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/* SPDX-License-Identifier: GPL-2.0-or-later
* The Original Code is:
* GXML/Graphite: Geometry and Graphics Programming Library + Utilities
* Copyright 2000 Bruno Levy <levy@loria.fr> */
/** \file
* \ingroup freestyle
*/
#include "matrix_util.h"
#include "BLI_math.h"
namespace Freestyle::OGF::MatrixUtil {
static const double EPS = 0.00001;
static int MAX_ITER = 100;
void semi_definite_symmetric_eigen(const double *mat, int n, double *eigen_vec, double *eigen_val)
{
double *a, *v;
double a_norm, a_normEPS, thr, thr_nn;
int nb_iter = 0;
int jj;
int i, j, k, ij, ik, l, m, lm, mq, lq, ll, mm, imv, im, iq, ilv, il, nn;
int *index;
double a_ij, a_lm, a_ll, a_mm, a_im, a_il;
double a_lm_2;
double v_ilv, v_imv;
double x;
double sinx, sinx_2, cosx, cosx_2, sincos;
double delta;
// Number of entries in mat
nn = (n * (n + 1)) / 2;
// Step 1: Copy mat to a
a = new double[nn];
for (ij = 0; ij < nn; ij++) {
a[ij] = mat[ij];
}
// Ugly Fortran-porting trick: indices for a are between 1 and n
a--;
// Step 2 : Init diagonalization matrix as the unit matrix
v = new double[n * n];
ij = 0;
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
if (i == j) {
v[ij++] = 1.0;
}
else {
v[ij++] = 0.0;
}
}
}
// Ugly Fortran-porting trick: indices for v are between 1 and n
v--;
// Step 3 : compute the weight of the non diagonal terms
ij = 1;
a_norm = 0.0;
for (i = 1; i <= n; i++) {
for (j = 1; j <= i; j++) {
if (i != j) {
a_ij = a[ij];
a_norm += a_ij * a_ij;
}
ij++;
}
}
if (a_norm != 0.0) {
a_normEPS = a_norm * EPS;
thr = a_norm;
// Step 4 : rotations
while (thr > a_normEPS && nb_iter < MAX_ITER) {
nb_iter++;
thr_nn = thr / nn;
for (l = 1; l < n; l++) {
for (m = l + 1; m <= n; m++) {
// compute sinx and cosx
lq = (l * l - l) / 2;
mq = (m * m - m) / 2;
lm = l + mq;
a_lm = a[lm];
a_lm_2 = a_lm * a_lm;
if (a_lm_2 < thr_nn) {
continue;
}
ll = l + lq;
mm = m + mq;
a_ll = a[ll];
a_mm = a[mm];
delta = a_ll - a_mm;
if (delta == 0.0) {
x = -M_PI / 4;
}
else {
x = -atan((a_lm + a_lm) / delta) / 2.0;
}
sinx = sin(x);
cosx = cos(x);
sinx_2 = sinx * sinx;
cosx_2 = cosx * cosx;
sincos = sinx * cosx;
// rotate L and M columns
ilv = n * (l - 1);
imv = n * (m - 1);
for (i = 1; i <= n; i++) {
if (!ELEM(i, l, m)) {
iq = (i * i - i) / 2;
if (i < m) {
im = i + mq;
}
else {
im = m + iq;
}
a_im = a[im];
if (i < l) {
il = i + lq;
}
else {
il = l + iq;
}
a_il = a[il];
a[il] = a_il * cosx - a_im * sinx;
a[im] = a_il * sinx + a_im * cosx;
}
ilv++;
imv++;
v_ilv = v[ilv];
v_imv = v[imv];
v[ilv] = cosx * v_ilv - sinx * v_imv;
v[imv] = sinx * v_ilv + cosx * v_imv;
}
x = a_lm * sincos;
x += x;
a[ll] = a_ll * cosx_2 + a_mm * sinx_2 - x;
a[mm] = a_ll * sinx_2 + a_mm * cosx_2 + x;
a[lm] = 0.0;
thr = fabs(thr - a_lm_2);
}
}
}
}
// Step 5: index conversion and copy eigen values
// back from Fortran to C++
a++;
for (i = 0; i < n; i++) {
k = i + (i * (i + 1)) / 2;
eigen_val[i] = a[k];
}
delete[] a;
// Step 6: sort the eigen values and eigen vectors
index = new int[n];
for (i = 0; i < n; i++) {
index[i] = i;
}
for (i = 0; i < (n - 1); i++) {
x = eigen_val[i];
k = i;
for (j = i + 1; j < n; j++) {
if (x < eigen_val[j]) {
k = j;
x = eigen_val[j];
}
}
eigen_val[k] = eigen_val[i];
eigen_val[i] = x;
jj = index[k];
index[k] = index[i];
index[i] = jj;
}
// Step 7: save the eigen vectors
// back from Fortran to C++
v++;
ij = 0;
for (k = 0; k < n; k++) {
ik = index[k] * n;
for (i = 0; i < n; i++) {
eigen_vec[ij++] = v[ik++];
}
}
delete[] v;
delete[] index;
}
//_________________________________________________________
} // namespace Freestyle::OGF::MatrixUtil
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