Math: Gram-Schmidt orthonormalization.

src/Math/Algorithms/CMakeLists.txt

@@ -1,5 +1,6 @@
 set(MagnumMathAlgorithms_HEADERS
-    GaussJordan.h)
+    GaussJordan.h
+    GramSchmidt.h)
 install(FILES ${MagnumMathAlgorithms_HEADERS} DESTINATION ${MAGNUM_INCLUDE_INSTALL_DIR}/Math/Algorithms)
 
 if(BUILD_TESTS)

src/Math/Algorithms/GramSchmidt.h

@@ -0,0 +1,51 @@
+#ifndef Magnum_Math_Algorithms_GramSchmidt_h
+#define Magnum_Math_Algorithms_GramSchmidt_h
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum 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 Lesser General Public License version 3 for more details.
+*/
+
+/** @file
+ * @brief Function Magnum::Math::Algorithms::gramSchmidtInPlace(), Magnum::Math::Algorithms::gramSchmidt()
+ */
+
+#include "Math/Matrix.h"
+
+namespace Magnum { namespace Math { namespace Algorithms {
+
+/**
+@brief Gram-schmidt matrix orthonormalization
+@param[in,out] matrix   Matrix to perform orthonormalization on
+*/
+template<std::size_t size, class T> void gramSchmidtInPlace(Matrix<size, T>& matrix) {
+    for(std::size_t i = 0; i != size; ++i) {
+        matrix[i] = matrix[i].normalized();
+        for(std::size_t j = i+1; j != size; ++j)
+            matrix[j] -= matrix[j].projected(matrix[i]);
+    }
+}
+
+/**
+@brief Gram-schmidt matrix orthonormalization
+
+Unlike gramSchmidtInPlace() returns the modified matrix instead of performing
+the orthonormalization in-place.
+*/
+template<std::size_t size, class T> Matrix<size, T> gramSchmidt(Matrix<size, T> matrix) {
+    gramSchmidtInPlace(matrix);
+    return matrix;
+}
+
+}}}
+
+#endif

src/Math/Algorithms/Test/CMakeLists.txt

@@ -1 +1,2 @@
 corrade_add_test(MathAlgorithmsGaussJordanTest GaussJordanTest.cpp LIBRARIES MagnumMathTestLib)
+corrade_add_test(MathAlgorithmsGramSchmidtTest GramSchmidtTest.cpp LIBRARIES MagnumMathTestLib)

src/Math/Algorithms/Test/GramSchmidtTest.cpp

@@ -0,0 +1,60 @@
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum 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 Lesser General Public License version 3 for more details.
+*/
+
+#include "GramSchmidtTest.h"
+
+#include "Math/Algorithms/GramSchmidt.h"
+
+CORRADE_TEST_MAIN(Magnum::Math::Algorithms::Test::GramSchmidtTest)
+
+namespace Magnum { namespace Math { namespace Algorithms { namespace Test {
+
+typedef Matrix<3, float> Matrix3;
+typedef Vector<3, float> Vector3;
+
+GramSchmidtTest::GramSchmidtTest() {
+    addTests(&GramSchmidtTest::test);
+}
+
+void GramSchmidtTest::test() {
+    Matrix3 m(
+        3.0f, 5.0f, 8.0f,
+        4.0f, 4.0f, 7.0f,
+        7.0f, -1.0f, 8.0f
+    );
+
+    Matrix3 normalized = Algorithms::gramSchmidt(m);
+
+    /* Verify the first vector is in direction of first original */
+    CORRADE_COMPARE(normalized[0], m[0].normalized());
+
+    /* Verify the vectors have unit length */
+    CORRADE_COMPARE(normalized[0].length(), 1.0f);
+    CORRADE_COMPARE(normalized[1].length(), 1.0f);
+    CORRADE_COMPARE(normalized[2].length(), 1.0f);
+
+    /* Verify the vectors are orthogonal */
+    CORRADE_COMPARE(Vector3::dot(normalized[0], normalized[1]), 0.0f);
+    CORRADE_COMPARE(Vector3::dot(normalized[0], normalized[2]), 0.0f);
+    CORRADE_COMPARE(Vector3::dot(normalized[1], normalized[2]), 0.0f);
+
+    /* Just to be sure */
+    Matrix3 expected( 0.303046f,  0.505076f,  0.808122f,
+                      0.928316f, -0.348119f, -0.130544f,
+                     -0.215388f, -0.789754f,  0.574367f);
+    CORRADE_COMPARE(normalized, expected);
+}
+
+}}}}

src/Math/Algorithms/Test/GramSchmidtTest.h

@@ -0,0 +1,31 @@
+#ifndef Magnum_Math_Algorithms_Test_GramSchmidtTest_h
+#define Magnum_Math_Algorithms_Test_GramSchmidtTest_h
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum 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 Lesser General Public License version 3 for more details.
+*/
+
+#include <TestSuite/Tester.h>
+
+namespace Magnum { namespace Math { namespace Algorithms { namespace Test {
+
+class GramSchmidtTest: public Corrade::TestSuite::Tester {
+    public:
+        GramSchmidtTest();
+
+        void test();
+};
+
+}}}}
+
+#endif