Non-linear Least Squares with Ceres Solver and external Fortran function

[Heinz Alfons]

Hi,

I'm new to C++ and trying to use Google's Ceres solver for solving a Non-linear Least Squares problem. I'm using an external fortran function that returns 10 values which I want to use as my loss values of the least squares problem. As I understand I need to somehow wrap each value in a residual block, however then in each block the Fortran function has to be recomputed. Is there a better way to do it? Maybe with some small example code? I've already been able to minimize the loss of the function using LBFGS as follows:

void minimizer() {
    struct Approx {
      bool operator()(const double* parameters, double* cost) const {
        cost[0] = fortran_minimizer_sum(parameters, additional_params);
        return true;
      }

      static ceres::FirstOrderFunction* Create() {
        constexpr int kNumParameters = 12;
        return new ceres::NumericDiffFirstOrderFunction<Approx,
                                                        ceres::CENTRAL,
                                                        kNumParameters>(new Approx);
      }
    };
   
    ceres::GradientProblemSolver::Options options;

    ceres::GradientProblemSolver::Summary summary;
    ceres::GradientProblem problem(Approx::Create());

    ceres::Solve(options, problem, parameters, &summary);
}

Now, how can I use the Trust Region solver of Ceres to to the same with a slightly different fortran function "fortran_minimizer" that doesn't only have one single cost/loss value but multiple loss values that I want to use as input to a Non-linear Least Squares solver?

Thank you

Heinz

[Heinz Alfons]

Sorry, the way I wrote it may be a bit confusing, the "fortran_minimizer" function I want to use returns 10 loss values that I want to use as my least squares. I wrote the helper function fortran_minimizer_sum that just computes the squared sum of these values in order to use it in the operator function.

[Dmitriy Korchemkin]

Heinz,

If you want to continue using numeric differentiation - you can use ceres::NumericDiffCostFunction . http://ceres-solver.org/nnls_modeling.html#_CPPv4N5ceres23NumericDiffCostFunctionE
Example in the documentation works with a single residual, but there are a number of examples for larger residual blocks in ceres/internal/numeric_diff_cost_function_test.cc ( + internal/ceres/numeric_diff_test_utils.h, internal/ceres/numeric_diff_test_utils.cc).

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Dmitriy A Korchemkin

[Heinz Alfons]

I want to use the Levenberg-Marquardt method, is that possible with ceres::NumericDiffCostFunction?

[Dmitriy Korchemkin]

Yes, you can use NumericDiffCostFunction with Levenberg-Marquardt optimizer; you can find a complete minimal example (from cost functor class to invocation of solver) in examples/examples/helloworld_numeric_diff.cc .

You'll need to change the number of residuals and parameters in template arguments according to your optimization problem. If dimensionality of residuals / parameters is unknown at compile time, there is a DynamicNumericDiffCostFunction class.

To view this discussion on the web visit https://groups.google.com/d/msgid/ceres-solver/b888673a-137e-46f4-a28a-73905c178fccn%40googlegroups.com.

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Dmitriy A Korchemkin