85 lines
2.7 KiB
Text
85 lines
2.7 KiB
Text
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/// @ref gtx_matrix_factorisation
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namespace glm
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{
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template <length_t C, length_t R, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER mat<C, R, T, Q> flipud(mat<C, R, T, Q> const& in)
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{
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mat<R, C, T, Q> tin = transpose(in);
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tin = fliplr(tin);
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mat<C, R, T, Q> out = transpose(tin);
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return out;
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}
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template <length_t C, length_t R, typename T, qualifier Q>
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GLM_FUNC_QUALIFIER mat<C, R, T, Q> fliplr(mat<C, R, T, Q> const& in)
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{
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mat<C, R, T, Q> out;
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for (length_t i = 0; i < C; i++)
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{
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out[i] = in[(C - i) - 1];
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}
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return out;
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}
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template <length_t C, length_t R, typename T, qualifier Q>
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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)
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{
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// Uses modified Gram-Schmidt method
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// Source: https://en.wikipedia.org/wiki/Gram<61>Schmidt_process
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// And https://en.wikipedia.org/wiki/QR_decomposition
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//For all the linearly independs columns of the input...
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// (there can be no more linearly independents columns than there are rows.)
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for (length_t i = 0; i < (C < R ? C : R); i++)
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{
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//Copy in Q the input's i-th column.
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q[i] = in[i];
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//j = [0,i[
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// Make that column orthogonal to all the previous ones by substracting to it the non-orthogonal projection of all the previous columns.
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// Also: Fill the zero elements of R
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for (length_t j = 0; j < i; j++)
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{
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q[i] -= dot(q[i], q[j])*q[j];
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r[j][i] = 0;
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}
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//Now, Q i-th column is orthogonal to all the previous columns. Normalize it.
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q[i] = normalize(q[i]);
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//j = [i,C[
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//Finally, compute the corresponding coefficients of R by computing the projection of the resulting column on the other columns of the input.
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for (length_t j = i; j < C; j++)
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{
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r[j][i] = dot(in[j], q[i]);
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}
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}
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}
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template <length_t C, length_t R, typename T, qualifier Q>
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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)
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{
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// From https://en.wikipedia.org/wiki/QR_decomposition:
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// 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.
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// QR decomposition is Gram<61>Schmidt orthogonalization of columns of A, started from the first column.
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// RQ decomposition is Gram<61>Schmidt orthogonalization of rows of A, started from the last row.
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mat<R, C, T, Q> tin = transpose(in);
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tin = fliplr(tin);
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mat<R, (C < R ? C : R), T, Q> tr;
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mat<(C < R ? C : R), C, T, Q> tq;
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qr_decompose(tin, tq, tr);
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tr = fliplr(tr);
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r = transpose(tr);
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r = fliplr(r);
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tq = fliplr(tq);
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q = transpose(tq);
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}
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} //namespace glm
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