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This commit is contained in:
Thomas Capricelli
@@ -20,6 +20,23 @@ public:
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const Scalar xtol = ei_sqrt(epsilon<Scalar>())
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);
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int solveNumericalDiff(
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Matrix< Scalar, Dynamic, 1 > &x,
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const Scalar tol = ei_sqrt(epsilon<Scalar>())
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);
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int solveNumericalDiff(
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Matrix< Scalar, Dynamic, 1 > &x,
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int &nfev,
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Matrix< Scalar, Dynamic, 1 > &diag,
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const int mode=1,
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int nb_of_subdiagonals = -1,
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int nb_of_superdiagonals = -1,
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const int maxfev = 2000,
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const Scalar factor = Scalar(100.),
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const Scalar xtol = ei_sqrt(epsilon<Scalar>()),
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const Scalar epsfcn = Scalar(0.)
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);
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Matrix< Scalar, Dynamic, 1 > fvec;
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Matrix< Scalar, Dynamic, Dynamic > fjac;
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Matrix< Scalar, Dynamic, 1 > R;
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@@ -357,3 +374,344 @@ algo_end:
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return info;
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}
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template<typename FunctorType, typename Scalar>
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int HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(
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Matrix< Scalar, Dynamic, 1 > &x,
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const Scalar tol
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)
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{
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const int n = x.size();
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int info, nfev=0;
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Matrix< Scalar, Dynamic, 1> diag;
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/* check the input parameters for errors. */
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if (n <= 0 || tol < 0.) {
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printf("HybridNonLinearSolver::solve() bad args : n,tol,...");
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return 0;
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}
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diag.setConstant(n, 1.);
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info = solveNumericalDiff(
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x,
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nfev,
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diag,
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2,
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-1, -1,
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(n+1)*200,
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100.,
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tol, Scalar(0.)
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);
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return (info==5)?4:info;
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}
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template<typename FunctorType, typename Scalar>
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int HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(
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Matrix< Scalar, Dynamic, 1 > &x,
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int &nfev,
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Matrix< Scalar, Dynamic, 1 > &diag,
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const int mode,
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int nb_of_subdiagonals,
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int nb_of_superdiagonals,
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const int maxfev,
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const Scalar factor,
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const Scalar xtol,
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const Scalar epsfcn
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)
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{
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const int n = x.size();
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Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n), wa3(n), wa4(n);
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if (nb_of_subdiagonals<0) nb_of_subdiagonals = n-1;
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if (nb_of_superdiagonals<0) nb_of_superdiagonals = n-1;
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qtf.resize(n);
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R.resize( (n*(n+1))/2);
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fjac.resize(n, n);
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fvec.resize(n);
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/* Local variables */
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int i, j, l, iwa[1];
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Scalar sum;
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int sing;
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int iter;
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Scalar temp;
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int msum, iflag;
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Scalar delta;
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int jeval;
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int ncsuc;
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Scalar ratio;
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Scalar fnorm;
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Scalar pnorm, xnorm, fnorm1;
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int nslow1, nslow2;
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int ncfail;
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Scalar actred, prered;
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int info;
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/* Function Body */
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info = 0;
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iflag = 0;
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nfev = 0;
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/* check the input parameters for errors. */
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if (n <= 0 || xtol < 0. || maxfev <= 0 || nb_of_subdiagonals < 0 || nb_of_superdiagonals < 0 || factor <= 0. )
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goto algo_end;
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if (mode == 2)
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for (j = 0; j < n; ++j)
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if (diag[j] <= 0.) goto algo_end;
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/* evaluate the function at the starting point */
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/* and calculate its norm. */
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iflag = functor.f(x, fvec);
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nfev = 1;
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if (iflag < 0)
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goto algo_end;
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fnorm = fvec.stableNorm();
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/* determine the number of calls to fcn needed to compute */
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/* the jacobian matrix. */
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/* Computing MIN */
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msum = std::min(nb_of_subdiagonals + nb_of_superdiagonals + 1, n);
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/* initialize iteration counter and monitors. */
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iter = 1;
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ncsuc = 0;
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ncfail = 0;
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nslow1 = 0;
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nslow2 = 0;
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/* beginning of the outer loop. */
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while (true) {
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jeval = true;
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/* calculate the jacobian matrix. */
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iflag = ei_fdjac1(functor, x, fvec, fjac,
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nb_of_subdiagonals, nb_of_superdiagonals, epsfcn);
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nfev += msum;
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if (iflag < 0)
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break;
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/* compute the qr factorization of the jacobian. */
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ei_qrfac<Scalar>(n, n, fjac.data(), fjac.rows(), false, iwa, 1, wa1.data(), wa2.data());
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/* on the first iteration and if mode is 1, scale according */
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/* to the norms of the columns of the initial jacobian. */
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if (iter == 1) {
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if (mode != 2)
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for (j = 0; j < n; ++j) {
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diag[j] = wa2[j];
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if (wa2[j] == 0.)
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diag[j] = 1.;
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}
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/* on the first iteration, calculate the norm of the scaled x */
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/* and initialize the step bound delta. */
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wa3 = diag.cwise() * x;
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xnorm = wa3.stableNorm();
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delta = factor * xnorm;
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if (delta == 0.)
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delta = factor;
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}
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/* form (q transpose)*fvec and store in qtf. */
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qtf = fvec;
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for (j = 0; j < n; ++j)
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if (fjac(j,j) != 0.) {
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sum = 0.;
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for (i = j; i < n; ++i)
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sum += fjac(i,j) * qtf[i];
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temp = -sum / fjac(j,j);
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for (i = j; i < n; ++i)
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qtf[i] += fjac(i,j) * temp;
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}
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/* copy the triangular factor of the qr factorization into r. */
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sing = false;
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for (j = 0; j < n; ++j) {
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l = j;
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if (j)
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for (i = 0; i < j; ++i) {
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R[l] = fjac(i,j);
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l = l + n - i -1;
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}
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R[l] = wa1[j];
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if (wa1[j] == 0.)
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sing = true;
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}
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/* accumulate the orthogonal factor in fjac. */
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ei_qform<Scalar>(n, n, fjac.data(), fjac.rows(), wa1.data());
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/* rescale if necessary. */
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/* Computing MAX */
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if (mode != 2)
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diag = diag.cwise().max(wa2);
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/* beginning of the inner loop. */
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while (true) {
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/* determine the direction p. */
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ei_dogleg<Scalar>(R, diag, qtf, delta, wa1);
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/* store the direction p and x + p. calculate the norm of p. */
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wa1 = -wa1;
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wa2 = x + wa1;
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wa3 = diag.cwise() * wa1;
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pnorm = wa3.stableNorm();
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/* on the first iteration, adjust the initial step bound. */
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if (iter == 1)
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delta = std::min(delta,pnorm);
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/* evaluate the function at x + p and calculate its norm. */
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iflag = functor.f(wa2, wa4);
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++nfev;
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if (iflag < 0)
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goto algo_end;
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fnorm1 = wa4.stableNorm();
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/* compute the scaled actual reduction. */
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actred = -1.;
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if (fnorm1 < fnorm) /* Computing 2nd power */
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actred = 1. - ei_abs2(fnorm1 / fnorm);
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/* compute the scaled predicted reduction. */
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l = 0;
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for (i = 0; i < n; ++i) {
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sum = 0.;
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for (j = i; j < n; ++j) {
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sum += R[l] * wa1[j];
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++l;
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}
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wa3[i] = qtf[i] + sum;
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}
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temp = wa3.stableNorm();
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prered = 0.;
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if (temp < fnorm) /* Computing 2nd power */
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prered = 1. - ei_abs2(temp / fnorm);
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/* compute the ratio of the actual to the predicted */
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/* reduction. */
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ratio = 0.;
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if (prered > 0.)
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ratio = actred / prered;
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/* update the step bound. */
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if (ratio < Scalar(.1)) {
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ncsuc = 0;
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++ncfail;
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delta = Scalar(.5) * delta;
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} else {
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ncfail = 0;
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++ncsuc;
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if (ratio >= Scalar(.5) || ncsuc > 1) /* Computing MAX */
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delta = std::max(delta, pnorm / Scalar(.5));
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if (ei_abs(ratio - 1.) <= Scalar(.1)) {
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delta = pnorm / Scalar(.5);
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}
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}
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/* test for successful iteration. */
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if (ratio >= Scalar(1e-4)) {
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/* successful iteration. update x, fvec, and their norms. */
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x = wa2;
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wa2 = diag.cwise() * x;
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fvec = wa4;
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xnorm = wa2.stableNorm();
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fnorm = fnorm1;
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++iter;
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}
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/* determine the progress of the iteration. */
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++nslow1;
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if (actred >= Scalar(.001))
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nslow1 = 0;
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if (jeval)
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++nslow2;
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if (actred >= Scalar(.1))
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nslow2 = 0;
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/* test for convergence. */
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if (delta <= xtol * xnorm || fnorm == 0.)
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info = 1;
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if (info != 0)
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goto algo_end;
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/* tests for termination and stringent tolerances. */
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if (nfev >= maxfev)
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info = 2;
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/* Computing MAX */
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if (Scalar(.1) * std::max(Scalar(.1) * delta, pnorm) <= epsilon<Scalar>() * xnorm)
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info = 3;
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if (nslow2 == 5)
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info = 4;
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if (nslow1 == 10)
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info = 5;
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if (info != 0)
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goto algo_end;
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/* criterion for recalculating jacobian approximation */
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/* by forward differences. */
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if (ncfail == 2)
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break;
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/* calculate the rank one modification to the jacobian */
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/* and update qtf if necessary. */
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for (j = 0; j < n; ++j) {
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sum = wa4.dot(fjac.col(j));
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wa2[j] = (sum - wa3[j]) / pnorm;
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wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm);
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if (ratio >= Scalar(1e-4))
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qtf[j] = sum;
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}
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/* compute the qr factorization of the updated jacobian. */
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ei_r1updt<Scalar>(n, n, R.data(), R.size(), wa1.data(), wa2.data(), wa3.data(), &sing);
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ei_r1mpyq<Scalar>(n, n, fjac.data(), fjac.rows(), wa2.data(), wa3.data());
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ei_r1mpyq<Scalar>(1, n, qtf.data(), 1, wa2.data(), wa3.data());
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/* end of the inner loop. */
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jeval = false;
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}
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/* end of the outer loop. */
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}
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algo_end:
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/* termination, either normal or user imposed. */
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if (iflag < 0)
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info = iflag;
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return info;
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}
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