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/*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* The Original Code is Copyright (C) 2015 by Blender Foundation
* All rights reserved.
*/
#pragma once
/** \file
* \ingroup bli
*/
#include "BLI_compiler_attrs.h"
#include "BLI_math_inline.h"
#ifdef __cplusplus
extern "C" {
#endif
#ifdef BLI_MATH_GCC_WARN_PRAGMA
# pragma GCC diagnostic push
# pragma GCC diagnostic ignored "-Wredundant-decls"
#endif
/* -------------------------------------------------------------------- */
/** \name Eigen Solvers
* \{ */
/**
* \brief Compute the eigen values and/or vectors of given 3D symmetric (aka adjoint) matrix.
*
* \param m3: the 3D symmetric matrix.
* \return r_eigen_values the computed eigen values (NULL if not needed).
* \return r_eigen_vectors the computed eigen vectors (NULL if not needed).
*/
bool BLI_eigen_solve_selfadjoint_m3(const float m3[3][3],
float r_eigen_values[3],
float r_eigen_vectors[3][3]);
/**
* \brief Compute the SVD (Singular Values Decomposition) of given 3D matrix (m3 = USV*).
*
* \param m3: the matrix to decompose.
* \return r_U the computed left singular vector of \a m3 (NULL if not needed).
* \return r_S the computed singular values of \a m3 (NULL if not needed).
* \return r_V the computed right singular vector of \a m3 (NULL if not needed).
*/
void BLI_svd_m3(const float m3[3][3], float r_U[3][3], float r_S[3], float r_V[3][3]);
/** \} */
/* -------------------------------------------------------------------- */
/** \name Simple Solvers
* \{ */
/**
* \brief Solve a tridiagonal system of equations:
*
* a[i] * r_x[i-1] + b[i] * r_x[i] + c[i] * r_x[i+1] = d[i]
*
* Ignores a[0] and c[count-1]. Uses the Thomas algorithm, e.g. see wiki.
*
* \param r_x: output vector, may be shared with any of the input ones
* \return true if success
*/
bool BLI_tridiagonal_solve(
const float *a, const float *b, const float *c, const float *d, float *r_x, int count);
/**
* \brief Solve a possibly cyclic tridiagonal system using the Sherman-Morrison formula.
*
* \param r_x: output vector, may be shared with any of the input ones
* \return true if success
*/
bool BLI_tridiagonal_solve_cyclic(
const float *a, const float *b, const float *c, const float *d, float *r_x, int count);
/**
* Generic 3 variable Newton's method solver.
*/
typedef void (*Newton3D_DeltaFunc)(void *userdata, const float x[3], float r_delta[3]);
typedef void (*Newton3D_JacobianFunc)(void *userdata, const float x[3], float r_jacobian[3][3]);
typedef bool (*Newton3D_CorrectionFunc)(void *userdata,
const float x[3],
float step[3],
float x_next[3]);
/**
* \brief Solve a generic f(x) = 0 equation using Newton's method.
*
* \param func_delta: Callback computing the value of f(x).
* \param func_jacobian: Callback computing the Jacobian matrix of the function at x.
* \param func_correction: Callback for forcing the search into an arbitrary custom domain.
* May be NULL.
* \param userdata: Data for the callbacks.
* \param epsilon: Desired precision.
* \param max_iterations: Limit on the iterations.
* \param trace: Enables logging to console.
* \param x_init: Initial solution vector.
* \param result: Final result.
* \return true if success
*/
bool BLI_newton3d_solve(Newton3D_DeltaFunc func_delta,
Newton3D_JacobianFunc func_jacobian,
Newton3D_CorrectionFunc func_correction,
void *userdata,
float epsilon,
int max_iterations,
bool trace,
const float x_init[3],
float result[3]);
#ifdef BLI_MATH_GCC_WARN_PRAGMA
# pragma GCC diagnostic pop
#endif
/** \} */
#ifdef __cplusplus
}
#endif
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