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C $Id: carmel.f 3304 2011-01-17 15:25:59Z brideout $
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C
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SUBROUTINE CARMEL(B,XI,VL)
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C
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C Private/Internal subroutine. Part of Apex coordinate computation
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C package. See COORD for public API. Computes scaler VL as a
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C function of B and XI.
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C
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C Input:
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C B - Scaler field strength value.
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C XI - integral invariant (see INTEG).
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C
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C Output:
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C VL - McIlwain's L-shell parameter i.e. Invariant Latitude
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C = ACOS(DSQRT(1.0D0/VL))/DTR
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C
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C .. Scalar Arguments ..
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DOUBLE PRECISION B,VL,XI
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C ..
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C .. Local Scalars ..
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DOUBLE PRECISION GG,XX
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C ..
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C .. Intrinsic Functions ..
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INTRINSIC DEXP,DLOG
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C ..
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IF (XI.GT.1.0D-36) THEN
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XX = 3.0D0*DLOG(XI)
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XX = XX + DLOG(B/0.311653D0)
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IF (XX.LE.-22.D0) THEN
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GG = .333338D0*XX + .30062102D0
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ELSE IF (XX.LE.-3.D0) THEN
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GG = ((((((((-8.1537735D-14*XX+8.3232531D-13)*XX+
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* 1.0066362D-9)*XX+8.1048663D-8)*XX+3.2916354D-6)*XX+
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* 8.2711096D-5)*XX+1.3714667D-3)*XX+.015017245D0)*XX+
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* .43432642D0)*XX + .62337691D0
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ELSE IF (XX.LE.3.D0) THEN
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GG = ((((((((2.6047023D-10*XX+2.3028767D-9)*XX-
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* 2.1997983D-8)*XX-5.3977642D-7)*XX-3.3408822D-6)*XX+
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* 3.8379917D-5)*XX+1.1784234D-3)*XX+1.4492441D-2)*XX+
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* .43352788D0)*XX + .6228644D0
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ELSE IF (XX.LE.11.7D0) THEN
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GG = ((((((((6.3271665D-10*XX-3.958306D-8)*XX+
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* 9.9766148D-07)*XX-1.2531932D-5)*XX+7.9451313D-5)*XX-
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* 3.2077032D-4)*XX+2.1680398D-3)*XX+1.2817956D-2)*XX+
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* .43510529D0)*XX + .6222355D0
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ELSE IF (XX.GT.23.D0) THEN
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GG = XX - 3.0460681D0
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ELSE
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GG = (((((2.8212095D-8*XX-3.8049276D-6)*XX+2.170224D-4)*XX-
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* 6.7310339D-3)*XX+.12038224D0)*XX-.18461796D0)*XX +
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* 2.0007187D0
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END IF
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VL = (((1.0D0+DEXP(GG))*0.311653D0)/B)**(1.D0/3.D0)
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C end compute l
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ELSE
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VL = (0.311653D0/B)**(1.D0/3.D0)
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END IF
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RETURN
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C
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END
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