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some more eigenization
This commit is contained in:
Thomas Capricelli
parent
a3034ee079
commit
ba2a9cce03
@ -186,7 +186,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveInit(
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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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@ -196,14 +195,12 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveInit(
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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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@ -224,7 +221,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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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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@ -235,11 +231,8 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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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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for (j = 0; j < n; ++j)
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diag[j] = (wa2[j]==0.) ? 1. : wa2[j];
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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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@ -260,7 +253,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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for(int ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors
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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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@ -273,76 +265,54 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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}
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/* copy the triangular factor of the qr factorization into r. */
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R = qrfac.matrixQR();
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sing = false;
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for (j = 0; j < n; ++j)
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if (wa1[j] == 0.) sing = true;
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sing = wa1.cwiseAbs().minCoeff()==0.;
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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.cwiseMax(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.cwiseProduct(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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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(i,j) * wa1[j];
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wa3[i] = qtf[i] + sum;
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}
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wa3 = R.template triangularView<Upper>()*wa1 + qtf;
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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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/* compute the ratio of the actual to the predicted 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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@ -350,7 +320,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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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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if (ratio >= Scalar(.5) || ncsuc > 1)
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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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@ -358,7 +328,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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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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@ -370,7 +339,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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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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@ -380,12 +348,10 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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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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@ -396,37 +362,27 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(
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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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wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );
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wa2 = fjac.transpose() * wa4;
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if (ratio >= Scalar(1e-4))
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qtf = wa2;
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wa2 = (wa2-wa3)/pnorm;
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/* compute the qr factorization of the updated jacobian. */
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ei_r1updt<Scalar>(n, n, R, 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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@ -493,7 +449,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(
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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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@ -503,14 +458,12 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(
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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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@ -544,11 +497,8 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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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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for (j = 0; j < n; ++j)
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diag[j] = (wa2[j]==0.) ? 1. : wa2[j];
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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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@ -569,7 +519,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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for(int ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors
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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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@ -583,74 +532,53 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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/* copy the triangular factor of the qr factorization into r. */
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R = qrfac.matrixQR();
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sing = false;
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for (j = 0; j < n; ++j)
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if (wa1[j] == 0.) sing = true;
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sing = wa1.cwiseAbs().minCoeff()==0.;
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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.cwiseMax(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.cwiseProduct(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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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(i,j) * wa1[j];
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wa3[i] = qtf[i] + sum;
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}
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wa3 = R.template triangularView<Upper>()*wa1 + qtf;
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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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/* compute the ratio of the actual to the predicted 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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@ -658,7 +586,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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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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if (ratio >= Scalar(.5) || ncsuc > 1)
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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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@ -666,7 +594,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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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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@ -678,7 +605,6 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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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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@ -688,12 +614,10 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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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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@ -703,35 +627,25 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(
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if (nslow1 == 10)
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return NotMakingProgressIterations;
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/* criterion for recalculating jacobian approximation */
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/* by forward differences. */
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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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wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );
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wa2 = fjac.transpose() * wa4;
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if (ratio >= Scalar(1e-4))
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qtf = wa2;
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wa2 = (wa2-wa3)/pnorm;
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/* compute the qr factorization of the updated jacobian. */
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ei_r1updt<Scalar>(n, n, R, 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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@ -8,46 +8,45 @@ void ei_dogleg(
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Matrix< Scalar, Dynamic, 1 > &x)
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{
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/* Local variables */
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int i, j, k;
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int i, j;
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Scalar sum, temp, alpha, bnorm;
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Scalar gnorm, qnorm;
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Scalar sgnorm;
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/* Function Body */
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const Scalar epsmch = epsilon<Scalar>();
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const int n = diag.size();
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Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n);
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const int n = qrfac.cols();
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assert(n==qtb.size());
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assert(n==x.size());
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assert(n==diag.size());
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Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n);
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for (k = 0; k < n; ++k) {
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j = n - k - 1;
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sum = 0.;
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for (i = j+1; i < n; ++i) {
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sum += qrfac(j,i) * x[i];
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}
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/* first, calculate the gauss-newton direction. */
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for (j = n-1; j >=0; --j) {
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temp = qrfac(j,j);
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if (temp == 0.) {
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for (i = 0; i <= j; ++i)
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temp = std::max(temp,ei_abs(qrfac(i,j)));
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temp = epsmch * temp;
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temp = epsmch * qrfac.col(j).head(j+1).maxCoeff();
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if (temp == 0.)
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temp = epsmch;
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}
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x[j] = (qtb[j] - sum) / temp;
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if (j==n-1)
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x[j] = qtb[j] / temp;
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else
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x[j] = (qtb[j] - qrfac.row(j).tail(n-j-1).dot(x.tail(n-j-1))) / temp;
|
||||
}
|
||||
|
||||
/* test whether the gauss-newton direction is acceptable. */
|
||||
|
||||
wa1.fill(0.);
|
||||
wa2 = diag.cwiseProduct(x);
|
||||
qnorm = wa2.stableNorm();
|
||||
if (qnorm <= delta)
|
||||
return;
|
||||
|
||||
// TODO : this path is not tested by Eigen unit tests
|
||||
|
||||
/* the gauss-newton direction is not acceptable. */
|
||||
/* next, calculate the scaled gradient direction. */
|
||||
|
||||
wa1.fill(0.);
|
||||
for (j = 0; j < n; ++j) {
|
||||
temp = qtb[j];
|
||||
for (i = j; i < n; ++i)
|
||||
@ -57,7 +56,6 @@ void ei_dogleg(
|
||||
|
||||
/* calculate the norm of the scaled gradient and test for */
|
||||
/* the special case in which the scaled gradient is zero. */
|
||||
|
||||
gnorm = wa1.stableNorm();
|
||||
sgnorm = 0.;
|
||||
alpha = delta / qnorm;
|
||||
@ -66,8 +64,9 @@ void ei_dogleg(
|
||||
|
||||
/* calculate the point along the scaled gradient */
|
||||
/* at which the quadratic is minimized. */
|
||||
|
||||
wa1.array() /= (diag*gnorm).array();
|
||||
// TODO : once unit tests cover this part,:
|
||||
// wa2 = qrfac.template triangularView<Upper>() * wa1;
|
||||
for (j = 0; j < n; ++j) {
|
||||
sum = 0.;
|
||||
for (i = j; i < n; ++i) {
|
||||
@ -79,7 +78,6 @@ void ei_dogleg(
|
||||
sgnorm = gnorm / temp / temp;
|
||||
|
||||
/* test whether the scaled gradient direction is acceptable. */
|
||||
|
||||
alpha = 0.;
|
||||
if (sgnorm >= delta)
|
||||
goto algo_end;
|
||||
@ -87,18 +85,14 @@ void ei_dogleg(
|
||||
/* the scaled gradient direction is not acceptable. */
|
||||
/* finally, calculate the point along the dogleg */
|
||||
/* at which the quadratic is minimized. */
|
||||
|
||||
bnorm = qtb.stableNorm();
|
||||
temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);
|
||||
/* Computing 2nd power */
|
||||
temp = temp - delta / qnorm * ei_abs2(sgnorm / delta) + ei_sqrt(ei_abs2(temp - delta / qnorm) + (1.-ei_abs2(delta / qnorm)) * (1.-ei_abs2(sgnorm / delta)));
|
||||
/* Computing 2nd power */
|
||||
alpha = delta / qnorm * (1. - ei_abs2(sgnorm / delta)) / temp;
|
||||
algo_end:
|
||||
|
||||
/* form appropriate convex combination of the gauss-newton */
|
||||
/* direction and the scaled gradient direction. */
|
||||
|
||||
temp = (1.-alpha) * std::min(sgnorm,delta);
|
||||
x = temp * wa1 + alpha * x;
|
||||
}
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user