Optimize PrepareDecoding: simplify Transition, batch CSFS with double

Transition.cpp: remove 7 dead methods, closed-form matrix exponentials
for SMC/SMC1, 3x3 block decomposition for CSC, binary search in
findIntervalForTime. Simplify getOmegas and decoding quantity assembly.

smcpp CSFS: add raw_sfs_batch() using double instead of adouble — the
original raw_sfs computed autodiff derivatives then discarded them.
Batch all 69 discretization intervals in one call instead of 69
separate calls. Output matches within machine epsilon (max abs 2e-15).

Author: pierpal

src/3rd_party/smcpp.cpp

@@ -1333,6 +1333,9 @@ std::vector<Matrix<T> > OnePopConditionedSFS<T>::compute(const PiecewiseConstant
   return csfs;
 }
 
+// Explicit instantiation for double (used by raw_sfs_batch to avoid autodiff overhead)
+template class OnePopConditionedSFS<double>;
+
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
@@ -1374,3 +1377,13 @@ Matrix<double> raw_sfs(const std::vector<double>& a, const std::vector<double>&
   Matrix<adouble> sfs = sfs_cython(n, pv, t1, t2, below_only);
   return sfs.unaryExpr([](adouble x){return x.value();});
 }
+
+// Added for PrepareDecoding: batched CSFS using double instead of adouble.
+// The original raw_sfs uses autodiff (adouble) then discards derivatives.
+// This version avoids that overhead and batches all intervals in one call.
+std::vector<Matrix<double>> raw_sfs_batch(const std::vector<double>& a, const std::vector<double>& s, const int n, const std::vector<double>& hidden_states) {
+  ParameterVector pv = make_params(a, s);
+  OnePopConditionedSFS<double> csfs(n);
+  PiecewiseConstantRateFunction<double> eta(pv, hidden_states);
+  return csfs.compute(eta);
+}

src/3rd_party/smcpp.hpp

@@ -29,4 +29,16 @@ void smcpp_init_cache();
 Matrix<double> raw_sfs(const std::vector<double>& a, const std::vector<double>& s, int n, double t1, double t2,
                        bool below_only = false);
 
+/**
+ * Compute raw SFS for all intervals at once, using double (no autodiff overhead).
+ *
+ * @param a normalised population sizes from the demographic history
+ * @param s discrete derivative of the times
+ * @param n number of samples
+ * @param hidden_states vector of interval boundaries [t0, t1, t2, ..., tM] giving M intervals
+ * @return vector of M raw SFS matrices
+ */
+std::vector<Matrix<double>> raw_sfs_batch(const std::vector<double>& a, const std::vector<double>& s, int n,
+                                          const std::vector<double>& hidden_states);
+
 #endif // PREPAREDECODING_SMCPP_HPP

src/PrepareDecoding.cpp

@@ -116,18 +116,24 @@ DecodingQuantities calculateCsfsAndDecodingQuantities(const Demography& demo, co
   std::vector<double> tos;
   std::vector<Matrix<double>> csfses;
 
-  // Must initialise smcpp cache once
-  smcpp_init_cache();
   for (auto i = 0ul; i < arrayDisc.size() - 1; ++i) {
+    froms.push_back(arrayDisc[i]);
+    tos.push_back(arrayDisc[i + 1]);
+  }
 
-    auto t0 = arrayDisc[i];
-    auto t1 = arrayDisc[i + 1];
-
-    froms.push_back(t0);
-    tos.push_back(t1);
-
-    csfses.emplace_back(raw_sfs(aVec, sVec, static_cast<int>(samples - 2u), t0 / (2. * N0), t1 / (2. * N0)) * theta);
-    csfses.back()(0, 0) = 1.0 - csfses.back().sum();
+  // Build hidden state boundaries for batched CSFS computation.
+  // Uses double (not autodiff) and computes all intervals in one call.
+  smcpp_init_cache();
+  std::vector<double> hiddenStates;
+  hiddenStates.reserve(arrayDisc.size());
+  for (const auto& d : arrayDisc)
+    hiddenStates.push_back(d / (2. * N0));
+
+  auto batchSfs = raw_sfs_batch(aVec, sVec, static_cast<int>(samples - 2u), hiddenStates);
+  for (auto& sfs : batchSfs) {
+    sfs *= theta;
+    sfs(0, 0) = 1.0 - sfs.sum();
+    csfses.push_back(std::move(sfs));
   }
 
   auto csfs = CSFS::load(arrayTime, arraySize, mutRate, samples, froms, tos, csfses);