SUBROUTINE DLARTG( F, G, CS, SN, R ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. DOUBLE PRECISION CS, F, G, R, SN * .. * * Purpose * ======= * * DLARTG generate a plane rotation so that * * [ CS SN ] . [ F ] = [ R ] where CS**2 + SN**2 = 1. * [ -SN CS ] [ G ] [ 0 ] * * This is a slower, more accurate version of the BLAS1 routine DROTG, * with the following other differences: * F and G are unchanged on return. * If G=0, then CS=1 and SN=0. * If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any * floating point operations (saves work in DBDSQR when * there are zeros on the diagonal). * * If F exceeds G in magnitude, CS will be positive. * * Arguments * ========= * * F (input) DOUBLE PRECISION * The first component of vector to be rotated. * * G (input) DOUBLE PRECISION * The second component of vector to be rotated. * * CS (output) DOUBLE PRECISION * The cosine of the rotation. * * SN (output) DOUBLE PRECISION * The sine of the rotation. * * R (output) DOUBLE PRECISION * The nonzero component of the rotated vector. * * This version has a few statements commented out for thread safety * (machine parameters are computed on each entry). 10 feb 03, SJH. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0D0 ) * .. * .. Local Scalars .. * LOGICAL FIRST INTEGER COUNT, I DOUBLE PRECISION EPS, F1, G1, SAFMIN, SAFMN2, SAFMX2, SCALE * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, INT, LOG, MAX, SQRT * .. * .. Save statement .. * SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 * .. * .. Data statements .. * DATA FIRST / .TRUE. / * .. * .. Executable Statements .. * * IF( FIRST ) THEN SAFMIN = DLAMCH( 'S' ) EPS = DLAMCH( 'E' ) SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / $ LOG( DLAMCH( 'B' ) ) / TWO ) SAFMX2 = ONE / SAFMN2 * FIRST = .FALSE. * END IF IF( G.EQ.ZERO ) THEN CS = ONE SN = ZERO R = F ELSE IF( F.EQ.ZERO ) THEN CS = ZERO SN = ONE R = G ELSE F1 = F G1 = G SCALE = MAX( ABS( F1 ), ABS( G1 ) ) IF( SCALE.GE.SAFMX2 ) THEN COUNT = 0 10 CONTINUE COUNT = COUNT + 1 F1 = F1*SAFMN2 G1 = G1*SAFMN2 SCALE = MAX( ABS( F1 ), ABS( G1 ) ) IF( SCALE.GE.SAFMX2 ) $ GO TO 10 R = SQRT( F1**2+G1**2 ) CS = F1 / R SN = G1 / R DO 20 I = 1, COUNT R = R*SAFMX2 20 CONTINUE ELSE IF( SCALE.LE.SAFMN2 ) THEN COUNT = 0 30 CONTINUE COUNT = COUNT + 1 F1 = F1*SAFMX2 G1 = G1*SAFMX2 SCALE = MAX( ABS( F1 ), ABS( G1 ) ) IF( SCALE.LE.SAFMN2 ) $ GO TO 30 R = SQRT( F1**2+G1**2 ) CS = F1 / R SN = G1 / R DO 40 I = 1, COUNT R = R*SAFMN2 40 CONTINUE ELSE R = SQRT( F1**2+G1**2 ) CS = F1 / R SN = G1 / R END IF IF( ABS( F ).GT.ABS( G ) .AND. CS.LT.ZERO ) THEN CS = -CS SN = -SN R = -R END IF END IF RETURN * * End of DLARTG * END