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rename NonLinear to NonLinearOptimization
This commit is contained in:
Thomas Capricelli
@@ -0,0 +1,725 @@
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template<typename FunctorType, typename Scalar=double>
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class HybridNonLinearSolver
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{
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public:
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HybridNonLinearSolver(FunctorType &_functor)
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: functor(_functor) { nfev=njev=iter = 0; fnorm= 0.; }
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enum Status {
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Running = -1,
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ImproperInputParameters = 0,
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RelativeErrorTooSmall = 1,
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TooManyFunctionEvaluation = 2,
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TolTooSmall = 3,
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NotMakingProgressJacobian = 4,
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NotMakingProgressIterations = 5,
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UserAksed = 6
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};
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struct Parameters {
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Parameters()
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: factor(Scalar(100.))
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, maxfev(1000)
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, xtol(ei_sqrt(epsilon<Scalar>()))
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, nb_of_subdiagonals(-1)
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, nb_of_superdiagonals(-1)
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, epsfcn(Scalar(0.)) {}
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Scalar factor;
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int maxfev; // maximum number of function evaluation
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Scalar xtol;
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int nb_of_subdiagonals;
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int nb_of_superdiagonals;
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Scalar epsfcn;
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};
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Status hybrj1(
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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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Status solveInit(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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Status solveOneStep(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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Status solve(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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Status hybrd1(
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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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Status solveNumericalDiffInit(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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Status solveNumericalDiffOneStep(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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Status solveNumericalDiff(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode=1
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);
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void resetParameters(void) { parameters = Parameters(); }
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Parameters parameters;
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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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Matrix< Scalar, Dynamic, 1 > qtf;
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Matrix< Scalar, Dynamic, 1 > diag;
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int nfev;
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int njev;
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int iter;
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Scalar fnorm;
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private:
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FunctorType &functor;
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int n;
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Scalar sum;
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bool sing;
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Scalar temp;
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Scalar delta;
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bool jeval;
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int ncsuc;
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Scalar ratio;
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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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Matrix< Scalar, Dynamic, 1 > wa1, wa2, wa3, wa4;
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};
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template<typename FunctorType, typename Scalar>
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typename HybridNonLinearSolver<FunctorType,Scalar>::Status
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HybridNonLinearSolver<FunctorType,Scalar>::hybrj1(
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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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n = x.size();
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/* check the input parameters for errors. */
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if (n <= 0 || tol < 0.)
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return ImproperInputParameters;
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resetParameters();
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parameters.maxfev = 100*(n+1);
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parameters.xtol = tol;
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diag.setConstant(n, 1.);
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return solve(
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x,
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2
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);
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}
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template<typename FunctorType, typename Scalar>
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typename HybridNonLinearSolver<FunctorType,Scalar>::Status
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HybridNonLinearSolver<FunctorType,Scalar>::solveInit(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode
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)
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{
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n = x.size();
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wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);
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fvec.resize(n);
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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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if (mode != 2)
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diag.resize(n);
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assert( (mode!=2 || diag.size()==n) || "When using mode==2, the caller must provide a valid 'diag'");
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/* Function Body */
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nfev = 0;
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njev = 0;
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/* check the input parameters for errors. */
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if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0. )
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return ImproperInputParameters;
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if (mode == 2)
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for (int j = 0; j < n; ++j)
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if (diag[j] <= 0.)
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return ImproperInputParameters;
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/* evaluate the function at the starting point */
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/* and calculate its norm. */
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nfev = 1;
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if ( functor(x, fvec) < 0)
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return UserAksed;
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fnorm = fvec.stableNorm();
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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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return Running;
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}
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template<typename FunctorType, typename Scalar>
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typename HybridNonLinearSolver<FunctorType,Scalar>::Status
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HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode
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)
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{
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int i, j, l, iwa[1];
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jeval = true;
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/* calculate the jacobian matrix. */
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if ( functor.df(x, fjac) < 0)
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return UserAksed;
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++njev;
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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, wa1.data(), wa2.data());
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if (iter == 1) {
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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 (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 = parameters.factor * xnorm;
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if (delta == 0.)
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delta = parameters.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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if ( functor(wa2, wa4) < 0)
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return UserAksed;
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++nfev;
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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 <= parameters.xtol * xnorm || fnorm == 0.)
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return RelativeErrorTooSmall;
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/* tests for termination and stringent tolerances. */
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if (nfev >= parameters.maxfev)
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return TooManyFunctionEvaluation;
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if (Scalar(.1) * std::max(Scalar(.1) * delta, pnorm) <= epsilon<Scalar>() * xnorm)
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return TolTooSmall;
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if (nslow2 == 5)
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return NotMakingProgressJacobian;
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if (nslow1 == 10)
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return NotMakingProgressIterations;
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/* criterion for recalculating jacobian. */
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if (ncfail == 2)
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break; // leave inner loop and go for the next outer loop iteration
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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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return Running;
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}
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template<typename FunctorType, typename Scalar>
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typename HybridNonLinearSolver<FunctorType,Scalar>::Status
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HybridNonLinearSolver<FunctorType,Scalar>::solve(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode
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)
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{
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Status status = solveInit(x, mode);
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while (status==Running)
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status = solveOneStep(x, mode);
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return status;
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}
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template<typename FunctorType, typename Scalar>
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typename HybridNonLinearSolver<FunctorType,Scalar>::Status
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HybridNonLinearSolver<FunctorType,Scalar>::hybrd1(
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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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n = x.size();
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/* check the input parameters for errors. */
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if (n <= 0 || tol < 0.)
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return ImproperInputParameters;
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resetParameters();
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parameters.maxfev = 200*(n+1);
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parameters.xtol = tol;
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diag.setConstant(n, 1.);
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return solveNumericalDiff(
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x,
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2
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);
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}
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template<typename FunctorType, typename Scalar>
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typename HybridNonLinearSolver<FunctorType,Scalar>::Status
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HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode
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)
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{
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n = x.size();
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if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;
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if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;
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wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);
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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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if (mode != 2)
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diag.resize(n);
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assert( (mode!=2 || diag.size()==n) || "When using mode==2, the caller must provide a valid 'diag'");
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/* Function Body */
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nfev = 0;
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njev = 0;
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/* check the input parameters for errors. */
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if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.nb_of_subdiagonals< 0 || parameters.nb_of_superdiagonals< 0 || parameters.factor <= 0. )
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return ImproperInputParameters;
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if (mode == 2)
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for (int j = 0; j < n; ++j)
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if (diag[j] <= 0.)
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return ImproperInputParameters;
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/* evaluate the function at the starting point */
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/* and calculate its norm. */
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nfev = 1;
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if ( functor(x, fvec) < 0)
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return UserAksed;
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fnorm = fvec.stableNorm();
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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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return Running;
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}
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template<typename FunctorType, typename Scalar>
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typename HybridNonLinearSolver<FunctorType,Scalar>::Status
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HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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Matrix< Scalar, Dynamic, 1 > &x,
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const int mode
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||||
)
|
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{
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int i, j, l, iwa[1];
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jeval = true;
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if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;
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if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;
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/* calculate the jacobian matrix. */
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if (ei_fdjac1(functor, x, fvec, fjac, parameters.nb_of_subdiagonals, parameters.nb_of_superdiagonals, parameters.epsfcn) <0)
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return UserAksed;
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nfev += std::min(parameters.nb_of_subdiagonals+parameters.nb_of_superdiagonals+ 1, n);
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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, wa1.data(), wa2.data());
|
||||
|
||||
/* on the first iteration and if mode is 1, scale according */
|
||||
/* to the norms of the columns of the initial jacobian. */
|
||||
|
||||
if (iter == 1) {
|
||||
if (mode != 2)
|
||||
for (j = 0; j < n; ++j) {
|
||||
diag[j] = wa2[j];
|
||||
if (wa2[j] == 0.)
|
||||
diag[j] = 1.;
|
||||
}
|
||||
|
||||
/* on the first iteration, calculate the norm of the scaled x */
|
||||
/* and initialize the step bound delta. */
|
||||
|
||||
wa3 = diag.cwise() * x;
|
||||
xnorm = wa3.stableNorm();
|
||||
delta = parameters.factor * xnorm;
|
||||
if (delta == 0.)
|
||||
delta = parameters.factor;
|
||||
}
|
||||
|
||||
/* form (q transpose)*fvec and store in qtf. */
|
||||
|
||||
qtf = fvec;
|
||||
for (j = 0; j < n; ++j)
|
||||
if (fjac(j,j) != 0.) {
|
||||
sum = 0.;
|
||||
for (i = j; i < n; ++i)
|
||||
sum += fjac(i,j) * qtf[i];
|
||||
temp = -sum / fjac(j,j);
|
||||
for (i = j; i < n; ++i)
|
||||
qtf[i] += fjac(i,j) * temp;
|
||||
}
|
||||
|
||||
/* copy the triangular factor of the qr factorization into r. */
|
||||
|
||||
sing = false;
|
||||
for (j = 0; j < n; ++j) {
|
||||
l = j;
|
||||
if (j)
|
||||
for (i = 0; i < j; ++i) {
|
||||
R[l] = fjac(i,j);
|
||||
l = l + n - i -1;
|
||||
}
|
||||
R[l] = wa1[j];
|
||||
if (wa1[j] == 0.)
|
||||
sing = true;
|
||||
}
|
||||
|
||||
/* accumulate the orthogonal factor in fjac. */
|
||||
|
||||
ei_qform<Scalar>(n, n, fjac.data(), fjac.rows(), wa1.data());
|
||||
|
||||
/* rescale if necessary. */
|
||||
|
||||
/* Computing MAX */
|
||||
if (mode != 2)
|
||||
diag = diag.cwise().max(wa2);
|
||||
|
||||
/* beginning of the inner loop. */
|
||||
|
||||
while (true) {
|
||||
|
||||
/* determine the direction p. */
|
||||
|
||||
ei_dogleg<Scalar>(R, diag, qtf, delta, wa1);
|
||||
|
||||
/* store the direction p and x + p. calculate the norm of p. */
|
||||
|
||||
wa1 = -wa1;
|
||||
wa2 = x + wa1;
|
||||
wa3 = diag.cwise() * wa1;
|
||||
pnorm = wa3.stableNorm();
|
||||
|
||||
/* on the first iteration, adjust the initial step bound. */
|
||||
|
||||
if (iter == 1)
|
||||
delta = std::min(delta,pnorm);
|
||||
|
||||
/* evaluate the function at x + p and calculate its norm. */
|
||||
|
||||
if ( functor(wa2, wa4) < 0)
|
||||
return UserAksed;
|
||||
++nfev;
|
||||
fnorm1 = wa4.stableNorm();
|
||||
|
||||
/* compute the scaled actual reduction. */
|
||||
|
||||
actred = -1.;
|
||||
if (fnorm1 < fnorm) /* Computing 2nd power */
|
||||
actred = 1. - ei_abs2(fnorm1 / fnorm);
|
||||
|
||||
/* compute the scaled predicted reduction. */
|
||||
|
||||
l = 0;
|
||||
for (i = 0; i < n; ++i) {
|
||||
sum = 0.;
|
||||
for (j = i; j < n; ++j) {
|
||||
sum += R[l] * wa1[j];
|
||||
++l;
|
||||
}
|
||||
wa3[i] = qtf[i] + sum;
|
||||
}
|
||||
temp = wa3.stableNorm();
|
||||
prered = 0.;
|
||||
if (temp < fnorm) /* Computing 2nd power */
|
||||
prered = 1. - ei_abs2(temp / fnorm);
|
||||
|
||||
/* compute the ratio of the actual to the predicted */
|
||||
/* reduction. */
|
||||
|
||||
ratio = 0.;
|
||||
if (prered > 0.)
|
||||
ratio = actred / prered;
|
||||
|
||||
/* update the step bound. */
|
||||
|
||||
if (ratio < Scalar(.1)) {
|
||||
ncsuc = 0;
|
||||
++ncfail;
|
||||
delta = Scalar(.5) * delta;
|
||||
} else {
|
||||
ncfail = 0;
|
||||
++ncsuc;
|
||||
if (ratio >= Scalar(.5) || ncsuc > 1) /* Computing MAX */
|
||||
delta = std::max(delta, pnorm / Scalar(.5));
|
||||
if (ei_abs(ratio - 1.) <= Scalar(.1)) {
|
||||
delta = pnorm / Scalar(.5);
|
||||
}
|
||||
}
|
||||
|
||||
/* test for successful iteration. */
|
||||
|
||||
if (ratio >= Scalar(1e-4)) {
|
||||
/* successful iteration. update x, fvec, and their norms. */
|
||||
x = wa2;
|
||||
wa2 = diag.cwise() * x;
|
||||
fvec = wa4;
|
||||
xnorm = wa2.stableNorm();
|
||||
fnorm = fnorm1;
|
||||
++iter;
|
||||
}
|
||||
|
||||
/* determine the progress of the iteration. */
|
||||
|
||||
++nslow1;
|
||||
if (actred >= Scalar(.001))
|
||||
nslow1 = 0;
|
||||
if (jeval)
|
||||
++nslow2;
|
||||
if (actred >= Scalar(.1))
|
||||
nslow2 = 0;
|
||||
|
||||
/* test for convergence. */
|
||||
|
||||
if (delta <= parameters.xtol * xnorm || fnorm == 0.)
|
||||
return RelativeErrorTooSmall;
|
||||
|
||||
/* tests for termination and stringent tolerances. */
|
||||
|
||||
if (nfev >= parameters.maxfev)
|
||||
return TooManyFunctionEvaluation;
|
||||
if (Scalar(.1) * std::max(Scalar(.1) * delta, pnorm) <= epsilon<Scalar>() * xnorm)
|
||||
return TolTooSmall;
|
||||
if (nslow2 == 5)
|
||||
return NotMakingProgressJacobian;
|
||||
if (nslow1 == 10)
|
||||
return NotMakingProgressIterations;
|
||||
|
||||
/* criterion for recalculating jacobian approximation */
|
||||
/* by forward differences. */
|
||||
|
||||
if (ncfail == 2)
|
||||
break; // leave inner loop and go for the next outer loop iteration
|
||||
|
||||
/* calculate the rank one modification to the jacobian */
|
||||
/* and update qtf if necessary. */
|
||||
|
||||
for (j = 0; j < n; ++j) {
|
||||
sum = wa4.dot(fjac.col(j));
|
||||
wa2[j] = (sum - wa3[j]) / pnorm;
|
||||
wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm);
|
||||
if (ratio >= Scalar(1e-4))
|
||||
qtf[j] = sum;
|
||||
}
|
||||
|
||||
/* compute the qr factorization of the updated jacobian. */
|
||||
|
||||
ei_r1updt<Scalar>(n, n, R.data(), R.size(), wa1.data(), wa2.data(), wa3.data(), &sing);
|
||||
ei_r1mpyq<Scalar>(n, n, fjac.data(), fjac.rows(), wa2.data(), wa3.data());
|
||||
ei_r1mpyq<Scalar>(1, n, qtf.data(), 1, wa2.data(), wa3.data());
|
||||
|
||||
/* end of the inner loop. */
|
||||
|
||||
jeval = false;
|
||||
}
|
||||
/* end of the outer loop. */
|
||||
|
||||
return Running;
|
||||
}
|
||||
|
||||
template<typename FunctorType, typename Scalar>
|
||||
typename HybridNonLinearSolver<FunctorType,Scalar>::Status
|
||||
HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(
|
||||
Matrix< Scalar, Dynamic, 1 > &x,
|
||||
const int mode
|
||||
)
|
||||
{
|
||||
Status status = solveNumericalDiffInit(x, mode);
|
||||
while (status==Running)
|
||||
status = solveNumericalDiffOneStep(x, mode);
|
||||
return status;
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user