You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
297 lines
8.7 KiB
297 lines
8.7 KiB
2 years ago
|
*> \brief \b CLARGV generates a vector of plane rotations with real cosines and complex sines.
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
*> \htmlonly
|
||
|
|
*> Download CLARGV + dependencies
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clargv.f">
|
||
|
|
*> [TGZ]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clargv.f">
|
||
|
|
*> [ZIP]</a>
|
||
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clargv.f">
|
||
|
|
*> [TXT]</a>
|
||
|
|
*> \endhtmlonly
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE CLARGV( N, X, INCX, Y, INCY, C, INCC )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* INTEGER INCC, INCX, INCY, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* REAL C( * )
|
||
|
|
* COMPLEX X( * ), Y( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> CLARGV generates a vector of complex plane rotations with real
|
||
|
|
*> cosines, determined by elements of the complex vectors x and y.
|
||
|
|
*> For i = 1,2,...,n
|
||
|
|
*>
|
||
|
|
*> ( c(i) s(i) ) ( x(i) ) = ( r(i) )
|
||
|
|
*> ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 )
|
||
|
|
*>
|
||
|
|
*> where c(i)**2 + ABS(s(i))**2 = 1
|
||
|
|
*>
|
||
|
|
*> The following conventions are used (these are the same as in CLARTG,
|
||
|
|
*> but differ from the BLAS1 routine CROTG):
|
||
|
|
*> If y(i)=0, then c(i)=1 and s(i)=0.
|
||
|
|
*> If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \param[in] N
|
||
|
|
*> \verbatim
|
||
|
|
*> N is INTEGER
|
||
|
|
*> The number of plane rotations to be generated.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] X
|
||
|
|
*> \verbatim
|
||
|
|
*> X is COMPLEX array, dimension (1+(N-1)*INCX)
|
||
|
|
*> On entry, the vector x.
|
||
|
|
*> On exit, x(i) is overwritten by r(i), for i = 1,...,n.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] INCX
|
||
|
|
*> \verbatim
|
||
|
|
*> INCX is INTEGER
|
||
|
|
*> The increment between elements of X. INCX > 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] Y
|
||
|
|
*> \verbatim
|
||
|
|
*> Y is COMPLEX array, dimension (1+(N-1)*INCY)
|
||
|
|
*> On entry, the vector y.
|
||
|
|
*> On exit, the sines of the plane rotations.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] INCY
|
||
|
|
*> \verbatim
|
||
|
|
*> INCY is INTEGER
|
||
|
|
*> The increment between elements of Y. INCY > 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] C
|
||
|
|
*> \verbatim
|
||
|
|
*> C is REAL array, dimension (1+(N-1)*INCC)
|
||
|
|
*> The cosines of the plane rotations.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] INCC
|
||
|
|
*> \verbatim
|
||
|
|
*> INCC is INTEGER
|
||
|
|
*> The increment between elements of C. INCC > 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup complexOTHERauxiliary
|
||
|
|
*
|
||
|
|
*> \par Further Details:
|
||
|
|
* =====================
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> 6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
|
||
|
|
*>
|
||
|
|
*> This version has a few statements commented out for thread safety
|
||
|
|
*> (machine parameters are computed on each entry). 10 feb 03, SJH.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE CLARGV( N, X, INCX, Y, INCY, C, INCC )
|
||
|
|
*
|
||
|
|
* -- LAPACK auxiliary routine --
|
||
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
INTEGER INCC, INCX, INCY, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
REAL C( * )
|
||
|
|
COMPLEX X( * ), Y( * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
REAL TWO, ONE, ZERO
|
||
|
|
PARAMETER ( TWO = 2.0E+0, ONE = 1.0E+0, ZERO = 0.0E+0 )
|
||
|
|
COMPLEX CZERO
|
||
|
|
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
* LOGICAL FIRST
|
||
|
|
INTEGER COUNT, I, IC, IX, IY, J
|
||
|
|
REAL CS, D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
|
||
|
|
$ SAFMN2, SAFMX2, SCALE
|
||
|
|
COMPLEX F, FF, FS, G, GS, R, SN
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
REAL SLAMCH, SLAPY2
|
||
|
|
EXTERNAL SLAMCH, SLAPY2
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC ABS, AIMAG, CMPLX, CONJG, INT, LOG, MAX, REAL,
|
||
|
|
$ SQRT
|
||
|
|
* ..
|
||
|
|
* .. Statement Functions ..
|
||
|
|
REAL ABS1, ABSSQ
|
||
|
|
* ..
|
||
|
|
* .. Save statement ..
|
||
|
|
* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2
|
||
|
|
* ..
|
||
|
|
* .. Data statements ..
|
||
|
|
* DATA FIRST / .TRUE. /
|
||
|
|
* ..
|
||
|
|
* .. Statement Function definitions ..
|
||
|
|
ABS1( FF ) = MAX( ABS( REAL( FF ) ), ABS( AIMAG( FF ) ) )
|
||
|
|
ABSSQ( FF ) = REAL( FF )**2 + AIMAG( FF )**2
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
* IF( FIRST ) THEN
|
||
|
|
* FIRST = .FALSE.
|
||
|
|
SAFMIN = SLAMCH( 'S' )
|
||
|
|
EPS = SLAMCH( 'E' )
|
||
|
|
SAFMN2 = SLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
|
||
|
|
$ LOG( SLAMCH( 'B' ) ) / TWO )
|
||
|
|
SAFMX2 = ONE / SAFMN2
|
||
|
|
* END IF
|
||
|
|
IX = 1
|
||
|
|
IY = 1
|
||
|
|
IC = 1
|
||
|
|
DO 60 I = 1, N
|
||
|
|
F = X( IX )
|
||
|
|
G = Y( IY )
|
||
|
|
*
|
||
|
|
* Use identical algorithm as in CLARTG
|
||
|
|
*
|
||
|
|
SCALE = MAX( ABS1( F ), ABS1( G ) )
|
||
|
|
FS = F
|
||
|
|
GS = G
|
||
|
|
COUNT = 0
|
||
|
|
IF( SCALE.GE.SAFMX2 ) THEN
|
||
|
|
10 CONTINUE
|
||
|
|
COUNT = COUNT + 1
|
||
|
|
FS = FS*SAFMN2
|
||
|
|
GS = GS*SAFMN2
|
||
|
|
SCALE = SCALE*SAFMN2
|
||
|
|
IF( SCALE.GE.SAFMX2 .AND. COUNT .LT. 20 )
|
||
|
|
$ GO TO 10
|
||
|
|
ELSE IF( SCALE.LE.SAFMN2 ) THEN
|
||
|
|
IF( G.EQ.CZERO ) THEN
|
||
|
|
CS = ONE
|
||
|
|
SN = CZERO
|
||
|
|
R = F
|
||
|
|
GO TO 50
|
||
|
|
END IF
|
||
|
|
20 CONTINUE
|
||
|
|
COUNT = COUNT - 1
|
||
|
|
FS = FS*SAFMX2
|
||
|
|
GS = GS*SAFMX2
|
||
|
|
SCALE = SCALE*SAFMX2
|
||
|
|
IF( SCALE.LE.SAFMN2 )
|
||
|
|
$ GO TO 20
|
||
|
|
END IF
|
||
|
|
F2 = ABSSQ( FS )
|
||
|
|
G2 = ABSSQ( GS )
|
||
|
|
IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN
|
||
|
|
*
|
||
|
|
* This is a rare case: F is very small.
|
||
|
|
*
|
||
|
|
IF( F.EQ.CZERO ) THEN
|
||
|
|
CS = ZERO
|
||
|
|
R = SLAPY2( REAL( G ), AIMAG( G ) )
|
||
|
|
* Do complex/real division explicitly with two real
|
||
|
|
* divisions
|
||
|
|
D = SLAPY2( REAL( GS ), AIMAG( GS ) )
|
||
|
|
SN = CMPLX( REAL( GS ) / D, -AIMAG( GS ) / D )
|
||
|
|
GO TO 50
|
||
|
|
END IF
|
||
|
|
F2S = SLAPY2( REAL( FS ), AIMAG( FS ) )
|
||
|
|
* G2 and G2S are accurate
|
||
|
|
* G2 is at least SAFMIN, and G2S is at least SAFMN2
|
||
|
|
G2S = SQRT( G2 )
|
||
|
|
* Error in CS from underflow in F2S is at most
|
||
|
|
* UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
|
||
|
|
* If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
|
||
|
|
* and so CS .lt. sqrt(SAFMIN)
|
||
|
|
* If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
|
||
|
|
* and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
|
||
|
|
* Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
|
||
|
|
CS = F2S / G2S
|
||
|
|
* Make sure abs(FF) = 1
|
||
|
|
* Do complex/real division explicitly with 2 real divisions
|
||
|
|
IF( ABS1( F ).GT.ONE ) THEN
|
||
|
|
D = SLAPY2( REAL( F ), AIMAG( F ) )
|
||
|
|
FF = CMPLX( REAL( F ) / D, AIMAG( F ) / D )
|
||
|
|
ELSE
|
||
|
|
DR = SAFMX2*REAL( F )
|
||
|
|
DI = SAFMX2*AIMAG( F )
|
||
|
|
D = SLAPY2( DR, DI )
|
||
|
|
FF = CMPLX( DR / D, DI / D )
|
||
|
|
END IF
|
||
|
|
SN = FF*CMPLX( REAL( GS ) / G2S, -AIMAG( GS ) / G2S )
|
||
|
|
R = CS*F + SN*G
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* This is the most common case.
|
||
|
|
* Neither F2 nor F2/G2 are less than SAFMIN
|
||
|
|
* F2S cannot overflow, and it is accurate
|
||
|
|
*
|
||
|
|
F2S = SQRT( ONE+G2 / F2 )
|
||
|
|
* Do the F2S(real)*FS(complex) multiply with two real
|
||
|
|
* multiplies
|
||
|
|
R = CMPLX( F2S*REAL( FS ), F2S*AIMAG( FS ) )
|
||
|
|
CS = ONE / F2S
|
||
|
|
D = F2 + G2
|
||
|
|
* Do complex/real division explicitly with two real divisions
|
||
|
|
SN = CMPLX( REAL( R ) / D, AIMAG( R ) / D )
|
||
|
|
SN = SN*CONJG( GS )
|
||
|
|
IF( COUNT.NE.0 ) THEN
|
||
|
|
IF( COUNT.GT.0 ) THEN
|
||
|
|
DO 30 J = 1, COUNT
|
||
|
|
R = R*SAFMX2
|
||
|
|
30 CONTINUE
|
||
|
|
ELSE
|
||
|
|
DO 40 J = 1, -COUNT
|
||
|
|
R = R*SAFMN2
|
||
|
|
40 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
50 CONTINUE
|
||
|
|
C( IC ) = CS
|
||
|
|
Y( IY ) = SN
|
||
|
|
X( IX ) = R
|
||
|
|
IC = IC + INCC
|
||
|
|
IY = IY + INCY
|
||
|
|
IX = IX + INCX
|
||
|
|
60 CONTINUE
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of CLARGV
|
||
|
|
*
|
||
|
|
END
|