From 019c9c0c5fc1f61dee93442b2c82926e7676ba21 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Vladim=C3=ADr=20Vondru=C5=A1?= <mosra@centrum.cz>
Date: Mon, 4 Feb 2013 18:46:37 +0100
Subject: [PATCH] Math: Gauss-Jordan algorithm as pure functions.

No need to wrap this in a class.
---
 src/Math/Algorithms/GaussJordan.h            | 79 +++++++++-----------
 src/Math/Algorithms/Test/GaussJordanTest.cpp |  4 +-
 2 files changed, 36 insertions(+), 47 deletions(-)

diff --git a/src/Math/Algorithms/GaussJordan.h b/src/Math/Algorithms/GaussJordan.h
index dc1734346..130403216 100644
--- a/src/Math/Algorithms/GaussJordan.h
+++ b/src/Math/Algorithms/GaussJordan.h
@@ -16,7 +16,7 @@
 */
 
 /** @file
- * @brief Class Magnum::Math::Algorithms::GaussJordan
+ * @brief Function Magnum::Math::Algorithms::gaussJordanInPlaceTransposed(), Magnum::Math::Algorithms::gaussJordanInPlace()
  */
 
 #include "Math/RectangularMatrix.h"
@@ -24,54 +24,25 @@
 namespace Magnum { namespace Math { namespace Algorithms {
 
 /**
-@brief Gauss-Jordan elimination
+@brief In-place Gauss-Jordan elimination on transposed matrices
+@param a     Transposed left side of augmented matrix
+@param t     Transposed right side of augmented matrix
+@return True if @p a is regular, false if @p a is singular (and thus the
+    system cannot be solved).
+
+As Gauss-Jordan elimination works on rows and matrices in OpenGL are
+column-major, it is more efficient to operate on transposed matrices and treat
+columns as rows. See also gaussJordanInPlace() which works with non-transposed matrices.
+
+The function eliminates matrix @p a and solves @p t in place. For efficiency
+reasons, only pure Gaussian elimination is done on @p a and the final
+backsubstitution is done only on @p t, as @p a would always end with identity
+matrix anyway.
 
 Based on ultra-compact Python code by Jarno Elonen,
 http://elonen.iki.fi/code/misc-notes/python-gaussj/index.html.
 */
-class GaussJordan {
-    public:
-        GaussJordan() = delete;
-
-        /**
-         * @brief Eliminate transposed matrices in place
-         * @param a     Transposed left side of augmented matrix
-         * @param t     Transposed right side of augmented matrix
-         * @return True if @p a is regular, false if @p a is singular (and
-         *      thus the system cannot be solved).
-         *
-         * As Gauss-Jordan elimination works on rows and matrices in OpenGL
-         * are column-major, it is more efficient to operate on transposed
-         * matrices and treat columns as rows. See also inPlace() which works
-         * with non-transposed matrices.
-         *
-         * The function eliminates matrix @p a and solves @p t in place. For
-         * efficiency reasons, only pure Gaussian elimination is done on @p a
-         * and the final backsubstitution is done only on @p t, as @p a would
-         * always end with identity matrix anyway.
-         */
-        template<std::size_t size, std::size_t rows, class T> static bool inPlaceTransposed(RectangularMatrix<size, size, T>& a, RectangularMatrix<size, rows, T>& t);
-
-        /**
-         * @brief Eliminate in place
-         *
-         * Transposes the matrices, calls inPlaceTransposed() on them and then
-         * transposes them back.
-         */
-        template<std::size_t size, std::size_t cols, class T> static bool inPlace(RectangularMatrix<size, size, T>& a, RectangularMatrix<cols, size, T>& t) {
-            a = a.transposed();
-            RectangularMatrix<size, cols, T> tTransposed = t.transposed();
-
-            bool ret = inPlaceTransposed(a, tTransposed);
-
-            a = a.transposed();
-            t = tTransposed.transposed();
-
-            return ret;
-        }
-};
-
-template<std::size_t size, std::size_t cols, class T> bool GaussJordan::inPlaceTransposed(RectangularMatrix<size, size, T>& a, RectangularMatrix<size, cols, T>& t) {
+template<std::size_t size, std::size_t rows, class T> bool gaussJordanInPlaceTransposed(RectangularMatrix<size, size, T>& a, RectangularMatrix<size, rows, T>& t) {
     for(std::size_t row = 0; row != size; ++row) {
         /* Find max pivot */
         std::size_t rowMax = row;
@@ -110,6 +81,24 @@ template<std::size_t size, std::size_t cols, class T> bool GaussJordan::inPlaceT
     return true;
 }
 
+/**
+@brief In-place Gauss-Jordan elimination
+
+Transposes the matrices, calls gaussJordanInPlaceTransposed() on them and then
+transposes them back.
+*/
+template<std::size_t size, std::size_t cols, class T> bool gaussJordanInPlace(RectangularMatrix<size, size, T>& a, RectangularMatrix<cols, size, T>& t) {
+    a = a.transposed();
+    RectangularMatrix<size, cols, T> tTransposed = t.transposed();
+
+    bool ret = gaussJordanInPlaceTransposed(a, tTransposed);
+
+    a = a.transposed();
+    t = tTransposed.transposed();
+
+    return ret;
+}
+
 }}}
 
 #endif
diff --git a/src/Math/Algorithms/Test/GaussJordanTest.cpp b/src/Math/Algorithms/Test/GaussJordanTest.cpp
index 1825769df..155144f84 100644
--- a/src/Math/Algorithms/Test/GaussJordanTest.cpp
+++ b/src/Math/Algorithms/Test/GaussJordanTest.cpp
@@ -42,7 +42,7 @@ void GaussJordanTest::singular() {
               Vector4(1.0f, 2.0f,  7.0f, 40.0f));
     RectangularMatrix<4, 1, float> t;
 
-    CORRADE_VERIFY(!GaussJordan::inPlaceTransposed(a, t));
+    CORRADE_VERIFY(!gaussJordanInPlaceTransposed(a, t));
 }
 
 void GaussJordanTest::invert() {
@@ -58,7 +58,7 @@ void GaussJordanTest::invert() {
 
     Matrix4 a2(a);
     Matrix4 inverse = Matrix4::fromDiagonal(Vector4(1.0f));
-    CORRADE_VERIFY(GaussJordan::inPlace(a2, inverse));
+    CORRADE_VERIFY(gaussJordanInPlace(a2, inverse));
 
     CORRADE_COMPARE(inverse, expectedInverse);
     CORRADE_COMPARE(a*inverse, Matrix4::fromDiagonal(Vector4(1.0f)));