85 lines
2.8 KiB
C++
85 lines
2.8 KiB
C++
/// @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
|