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91 lines
3.2 KiB
91 lines
3.2 KiB
namespace Eigen {
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namespace internal {
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// TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt
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template <typename Scalar>
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void qrsolv(
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Matrix< Scalar, Dynamic, Dynamic > &s,
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// TODO : use a PermutationMatrix once lmpar is no more:
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const VectorXi &ipvt,
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const Matrix< Scalar, Dynamic, 1 > &diag,
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const Matrix< Scalar, Dynamic, 1 > &qtb,
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Matrix< Scalar, Dynamic, 1 > &x,
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Matrix< Scalar, Dynamic, 1 > &sdiag)
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{
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typedef DenseIndex Index;
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/* Local variables */
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Index i, j, k, l;
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Scalar temp;
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Index n = s.cols();
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Matrix< Scalar, Dynamic, 1 > wa(n);
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JacobiRotation<Scalar> givens;
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/* Function Body */
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// the following will only change the lower triangular part of s, including
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// the diagonal, though the diagonal is restored afterward
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/* copy r and (q transpose)*b to preserve input and initialize s. */
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/* in particular, save the diagonal elements of r in x. */
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x = s.diagonal();
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wa = qtb;
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s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();
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/* eliminate the diagonal matrix d using a givens rotation. */
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for (j = 0; j < n; ++j) {
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/* prepare the row of d to be eliminated, locating the */
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/* diagonal element using p from the qr factorization. */
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l = ipvt[j];
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if (diag[l] == 0.)
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break;
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sdiag.tail(n-j).setZero();
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sdiag[j] = diag[l];
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/* the transformations to eliminate the row of d */
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/* modify only a single element of (q transpose)*b */
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/* beyond the first n, which is initially zero. */
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Scalar qtbpj = 0.;
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for (k = j; k < n; ++k) {
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/* determine a givens rotation which eliminates the */
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/* appropriate element in the current row of d. */
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givens.makeGivens(-s(k,k), sdiag[k]);
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/* compute the modified diagonal element of r and */
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/* the modified element of ((q transpose)*b,0). */
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s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];
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temp = givens.c() * wa[k] + givens.s() * qtbpj;
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qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
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wa[k] = temp;
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/* accumulate the tranformation in the row of s. */
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for (i = k+1; i<n; ++i) {
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temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
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sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
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s(i,k) = temp;
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}
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}
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}
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/* solve the triangular system for z. if the system is */
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/* singular, then obtain a least squares solution. */
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Index nsing;
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for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}
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wa.tail(n-nsing).setZero();
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s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));
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// restore
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sdiag = s.diagonal();
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s.diagonal() = x;
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/* permute the components of z back to components of x. */
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for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];
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}
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} // end namespace internal
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} // end namespace Eigen
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