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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_gaussian_h__
#define __math_gaussian_h__
#include "math/math.h"
#include "math/vector.h"
namespace MR {
namespace Math {
namespace Gaussian {
template <typename T> inline T lnP (const T measured, const T actual, const T one_over_noise_squared)
{
return (0.5 * (one_over_noise_squared * pow2 (actual - measured) - log (one_over_noise_squared)));
}
template <typename T> inline T lnP (const T measured, const T actual, const T one_over_noise_squared, T& dP_dactual, T& dP_dN)
{
assert (one_over_noise_squared > 0.0);
dP_dN = pow2 (actual - measured);
dP_dactual = one_over_noise_squared * dP_dN;
dP_dN = 0.5 * (dP_dN - 1.0/one_over_noise_squared);
return (0.5 * (dP_dactual - log(one_over_noise_squared)));
}
template <typename T> inline T lnP (const int N, const T* measured, const T* actual, const T one_over_noise_squared)
{
assert (one_over_noise_squared > 0.0);
T lnP = 0.0;
for (int i = 0; i < N; i++)
lnP += pow2 (actual[i] - measured[i]);
lnP *= one_over_noise_squared;
lnP -= N * log (one_over_noise_squared);
return (0.5*lnP);
}
template <typename T> inline T lnP (const int N, const T* measured, const T* actual, const T one_over_noise_squared, T* dP_dactual, T& dP_dN)
{
assert (one_over_noise_squared > 0.0);
T lnP = 0.0;
dP_dN = 0.0;
for (int i = 0; i < N; i++) {
T diff = actual[i] - measured[i];
dP_dactual[i] = one_over_noise_squared * diff;
lnP += pow2 (diff);
}
dP_dN = 0.5 * (lnP - T(N)/one_over_noise_squared);
lnP *= one_over_noise_squared;
lnP -= N * log (one_over_noise_squared);
return (0.5*lnP);
}
template <typename T> inline T lnP (const Vector<T>& measured, const Vector<T>& actual, const T one_over_noise_squared)
{
assert (one_over_noise_squared > 0.0);
assert (measured.size() == actual.size());
T lnP = 0.0;
for (size_t i = 0; i < measured.size(); i++)
lnP += pow2 (actual[i] - measured[i]);
lnP *= one_over_noise_squared;
lnP -= measured.size() * log (one_over_noise_squared);
return (0.5*lnP);
}
template <typename T> inline T lnP (const Vector<T>& measured, const Vector<T>& actual, const T one_over_noise_squared, Vector<T>& dP_dactual, T& dP_dN)
{
assert (one_over_noise_squared > 0.0);
assert (measured.size() == actual.size());
assert (measured.size() == dP_dactual.size());
T lnP = 0.0;
dP_dN = 0.0;
for (size_t i = 0; i < measured.size(); i++) {
T diff = actual[i] - measured[i];
dP_dactual[i] = one_over_noise_squared * diff;
lnP += pow2 (diff);
}
dP_dN = 0.5 * (lnP - T(measured.size())/one_over_noise_squared);
lnP *= one_over_noise_squared;
lnP -= measured.size() * log (one_over_noise_squared);
return (0.5*lnP);
}
}
}
}
#endif
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