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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
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