![]() |
LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
|
00001 *> \brief \b CLARGV 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CLARGV + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clargv.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clargv.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clargv.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CLARGV( N, X, INCX, Y, INCY, C, INCC ) 00022 * 00023 * .. Scalar Arguments .. 00024 * INTEGER INCC, INCX, INCY, N 00025 * .. 00026 * .. Array Arguments .. 00027 * REAL C( * ) 00028 * COMPLEX X( * ), Y( * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> CLARGV generates a vector of complex plane rotations with real 00038 *> cosines, determined by elements of the complex vectors x and y. 00039 *> For i = 1,2,...,n 00040 *> 00041 *> ( c(i) s(i) ) ( x(i) ) = ( r(i) ) 00042 *> ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 ) 00043 *> 00044 *> where c(i)**2 + ABS(s(i))**2 = 1 00045 *> 00046 *> The following conventions are used (these are the same as in CLARTG, 00047 *> but differ from the BLAS1 routine CROTG): 00048 *> If y(i)=0, then c(i)=1 and s(i)=0. 00049 *> If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real. 00050 *> \endverbatim 00051 * 00052 * Arguments: 00053 * ========== 00054 * 00055 *> \param[in] N 00056 *> \verbatim 00057 *> N is INTEGER 00058 *> The number of plane rotations to be generated. 00059 *> \endverbatim 00060 *> 00061 *> \param[in,out] X 00062 *> \verbatim 00063 *> X is COMPLEX array, dimension (1+(N-1)*INCX) 00064 *> On entry, the vector x. 00065 *> On exit, x(i) is overwritten by r(i), for i = 1,...,n. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] INCX 00069 *> \verbatim 00070 *> INCX is INTEGER 00071 *> The increment between elements of X. INCX > 0. 00072 *> \endverbatim 00073 *> 00074 *> \param[in,out] Y 00075 *> \verbatim 00076 *> Y is COMPLEX array, dimension (1+(N-1)*INCY) 00077 *> On entry, the vector y. 00078 *> On exit, the sines of the plane rotations. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] INCY 00082 *> \verbatim 00083 *> INCY is INTEGER 00084 *> The increment between elements of Y. INCY > 0. 00085 *> \endverbatim 00086 *> 00087 *> \param[out] C 00088 *> \verbatim 00089 *> C is REAL array, dimension (1+(N-1)*INCC) 00090 *> The cosines of the plane rotations. 00091 *> \endverbatim 00092 *> 00093 *> \param[in] INCC 00094 *> \verbatim 00095 *> INCC is INTEGER 00096 *> The increment between elements of C. INCC > 0. 00097 *> \endverbatim 00098 * 00099 * Authors: 00100 * ======== 00101 * 00102 *> \author Univ. of Tennessee 00103 *> \author Univ. of California Berkeley 00104 *> \author Univ. of Colorado Denver 00105 *> \author NAG Ltd. 00106 * 00107 *> \date November 2011 00108 * 00109 *> \ingroup complexOTHERauxiliary 00110 * 00111 *> \par Further Details: 00112 * ===================== 00113 *> 00114 *> \verbatim 00115 *> 00116 *> 6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel 00117 *> 00118 *> This version has a few statements commented out for thread safety 00119 *> (machine parameters are computed on each entry). 10 feb 03, SJH. 00120 *> \endverbatim 00121 *> 00122 * ===================================================================== 00123 SUBROUTINE CLARGV( N, X, INCX, Y, INCY, C, INCC ) 00124 * 00125 * -- LAPACK auxiliary routine (version 3.4.0) -- 00126 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00128 * November 2011 00129 * 00130 * .. Scalar Arguments .. 00131 INTEGER INCC, INCX, INCY, N 00132 * .. 00133 * .. Array Arguments .. 00134 REAL C( * ) 00135 COMPLEX X( * ), Y( * ) 00136 * .. 00137 * 00138 * ===================================================================== 00139 * 00140 * .. Parameters .. 00141 REAL TWO, ONE, ZERO 00142 PARAMETER ( TWO = 2.0E+0, ONE = 1.0E+0, ZERO = 0.0E+0 ) 00143 COMPLEX CZERO 00144 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) ) 00145 * .. 00146 * .. Local Scalars .. 00147 * LOGICAL FIRST 00148 INTEGER COUNT, I, IC, IX, IY, J 00149 REAL CS, D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN, 00150 $ SAFMN2, SAFMX2, SCALE 00151 COMPLEX F, FF, FS, G, GS, R, SN 00152 * .. 00153 * .. External Functions .. 00154 REAL SLAMCH, SLAPY2 00155 EXTERNAL SLAMCH, SLAPY2 00156 * .. 00157 * .. Intrinsic Functions .. 00158 INTRINSIC ABS, AIMAG, CMPLX, CONJG, INT, LOG, MAX, REAL, 00159 $ SQRT 00160 * .. 00161 * .. Statement Functions .. 00162 REAL ABS1, ABSSQ 00163 * .. 00164 * .. Save statement .. 00165 * SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 00166 * .. 00167 * .. Data statements .. 00168 * DATA FIRST / .TRUE. / 00169 * .. 00170 * .. Statement Function definitions .. 00171 ABS1( FF ) = MAX( ABS( REAL( FF ) ), ABS( AIMAG( FF ) ) ) 00172 ABSSQ( FF ) = REAL( FF )**2 + AIMAG( FF )**2 00173 * .. 00174 * .. Executable Statements .. 00175 * 00176 * IF( FIRST ) THEN 00177 * FIRST = .FALSE. 00178 SAFMIN = SLAMCH( 'S' ) 00179 EPS = SLAMCH( 'E' ) 00180 SAFMN2 = SLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / 00181 $ LOG( SLAMCH( 'B' ) ) / TWO ) 00182 SAFMX2 = ONE / SAFMN2 00183 * END IF 00184 IX = 1 00185 IY = 1 00186 IC = 1 00187 DO 60 I = 1, N 00188 F = X( IX ) 00189 G = Y( IY ) 00190 * 00191 * Use identical algorithm as in CLARTG 00192 * 00193 SCALE = MAX( ABS1( F ), ABS1( G ) ) 00194 FS = F 00195 GS = G 00196 COUNT = 0 00197 IF( SCALE.GE.SAFMX2 ) THEN 00198 10 CONTINUE 00199 COUNT = COUNT + 1 00200 FS = FS*SAFMN2 00201 GS = GS*SAFMN2 00202 SCALE = SCALE*SAFMN2 00203 IF( SCALE.GE.SAFMX2 ) 00204 $ GO TO 10 00205 ELSE IF( SCALE.LE.SAFMN2 ) THEN 00206 IF( G.EQ.CZERO ) THEN 00207 CS = ONE 00208 SN = CZERO 00209 R = F 00210 GO TO 50 00211 END IF 00212 20 CONTINUE 00213 COUNT = COUNT - 1 00214 FS = FS*SAFMX2 00215 GS = GS*SAFMX2 00216 SCALE = SCALE*SAFMX2 00217 IF( SCALE.LE.SAFMN2 ) 00218 $ GO TO 20 00219 END IF 00220 F2 = ABSSQ( FS ) 00221 G2 = ABSSQ( GS ) 00222 IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN 00223 * 00224 * This is a rare case: F is very small. 00225 * 00226 IF( F.EQ.CZERO ) THEN 00227 CS = ZERO 00228 R = SLAPY2( REAL( G ), AIMAG( G ) ) 00229 * Do complex/real division explicitly with two real 00230 * divisions 00231 D = SLAPY2( REAL( GS ), AIMAG( GS ) ) 00232 SN = CMPLX( REAL( GS ) / D, -AIMAG( GS ) / D ) 00233 GO TO 50 00234 END IF 00235 F2S = SLAPY2( REAL( FS ), AIMAG( FS ) ) 00236 * G2 and G2S are accurate 00237 * G2 is at least SAFMIN, and G2S is at least SAFMN2 00238 G2S = SQRT( G2 ) 00239 * Error in CS from underflow in F2S is at most 00240 * UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS 00241 * If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN, 00242 * and so CS .lt. sqrt(SAFMIN) 00243 * If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN 00244 * and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS) 00245 * Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S 00246 CS = F2S / G2S 00247 * Make sure abs(FF) = 1 00248 * Do complex/real division explicitly with 2 real divisions 00249 IF( ABS1( F ).GT.ONE ) THEN 00250 D = SLAPY2( REAL( F ), AIMAG( F ) ) 00251 FF = CMPLX( REAL( F ) / D, AIMAG( F ) / D ) 00252 ELSE 00253 DR = SAFMX2*REAL( F ) 00254 DI = SAFMX2*AIMAG( F ) 00255 D = SLAPY2( DR, DI ) 00256 FF = CMPLX( DR / D, DI / D ) 00257 END IF 00258 SN = FF*CMPLX( REAL( GS ) / G2S, -AIMAG( GS ) / G2S ) 00259 R = CS*F + SN*G 00260 ELSE 00261 * 00262 * This is the most common case. 00263 * Neither F2 nor F2/G2 are less than SAFMIN 00264 * F2S cannot overflow, and it is accurate 00265 * 00266 F2S = SQRT( ONE+G2 / F2 ) 00267 * Do the F2S(real)*FS(complex) multiply with two real 00268 * multiplies 00269 R = CMPLX( F2S*REAL( FS ), F2S*AIMAG( FS ) ) 00270 CS = ONE / F2S 00271 D = F2 + G2 00272 * Do complex/real division explicitly with two real divisions 00273 SN = CMPLX( REAL( R ) / D, AIMAG( R ) / D ) 00274 SN = SN*CONJG( GS ) 00275 IF( COUNT.NE.0 ) THEN 00276 IF( COUNT.GT.0 ) THEN 00277 DO 30 J = 1, COUNT 00278 R = R*SAFMX2 00279 30 CONTINUE 00280 ELSE 00281 DO 40 J = 1, -COUNT 00282 R = R*SAFMN2 00283 40 CONTINUE 00284 END IF 00285 END IF 00286 END IF 00287 50 CONTINUE 00288 C( IC ) = CS 00289 Y( IY ) = SN 00290 X( IX ) = R 00291 IC = IC + INCC 00292 IY = IY + INCY 00293 IX = IX + INCX 00294 60 CONTINUE 00295 RETURN 00296 * 00297 * End of CLARGV 00298 * 00299 END