[SymForce] Add eigen_sparse_solver

For use with e.g. any of the CHOLMOD solvers from CholmodSupport

Topic: sf-eigen-sparse
GitOrigin-RevId: 76bb2cb5d1bf62f9b3e3f12a593b532850d1368c

symforce/opt/eigen_sparse_solver.h

@@ -0,0 +1,112 @@
+/* ----------------------------------------------------------------------------
+ * SymForce - Copyright 2022, Skydio, Inc.
+ * This source code is under the Apache 2.0 license found in the LICENSE file.
+ * ---------------------------------------------------------------------------- */
+
+#pragma once
+
+#include <Eigen/Core>
+#include <Eigen/SparseCore>
+
+#include "./assert.h"
+
+namespace sym {
+
+/**
+ * A thin wrapper around Eigen's Sparse Solver interface for use in nonlinear solver classes like
+ * sym::LevenbergMarquardtSolver.
+ *
+ * Can be specialized with anything satisfying the SparseSolver concept.
+ *
+ * For example, can be used like:
+ *
+ *     using LinearSolver =
+ *         sym::EigenSparseSolver<double, Eigen::CholmodDecomposition<Eigen::SparseMatrix<double>>>;
+ *     using NonlinearSolver = sym::LevenbergMarquardtSolver<double, LinearSolver>;
+ *     using Optimizer = sym::Optimizer<double, NonlinearSolver>;
+ *
+ *     Optimizer optimizer{...};
+ */
+template <typename Scalar, typename EigenSolver>
+class EigenSparseSolver {
+ public:
+  using MatrixType = Eigen::SparseMatrix<Scalar>;
+
+ private:
+  EigenSolver solver_;
+
+ public:
+  using RhsType = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
+
+  /**
+   * Factorize A and store internally.
+   * @param A a symmetric positive definite matrix.
+   * @returns true if factorization succeeded, and false if failed.
+   */
+  bool Factorize(const MatrixType& A) {
+    solver_.compute(A);
+    return solver_.info() == Eigen::Success;
+  }
+
+  /**
+   * @returns x for A x = b, where x and b are dense
+   * @pre this->Factorize has already been called and succeeded.
+   */
+  template <typename Rhs>
+  RhsType Solve(const Eigen::MatrixBase<Rhs>& b) const {
+    return solver_.solve(b);
+  }
+
+  /**
+   * Solves in place for x in A x = b, where x and b are dense
+   *
+   * Eigen solvers cannot actually solve in place, so this solves, then copies back into the
+   * argument.
+   *
+   * @pre this->Factorize has already been called and succeeded.
+   */
+  template <typename Rhs>
+  void SolveInPlace(Eigen::MatrixBase<Rhs>& b) const {
+    b = solver_.solve(b);
+  }
+
+  /**
+   * @returns the lower triangular matrix L such that P^T * L * D * L^T * P = A, where A is the
+   * last matrix to have been factorized with this->Factorize and D is a diagonal matrix
+   * with positive diagonal entries, and P is a permutation matrix.
+   *
+   * @pre this->Factorize has already been called and succeeded.
+   */
+  MatrixType L() const {
+    return {};
+  }
+
+  /**
+   * @returns the diagonal matrix D such that P^T * L * D * L^T * P = A, where A is the
+   * last matrix to have been factorized with this->Factorize, L is lower triangular with
+   * unit diagonal, and P is a permutation matrix
+   * @pre this->Factorize has already been called and succeeded.
+   */
+  MatrixType D() const {
+    return {};
+  }
+
+  /**
+   * @returns the permutation matrix P such that P^T * L * D * L^T * P = A, where A is the
+   * last matrix to have been factorized with this->Factorize, L is lower triangular with
+   * unit diagonal, and D is a diagonal matrix
+   * @pre this->Factorize has already been called and succeeded.
+   */
+  Eigen::PermutationMatrix<Eigen::Dynamic> Permutation() const {
+    return {};
+  }
+
+  /**
+   * Defined to satisfy interface. No analysis is needed so is a no-op.
+   */
+  void AnalyzeSparsityPattern(const MatrixType& A) {
+    solver_.analyzePattern(A);
+  }
+};
+
+}  // namespace sym