Math: Added Algorithms::qr().

src/Magnum/Math/Algorithms/CMakeLists.txt

@@ -26,6 +26,7 @@
 set(MagnumMathAlgorithms_HEADERS
     GaussJordan.h
     GramSchmidt.h
+    Qr.h
     Svd.h)
 
 # Force IDEs to display all header files in project view

src/Magnum/Math/Algorithms/Qr.h

@@ -0,0 +1,59 @@
+#ifndef Magnum_Math_Algorithms_Qr_h
+#define Magnum_Math_Algorithms_Qr_h
+/*
+    This file is part of Magnum.
+
+    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016
+              Vladimír Vondruš <mosra@centrum.cz>
+
+    Permission is hereby granted, free of charge, to any person obtaining a
+    copy of this software and associated documentation files (the "Software"),
+    to deal in the Software without restriction, including without limitation
+    the rights to use, copy, modify, merge, publish, distribute, sublicense,
+    and/or sell copies of the Software, and to permit persons to whom the
+    Software is furnished to do so, subject to the following conditions:
+
+    The above copyright notice and this permission notice shall be included
+    in all copies or substantial portions of the Software.
+
+    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+    DEALINGS IN THE SOFTWARE.
+*/
+
+/** @file
+ * @brief Function @ref Magnum::Math::Algorithms::qr()
+ */
+
+#include "Magnum/Math/Matrix.h"
+
+namespace Magnum { namespace Math { namespace Algorithms {
+
+/**
+@brief QR decomposition
+
+Calculated using classic Gram-Schmidt process.
+*/
+template<std::size_t size, class T> std::pair<Matrix<size, T>, Matrix<size, T>> qr(const Matrix<size, T>& matrix) {
+    Matrix<size, T> q, r;
+
+    for(std::size_t k = 0; k != size; ++k) {
+        Vector<size, T> p = matrix[k];
+        for(std::size_t j = 0; j != k; ++j) {
+            r[k][j] = Math::dot(p, q[j]);
+            p -= q[j]*r[k][j];
+        }
+        r[k][k] = p.length();
+        q[k] = p/r[k][k];
+    }
+
+    return {q, r};
+}
+
+}}}
+
+#endif

src/Magnum/Math/Algorithms/Test/CMakeLists.txt

@@ -25,4 +25,5 @@
 
 corrade_add_test(MathAlgorithmsGaussJordanTest GaussJordanTest.cpp LIBRARIES MagnumMathTestLib)
 corrade_add_test(MathAlgorithmsGramSchmidtTest GramSchmidtTest.cpp LIBRARIES MagnumMathTestLib)
+corrade_add_test(MathAlgorithmsQrTest QrTest.cpp LIBRARIES MagnumMathTestLib)
 corrade_add_test(MathAlgorithmsSvdTest SvdTest.cpp LIBRARIES MagnumMathTestLib)

src/Magnum/Math/Algorithms/Test/QrTest.cpp

@@ -0,0 +1,69 @@
+/*
+    This file is part of Magnum.
+
+    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016
+              Vladimír Vondruš <mosra@centrum.cz>
+
+    Permission is hereby granted, free of charge, to any person obtaining a
+    copy of this software and associated documentation files (the "Software"),
+    to deal in the Software without restriction, including without limitation
+    the rights to use, copy, modify, merge, publish, distribute, sublicense,
+    and/or sell copies of the Software, and to permit persons to whom the
+    Software is furnished to do so, subject to the following conditions:
+
+    The above copyright notice and this permission notice shall be included
+    in all copies or substantial portions of the Software.
+
+    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+    DEALINGS IN THE SOFTWARE.
+*/
+
+#include <tuple>
+#include <Corrade/TestSuite/Tester.h>
+
+#include "Magnum/Math/Matrix3.h"
+#include "Magnum/Math/Algorithms/Qr.h"
+
+namespace Magnum { namespace Math { namespace Algorithms { namespace Test {
+
+struct QrTest: Corrade::TestSuite::Tester {
+    explicit QrTest();
+
+    void test();
+};
+
+typedef Matrix3<Float> Matrix3;
+
+QrTest::QrTest() {
+    addTests({&QrTest::test});
+}
+
+void QrTest::test() {
+    Matrix3 a{{  0.0f,   3.0f,   4.0f},
+              {-20.0f,  27.0f,  11.0f},
+              {-14.0f,  -4.0f,  -2.0f}};
+
+    Matrix3 q, r;
+    std::tie(q, r) = Algorithms::qr(a);
+
+    CORRADE_COMPARE(q*r, a);
+
+    Matrix3 qExpected = Matrix3{{  0.0f,  15.0f, 20.0f},
+                                {-20.0f,  12.0f, -9.0f},
+                                {-15.0f, -16.0f, 12.0f}}/25.0f;
+    CORRADE_COMPARE(q, qExpected);
+
+    Matrix3 rExpected{{ 5.0f,  0.0f,  0.0f},
+                      {25.0f, 25.0f,  0.0f},
+                      {-4.0f, 10.0f, 10.0f}};
+    CORRADE_COMPARE(r, rExpected);
+}
+
+}}}}
+
+CORRADE_TEST_MAIN(Magnum::Math::Algorithms::Test::QrTest)