Merge branch 'timoore/effects'

[simgear.git] / simgear / math / leastsqs.hxx

diff --git a/simgear/math/leastsqs.hxx b/simgear/math/leastsqs.hxx
index 16d6ad09663b3a08ac24b3eed88ffc0f9b1bb37d..3889cf7a3e15bdc1a4f5a9cea63dd7f33d843fff 100644 (file)
--- a/simgear/math/leastsqs.hxx
+++ b/simgear/math/leastsqs.hxx
@@ -1,69 +1,79 @@
-// leastsqs.h -- Implements a simple linear least squares best fit routine
-//
+/**
+ * \file leastsqs.hxx
+ * Implements a simple linear least squares best fit routine.
+ */
+
 // Written by Curtis Olson, started September 1997.
 //
-// Copyright (C) 1997  Curtis L. Olson  - curt@infoplane.com
+// Copyright (C) 1997  Curtis L. Olson  - http://www.flightgear.org/~curt
 //
-// 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 library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Library 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,
+// This library 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.
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+// Library 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., 675 Mass Ave, Cambridge, MA 02139, USA.
+// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 //
 // $Id$
-///
 
 
 #ifndef _LEASTSQS_H
 #define _LEASTSQS_H
 
 
-#ifndef __cplusplus                                                          
+#ifndef __cplusplus
 # error This library requires C++
-#endif                                   
-
+#endif
 
-/* 
-Least squares fit:
 
-y = b0 + b1x
+/**
+Classical least squares fit:
 
-     n*sum(xi*yi) - (sum(xi)*sum(yi))
-b1 = --------------------------------
-     n*sum(xi^2) - (sum(xi))^2
+\f[
+    y = b_0 + b_1 * x
+\f]
 
+\f[
+    b_1 = \frac{n * \sum_0^{i-1} (x_i*y_i) - \sum_0^{i-1} x_i* \sum_0^{i-1} y_i}
+          {n*\sum_0^{i-1} x_i^2 - (\sum_0^{i-1} x_i)^2}
+\f]
 
-b0 = sum(yi)/n - b1*(sum(xi)/n)
+\f[
+    b_0 = \frac{\sum_0^{i-1} y_i}{n} - b_1 * \frac{\sum_0^{i-1} x_i}{n}
+\f]
 */
-
 void least_squares(double *x, double *y, int n, double *m, double *b);
 
-/* incrimentally update existing values with a new data point */
+
+/**
+ * Incrimentally update existing values with a new data point.
+ */
 void least_squares_update(double x, double y, double *m, double *b);
 
 
-/* 
-  return the least squares error:
+/**
+  @return the least squares error:.
+\f[
 
-              (y[i] - y_hat[i])^2
-              -------------------
-                      n
+    \frac{(y_i - \hat{y}_i)^2}{n}
+\f]
 */
 double least_squares_error(double *x, double *y, int n, double m, double b);
 
 
-/* 
-  return the maximum least squares error:
+/**
+  @return the maximum least squares error.
 
-              (y[i] - y_hat[i])^2
+\f[
+    (y_i - \hat{y}_i)^2
+\f]
 */
 double least_squares_max_error(double *x, double *y, int n, double m, double b);