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vendor/include/glm/gtx/matrix_factorisation.inl

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+/// @ref gtx_matrix_factorisation
+
+namespace glm
+{
+	template <length_t C, length_t R, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER mat<C, R, T, Q> flipud(mat<C, R, T, Q> const& in)
+	{
+		mat<R, C, T, Q> tin = transpose(in);
+		tin = fliplr(tin);
+		mat<C, R, T, Q> out = transpose(tin);
+
+		return out;
+	}
+
+	template <length_t C, length_t R, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER mat<C, R, T, Q> fliplr(mat<C, R, T, Q> const& in)
+	{
+		mat<C, R, T, Q> out;
+		for (length_t i = 0; i < C; i++)
+		{
+			out[i] = in[(C - i) - 1];
+		}
+
+		return out;
+	}
+
+	template <length_t C, length_t R, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER void qr_decompose(mat<C, R, T, Q> const& in, mat<(C < R ? C : R), R, T, Q>& q, mat<C, (C < R ? C : R), T, Q>& r)
+	{
+		// Uses modified Gram-Schmidt method
+		// Source: https://en.wikipedia.org/wiki/Gram–Schmidt_process
+		// And https://en.wikipedia.org/wiki/QR_decomposition
+
+		//For all the linearly independs columns of the input...
+		// (there can be no more linearly independents columns than there are rows.)
+		for (length_t i = 0; i < (C < R ? C : R); i++)
+		{
+			//Copy in Q the input's i-th column.
+			q[i] = in[i];
+
+			//j = [0,i[
+			// Make that column orthogonal to all the previous ones by substracting to it the non-orthogonal projection of all the previous columns.
+			// Also: Fill the zero elements of R
+			for (length_t j = 0; j < i; j++)
+			{
+				q[i] -= dot(q[i], q[j])*q[j];
+				r[j][i] = 0;
+			}
+
+			//Now, Q i-th column is orthogonal to all the previous columns. Normalize it.
+			q[i] = normalize(q[i]);
+
+			//j = [i,C[
+			//Finally, compute the corresponding coefficients of R by computing the projection of the resulting column on the other columns of the input.
+			for (length_t j = i; j < C; j++)
+			{
+				r[j][i] = dot(in[j], q[i]);
+			}
+		}
+	}
+
+	template <length_t C, length_t R, typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER void rq_decompose(mat<C, R, T, Q> const& in, mat<(C < R ? C : R), R, T, Q>& r, mat<C, (C < R ? C : R), T, Q>& q)
+	{
+		// From https://en.wikipedia.org/wiki/QR_decomposition:
+		// The RQ decomposition transforms a matrix A into the product of an upper triangular matrix R (also known as right-triangular) and an orthogonal matrix Q. The only difference from QR decomposition is the order of these matrices.
+		// QR decomposition is Gram–Schmidt orthogonalization of columns of A, started from the first column.
+		// RQ decomposition is Gram–Schmidt orthogonalization of rows of A, started from the last row.
+
+		mat<R, C, T, Q> tin = transpose(in);
+		tin = fliplr(tin);
+
+		mat<R, (C < R ? C : R), T, Q> tr;
+		mat<(C < R ? C : R), C, T, Q> tq;
+		qr_decompose(tin, tq, tr);
+
+		tr = fliplr(tr);
+		r = transpose(tr);
+		r = fliplr(r);
+
+		tq = fliplr(tq);
+		q = transpose(tq);
+	}
+} //namespace glm