Add BLI_math_statistics, where stats tool shall be!

For now, only contains some 3x3 matrix covariance computing.

source/blender/blenlib/BLI_math.h

@@ -74,5 +74,6 @@
 #include "BLI_math_geom.h"
 #include "BLI_math_interp.h"
 #include "BLI_math_solvers.h"
+#include "BLI_math_statistics.h"
 
 #endif /* __BLI_MATH_H__ */

source/blender/blenlib/BLI_math_statistics.h

@@ -0,0 +1,70 @@
+/*
+ * ***** 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 *****
+ * */
+
+#ifndef __BLI_MATH_STATISTICS_H__
+#define __BLI_MATH_STATISTICS_H__
+
+/** \file BLI_math_statistics.h
+ *  \ingroup bli
+ */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include "BLI_compiler_attrs.h"
+#include "BLI_math_inline.h"
+
+#ifdef BLI_MATH_GCC_WARN_PRAGMA
+#  pragma GCC diagnostic push
+#  pragma GCC diagnostic ignored "-Wredundant-decls"
+#endif
+
+/********************************** Covariance Matrices *********************************/
+
+void BLI_covariance_m_vn_ex(
+        const int n, const float *cos_vn, const int nbr_cos_v3, const float *center, const bool use_sample_correction,
+        float *r_covmat);
+void BLI_covariance_m3_v3n(
+        const float (*cos_v3)[3], const int nbr_cos_v3, const bool use_sample_correction,
+        float r_covmat[3][3], float r_center[3]);
+
+/**************************** Inline Definitions ******************************/
+#if 0  /* None so far. */
+#  if BLI_MATH_DO_INLINE
+#    include "intern/math_geom_inline.c"
+#  endif
+#endif
+
+#ifdef BLI_MATH_GCC_WARN_PRAGMA
+#  pragma GCC diagnostic pop
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* __BLI_MATH_STATISTICS_H__ */
+

source/blender/blenlib/CMakeLists.txt

@@ -85,6 +85,7 @@ set(SRC
 	intern/math_matrix.c
 	intern/math_rotation.c
 	intern/math_solvers.c
+	intern/math_statistics.c
 	intern/math_vector.c
 	intern/math_vector_inline.c
 	intern/noise.c
@@ -165,6 +166,7 @@ set(SRC
 	BLI_math_matrix.h
 	BLI_math_rotation.h
 	BLI_math_solvers.h
+	BLI_math_statistics.h
 	BLI_math_vector.h
 	BLI_memarena.h
 	BLI_mempool.h

source/blender/blenlib/intern/math_statistics.c

@@ -0,0 +1,116 @@
+/*
+ * ***** 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_statistics.c
+ *  \ingroup bli
+ */
+
+#include "MEM_guardedalloc.h"
+
+#include "BLI_math.h"
+#include "BLI_utildefines.h"
+
+#include "BLI_strict_flags.h"
+
+/********************************** Covariance Matrices *********************************/
+
+/**
+ * \brief Compute the covariance matrix of given set of nD coordinates.
+ *
+ * \param n the dimension of the vectors (and hence, of the covairance matrix to compute).
+ * \param cos_vn the nD points to compute covariance from.
+ * \param nbr_cos_vn the number of nD coordinates in cos_vn.
+ * \param center the center (or mean point) of cos_vn. If NULL, it is assumed cos_vn is already centered.
+ * \param use_sample_correction whether to apply sample correction
+ *                              (i.e. get 'sample varince' instead of 'population variance').
+ * \return r_covmat the computed covariance matrix.
+ */
+void BLI_covariance_m_vn_ex(
+        const int n, const float *cos_vn, const int nbr_cos_vn, const float *center, const bool use_sample_correction,
+        float *r_covmat)
+{
+	int i, j, k;
+
+	/* Note about that division: see https://en.wikipedia.org/wiki/Bessel%27s_correction.
+	 * In a nutshell, it must be 1 / (n - 1) for 'sample data', and 1 / n for 'population data'...
+	 */
+	const float covfac = 1.0f / (float)(use_sample_correction ? nbr_cos_vn - 1 : nbr_cos_vn);
+
+	memset(r_covmat, 0, sizeof(*r_covmat) * (size_t)(n * n));
+
+#pragma omp parallel for default(shared) private(i, j, k) schedule(static) if((nbr_cos_vn * n) >= 10000)
+	for (i = 0; i < n; i++) {
+		for (j = i; j < n; j++) {
+			r_covmat[i * n + j] = 0.0f;
+			if (center) {
+				for (k = 0; k < nbr_cos_vn; k++) {
+					r_covmat[i * n + j] += (cos_vn[k * n + i] - center[i]) * (cos_vn[k * n + j] - center[j]);
+				}
+			}
+			else {
+				for (k = 0; k < nbr_cos_vn; k++) {
+					r_covmat[i * n + j] += cos_vn[k * n + i] * cos_vn[k * n + j];
+				}
+			}
+			r_covmat[i * n + j] *= covfac;
+		}
+	}
+	/* Covariance matrices are always symetrical, so we can compute only one half of it (as done above),
+	 * and copy it to the other half! */
+	for (i = 1; i < n; i++) {
+		for (j = 0; j < i; j++) {
+			r_covmat[i * n + j] = r_covmat[j * n + i];
+		}
+	}
+}
+
+/**
+ * \brief Compute the covariance matrix of given set of 3D coordinates.
+ *
+ * \param cos_v3 the 3D points to compute covariance from.
+ * \param nbr_cos_v3 the number of 3D coordinates in cos_v3.
+ * \return r_covmat the computed covariance matrix.
+ * \return r_center the computed center (mean) of 3D points (may be NULL).
+ */
+void BLI_covariance_m3_v3n(
+        const float (*cos_v3)[3], const int nbr_cos_v3, const bool use_sample_correction,
+        float r_covmat[3][3], float r_center[3])
+{
+	float center[3];
+	const float mean_fac = 1.0f / (float)nbr_cos_v3;
+	int i;
+
+	zero_v3(center);
+	for (i = 0; i < nbr_cos_v3; i++) {
+		/* Applying mean_fac here rather than once at the end reduce compute errors... */
+		madd_v3_v3fl(center, cos_v3[i], mean_fac);
+	}
+
+	if (r_center) {
+		copy_v3_v3(r_center, center);
+	}
+
+	BLI_covariance_m_vn_ex(3, (const float *)cos_v3, nbr_cos_v3, center, use_sample_correction, (float *)r_covmat);
+}