blender-archive/source/blender/freestyle/intern/geometry/matrix_util.cpp

/*
 * ***** 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:
 *   GXML/Graphite: Geometry and Graphics Programming Library + Utilities
 *   Copyright (C) 2000 Bruno Levy
 *   Contact: Bruno Levy
 *      levy@loria.fr
 *      ISA Project
 *      LORIA, INRIA Lorraine,
 *      Campus Scientifique, BP 239
 *      54506 VANDOEUVRE LES NANCY CEDEX
 *      FRANCE
 *
 * Contributor(s): none yet.
 *
 * ***** END GPL LICENSE BLOCK *****
 */

/** \file blender/freestyle/intern/geometry/matrix_util.cpp
 *  \ingroup freestyle
 *  \author Bruno Levy
 */

#include "matrix_util.h"

#include "BLI_math.h"

namespace Freestyle {

namespace OGF {

namespace 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 ((i != l) && (i != 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 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;
		return;
	}

//_________________________________________________________

}  // MatrixUtil namespace

}  // OGF namespace

} /* namespace Freestyle */