LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clargv.f
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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 
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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
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