|
|
@@ -1,9 +1,11 @@
|
|
|
/// @ref gtx_matrix_factorisation
|
|
|
/// @file glm/gtx/matrix_factorisation.inl
|
|
|
|
|
|
-namespace glm {
|
|
|
+namespace glm
|
|
|
+{
|
|
|
template <length_t C, length_t R, typename T, precision P, template<length_t, length_t, typename, precision> class matType>
|
|
|
- GLM_FUNC_QUALIFIER matType<C, R, T, P> flipud(const matType<C, R, T, P>& in) {
|
|
|
+ GLM_FUNC_QUALIFIER matType<C, R, T, P> flipud(matType<C, R, T, P> const& in)
|
|
|
+ {
|
|
|
matType<R, C, T, P> tin = transpose(in);
|
|
|
tin = fliplr(tin);
|
|
|
matType<C, R, T, P> out = transpose(tin);
|
|
|
@@ -12,9 +14,11 @@ namespace glm {
|
|
|
}
|
|
|
|
|
|
template <length_t C, length_t R, typename T, precision P, template<length_t, length_t, typename, precision> class matType>
|
|
|
- GLM_FUNC_QUALIFIER matType<C, R, T, P> fliplr(const matType<C, R, T, P>& in) {
|
|
|
+ GLM_FUNC_QUALIFIER matType<C, R, T, P> fliplr(matType<C, R, T, P> const& in)
|
|
|
+ {
|
|
|
matType<C, R, T, P> out;
|
|
|
- for (length_t i = 0; i < C; i++) {
|
|
|
+ for (length_t i = 0; i < C; i++)
|
|
|
+ {
|
|
|
out[i] = in[(C - i) - 1];
|
|
|
}
|
|
|
|
|
|
@@ -22,21 +26,24 @@ namespace glm {
|
|
|
}
|
|
|
|
|
|
template <length_t C, length_t R, typename T, precision P, template<length_t, length_t, typename, precision> class matType>
|
|
|
- GLM_FUNC_QUALIFIER void qr_decompose(matType<(C < R ? C : R), R, T, P>& q, matType<C, (C < R ? C : R), T, P>& r, const matType<C, R, T, P>& in) {
|
|
|
+ GLM_FUNC_QUALIFIER void qr_decompose(matType<C, R, T, P> const& in, matType<(C < R ? C : R), R, T, P>& q, matType<C, (C < R ? C : R), T, P>& 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++) {
|
|
|
+ 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++) {
|
|
|
+ for (length_t j = 0; j < i; j++)
|
|
|
+ {
|
|
|
q[i] -= dot(q[i], q[j])*q[j];
|
|
|
r[j][i] = 0;
|
|
|
}
|
|
|
@@ -46,14 +53,16 @@ namespace glm {
|
|
|
|
|
|
//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++) {
|
|
|
+ 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, precision P, template<length_t, length_t, typename, precision> class matType>
|
|
|
- GLM_FUNC_QUALIFIER void rq_decompose(matType<(C < R ? C : R), R, T, P>& r, matType<C, (C < R ? C : R), T, P>& q, const matType<C, R, T, P>& in) {
|
|
|
+ GLM_FUNC_QUALIFIER void rq_decompose(matType<C, R, T, P> const& in, matType<(C < R ? C : R), R, T, P>& r, matType<C, (C < R ? C : R), T, P>& 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.
|