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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLAQSP 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLAQSP + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqsp.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqsp.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqsp.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZLAQSP( 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 S( * ) 00030 * COMPLEX*16 AP( * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> ZLAQSP equilibrates a symmetric matrix A using the scaling factors 00040 *> in the vector S. 00041 *> \endverbatim 00042 * 00043 * Arguments: 00044 * ========== 00045 * 00046 *> \param[in] UPLO 00047 *> \verbatim 00048 *> UPLO is CHARACTER*1 00049 *> Specifies whether the upper or lower triangular part of the 00050 *> symmetric matrix A is stored. 00051 *> = 'U': Upper triangular 00052 *> = 'L': Lower triangular 00053 *> \endverbatim 00054 *> 00055 *> \param[in] N 00056 *> \verbatim 00057 *> N is INTEGER 00058 *> The order of the matrix A. N >= 0. 00059 *> \endverbatim 00060 *> 00061 *> \param[in,out] AP 00062 *> \verbatim 00063 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 00064 *> On entry, the upper or lower triangle of the symmetric matrix 00065 *> A, packed columnwise in a linear array. The j-th column of A 00066 *> is stored in the array AP as follows: 00067 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00068 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00069 *> 00070 *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in 00071 *> the same storage format as A. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] S 00075 *> \verbatim 00076 *> S is DOUBLE PRECISION array, dimension (N) 00077 *> The scale factors for A. 00078 *> \endverbatim 00079 *> 00080 *> \param[in] SCOND 00081 *> \verbatim 00082 *> SCOND is DOUBLE PRECISION 00083 *> Ratio of the smallest S(i) to the largest S(i). 00084 *> \endverbatim 00085 *> 00086 *> \param[in] AMAX 00087 *> \verbatim 00088 *> AMAX is DOUBLE PRECISION 00089 *> Absolute value of largest matrix entry. 00090 *> \endverbatim 00091 *> 00092 *> \param[out] EQUED 00093 *> \verbatim 00094 *> EQUED is CHARACTER*1 00095 *> Specifies whether or not equilibration was done. 00096 *> = 'N': No equilibration. 00097 *> = 'Y': Equilibration was done, i.e., A has been replaced by 00098 *> diag(S) * A * diag(S). 00099 *> \endverbatim 00100 * 00101 *> \par Internal Parameters: 00102 * ========================= 00103 *> 00104 *> \verbatim 00105 *> THRESH is a threshold value used to decide if scaling should be done 00106 *> based on the ratio of the scaling factors. If SCOND < THRESH, 00107 *> scaling is done. 00108 *> 00109 *> LARGE and SMALL are threshold values used to decide if scaling should 00110 *> be done based on the absolute size of the largest matrix element. 00111 *> If AMAX > LARGE or AMAX < SMALL, scaling is done. 00112 *> \endverbatim 00113 * 00114 * Authors: 00115 * ======== 00116 * 00117 *> \author Univ. of Tennessee 00118 *> \author Univ. of California Berkeley 00119 *> \author Univ. of Colorado Denver 00120 *> \author NAG Ltd. 00121 * 00122 *> \date November 2011 00123 * 00124 *> \ingroup complex16OTHERauxiliary 00125 * 00126 * ===================================================================== 00127 SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED ) 00128 * 00129 * -- LAPACK auxiliary routine (version 3.4.0) -- 00130 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00132 * November 2011 00133 * 00134 * .. Scalar Arguments .. 00135 CHARACTER EQUED, UPLO 00136 INTEGER N 00137 DOUBLE PRECISION AMAX, SCOND 00138 * .. 00139 * .. Array Arguments .. 00140 DOUBLE PRECISION S( * ) 00141 COMPLEX*16 AP( * ) 00142 * .. 00143 * 00144 * ===================================================================== 00145 * 00146 * .. Parameters .. 00147 DOUBLE PRECISION ONE, THRESH 00148 PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 ) 00149 * .. 00150 * .. Local Scalars .. 00151 INTEGER I, J, JC 00152 DOUBLE PRECISION CJ, LARGE, SMALL 00153 * .. 00154 * .. External Functions .. 00155 LOGICAL LSAME 00156 DOUBLE PRECISION DLAMCH 00157 EXTERNAL LSAME, DLAMCH 00158 * .. 00159 * .. Executable Statements .. 00160 * 00161 * Quick return if possible 00162 * 00163 IF( N.LE.0 ) THEN 00164 EQUED = 'N' 00165 RETURN 00166 END IF 00167 * 00168 * Initialize LARGE and SMALL. 00169 * 00170 SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) 00171 LARGE = ONE / SMALL 00172 * 00173 IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN 00174 * 00175 * No equilibration 00176 * 00177 EQUED = 'N' 00178 ELSE 00179 * 00180 * Replace A by diag(S) * A * diag(S). 00181 * 00182 IF( LSAME( UPLO, 'U' ) ) THEN 00183 * 00184 * Upper triangle of A is stored. 00185 * 00186 JC = 1 00187 DO 20 J = 1, N 00188 CJ = S( J ) 00189 DO 10 I = 1, J 00190 AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 ) 00191 10 CONTINUE 00192 JC = JC + J 00193 20 CONTINUE 00194 ELSE 00195 * 00196 * Lower triangle of A is stored. 00197 * 00198 JC = 1 00199 DO 40 J = 1, N 00200 CJ = S( J ) 00201 DO 30 I = J, N 00202 AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J ) 00203 30 CONTINUE 00204 JC = JC + N - J + 1 00205 40 CONTINUE 00206 END IF 00207 EQUED = 'Y' 00208 END IF 00209 * 00210 RETURN 00211 * 00212 * End of ZLAQSP 00213 * 00214 END