Eigen::internal::igamma_series_impl< Scalar, mode > Struct Template Reference

#include <SpecialFunctionsImpl.h>

Static Public Member Functions
static EIGEN_DEVICE_FUNC Scalar	run (Scalar a, Scalar x)

Member Function Documentation

run()

template<typename Scalar , IgammaComputationMode mode>

static EIGEN_DEVICE_FUNC Scalar Eigen::internal::igamma_series_impl< Scalar, mode >::run ( Scalar  a, Scalar  x  )

inlinestatic

                                                          {
    const Scalar zero = 0;
    const Scalar one = 1;
    const Scalar machep = cephes_helper<Scalar>::machep();
 
    Scalar ax = main_igamma_term<Scalar>(a, x);
 
    // This is independent of mode. If this value is zero,
    // then the function value is zero. If the function value is zero,
    // then we are in a neighborhood where the function value evaluates to zero,
    // so the derivative is zero.
    if (ax == zero) {
      return zero;
    }
 
    ax /= a;
 
    /* power series */
    Scalar r = a;
    Scalar c = one;
    Scalar ans = one;
 
    Scalar dc_da = zero;
    Scalar dans_da = zero;
 
    for (int i = 0; i < igamma_num_iterations<Scalar, mode>(); i++) {
      r += one;
      Scalar term = x / r;
      Scalar dterm_da = -x / (r * r);
      dc_da = term * dc_da + dterm_da * c;
      dans_da += dc_da;
      c *= term;
      ans += c;
 
      if (mode == VALUE) {
        if (c <= machep * ans) {
          break;
        }
      } else {
        if (numext::abs(dc_da) <= machep * numext::abs(dans_da)) {
          break;
        }
      }
    }
 
    Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a + one);
    Scalar dax_da = ax * dlogax_da;
 
    switch (mode) {
      case VALUE:
        return ans * ax;
      case DERIVATIVE:
        return ans * dax_da + dans_da * ax;
      case SAMPLE_DERIVATIVE:
      default:  // this is needed to suppress clang warning
        return -(dans_da + ans * dlogax_da) * x / a;
    }
  }

References a, Eigen::numext::abs(), plotDoE::ax, calibrate::c, Eigen::internal::DERIVATIVE, i, Eigen::numext::log(), Eigen::internal::cephes_helper< Scalar >::machep(), UniformPSDSelfTest::r, Eigen::internal::digamma_impl< Scalar >::run(), Eigen::internal::SAMPLE_DERIVATIVE, Eigen::internal::VALUE, Eigen::numext::x, and zero().

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The documentation for this struct was generated from the following file:

• SpecialFunctionsImpl.h