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*DECK SROTG
SUBROUTINE SROTG (SA, SB, SC, SS)
C***BEGIN PROLOGUE SROTG
C***PURPOSE Construct a plane Givens rotation.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B10
C***TYPE SINGLE PRECISION (SROTG-S, DROTG-D, CROTG-C)
C***KEYWORDS BLAS, GIVENS ROTATION, GIVENS TRANSFORMATION,
C LINEAR ALGEBRA, VECTOR
C***AUTHOR Lawson, C. L., (JPL)
C Hanson, R. J., (SNLA)
C Kincaid, D. R., (U. of Texas)
C Krogh, F. T., (JPL)
C***DESCRIPTION
C
C B L A S Subprogram
C Description of Parameters
C
C --Input--
C SA single precision scalar
C SB single precision scalar
C
C --Output--
C SA single precision result R
C SB single precision result Z
C SC single precision result
C SS single precision result
C
C Construct the Givens transformation
C
C ( SC SS )
C G = ( ) , SC**2 + SS**2 = 1 ,
C (-SS SC )
C
C which zeros the second entry of the 2-vector (SA,SB)**T.
C
C The quantity R = (+/-)SQRT(SA**2 + SB**2) overwrites SA in
C storage. The value of SB is overwritten by a value Z which
C allows SC and SS to be recovered by the following algorithm:
C
C If Z=1 set SC=0.0 and SS=1.0
C If ABS(Z) .LT. 1 set SC=SQRT(1-Z**2) and SS=Z
C If ABS(Z) .GT. 1 set SC=1/Z and SS=SQRT(1-SC**2)
C
C Normally, the subprogram SROT(N,SX,INCX,SY,INCY,SC,SS) will
C next be called to apply the transformation to a 2 by N matrix.
C
C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
C Krogh, Basic linear algebra subprograms for Fortran
C usage, Algorithm No. 539, Transactions on Mathematical
C Software 5, 3 (September 1979), pp. 308-323.
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 791001 DATE WRITTEN
C 861211 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE SROTG
C***FIRST EXECUTABLE STATEMENT SROTG
IF (ABS(SA) .LE. ABS(SB)) GO TO 10
C
C *** HERE ABS(SA) .GT. ABS(SB) ***
C
U = SA + SA
V = SB / U
C
C NOTE THAT U AND R HAVE THE SIGN OF SA
C
R = SQRT(0.25E0 + V**2) * U
C
C NOTE THAT SC IS POSITIVE
C
SC = SA / R
SS = V * (SC + SC)
SB = SS
SA = R
RETURN
C
C *** HERE ABS(SA) .LE. ABS(SB) ***
C
10 IF (SB .EQ. 0.0E0) GO TO 20
U = SB + SB
V = SA / U
C
C NOTE THAT U AND R HAVE THE SIGN OF SB
C (R IS IMMEDIATELY STORED IN SA)
C
SA = SQRT(0.25E0 + V**2) * U
C
C NOTE THAT SS IS POSITIVE
C
SS = SB / SA
SC = V * (SS + SS)
IF (SC .EQ. 0.0E0) GO TO 15
SB = 1.0E0 / SC
RETURN
15 SB = 1.0E0
RETURN
C
C *** HERE SA = SB = 0.0 ***
C
20 SC = 1.0E0
SS = 0.0E0
RETURN
C
END
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