Add benchmarks for unsupported modules and extend supported benchmarks

libeigen/eigen!2179

Closes #3036

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>

unsupported/benchmarks/MatrixFunctions/bench_matrix_exponential.cpp

@@ -0,0 +1,52 @@
+// Benchmarks for matrix exponential.
+// Critical for Sophus Lie group operations (SLAM, visual odometry).
+
+#include <benchmark/benchmark.h>
+#include <Eigen/Core>
+#include <unsupported/Eigen/MatrixFunctions>
+
+using namespace Eigen;
+
+#ifndef SCALAR
+#define SCALAR double
+#endif
+
+typedef SCALAR Scalar;
+
+static void BM_MatrixExp(benchmark::State& state) {
+  int n = state.range(0);
+  typedef Matrix<Scalar, Dynamic, Dynamic> MatrixType;
+
+  // Generate a random matrix with reasonable spectral radius.
+  MatrixType A = MatrixType::Random(n, n) / Scalar(n);
+  MatrixType result(n, n);
+
+  for (auto _ : state) {
+    result = A.exp();
+    benchmark::DoNotOptimize(result.data());
+    benchmark::ClobberMemory();
+  }
+}
+
+// Fixed-size specializations for Lie group sizes.
+template <int N>
+static void BM_MatrixExp_Fixed(benchmark::State& state) {
+  typedef Matrix<Scalar, N, N> MatrixType;
+
+  MatrixType A = MatrixType::Random() / Scalar(N);
+  MatrixType result;
+
+  for (auto _ : state) {
+    result = A.exp();
+    benchmark::DoNotOptimize(result.data());
+    benchmark::ClobberMemory();
+  }
+}
+
+// Dynamic sizes: Lie groups (2,3,4) plus larger.
+BENCHMARK(BM_MatrixExp)->Arg(2)->Arg(3)->Arg(4)->Arg(8)->Arg(16)->Arg(32)->Arg(64)->Arg(128);
+
+// Fixed-size Lie group dimensions.
+BENCHMARK(BM_MatrixExp_Fixed<2>);
+BENCHMARK(BM_MatrixExp_Fixed<3>);
+BENCHMARK(BM_MatrixExp_Fixed<4>);