More comments

Fix RQ test
Slight optimisation in QR

glm/gtx/matrix_factorisation.hpp

@@ -27,7 +27,6 @@
 /*
 Suggestions:
  - Move helper functions flipud and flip lr to another file: They may be helpful in more general circumstances.
- - When rq_decompose is fed a matrix that has more rows than columns, the resulting r matrix is NOT upper triangular. Is that a bug?
  - Implement other types of matrix factorisation, such as: QL and LQ, L(D)U, eigendecompositions, etc...
 */
 
@@ -46,15 +45,16 @@ namespace glm{
 	GLM_FUNC_DECL matType<C, R, T, P> fliplr(const matType<C, R, T, P>& in);
 
 	/// Performs QR factorisation of a matrix.
-	/// Returns 2 matrices, q and r, such that q columns are orthonormal, r is an upper triangular matrix, and q*r=in.
-	/// r is a square matrix whose dimensions are the same than the width of the input matrix, and q has the same dimensions than the input matrix.
+	/// Returns 2 matrices, q and r, such that the columns of q are orthonormal and span the same subspace than those of the input matrix, r is an upper triangular matrix, and q*r=in.
+	/// Given an n-by-m input matrix, q has dimensions min(n,m)-by-m, and r has dimensions n-by-min(n,m).
 	/// From GLM_GTX_matrix_factorisation extension.
 	template <length_t C, length_t R, typename T, precision P, template<length_t, length_t, typename, precision> class matType>
 	GLM_FUNC_DECL void qr_decompose(matType<std::min(C, R), R, T, P>& q, matType<C, std::min(C, R), T, P>& r, const matType<C, R, T, P>& in);
 
 	/// Performs RQ factorisation of a matrix.
-	/// Returns 2 matrices, r and q, such that r is an upper triangular matrix, q rows are orthonormal, and r*q=in.
-	/// q has the same dimensions than the input matrix, and r is a square matrix whose dimensions are the same than the height of the input matrix.
+	/// Returns 2 matrices, r and q, such that r is an upper triangular matrix, the rows of q are orthonormal and span the same subspace than those of the input matrix, and r*q=in.
+	/// Note that in the context of RQ factorisation, the diagonal is seen as starting in the lower-right corner of the matrix, instead of the usual upper-left.
+	/// Given an n-by-m input matrix, r has dimensions min(n,m)-by-m, and q has dimensions n-by-min(n,m).
 	/// From GLM_GTX_matrix_factorisation extension.
 	template <length_t C, length_t R, typename T, precision P, template<length_t, length_t, typename, precision> class matType>
 	GLM_FUNC_DECL void rq_decompose(matType<std::min(C, R), R, T, P>& r, matType<C, std::min(C, R), T, P>& q, const matType<C, R, T, P>& in);

glm/gtx/matrix_factorisation.inl

@@ -29,21 +29,25 @@ namespace glm {
 		// 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 < std::min(R, C); 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]);
-		}
-
-		for (length_t i = 0; i < std::min(R, C); i++) {
-			for (length_t j = 0; j < i; j++) {
-				r[j][i] = 0;
-			}
 
+			//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]);
 			}

test/gtx/gtx_matrix_factorisation.cpp

@@ -22,17 +22,17 @@ int test_qr(matType<C, R, T, P> m) {
 
 	//Test if the columns of q are orthonormal
 	for (glm::length_t i = 0; i < std::min(C, R); i++) {
-		if ((length(q[i]) - 1) > epsilon) return 1;
+		if ((length(q[i]) - 1) > epsilon) return 2;
 
 		for (glm::length_t j = 0; j<i; j++) {
-			if (abs(dot(q[i], q[j])) > epsilon) return 1;
+			if (abs(dot(q[i], q[j])) > epsilon) return 3;
 		}
 	}
 
 	//Test if the matrix r is upper triangular
 	for (glm::length_t i = 0; i < C; i++) {
 		for (glm::length_t j = i + 1; j < std::min(C, R); j++) {
-			if (r[i][j] != 0) return 1;
+			if (r[i][j] != 0) return 4;
 		}
 	}
 
@@ -61,17 +61,17 @@ int test_rq(matType<C, R, T, P> m) {
 	matType<std::min(C, R), C, T, P> tq = transpose(q);
 
 	for (glm::length_t i = 0; i < std::min(C, R); i++) {
-		if ((length(tq[i]) - 1) > epsilon) return 1;
+		if ((length(tq[i]) - 1) > epsilon) return 2;
 
 		for (glm::length_t j = 0; j<i; j++) {
-			if (abs(dot(tq[i], tq[j])) > epsilon) return 1;
+			if (abs(dot(tq[i], tq[j])) > epsilon) return 3;
 		}
 	}
 	
 	//Test if the matrix r is upper triangular
 	for (glm::length_t i = 0; i < std::min(C, R); i++) {
-		for (glm::length_t j = i + 1; j < R; j++) {
-			if (r[i][j] != 0) return 1;
+		for (glm::length_t j = R - std::min(C, R) + i + 1; j < R; j++) {
+			if (r[i][j] != 0) return 4;
 		}
 	}
 
@@ -85,19 +85,19 @@ int main()
 	if(test_qr(glm::dmat3(12, 6, -4, -51, 167, 24, 4, -68, -41))) return 1;
 
 	//Test RQ square
-	if (test_rq(glm::dmat3(12, 6, -4, -51, 167, 24, 4, -68, -41))) return 1;
+	if (test_rq(glm::dmat3(12, 6, -4, -51, 167, 24, 4, -68, -41))) return 2;
 
 	//Test QR triangular 1
-	if (test_qr(glm::dmat3x4(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 1;
+	if (test_qr(glm::dmat3x4(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 3;
 
 	//Test QR triangular 2
-	if (test_qr(glm::dmat4x3(12, 6, -4, -51, 167, 24,  4, -68, -41, 7, 2, 15))) return 1;
+	if (test_qr(glm::dmat4x3(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 4;
 
 	//Test RQ triangular 1 : Fails at the triangular test
-	//if (test_rq(glm::dmat3x4(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 1;
+	if (test_rq(glm::dmat3x4(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 5;
 
 	//Test QR triangular 2
-	if (test_rq(glm::dmat4x3(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 1;
+	if (test_rq(glm::dmat4x3(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 6;
 
 	return 0;
 }