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/* Copyright 2015 The Chromium OS Authors. All rights reserved.
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "common.h"
#include "mat33.h"
#include "math.h"
#include "util.h"
#define K_EPSILON 1E-5f
void init_zero_matrix(mat33_t A)
{
memset(A, 0, sizeof(mat33_t));
}
void init_diagonal_matrix(mat33_t A, float x)
{
size_t i;
init_zero_matrix(A);
for (i = 0; i < 3; ++i)
A[i][i] = x;
}
void mat33_scalar_mul(mat33_t A, float c)
{
size_t i;
for (i = 0; i < 3; ++i) {
size_t j;
for (j = 0; j < 3; ++j)
A[i][j] *= c;
}
}
void mat33_swap_rows(mat33_t A, const size_t i, const size_t j)
{
const size_t N = 3;
size_t k;
if (i == j)
return;
for (k = 0; k < N; ++k) {
float tmp = A[i][k];
A[i][k] = A[j][k];
A[j][k] = tmp;
}
}
/*
* Returns the eigenvalues and corresponding eigenvectors of the _symmetric_
* matrix.
* The i-th eigenvalue corresponds to the eigenvector in the i-th _row_ of
* "eigenvecs".
*/
void mat33_get_eigenbasis(mat33_t S, vec3_t e_vals, mat33_t e_vecs)
{
const size_t N = 3;
size3_t ind;
size_t i, j, k, l, m;
for (k = 0; k < N; ++k) {
ind[k] = mat33_maxind(S, k);
e_vals[k] = S[k][k];
}
init_diagonal_matrix(e_vecs, 1.0f);
for (;;) {
float y, t, s, c, p, sum;
m = 0;
for (k = 1; k + 1 < N; ++k) {
if (fabsf(S[k][ind[k]]) >
fabsf(S[m][ind[m]])) {
m = k;
}
}
k = m;
l = ind[m];
p = S[k][l];
if (fabsf(p) < K_EPSILON)
break;
y = (e_vals[l] - e_vals[k]) * 0.5f;
t = fabsf(y) + sqrtf(p * p + y * y);
s = sqrtf(p * p + t * t);
c = t / s;
s = p / s;
t = p * p / t;
if (y < 0.0f) {
s = -s;
t = -t;
}
S[k][l] = 0.0f;
e_vals[k] -= t;
e_vals[l] += t;
for (i = 0; i < k; ++i)
mat33_rotate(S, c, s, i, k, i, l);
for (i = k + 1; i < l; ++i)
mat33_rotate(S, c, s, k, i, i, l);
for (i = l + 1; i < N; ++i)
mat33_rotate(S, c, s, k, i, l, i);
for (i = 0; i < N; ++i) {
float tmp = c * e_vecs[k][i] - s * e_vecs[l][i];
e_vecs[l][i] = s * e_vecs[k][i] + c * e_vecs[l][i];
e_vecs[k][i] = tmp;
}
ind[k] = mat33_maxind(S, k);
ind[l] = mat33_maxind(S, l);
sum = 0.0f;
for (i = 0; i < N; ++i)
for (j = i + 1; j < N; ++j)
sum += fabsf(S[i][j]);
if (sum < K_EPSILON)
break;
}
for (k = 0; k < N; ++k) {
m = k;
for (l = k + 1; l < N; ++l)
if (e_vals[l] > e_vals[m])
m = l;
if (k != m) {
float tmp = e_vals[k];
e_vals[k] = e_vals[m];
e_vals[m] = tmp;
mat33_swap_rows(e_vecs, k, m);
}
}
}
/* index of largest off-diagonal element in row k */
size_t mat33_maxind(mat33_t A, size_t k)
{
const size_t N = 3;
size_t i, m = k + 1;
for (i = k + 2; i < N; ++i)
if (fabsf(A[k][i]) > fabsf(A[k][m]))
m = i;
return m;
}
void mat33_rotate(mat33_t A, float c, float s,
size_t k, size_t l, size_t i, size_t j)
{
float tmp = c * A[k][l] - s * A[i][j];
A[i][j] = s * A[k][l] + c * A[i][j];
A[k][l] = tmp;
}
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