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108 lines
3 KiB
Fortran
108 lines
3 KiB
Fortran
*DECK DROTG
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SUBROUTINE DROTG (DA, DB, DC, DS)
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C***BEGIN PROLOGUE DROTG
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C***PURPOSE Construct a plane Givens rotation.
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C***LIBRARY SLATEC (BLAS)
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C***CATEGORY D1B10
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C***TYPE DOUBLE PRECISION (SROTG-S, DROTG-D, CROTG-C)
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C***KEYWORDS BLAS, GIVENS ROTATION, GIVENS TRANSFORMATION,
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C LINEAR ALGEBRA, VECTOR
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C***AUTHOR Lawson, C. L., (JPL)
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C Hanson, R. J., (SNLA)
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C Kincaid, D. R., (U. of Texas)
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C Krogh, F. T., (JPL)
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C***DESCRIPTION
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C
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C B L A S Subprogram
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C Description of Parameters
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C
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C --Input--
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C DA double precision scalar
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C DB double precision scalar
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C
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C --Output--
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C DA double precision result R
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C DB double precision result Z
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C DC double precision result
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C DS double precision result
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C
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C Construct the Givens transformation
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C
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C ( DC DS )
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C G = ( ) , DC**2 + DS**2 = 1 ,
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C (-DS DC )
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C
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C which zeros the second entry of the 2-vector (DA,DB)**T .
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C
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C The quantity R = (+/-)SQRT(DA**2 + DB**2) overwrites DA in
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C storage. The value of DB is overwritten by a value Z which
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C allows DC and DS to be recovered by the following algorithm.
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C
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C If Z=1 set DC=0.0 and DS=1.0
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C If ABS(Z) .LT. 1 set DC=SQRT(1-Z**2) and DS=Z
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C If ABS(Z) .GT. 1 set DC=1/Z and DS=SQRT(1-DC**2)
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C
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C Normally, the subprogram DROT(N,DX,INCX,DY,INCY,DC,DS) will
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C next be called to apply the transformation to a 2 by N matrix.
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C
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C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
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C Krogh, Basic linear algebra subprograms for Fortran
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C usage, Algorithm No. 539, Transactions on Mathematical
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C Software 5, 3 (September 1979), pp. 308-323.
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C***ROUTINES CALLED (NONE)
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C***REVISION HISTORY (YYMMDD)
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C 791001 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890531 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE DROTG
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DOUBLE PRECISION DA, DB, DC, DS, U, V, R
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C***FIRST EXECUTABLE STATEMENT DROTG
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IF (ABS(DA) .LE. ABS(DB)) GO TO 10
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C
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C *** HERE ABS(DA) .GT. ABS(DB) ***
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C
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U = DA + DA
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V = DB / U
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C
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C NOTE THAT U AND R HAVE THE SIGN OF DA
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C
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R = SQRT(0.25D0 + V**2) * U
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C
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C NOTE THAT DC IS POSITIVE
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C
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DC = DA / R
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DS = V * (DC + DC)
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DB = DS
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DA = R
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RETURN
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C
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C *** HERE ABS(DA) .LE. ABS(DB) ***
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C
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10 IF (DB .EQ. 0.0D0) GO TO 20
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U = DB + DB
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V = DA / U
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C
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C NOTE THAT U AND R HAVE THE SIGN OF DB
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C (R IS IMMEDIATELY STORED IN DA)
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C
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DA = SQRT(0.25D0 + V**2) * U
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C
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C NOTE THAT DS IS POSITIVE
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C
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DS = DB / DA
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DC = V * (DS + DS)
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IF (DC .EQ. 0.0D0) GO TO 15
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DB = 1.0D0 / DC
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RETURN
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15 DB = 1.0D0
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RETURN
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C
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C *** HERE DA = DB = 0.0 ***
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C
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20 DC = 1.0D0
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DS = 0.0D0
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RETURN
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C
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END
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