Add a matrix version of GaussianQuadrature5

Change-Id: I205c37c825ce0abdf31bc2821e82e0d89505a056
Signed-off-by: Austin Schuh <austin.linux@gmail.com>
diff --git a/frc971/control_loops/fixed_quadrature.h b/frc971/control_loops/fixed_quadrature.h
index 572c235..22d4984 100644
--- a/frc971/control_loops/fixed_quadrature.h
+++ b/frc971/control_loops/fixed_quadrature.h
@@ -1,6 +1,7 @@
 #ifndef FRC971_CONTROL_LOOPS_FIXED_QUADRATURE_H_
 #define FRC971_CONTROL_LOOPS_FIXED_QUADRATURE_H_
 
+#include <Eigen/Dense>
 #include <array>
 
 namespace frc971 {
@@ -9,8 +10,8 @@
 // Implements Gaussian Quadrature integration (5th order).  fn is the function to
 // integrate.  It must take 1 argument of type T.  The integration is between a
 // and b.
-template <typename F, typename T>
-T GaussianQuadrature5(const F &fn, T a, T b) {
+template <typename T, typename F>
+double GaussianQuadrature5(const F &fn, T a, T b) {
   // Pulled from Python.
   // numpy.set_printoptions(precision=20)
   // scipy.special.p_roots(5)
@@ -31,6 +32,30 @@
   return answer;
 }
 
+template <size_t N, typename F>
+Eigen::Matrix<double, N, 1> MatrixGaussianQuadrature5(const F &fn, double a,
+                                                      double b) {
+  // Pulled from Python.
+  // numpy.set_printoptions(precision=20)
+  // scipy.special.p_roots(5)
+  const ::std::array<double, 5> x{{
+      -9.06179845938663630633e-01, -5.38469310105682885670e-01,
+      3.24607628916367383789e-17, 5.38469310105683218737e-01,
+      9.06179845938663408589e-01}};
+
+  const ::std::array<double, 5> w{{
+      0.23692688505618844652, 0.4786286704993669705, 0.56888888888888811124,
+      0.47862867049936674846, 0.23692688505618875183}};
+
+  Eigen::Matrix<double, N, 1> answer;
+  answer.setZero();
+  for (int i = 0; i < 5; ++i) {
+    const double y = (b - a) * (x[i] + 1) / 2.0 + a;
+    answer += (b - a) / 2.0 * w[i] * fn(y);
+  }
+  return answer;
+}
+
 }  // namespace control_loops
 }  // namespace frc971