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/*
* ***** BEGIN GPL LICENSE BLOCK *****
*
* 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.
*
* The Original Code is: all of this file.
*
* ***** END GPL LICENSE BLOCK *****
* */
/** \file blender/blenlib/intern/math_solvers.c
* \ingroup bli
*/
#include "MEM_guardedalloc.h"
#include "BLI_math.h"
#include "BLI_utildefines.h"
#include "BLI_strict_flags.h"
#include "eigen_capi.h"
/********************************** 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])
{
#ifndef NDEBUG
/* We must assert given matrix is self-adjoint (i.e. symmetric) */
if ((m3[0][1] != m3[1][0]) ||
(m3[0][2] != m3[2][0]) ||
(m3[1][2] != m3[2][1]))
{
BLI_assert(0);
}
#endif
return EIG_self_adjoint_eigen_solve(3, (const float *)m3, r_eigen_values, (float *)r_eigen_vectors);
}
/**
* \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])
{
EIG_svd_square_matrix(3, (const float *)m3, (float *)r_U, (float *)r_S, (float *)r_V);
}
/***************************** Simple Solvers ************************************/
/**
* \brief Solve a tridiagonal system of equations:
*
* a[i] * x[i-1] + b[i] * x[i] + c[i] * x[i+1] = d[i]
*
* Ignores a[0] and c[count-1]. Uses Thomas algorithm, e.g. see wiki.
*
* \param 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 *x, const int count)
{
if (count < 0)
return false;
size_t bytes = sizeof(float)*(unsigned)count;
float *c1 = (float *)MEM_mallocN(bytes*2, "tridiagonal_c1d1");
float *d1 = c1 + count;
if (!c1)
return false;
int i;
double c_prev, d_prev, x_prev;
/* forward pass */
c_prev = ((double)c[0]) / b[0];
d_prev = ((double)d[0]) / b[0];
c1[0] = ((float)c_prev);
d1[0] = ((float)d_prev);
for (i = 1; i < count; i++) {
double denum = b[i] - a[i]*c_prev;
c_prev = c[i] / denum;
d_prev = (d[i] - a[i]*d_prev) / denum;
c1[i] = ((float)c_prev);
d1[i] = ((float)d_prev);
}
/* back pass */
x_prev = d_prev;
x[--i] = ((float)x_prev);
while (--i >= 0) {
x_prev = d1[i] - c1[i] * x_prev;
x[i] = ((float)x_prev);
}
MEM_freeN(c1);
return isfinite(x_prev);
}
/**
* \brief Solve a possibly cyclic tridiagonal system using the Sherman-Morrison formula.
*
* \param 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 *x, const int count)
{
if (count < 1)
return false;
float a0 = a[0], cN = c[count-1];
if (a0 == 0.0f && cN == 0.0f) {
return BLI_tridiagonal_solve(a, b, c, d, x, count);
}
size_t bytes = sizeof(float)*(unsigned)count;
float *tmp = (float*)MEM_mallocN(bytes*2, "tridiagonal_ex");
float *b2 = tmp + count;
if (!tmp)
return false;
/* prepare the noncyclic system; relies on tridiagonal_solve ignoring values */
memcpy(b2, b, bytes);
b2[0] -= a0;
b2[count-1] -= cN;
memset(tmp, 0, bytes);
tmp[0] = a0;
tmp[count-1] = cN;
/* solve for partial solution and adjustment vector */
bool success =
BLI_tridiagonal_solve(a, b2, c, tmp, tmp, count) &&
BLI_tridiagonal_solve(a, b2, c, d, x, count);
/* apply adjustment */
if (success) {
float coeff = (x[0] + x[count-1]) / (1.0f + tmp[0] + tmp[count-1]);
for (int i = 0; i < count; i++)
x[i] -= coeff * tmp[i];
}
MEM_freeN(tmp);
return success;
}
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