Math: generalize Gram-Schmidt algorithm for non-square matrices.

src/Math/Algorithms/GramSchmidt.h

@@ -19,29 +19,30 @@
  * @brief Function Magnum::Math::Algorithms::gramSchmidtInPlace(), Magnum::Math::Algorithms::gramSchmidt()
  */
 
-#include "Math/Matrix.h"
+#include "Math/RectangularMatrix.h"
 
 namespace Magnum { namespace Math { namespace Algorithms {
 
 /**
-@brief Gram-schmidt matrix orthonormalization
+@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) {
+template<std::size_t cols, std::size_t rows, class T> void gramSchmidtInPlace(RectangularMatrix<cols, rows, T>& matrix) {
-    for(std::size_t i = 0; i != size; ++i) {
+    static_assert(cols <= rows, "Unsupported matrix aspect ratio");
+    for(std::size_t i = 0; i != cols; ++i) {
         matrix[i] = matrix[i].normalized();
-        for(std::size_t j = i+1; j != size; ++j)
+        for(std::size_t j = i+1; j != cols; ++j)
             matrix[j] -= matrix[j].projected(matrix[i]);
     }
 }
 
 /**
-@brief Gram-schmidt matrix orthonormalization
+@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) {
+template<std::size_t cols, std::size_t rows, class T> RectangularMatrix<cols, rows, T> gramSchmidt(RectangularMatrix<cols, rows, T> matrix) {
     gramSchmidtInPlace(matrix);
     return matrix;
 }

src/Math/Algorithms/Test/GramSchmidtTest.cpp

@@ -26,7 +26,7 @@ class GramSchmidtTest: public Corrade::TestSuite::Tester {
         void test();
 };
 
-typedef Matrix<3, float> Matrix3;
+typedef RectangularMatrix<3, 3, float> Matrix3;
 typedef Vector<3, float> Vector3;
 
 GramSchmidtTest::GramSchmidtTest() {