If status is good on entry this routine will calculate the differential of chi-squared with respect to A(J) and A(K). It does this numerically by calling the supplied routine XISQ_ROUTINE to calculate chi-squared at [A(J)$+$DELTA_AJ,A(K)$+$DELTA_AK], [A(J)-DELTA_AJ,A(K)$+$DELTA_AK], [A(J)$+$DELTA_AJ,A(K)-DELTA_AK] and [A(J)-DELTA_AJ,A(K)-DELTA_AK]. The result is then calculated using the formula:-

$$\begin{array}{cc}\begin{array}{rl}\frac{{\partial }^2{\chi }^2}{\partial AJ\partial AK}=& {\chi }^2\left(AJ+\delta AJ,AK+\delta AK\right)\\ & -{\chi }^2\left(AJ-\delta AJ,AK+\delta AK\right)\\ & -\frac{{\chi }^2\left(AJ-\delta AJ,AK+\delta AK\right)+{\chi }^2\left(AJ-\delta AJ,AK-\delta AK\right)}{4\delta AJ\delta AK}\\ \end{array}& \end{array}$$

(42)

DELTA_AJ is equal to the absolute value of 0.001 $\ast$ A(J) or, if this is zero, 0.001. DELTA_AK is calculated in a similar way.

CALL SCULIB_FIT_D2XISQ_DAJK (XISQ_ROUTINE, N, A, J, K, D2XISQ_DAJK, STATUS)

XISQ_ROUTINE (XISQ, N, A, STATUS) = EXTERNAL ROUTINE (Given)

N = INTEGER (Given)

A(N) = DOUBLE PRECISION (Given and returned)

J = INTEGER (Given)

K = INTEGER (Given)

D2XISQ_DAJK = DOUBLE PRECISION (Returned)

STATUS = INTEGER (Given and returned)

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