Public Shared Function s14ac ( _ x As Double, _ <OutAttribute> ByRef ifail As Integer _ ) As Double
public: static double s14ac( double x, [OutAttribute] int% ifail )
- Type: System..::..DoubleOn entry: the argument of the function.Constraint: .
s14ac returns a value of the function . The psi function is computed without the logarithmic term so that when is large, sums or differences of psi functions may be computed without unnecessary loss of precision, by analytically combining the logarithmic terms. For example, the difference has an asymptotic behaviour for large given by .
Computing directly would amount to subtracting two large numbers which are close to and to produce a small number close to , resulting in a loss of significant digits. However, using this method to compute , we can compute , and the dominant logarithmic term may be computed accurately from its power series when is large. Thus we avoid the unnecessary loss of precision.
The method is derived from the method PSIFN in Amos (1983).
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Amos D E (1983) Algorithm 610: A portable FORTRAN subroutine for derivatives of the psi function ACM Trans. Math. Software 9 494–502
Errors or warnings detected by the method:
On entry, . s14ac returns the value zero.
All constants in s14ac are given to approximately digits of precision. Calling the number of digits of precision in the floating-point arithmetic being used , then clearly the maximum number of correct digits in the results obtained is limited by .
With the above proviso, results returned by this method should be accurate almost to full precision, except at points close to the zero of , , where only absolute rather than relative accuracy can be obtained.
The example program reads values of the argument from a file, evaluates the function at each value of and prints the results.