SCULIB_SKYFUNC

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SCULIB_SKYFUNC_2

calculate f(x) and its Jacobian for NAG non-linear fitting routine E04UPF when fitting B and TAU in sky-dip analysis

Description:

E04UPF is a NAG routine that is used to fit a theoretical sky-dip curve to the measured data by varying B and TAU. This routine is called by E04UPF to calculate the M sub-functions f(x) at the current solution vector X, and/or the Jacobian matrix. Please see the NAG manual if you need to know more about E04UPF.

The solution vector is composed as follows:-

x(1) = B
x(2) = TAU

For each of the M measured airmasses the subfunction f(x) is:-

f (x) = J_{}

theory (Airmass(i)) - J_meas (Airmass(i))

J_{}

noise (Airmass(i)) (84)

where:-

J_{}

theory = (1-

η_{}

tel) J_tel + $η_{}$

telJ_atm (1-B $e x p (- τ A i r m a s s)) (85)$

The corresponding Jacobian has component (i,j):-

\frac{\partial f (x)}{\partial x (j)} = \frac{\partial}{\partial x (j)} J_{}

theory(Airmass(i))

\times \frac{1}{J_{}}

noise(i) (86)

leading to:

\frac{\partial f (i)}{\partial x (1)} = - η_{}

tel J_atm

e x p (- τ A (i)) (87)

\frac{\partial f (i)}{\partial x (2)} = A (i) B η_{}

tel J_atm

e x p (- τ A (i)) (88)

The array USER is used to get the necessary ancillary information into the routine:-

USER (1) = J_TEL
USER (2) = J_ATM
USER (3) = ETA_TEL
USER (4:M $+$ 3) = the measured airmasses
USER (M $+$ 4:2M $+$ 3) = the measured sky temperatures
USER (2M $+$ 4:3M $+$ 3) = the errors on the measured sky temperatures

SCULIB_SKYFUNC_2

Description:

Invocation

Arguments

See NAG manual description of OBJFUN parameter in E04UPF.

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