SUBROUTINE CLARGV( N, X, INCX, Y, INCY, C, INCC ) * * -- LAPACK auxiliary routine (version 3.0) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * June 30, 1999 * 9-15-00: New version continuous in r(i) (eca) * 12-4-00: Give D the sign of Re(f) for |g| > |f| (eca) * * .. Scalar Arguments .. INTEGER INCC, INCX, INCY, N * .. * .. Array Arguments .. REAL C( * ) COMPLEX X( * ), Y( * ) * .. * * Purpose * ======= * * 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. * * Arguments * ========= * * N (input) INTEGER * The number of plane rotations to be generated. * * X (input/output) 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. * * INCX (input) INTEGER * The increment between elements of X. INCX > 0. * * Y (input/output) COMPLEX array, dimension (1+(N-1)*INCY) * On entry, the vector y. * On exit, the sines of the plane rotations. * * INCY (input) INTEGER * The increment between elements of Y. INCY > 0. * * C (output) REAL array, dimension (1+(N-1)*INCC) * The cosines of the plane rotations. * * INCC (input) INTEGER * The increment between elements of C. INCC > 0. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) COMPLEX CZERO PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, IC, IX, IY REAL CS, D, F1, F2, G1, G2 COMPLEX F, FS, G, GS, R, SN, Z * .. * .. Intrinsic Functions .. INTRINSIC ABS, AIMAG, CONJG, MAX, REAL, SQRT * .. * .. Statement Functions .. REAL ABS1, ABSSQ * .. * .. Statement Function definitions .. ABS1( Z ) = MAX( ABS( REAL( Z ) ), ABS( AIMAG( Z ) ) ) ABSSQ( Z ) = REAL( Z )**2 + AIMAG( Z )**2 * .. * .. Executable Statements .. * IX = 1 IY = 1 IC = 1 DO 60 I = 1, N F = X( IX ) G = Y( IY ) * * Use identical algorithm as in CLARTG * IF( G.EQ.CZERO ) THEN C( IC ) = SIGN( ONE, REAL(F) ) X( IX ) = F*C( IC ) ELSE IF( F.EQ.CZERO ) THEN C( IC ) = ZERO Y( IY ) = CONJG(G) / ABS( G ) X( IX ) = ABS( G ) ELSE F1 = ABS1(F) G1 = ABS1(G) IF( F1.GE.G1 ) THEN FS = F / F1 F2 = ABSSQ( FS ) GS = G / F1 G2 = ABSSQ( GS ) D = SIGN( SQRT( ONE + G2 / F2 ), REAL(F) ) CS = ONE / D C( IC ) = CS Y( IY ) = CONJG( GS )*FS*( CS / F2 ) X( IX ) = F*D ELSE FS = F / G1 F2 = ABSSQ( FS ) GS = G / G1 G2 = ABSSQ( GS ) D = SIGN( G1*SQRT( F2 + G2 ), REAL(F) ) F1 = ABS( F ) FS = F / F1 C( IC ) = F1 / D Y( IY ) = ( CONJG( G ) / D )*FS X( IX ) = FS*D END IF END IF IC = IC + INCC IX = IX + INCX IY = IY + INCY 60 CONTINUE RETURN * * End of CLARGV * END