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27.14.2 Energy Derivative Test

The energy derivative test is invoked by the DERIV keyword. The code works by computing numerical derivatives of energy as shown: dU(x_i)/dx_i (x_i) = (U(x_i+h) - U(x_i-h)) / 2h and comparing them against the analytic derivatives computed by the code. Statistics of the differences are calculated and a histogram of the differences is displayed.

The keyword, DELTA, specifies the value of h in the above expression. The default value is 0.001. For single precision arithmetic, this value is close to optimum.1 The keyword, CUT, specifies a printing cutoff. Any difference in derivative whose magnitude exceeds this value will be individually displayed.


[1] See S.D. Conte and C. de Boor, Elementary Numerical Analysis, an Algorithmic Approach, McGraw-Hill Book Company, New York 1972, p. 282