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/* Copyright (c) 2008-2022 the MRtrix3 contributors.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* Covered Software is provided under this License on an "as is"
* basis, without warranty of any kind, either expressed, implied, or
* statutory, including, without limitation, warranties that the
* Covered Software is free of defects, merchantable, fit for a
* particular purpose or non-infringing.
* See the Mozilla Public License v. 2.0 for more details.
*
* For more details, see http://www.mrtrix.org/.
*/
#ifndef __math_welch_satterthwaite_h__
#define __math_welch_satterthwaite_h__
#include "math/math.h"
namespace MR {
namespace Math {
template <class VarArrayType, class CountArrayType>
default_type welch_satterthwaite (const VarArrayType& variances, const CountArrayType& counts)
{
assert (size_t(variances.size()) == size_t(counts.size()));
default_type numerator = 0.0, denominator = 0.0;
for (size_t i = 0; i != size_t(variances.size()); ++i) {
const default_type ks2 = (1.0 / (counts[i] - 1)) * variances[i];
numerator += ks2;
denominator += Math::pow2 (ks2) / (counts[i] - 1);
}
return Math::pow2 (numerator) / denominator;
}
}
}
#endif
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