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pFq: Change pnorm to p_abs_error.

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Update docs to reflect the fact that this is an error estimate.
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jzmaddock
2019-07-28 17:48:04 +01:00
parent b0d3662ab6
commit ae2caa30fd
2 changed files with 25 additions and 19 deletions
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19
doc/sf/hypergeometric.qbk
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@@ -420,16 +420,16 @@ are destroyed by cancellation.
namespace boost { namespace math {
template <class Seq, class Real>
``__sf_result`` hypergeometric_pFq(const Seq& aj, const Seq& bj, const Real& z, Real* pNorm, const Policy& pol);
``__sf_result`` hypergeometric_pFq(const Seq& aj, const Seq& bj, const Real& z, Real* p_abs_error, const Policy& pol);
template <class Seq, class Real>
``__sf_result`` hypergeometric_pFq(const Seq& aj, const Seq& bj, const Real& z, Real* pNorm = 0)
``__sf_result`` hypergeometric_pFq(const Seq& aj, const Seq& bj, const Real& z, Real* p_abs_error = 0)
template <class R, class Real>
``__sf_result`` hypergeometric_pFq(const std::initializer_list<R>& aj, const std::initializer_list<R>& bj, const Real& z, Real* pNorm, const Policy& pol);
``__sf_result`` hypergeometric_pFq(const std::initializer_list<R>& aj, const std::initializer_list<R>& bj, const Real& z, Real* p_abs_error, const Policy& pol);
template <class R, class Real>
``__sf_result`` hypergeometric_pFq(const std::initializer_list<R>& aj, const std::initializer_list<R>& bj, const Real& z, Real* pNorm = 0)
``__sf_result`` hypergeometric_pFq(const std::initializer_list<R>& aj, const std::initializer_list<R>& bj, const Real& z, Real* p_abs_error = 0)
}} // namespaces
@@ -444,10 +444,8 @@ It is most naturally used via initializer lists as in:
double h = hypergeometric_pFq({2,3,4}, {5,6,7,8}, z); // Calculate 3F4
The optional ['norm] argument calculates the norm of the sum and can be used for error estimation, which is to say the ['absolute error]
in the result is estimated to be:
norm * std::numeric_limits<decltype(norm)>::epsilon();
The optional ['p_abs_error] argument calculates an estimate of the absolute error in the result from the
L1 norm of the sum, plus some other factors (see implementation below).
You should divide this value by the result to get an estimate of ['relative error].
@@ -467,8 +465,9 @@ result. For other /p/ and /q/ values, predicting the exact locations of the max
simply restart summation at the point where each b[sub j] passes the origin: this will eventually reach
all the significant terms of the sum, but the key word may well be "eventually".
The error term /norm/ is normally simply the sum of the absolute values of each term. However,
if it was necessary for the summation to skip forward, then /norm/ is adjusted to account for the
The error term /p_abs_error/ is normally simply the sum of the absolute values of each term multiplied
by machine epsilon for type `Real`. However,
if it was necessary for the summation to skip forward, then /p_abs_error/ is adjusted to account for the
error inherent in calculating the N'th term via logarithms.
[endsect]