096 *> = 'Y': Equilibration was done, i.e., A has been replaced by 00097 *> diag(S) * A * diag(S). 00098 *> \endverbatim 00099 * 00100 *> \par Internal Parameters: 00101 * ========================= 00102 *> 00103 *> \verbatim 00104 *> THRESH is a threshold value used to decide if scaling should be done 00105 *> based on the ratio of the scaling factors. If SCOND < THRESH, 00106 *> scaling is done. 00107 *> 00108 *> LARGE and SMALL are threshold values used to decide if scaling should 00109 *> be done based on the absolute size of the largest matrix element. 00110 *> If AMAX > LARGE or AMAX < SMALL, scaling is done. 00111 *> \endverbatim 00112 * 00113 * Authors: 00114 * ======== 00115 * 00116 *> \author Univ. of Tennessee 00117 *> \author Univ. of California Berkeley 00118 *> \author Univ. of Colorado Denver 00119 *> \author NAG Ltd. 00120 * 00121 *> \date November 2011 00122 * 00123 *> \ingroup doubleOTHERauxiliary 00124 * 00125 * ===================================================================== 00126 SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) 00127 * 00128 * -- LAPACK auxiliary routine (version 3.4.0) -- 00129 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00131 * November 2011 00132 * 00133 * .. Scalar Arguments .. 00134 CHARACTER EQUED, UPLO 00135 INTEGER N 00136 DOUBLE PRECISION AMAX, SCOND 00137 * .. 00138 * .. Array Arguments .. 00139 DOUBLE PRECISION AP( * ), S( * ) 00140 * .. 00141 * 00142 * ===================================================================== 00143 * 00144 * .. Parameters .. 00145 DOUBLE PRECISION ONE, THRESH 00146 PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 ) 00147 * .. 00148 * .. Local Scalars .. 00149 INTEGER I, J, JC 00150 DOUBLE PRECISION CJ, LARGE, SMALL 00151 * .. 00152 * .. External Functions .. 00153 LOGICAL LSAME 00154 DOUBLE PRECISION DLAMCH 00155 EXTERNAL LSAME, DLAMCH 00156 * .. 00157 * .. Executable Statements .. 00158 * 00159 * Quick return if possible 00160 * 00161 IF( N.LE.0 ) THEN 00162 EQUED = 'N' 00163 RETURN 00164 END IF 00165 * 00166 * Initialize LARGE and SMALL. 00167 * 00168 SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) 00169 LARGE = ONE / SMALL 00170 * 00171 IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN 00172 * 00173 * No equilibration 00174 * 00175 EQUED = 'N' 00176 ELSE 00177 * 00178 * Replace A by diag(S) * A * diag(S). 00179 * 00180 IF( LSAME( UPLO, 'U' ) ) THEN 00181 * 00182 * Upper triangle of A is stored. 00183 * 00184 JC = 1 00185 DO 20 J = 1, N 00186 CJ = S( J ) 00187 DO 10 I = 1, J 00188 AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 ) 00189 10 CONTINUE 00190 JC = JC + J 00191 20 CONTINUE 00192 ELSE 00193 * 00194 * Lower triangle of A is stored. 00195 * 00196 JC = 1 00197 DO 40 J = 1, N 00198 CJ = S( J ) 00199 DO 30 I = J, N 00200 AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J ) 00201 30 CONTINUE 00202 JC = JC + N - J + 1 00203 40 CONTINUE 00204 END IF 00205 EQUED = 'Y' 00206 END IF 00207 * 00208 RETURN 00209 * 00210 * End of DLAQSP 00211 * 00212 END