diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index 5808db668..ee10093a0 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -45,6 +45,13 @@ jobs:
           sudo apt-get update -q -y
           sudo apt-get install -q -y clang-${{ matrix.clang-version }} lld-${{ matrix.clang-version }} libomp-${{ matrix.clang-version }}-dev libeigen3-dev libboost-dev
           sudo ln -sf $(which ld.lld-${{ matrix.clang-version }}) /usr/local/bin/ld.lld
+      # Install Rust
+      - name: Install Rust
+        uses: actions-rs/toolchain@v1
+        with:
+          toolchain: stable
+          override: true
+          profile: minimal
 
       - name: Setup cmake
         uses: jwlawson/actions-setup-cmake@v2
@@ -55,7 +62,7 @@ jobs:
         run: |
           mkdir build
           cd build
-          cmake .. -DCMAKE_POLICY_VERSION_MINIMUM=3.5 -DIQTREE_FLAGS=static -DCMAKE_C_COMPILER=$(which clang-${{ matrix.clang-version }}) -DCMAKE_CXX_COMPILER=$(which clang++-${{ matrix.clang-version }})
+          cmake .. -DUSE_MUTSEL=ON -DCMAKE_POLICY_VERSION_MINIMUM=3.5 -DIQTREE_FLAGS=static -DCMAKE_C_COMPILER=$(which clang-${{ matrix.clang-version }}) -DCMAKE_CXX_COMPILER=$(which clang++-${{ matrix.clang-version }})
           make -j
           make package
           file iqtree3 | grep x86-64
@@ -109,11 +116,18 @@ jobs:
           sudo apt-get update -q -y
           sudo apt-get install -q -y gcc g++ libeigen3-dev libboost-dev
 
+      # Install Rust
+      - name: Install Rust
+        uses: actions-rs/toolchain@v1
+        with:
+          toolchain: stable
+          override: true
+          profile: minimal
       - name: Build
         run: |
           mkdir build
           cd build
-          cmake .. -DIQTREE_FLAGS=static
+          cmake .. -DIQTREE_FLAGS=static -DUSE_MUTSEL=ON 
           make -j
           make package
           file iqtree3 | grep aarch64
@@ -199,6 +213,13 @@ jobs:
       - name: Install dependencies
         run: brew install make eigen boost libomp
 
+      # Install Rust
+      - name: Install Rust
+        uses: actions-rs/toolchain@v1
+        with:
+          toolchain: stable
+          override: true
+          profile: minimal
       - name: Build
         run: |
           set -x
@@ -206,7 +227,7 @@ jobs:
           cd build
           export CPPFLAGS="-I/usr/local/opt/libomp/include"
           export CXXFLAGS="-I/usr/local/opt/libomp/include"
-          cmake .. -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ -DEIGEN3_INCLUDE_DIR=$(brew --prefix eigen)/include/eigen3
+          cmake .. -DUSE_MUTSEL=ON -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ -DEIGEN3_INCLUDE_DIR=$(brew --prefix eigen)/include/eigen3
           make -j
           make package
           file iqtree3 | grep x86_64
@@ -256,6 +277,13 @@ jobs:
       - name: Install dependencies
         run: brew install make eigen boost libomp
 
+      # Install Rust
+      - name: Install Rust
+        uses: actions-rs/toolchain@v1
+        with:
+          toolchain: stable
+          override: true
+          profile: minimal
       - name: Build
         run: |
           set -x
@@ -263,7 +291,7 @@ jobs:
           cd build
           export CPPFLAGS="-I/opt/homebrew/opt/libomp/include"
           export CXXFLAGS="-I/opt/homebrew/opt/libomp/include"
-          cmake .. -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ -DEIGEN3_INCLUDE_DIR=$(brew --prefix eigen)/include/eigen3
+          cmake .. -DUSE_MUTSEL=ON -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ -DEIGEN3_INCLUDE_DIR=$(brew --prefix eigen)/include/eigen3
           make -j
           make package
           file iqtree3 | grep arm64
@@ -378,6 +406,14 @@ jobs:
         shell: cmd
         run: choco install eigen
 
+      # Install Rust
+      - name: Install Rust
+        uses: actions-rs/toolchain@v1
+        with:
+          toolchain: stable
+          override: true
+          profile: minimal
+          target: x86_64-pc-windows-gnu
       - name: Compile
         shell: cmd
         run: |
@@ -385,14 +421,19 @@ jobs:
           mkdir build
           cd build
           cmake -G "MinGW Makefiles" ^
+            -DUSE_MUTSEL=ON ^
             -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++ ^
-            -DCMAKE_C_FLAGS=--target=x86_64-pc-windows-gnu ^
-            -DCMAKE_CXX_FLAGS=--target=x86_64-pc-windows-gnu ^
+            -DCMAKE_C_FLAGS="--target=x86_64-pc-windows-gnu --sysroot=C:/mingw64 -B C:/mingw64/bin" ^
+            -DCMAKE_CXX_FLAGS="--target=x86_64-pc-windows-gnu --sysroot=C:/mingw64 -B C:/mingw64/bin" ^
             -DCMAKE_MAKE_PROGRAM=mingw32-make ^
             -DBoost_INCLUDE_DIR="C:/local/boost/include" ^
             -DBoost_LIBRARY_DIRS="C:/local/boost/lib" ^
             -DCMAKE_POLICY_VERSION_MINIMUM=3.5 ^
-            -DIQTREE_FLAGS="static cpp14" ..
+            -DIQTREE_FLAGS="static" ..
+            
+          type CMakeFiles\iqtree3.dir\link.txt
+          type CMakeFiles\iqtree3.dir\linkLibs.rsp
+
           make -j
           make package
         env:
diff --git a/.gitignore b/.gitignore
index 031049267..43f47d455 100644
--- a/.gitignore
+++ b/.gitignore
@@ -35,3 +35,4 @@ zlib-1.2.7/
 /.direnv/
 /.envrc
 softwipe_build
+mutsel_rust/target/
\ No newline at end of file
diff --git a/.vscode/settings.json b/.vscode/settings.json
deleted file mode 100644
index 0db587396..000000000
--- a/.vscode/settings.json
+++ /dev/null
@@ -1,3 +0,0 @@
-{
-    "cmake.configureOnOpen": true
-}
\ No newline at end of file
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 0c4637498..2c21c837e 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -284,6 +284,43 @@ else()
     message("Integrate CMAPLE_AA: OFF")
 endif()
 
+##################################################################
+# Include Rust dependecies: phylo_grad, MUTSEL model
+##################################################################
+
+if (USE_MUTSEL STREQUAL "ON")
+    message("Compile Rust Dependencies: ON")
+    if (WIN32)
+        set(MUTSEL_RUST_LIB_FILE "x86_64-pc-windows-gnu/release/libmutsel_rust.a")
+    else()
+        set(MUTSEL_RUST_LIB_FILE "release/libmutsel_rust.a")
+    endif()
+    set(MUTSEL_RUST_LIB_PATH "${CMAKE_SOURCE_DIR}/mutsel_rust/target/${MUTSEL_RUST_LIB_FILE}")
+
+    if (WIN32)
+        set(CARGO_TARGET --target x86_64-pc-windows-gnu)
+    else()
+        set(CARGO_TARGET "")
+    endif()
+
+
+    include(ExternalProject)
+    ExternalProject_Add(
+        mutsel
+        SOURCE_DIR "${CMAKE_SOURCE_DIR}/mutsel_rust"  # Where your Rust source is
+        CONFIGURE_COMMAND ""                           # No configure step for Rust
+        BUILD_COMMAND cargo build --release --lib ${CARGO_TARGET}
+        BUILD_BYPRODUCTS "${MUTSEL_RUST_LIB_PATH}"
+        INSTALL_COMMAND ""  # No install step for Rust
+        BUILD_IN_SOURCE 1  # Build in source directory
+        LOG_BUILD ON
+        LOG_OUTPUT_ON_FAILURE ON
+    )
+    add_definitions(-DUSE_MUTSEL)
+else()
+    message("Compile Rust Dependencies: OFF")
+endif()
+
 ##################################################################
 # build IQTREE library
 ##################################################################
@@ -313,16 +350,10 @@ elseif (APPLE)
         # set the first version of mac 11 that supports ARM
         set(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} --target=arm64-apple-macos11.0.1")
 	else()
-		# to be compatible back to Mac OS X 10.7
-    	if (IQTREE_FLAGS MATCHES "oldmac")
-        	add_definitions("-mmacosx-version-min=10.5")
-        	set(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} -mmacosx-version-min=10.5")
-    	else()
-            # supports the first version changed from OS X to macOS
-        	add_definitions("--target=x86_64-apple-macos10.12")
-            set(CMAKE_OSX_DEPLOYMENT_TARGET 10.12)
-            set(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} --target=x86_64-apple-macos10.12")
-    	endif()
+        # supports the first version changed from OS X to macOS
+        add_definitions("--target=x86_64-apple-macos11.0.1")
+        set(CMAKE_OSX_DEPLOYMENT_TARGET 11.0.1)
+        set(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} --target=x86_64-apple-macos11.0.1")
 	endif()
     SET(CMAKE_FIND_LIBRARY_SUFFIXES .a ${CMAKE_FIND_LIBRARY_SUFFIXES})
 elseif (UNIX)
@@ -1017,7 +1048,8 @@ endif()
 
 # basic linking librararies
 target_link_libraries(iqtree3 pll ncl nclextra utils pda lbfgsb whtest sprng vectorclass model
-    gsl alignment tree simulator terrace yaml-cpp phyloYAML main ${TARGET_CMAPLE} ${PLATFORM_LIB} ${STD_LIB} ${THREAD_LIB} ${ATOMIC_LIB})
+    gsl alignment tree simulator terrace yaml-cpp phyloYAML main ${TARGET_CMAPLE} ${PLATFORM_LIB} ${STD_LIB} ${THREAD_LIB} ${ATOMIC_LIB} ${CMAKE_DL_LIBS})
+
 
 # Link the bundled LLVM libomp.a even for GCC builds
 # dl is needed by libomp on Linux for dlsym
diff --git a/alignment/alignment.cpp b/alignment/alignment.cpp
index 111987cf9..9a4a9526b 100644
--- a/alignment/alignment.cpp
+++ b/alignment/alignment.cpp
@@ -4102,6 +4102,15 @@ void Alignment::createBootstrapAlignment(Alignment *aln, IntVector* pattern_freq
                         memcpy(state_freq, aln->ptn_state_freq[ptn], num_states*sizeof(double));
                     }
                     ptn_state_freq.push_back(state_freq);
+                    if (!aln->site_rate_matrices.empty()) {
+                        /* Minh/Thomas: Better change 190 to num_states*(numstates-1)/2 so that if you want to
+                         extend the model in the future, no change is needed here
+                         Also: This is only for reversible models. For non-rev models
+                         you need to store the full matrix, i.e., num_states*num_states entries
+                         */
+                        const double *rate_matrix = aln->site_rate_matrices.data() + ptn * 190;
+                        site_rate_matrices.insert(site_rate_matrices.end(), rate_matrix, rate_matrix + 190);
+                    }
                 }
                 if (pattern_freq) {
                     ((*pattern_freq)[ptn])++;
@@ -4186,6 +4195,9 @@ void Alignment::createBootstrapAlignment(Alignment *aln, IntVector* pattern_freq
     		out_site += site_vec[part+1];
     	}
     }
+    if (!aln->site_rate_matrices.empty()) {
+        ASSERT(aln->site_rate_matrices.size() == aln->getNPattern() * 190);
+    }
     if (aln->isSSF()) {
         ASSERT(ptn_state_freq.size() == getNPattern());
     }
diff --git a/alignment/alignment.h b/alignment/alignment.h
index e011d84da..f42233a1c 100644
--- a/alignment/alignment.h
+++ b/alignment/alignment.h
@@ -949,6 +949,10 @@ class Alignment : public vector<Pattern>, public CharSet, public StateSpace {
     /** pattern index to state frequency vector map */
     vector<double*> ptn_state_freq;
 
+    /** site to rate matrix. Stored in row-major order [num_sites, 190] used for MUTSEL */
+    vector<double> site_rate_matrices;
+    // Minh/Thomas: TODO rename this to ptn_rate_matrices to avoid confusions
+    
     /**
      * @return true if data type is SEQ_CODON and state is a stop codon
      */
diff --git a/main/CMakeLists.txt b/main/CMakeLists.txt
index 5c7916294..ab989d385 100644
--- a/main/CMakeLists.txt
+++ b/main/CMakeLists.txt
@@ -14,6 +14,7 @@ add_library(main
     terraceanalysis.h
 )
 
+
 if (USE_BOOSTER)
     target_link_libraries(main booster)
 endif()
@@ -58,4 +59,4 @@ if (USE_CMAPLE)
         
         target_link_libraries(main-aa pda whtest vectorclass terrace maple-aa)
     endif()
-endif()
+endif()
\ No newline at end of file
diff --git a/main/main.cpp b/main/main.cpp
index 94435557e..784f2c695 100644
--- a/main/main.cpp
+++ b/main/main.cpp
@@ -64,6 +64,7 @@
 #include "utils/operatingsystem.h" //for getOSName()
 #include <stdlib.h>
 #include "vectorclass/instrset.h"
+#include "main/outstreambuf.h"
 #include "alignment/alignment.h"
 
 #include "utils/MPIHelper.h"
@@ -1686,30 +1687,6 @@ void processNCBITree(Params &params) {
     }
 }
 
-/* write simultaneously to cout/cerr and a file */
-class outstreambuf : public streambuf {
-public:
-    outstreambuf* open( const char* name, ios::openmode mode = ios::out);
-    bool is_open();
-    outstreambuf* close();
-    ~outstreambuf() { close(); }
-    streambuf *get_fout_buf() {
-        return fout_buf;
-    }
-    streambuf *get_cout_buf() {
-        return cout_buf;
-    }
-    ofstream *get_fout() {
-        return &fout;
-    }
-    
-protected:
-    ofstream fout;
-    streambuf *cout_buf;
-    streambuf *fout_buf;
-    virtual int     overflow( int c = EOF);
-    virtual int     sync();
-};
 
 outstreambuf* outstreambuf::open( const char* name, ios::openmode mode) {
     if (!(Params::getInstance().suppress_output_flags & OUT_LOG)) {
diff --git a/main/outstreambuf.h b/main/outstreambuf.h
new file mode 100644
index 000000000..d94acd048
--- /dev/null
+++ b/main/outstreambuf.h
@@ -0,0 +1,33 @@
+#ifndef OUTSTREAMBUF_H
+#define OUTSTREAMBUF_H
+
+#include <fstream>
+#include <streambuf>
+#include <iostream>
+
+/* write simultaneously to cout/cerr and a file */
+class outstreambuf : public std::streambuf {
+public:
+    outstreambuf* open( const char* name, std::ios::openmode mode = std::ios::out);
+    bool is_open();
+    outstreambuf* close();
+    ~outstreambuf() { close(); }
+    std::streambuf *get_fout_buf() {
+        return fout_buf;
+    }
+    std::streambuf *get_cout_buf() {
+        return cout_buf;
+    }
+    std::ofstream *get_fout() {
+        return &fout;
+    }
+    
+protected:
+    std::ofstream fout;
+    std::streambuf *cout_buf;
+    std::streambuf *fout_buf;
+    virtual int     overflow( int c = EOF);
+    virtual int     sync();
+};
+
+#endif // OUTSTREAMBUF_H
\ No newline at end of file
diff --git a/main/phyloanalysis.cpp b/main/phyloanalysis.cpp
index c2dac05a5..46918dda9 100644
--- a/main/phyloanalysis.cpp
+++ b/main/phyloanalysis.cpp
@@ -67,6 +67,10 @@
 #include <Eigen/Eigenvalues>
 #include <unsupported/Eigen/MatrixFunctions>
 
+#include "utils/mutsel_wrapper.h"
+#include "utils/self_process.h"
+#include <filesystem>
+
 using namespace Eigen;
 using Eigen::Map;
 
@@ -2570,7 +2574,30 @@ void runApproximateBranchLengths(Params &params, IQTree &iqtree) {
 
 }
 
+// For MUTSEL model write a different file since we here only have the actual substitution rate
+void printMutselSiteRates(Alignment &alignment, const char *rate_file) {
+    DoubleVector site_rates = computeMutselSiteRates(alignment);
+    try {
+        ofstream out;
+        out.exceptions(ios::failbit | ios::badbit);
+        out.open(rate_file);
+        out.setf(ios::fixed, ios::floatfield);
+        out.precision(5);
+        out << "Site\tRate" << endl;
+        for (size_t i = 0; i < site_rates.size(); ++i)
+            out << i + 1 << "\t" << site_rates[i] << endl;
+        out.close();
+    } catch (ios::failure) {
+        outError(ERR_WRITE_OUTPUT, rate_file);
+    }
+    cout << "Site rates printed to " << rate_file << endl;
+}
+
 void printSiteRates(IQTree &iqtree, const char *rate_file, bool bayes) {
+    if (Params::getInstance().model_name.rfind("MUTSEL") == 0) {
+        printMutselSiteRates(*iqtree.aln, rate_file);
+        return;
+    }
     try {
         ofstream out;
         out.exceptions(ios::failbit | ios::badbit);
@@ -2588,7 +2615,7 @@ void printSiteRates(IQTree &iqtree, const char *rate_file, bool bayes) {
             << "#   Site:   Site ID within partition (starting from 1 for each partition)" << endl;
         } else
             out << "#   Site:   Alignment site ID" << endl;
-        
+
         if (bayes)
             out << "#   Rate:   Posterior mean site rate weighted by posterior probability" << endl
                 << "#   Cat:    Category with highest posterior (0=invariable, 1=slow, etc)" << endl
@@ -5196,19 +5223,65 @@ void runPhyloAnalysis(Params &params, Checkpoint *checkpoint, IQTree *&tree, Ali
 
         // Initialize site-frequency model
         if (params.tree_freq_file) {
-            if (checkpoint->getBool("finishedSiteFreqFile")) {
-                alignment->readSiteStateFreq(((string)params.out_prefix + ".sitefreq").c_str());
-                params.print_site_state_freq = WSF_NONE;
-                cout << "CHECKPOINT: Site frequency model restored" << endl;
+            if ((std::string)params.tree_freq_file == "AUTO") {
+                /* Minh/Thomas comments: the design of spawning process is not great
+                 because you need to load the alignment again causing overhead.
+                 It's better to run inside IQ-TREE. Suggest that we do not
+                 announce -ft AUTO option for now, and just ask users to explicitly
+                 infer a guide tree themselves.
+                 */
+                cout << "INFO: Automatic guide tree inference using LG+F+G4" << endl;
+                auto guide_tree_out = (std::string)params.out_prefix + ".guide_tree";
+                if (fileExists(guide_tree_out + ".treefile")) {
+                    cout << "INFO: Guide tree already exists at " << guide_tree_out + ".treefile" << endl;
+                    params.tree_freq_file = strdup((guide_tree_out + ".treefile").c_str());
+                } else {
+                    cout << "INFO: Guide tree does not exist, inferring..." << endl;
+                    auto arguments = std::vector<std::string>{"-s", (std::string)params.aln_file, "-m", "LG+F+G4", "-nt", std::to_string(params.num_threads), "-pre", guide_tree_out};
+                    auto process = selfproc::spawn_self(arguments);
+                    auto exit_code = process.wait();
+                    if (exit_code != 0) {
+                        outError("Guide tree inference failed with exit code " + std::to_string(exit_code));
+                        exit(1);
+                    }
+                    cout << "INFO: Guide tree written to " << guide_tree_out + ".treefile" << endl;
+                    params.tree_freq_file = strdup((guide_tree_out + ".treefile").c_str());
+                }
+            }
+            if (params.model_name.rfind("MUTSEL") == 0) {
+                if (checkpoint->getBool("finishedSiteModelFile")) {
+                    read_site_model_file((string)params.out_prefix + ".sitemodel", *alignment);
+                    alignment->model_name = params.model_name;
+                    params.print_site_state_freq = WSF_NONE;
+                    cout << "CHECKPOINT: Site model restored" << endl;
+                } else {
+                    computeMutselSiteFrequencyModel(params, alignment);
+                    alignment->model_name = params.model_name;
+                    checkpoint->putBool("finishedSiteModelFile", true);
+                    checkpoint->dump();
+                }
             } else {
-                computeSiteFrequencyModel(params, alignment);
-                checkpoint->putBool("finishedSiteFreqFile", true);
-                checkpoint->dump();
+                if (checkpoint->getBool("finishedSiteFreqFile")) {
+                    alignment->readSiteStateFreq(((string)params.out_prefix + ".sitefreq").c_str());
+                    params.print_site_state_freq = WSF_NONE;
+                    cout << "CHECKPOINT: Site frequency model restored" << endl;
+                } else {
+                    computeSiteFrequencyModel(params, alignment);
+                    checkpoint->putBool("finishedSiteFreqFile", true);
+                    checkpoint->dump();
+                }
             }
         }
         if (params.site_freq_file) {
             alignment->readSiteStateFreq(params.site_freq_file);
         }
+        if (!params.site_model_file.empty()) {
+            read_site_model_file(params.site_model_file, *alignment);
+            std::cout << "INFO: Site model read from " << params.site_model_file << std::endl;
+            alignment->model_name = "MUTSEL";
+            params.model_name = alignment->model_name;
+            params.print_site_state_freq = WSF_NONE;
+        }
     }
 
     if (params.symtest) {
@@ -5225,6 +5298,14 @@ void runPhyloAnalysis(Params &params, Checkpoint *checkpoint, IQTree *&tree, Ali
     tree = newIQTree(params, alignment);
 
     tree->setCheckpoint(checkpoint);
+    // Increase the maximum branch length if MutSel is used because the time unit is different.
+    if (params.model_name.rfind("MUTSEL") == 0) {
+        // Minh/Thomas: Better have some option like --max-mutsel-brlen with the
+        // default of 200.0. So users can change. We don't like hard-coded
+        // constant in the code
+        // Also this has to be in the utils.cpp file, not here, which is hard to debug.
+        params.max_branch_length = 200.0;
+    }
     if (tree->isTreeMix()) {
         ((IQTreeMix*) tree)->setMinBranchLen(params);
     } else if (params.min_branch_length <= 0.0) {
@@ -5243,6 +5324,7 @@ void runPhyloAnalysis(Params &params, Checkpoint *checkpoint, IQTree *&tree, Ali
             cout << "NOTE: minimal branch length is increased to " << params.min_branch_length << " because PoMo infers number of mutations and frequency shifts" << endl;
             cout.precision(3);
         }
+
     }
     // Increase the minimum branch length if PoMo is used.
     if (alignment->seq_type == SEQ_POMO) {
diff --git a/model/modelfactory.cpp b/model/modelfactory.cpp
index a45f1a842..d677312e6 100644
--- a/model/modelfactory.cpp
+++ b/model/modelfactory.cpp
@@ -639,39 +639,64 @@ ModelFactory::ModelFactory(Params &params, string &model_name, PhyloTree *tree,
 //        fused_mix_rate &= model->isMixture() && site_rate->getNRate() > 1;
     } else {
         // site-specific model
-        if (model_str == "JC" || model_str == "POISSON")
-            outError("JC is not suitable for site-specific model");
-        model = new ModelSet(model_str.c_str(), tree);
-        ModelSet *models = (ModelSet*)model; // assign pointer for convenience
-        models->init((params.freq_type != FREQ_UNKNOWN) ? params.freq_type : FREQ_EMPIRICAL);
-        double *state_freq = new double[model->num_states];
-        double *rates = new double[model->getNumRateEntries()];
-        for (size_t i = 0; i < tree->aln->ptn_state_freq.size(); ++i) {
-            ModelMarkov *modeli;
-            if (i == 0) {
-                modeli = (ModelMarkov*)createModel(model_str, models_block, (params.freq_type != FREQ_UNKNOWN) ? params.freq_type : FREQ_EMPIRICAL, "", tree);
-                modeli->getStateFrequency(state_freq);
-                modeli->getRateMatrix(rates);
-            } else {
-                modeli = (ModelMarkov*)createModel(model_str, models_block, FREQ_EQUAL, "", tree);
-                modeli->setStateFrequency(state_freq);
-                modeli->setRateMatrix(rates);
+
+        if (tree->aln->site_rate_matrices.empty()) {
+            // PMSF
+            if (model_str == "JC" || model_str == "POISSON")
+                outError("JC is not suitable for site-specific model");
+            model = new ModelSet(model_str.c_str(), tree);
+            ModelSet *models = (ModelSet*)model; // assign pointer for convenience
+            models->init((params.freq_type != FREQ_UNKNOWN) ? params.freq_type : FREQ_EMPIRICAL);
+            double *state_freq = new double[model->num_states];
+            double *rates = new double[model->getNumRateEntries()];
+            for (size_t i = 0; i < tree->aln->ptn_state_freq.size(); ++i) {
+                ModelMarkov *modeli;
+                if (i == 0) {
+                    modeli = (ModelMarkov*)createModel(model_str, models_block, (params.freq_type != FREQ_UNKNOWN) ? params.freq_type : FREQ_EMPIRICAL, "", tree);
+                    modeli->getStateFrequency(state_freq);
+                    modeli->getRateMatrix(rates);
+                } else {
+                    modeli = (ModelMarkov*)createModel(model_str, models_block, FREQ_EQUAL, "", tree);
+                    modeli->setStateFrequency(state_freq);
+                    modeli->setRateMatrix(rates);
+                }
+                if (tree->aln->ptn_state_freq[i])
+                    modeli->setStateFrequency (tree->aln->ptn_state_freq[i]);
+
+                modeli->init(FREQ_USER_DEFINED);
+                models->push_back(modeli);
             }
-            if (tree->aln->ptn_state_freq[i])
+            delete [] rates;
+            delete [] state_freq;
+
+            models->joinEigenMemory();
+            models->decomposeRateMatrix();
+        } else {
+            // MUTSEL
+            ModelSet *models = new ModelSet(model_str.c_str(), tree);
+            
+            models->init((params.freq_type != FREQ_UNKNOWN) ? params.freq_type : FREQ_EMPIRICAL);
+            models->fixParameters(true);
+            
+            for (size_t i = 0; i < tree->aln->ptn_state_freq.size(); ++i) {
+                ModelMarkov *modeli = new ModelMarkov(tree, true, true); // dummy model for getting num_states and num_rate_entries
                 modeli->setStateFrequency(tree->aln->ptn_state_freq[i]);
+                modeli->setRateMatrix(tree->aln->site_rate_matrices.data() + i * 190);
+                
+                // Minh/Thomas: Important to note: site Q matrices are not normalised
+                // But make sure to normalise across all sites, i.e.
+                // (1/nsites) * sum_i mu_i = 1.0, where mu_i = -sum_j pi^i_j * Q^i_{jj}
+                modeli->normalize_matrix = false;
+                modeli->init(FREQ_USER_DEFINED);
+                modeli->fixParameters(true);
+                models->push_back(modeli);
+            }
+            
+            models->joinEigenMemory();
+            models->decomposeRateMatrix();
 
-            modeli->init(FREQ_USER_DEFINED);
-            models->push_back(modeli);
+            model = models;
         }
-        delete [] rates;
-        delete [] state_freq;
-
-        models->joinEigenMemory();
-        models->decomposeRateMatrix();
-
-        // delete information of the old alignment
-//        tree->aln->ordered_pattern.clear();
-//        tree->deleteAllPartialLh();
     }
 
 //    if (model->isMixture())
diff --git a/mutsel_rust/Cargo.lock b/mutsel_rust/Cargo.lock
new file mode 100644
index 000000000..efae748ad
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+ "lzma-sys",
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+ "yoke-derive",
+ "zerofrom",
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+ "synstructure",
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+ "synstructure",
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+ "indexmap",
+ "memchr",
+ "typed-path",
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+
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diff --git a/mutsel_rust/Cargo.toml b/mutsel_rust/Cargo.toml
new file mode 100644
index 000000000..c5e058a86
--- /dev/null
+++ b/mutsel_rust/Cargo.toml
@@ -0,0 +1,28 @@
+[package]
+name = "mutsel_rust"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]
+anyhow = "1.0.100"
+candle-core = "0.9.2"
+candle-nn = "0.9.2"
+lazy_static = "1.5.0"
+phylo_grad = { git = "https://github.com/soedinglab/phylo_grad", rev="939dedb07605411bd6b2dbb4d3d733f842a15ff5"}
+rayon = "1.11.0"
+phylotree = "0.1.3"
+seq_io = "0.3.4"
+libc = "0.2.182"
+spec_math = "0.1.6"
+
+[lib]
+name = "mutsel_rust"
+crate-type = ["staticlib", "rlib"]
+
+[profile.release]
+lto = false # There seems to be an issue with LLVM which makes the code slower when using lto
+panic = 'abort'
+
+[profile.dev]
+panic = 'abort'
+
diff --git a/mutsel_rust/src/data.rs b/mutsel_rust/src/data.rs
new file mode 100644
index 000000000..7287d87c6
--- /dev/null
+++ b/mutsel_rust/src/data.rs
@@ -0,0 +1,7854 @@
+use candle_core::Tensor;
+
+pub const LG_TXT : &'static str = "
+0.425093 
+0.276818 0.751878 
+0.395144 0.123954 5.076149 
+2.489084 0.534551 0.528768 0.062556 
+0.969894 2.807908 1.695752 0.523386 0.084808 
+1.038545 0.363970 0.541712 5.243870 0.003499 4.128591 
+2.066040 0.390192 1.437645 0.844926 0.569265 0.267959 0.348847 
+0.358858 2.426601 4.509238 0.927114 0.640543 4.813505 0.423881 0.311484 
+0.149830 0.126991 0.191503 0.010690 0.320627 0.072854 0.044265 0.008705 0.108882 
+0.395337 0.301848 0.068427 0.015076 0.594007 0.582457 0.069673 0.044261 0.366317 4.145067 
+0.536518 6.326067 2.145078 0.282959 0.013266 3.234294 1.807177 0.296636 0.697264 0.159069 0.137500 
+1.124035 0.484133 0.371004 0.025548 0.893680 1.672569 0.173735 0.139538 0.442472 4.273607 6.312358 0.656604 
+0.253701 0.052722 0.089525 0.017416 1.105251 0.035855 0.018811 0.089586 0.682139 1.112727 2.592692 0.023918 1.798853 
+1.177651 0.332533 0.161787 0.394456 0.075382 0.624294 0.419409 0.196961 0.508851 0.078281 0.249060 0.390322 0.099849 0.094464 
+4.727182 0.858151 4.008358 1.240275 2.784478 1.223828 0.611973 1.739990 0.990012 0.064105 0.182287 0.748683 0.346960 0.361819 1.338132 
+2.139501 0.578987 2.000679 0.425860 1.143480 1.080136 0.604545 0.129836 0.584262 1.033739 0.302936 1.136863 2.020366 0.165001 0.571468 6.472279 
+0.180717 0.593607 0.045376 0.029890 0.670128 0.236199 0.077852 0.268491 0.597054 0.111660 0.619632 0.049906 0.696175 2.457121 0.095131 0.248862 0.140825 
+0.218959 0.314440 0.612025 0.135107 1.165532 0.257336 0.120037 0.054679 5.306834 0.232523 0.299648 0.131932 0.481306 7.803902 0.089613 0.400547 0.245841 3.151815 
+2.547870 0.170887 0.083688 0.037967 1.959291 0.210332 0.245034 0.076701 0.119013 10.649107 1.702745 0.185202 1.898718 0.654683 0.296501 0.098369 2.188158 0.189510 0.249313
+";
+
+pub const CODON_TXT: &'static str = "
+0.013119 
+0.013119 0.013119 
+1.652941 0.013119 6.572407 
+0.013119 2.199548 0.013119 0.013119 
+0.013119 2.199548 0.013119 0.013119 0.013119 
+1.652941 0.013119 0.013119 6.572407 0.013119 3.292763 
+1.652941 2.199548 0.013119 3.292763 1.652941 0.013119 3.292763 
+0.013119 2.199548 3.292763 3.292763 0.013119 6.572407 0.013119 0.013119 
+0.013119 0.377524 2.199548 0.013119 0.013119 0.013119 0.013119 0.013119 0.013119 
+0.013119 0.741928 0.013119 0.013119 0.013119 1.106333 0.013119 0.013119 1.106333 1.470738 
+0.013119 2.199548 6.572407 0.013119 0.013119 3.292763 6.572407 0.013119 0.013119 1.106333 0.013119 
+0.013119 1.106333 0.013119 0.013119 0.013119 0.013119 0.013119 0.013119 0.013119 8.758837 2.199548 3.292763 
+0.013119 0.013119 0.013119 0.013119 3.292763 0.013119 0.013119 0.013119 0.013119 2.199548 4.385978 0.013119 0.013119 
+1.652941 1.106333 0.013119 0.013119 0.013119 1.652941 0.013119 0.013119 1.652941 0.013119 2.199548 0.013119 0.013119 0.013119 
+1.106333 1.106333 2.199548 0.013119 2.199548 0.013119 0.013119 1.106333 0.013119 0.741928 0.741928 0.013119 0.013119 2.199548 2.199548 
+3.292763 0.559726 1.652941 0.013119 0.013119 0.013119 0.013119 0.013119 0.013119 3.292763 0.013119 1.652941 3.292763 0.013119 1.652941 1.652941 
+0.013119 3.292763 0.013119 0.013119 6.572407 0.013119 0.013119 1.652941 0.013119 0.013119 1.106333 0.013119 0.013119 0.013119 0.013119 1.106333 0.013119 
+0.013119 0.013119 3.292763 3.292763 6.572407 0.013119 0.013119 0.013119 6.572407 0.013119 0.013119 0.013119 0.013119 3.292763 0.013119 1.106333 0.013119 0.013119 
+3.292763 0.013119 0.013119 1.652941 0.013119 0.013119 1.652941 1.652941 0.013119 3.292763 1.652941 0.013119 3.292763 1.652941 0.013119 0.013119 0.013119 0.013119 0.013119";
+
+pub const CODON2_TXT: &'static str = "
+0.000023 
+0.000023 0.000023 
+1.747002 0.000023 6.987938 
+0.000023 2.329328 0.000023 0.000023 
+0.000023 2.329328 0.000023 0.000023 0.000023 
+1.747002 0.000023 0.000023 6.987938 0.000023 3.493980 
+1.747002 2.329328 0.000023 3.493980 1.747002 0.000023 3.493980 
+0.000023 2.329328 3.493980 3.493980 0.000023 6.987938 0.000023 0.000023 
+0.000023 0.388240 2.329328 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 
+0.000023 0.776458 0.000023 0.000023 0.000023 1.164675 0.000023 0.000023 1.164675 1.552893 
+0.000023 2.329328 6.987938 0.000023 0.000023 3.493980 6.987938 0.000023 0.000023 1.164675 0.000023 
+0.000023 1.164675 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 9.317243 2.329328 3.493980 
+0.000023 0.000023 0.000023 0.000023 3.493980 0.000023 0.000023 0.000023 0.000023 2.329328 4.658633 0.000023 0.000023 
+1.747002 1.164675 0.000023 0.000023 0.000023 1.747002 0.000023 0.000023 1.747002 0.000023 2.329328 0.000023 0.000023 0.000023 
+1.164675 1.164675 2.329328 0.000023 2.329328 0.000023 0.000023 1.164675 0.000023 0.776458 0.776458 0.000023 0.000023 2.329328 2.329328 
+3.493980 0.582349 1.747002 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 3.493980 0.000023 1.747002 3.493980 0.000023 1.747002 1.747002 
+0.000023 3.493980 0.000023 0.000023 6.987938 0.000023 0.000023 1.747002 0.000023 0.000023 1.164675 0.000023 0.000023 0.000023 0.000023 1.164675 0.000023 
+0.000023 0.000023 3.493980 3.493980 6.987938 0.000023 0.000023 0.000023 6.987938 0.000023 0.000023 0.000023 0.000023 3.493980 0.000023 1.164675 0.000023 0.000023 
+3.493980 0.000023 0.000023 1.747002 0.000023 0.000023 1.747002 1.747002 0.000023 3.493980 1.747002 0.000023 3.493980 1.747002 0.000023 0.000023 0.000023 0.000023 0.000023 
+
+0.065574 0.098361 0.032787 0.032787 0.032787 0.032787 0.032787 0.065574 0.032787 0.049180 0.098361 0.032787 0.016393 0.032787 0.065574 0.098361 0.065574 0.016393 0.032787 0.065574";
+
+/// Load a lower-triangular rate matrix from a whitespace-separated string
+/// It will load the first 190 values into a 20x20 matrix
+/// Diagonal and upper-triangular values are set to zero
+pub fn load_lower_R(matrix: &str) -> Tensor {
+    let vals = matrix
+        .split_whitespace()
+        .map(|s| s.parse::<f64>().unwrap())
+        .collect::<Vec<f64>>();
+
+    let mut data = vec![0.0; 20 * 20];
+    let mut index = 0;
+    for i in 1..20 {
+        for j in 0..i {
+            data[i * 20 + j] = vals[index];
+            index += 1;
+        }
+    }
+    Tensor::from_vec(data, &[20, 20], &candle_core::Device::Cpu).unwrap()
+}
+
+pub fn load_lower_R_with_equi(matrix: &str) -> Tensor {
+    let vals = matrix
+        .split_whitespace()
+        .map(|s| s.parse::<f64>().unwrap())
+        .collect::<Vec<f64>>();
+
+    let mut data = vec![0.0; 20 * 20];
+    let mut index = 0;
+    for i in 1..20 {
+        for j in 0..i {
+            data[i * 20 + j] = vals[index];
+            index += 1;
+        }
+    }
+    for i in 0..20 {
+        data[i * 20 + i] = vals[index];
+        index += 1;
+    }
+    Tensor::from_vec(data, &[20, 20], &candle_core::Device::Cpu).unwrap()
+}
+
+pub const C20: &'static [[f64; 20]] = &[
+    [
+        0.0862412505,
+        0.0171943793,
+        0.0791293376,
+        0.0329908619,
+        0.0130504558,
+        0.0169046938,
+        0.0184526503,
+        0.0366905299,
+        0.0108013340,
+        0.0097907148,
+        0.0112826424,
+        0.0220195221,
+        0.0087821483,
+        0.0044155335,
+        0.0189273201,
+        0.3178152357,
+        0.2711700523,
+        0.0015317305,
+        0.0048342853,
+        0.0179753220,
+    ],
+    [
+        0.2035582865,
+        0.0050980810,
+        0.0077052407,
+        0.0031656079,
+        0.0348667285,
+        0.0064044073,
+        0.0070859400,
+        0.0195235515,
+        0.0024392035,
+        0.1152573291,
+        0.0789777393,
+        0.0042380850,
+        0.0309187017,
+        0.0112429356,
+        0.0164189221,
+        0.0496777139,
+        0.1118946615,
+        0.0017762569,
+        0.0048448213,
+        0.2849057867,
+    ],
+    [
+        0.0211547413,
+        0.0014946177,
+        0.0012755030,
+        0.0005492865,
+        0.0048188557,
+        0.0012328812,
+        0.0014539632,
+        0.0011430874,
+        0.0011346394,
+        0.3928460626,
+        0.1250644210,
+        0.0013579946,
+        0.0209788805,
+        0.0128251737,
+        0.0020247248,
+        0.0026240726,
+        0.0171914121,
+        0.0011591071,
+        0.0036027969,
+        0.3860677787,
+    ],
+    [
+        0.0376903543,
+        0.2885196153,
+        0.0365411474,
+        0.0109469400,
+        0.0064073829,
+        0.0893564381,
+        0.0358365464,
+        0.0191106776,
+        0.0329513951,
+        0.0101711878,
+        0.0237495504,
+        0.2897626974,
+        0.0096528870,
+        0.0036349802,
+        0.0105337370,
+        0.0356313768,
+        0.0355926500,
+        0.0027925238,
+        0.0066557222,
+        0.0144621902,
+    ],
+    [
+        0.0084597802,
+        0.0053589922,
+        0.0072525884,
+        0.0024487852,
+        0.0084909000,
+        0.0042781483,
+        0.0025055486,
+        0.0024277107,
+        0.0433214027,
+        0.0097713028,
+        0.0380507037,
+        0.0026741007,
+        0.0080724771,
+        0.3420463838,
+        0.0021418673,
+        0.0080418935,
+        0.0055322116,
+        0.0494840193,
+        0.4375001561,
+        0.0121410277,
+    ],
+    [
+        0.1759898886,
+        0.0290429175,
+        0.0332845569,
+        0.1301263816,
+        0.0017558693,
+        0.0707183953,
+        0.2182166681,
+        0.0409535143,
+        0.0130708195,
+        0.0085622087,
+        0.0159530702,
+        0.0542946169,
+        0.0054045759,
+        0.0025276980,
+        0.0371020404,
+        0.0793480500,
+        0.0540083424,
+        0.0010592104,
+        0.0036259116,
+        0.0249552645,
+    ],
+    [
+        0.1634397322,
+        0.0195541184,
+        0.0438701833,
+        0.0374272612,
+        0.0088659891,
+        0.0137554758,
+        0.0220611924,
+        0.5296717726,
+        0.0090006141,
+        0.0017569353,
+        0.0061156267,
+        0.0167117975,
+        0.0029390787,
+        0.0030641349,
+        0.0126457766,
+        0.0829342776,
+        0.0142835614,
+        0.0028640685,
+        0.0032398299,
+        0.0057985736,
+    ],
+    [
+        0.0917468761,
+        0.0265853306,
+        0.0290699087,
+        0.0133818895,
+        0.0284015012,
+        0.0255084506,
+        0.0196875685,
+        0.0249898794,
+        0.0449766405,
+        0.0583555688,
+        0.1155009222,
+        0.0164915955,
+        0.0395994595,
+        0.0998479096,
+        0.0209916159,
+        0.0736482742,
+        0.0661518462,
+        0.0246463919,
+        0.0972327226,
+        0.0831856483,
+    ],
+    [
+        0.0646700714,
+        0.0988015996,
+        0.0228907308,
+        0.0168733856,
+        0.0077117603,
+        0.0996414875,
+        0.0544977962,
+        0.0148893975,
+        0.0313851988,
+        0.0505983315,
+        0.1844282999,
+        0.0907931290,
+        0.0774839960,
+        0.0219148172,
+        0.0105004469,
+        0.0321196170,
+        0.0411766062,
+        0.0084303030,
+        0.0206106035,
+        0.0505824221,
+    ],
+    [
+        0.0135993865,
+        0.0043408375,
+        0.0018469375,
+        0.0007951703,
+        0.0100090240,
+        0.0046420778,
+        0.0018011758,
+        0.0026794645,
+        0.0072401918,
+        0.0814026713,
+        0.3661422246,
+        0.0025158135,
+        0.0734965132,
+        0.2640965246,
+        0.0038994134,
+        0.0043668760,
+        0.0075248451,
+        0.0261564898,
+        0.0660970801,
+        0.0573472826,
+    ],
+    [
+        0.1478036236,
+        0.0842845089,
+        0.0726630217,
+        0.0534743238,
+        0.0048825808,
+        0.0757166156,
+        0.0727246460,
+        0.0907725939,
+        0.0262288856,
+        0.0035781075,
+        0.0126777221,
+        0.1051660098,
+        0.0059621792,
+        0.0029903868,
+        0.0156558198,
+        0.1459903343,
+        0.0634877444,
+        0.0015928454,
+        0.0050760739,
+        0.0092719768,
+    ],
+    [
+        0.0186377412,
+        0.0042055165,
+        0.0019865236,
+        0.0008329696,
+        0.0054968852,
+        0.0065890091,
+        0.0020248504,
+        0.0021713483,
+        0.0023665991,
+        0.2020809776,
+        0.4370381920,
+        0.0029120653,
+        0.1241860384,
+        0.0385383157,
+        0.0040672279,
+        0.0046177381,
+        0.0149904396,
+        0.0026871667,
+        0.0056324117,
+        0.1189379840,
+    ],
+    [
+        0.0477624336,
+        0.0505742667,
+        0.0209574273,
+        0.0141349161,
+        0.0075791708,
+        0.0429296799,
+        0.0462688073,
+        0.0052327914,
+        0.0165351815,
+        0.1741496627,
+        0.1121253570,
+        0.0577575020,
+        0.0330288046,
+        0.0130691347,
+        0.0124374733,
+        0.0264988925,
+        0.0951754678,
+        0.0031660482,
+        0.0112465746,
+        0.2093704079,
+    ],
+    [
+        0.4164189845,
+        0.0056100821,
+        0.0091701381,
+        0.0045131748,
+        0.0406937949,
+        0.0061320495,
+        0.0063229801,
+        0.0946185184,
+        0.0031057404,
+        0.0076443223,
+        0.0099885414,
+        0.0038941773,
+        0.0069323155,
+        0.0048438356,
+        0.0187840756,
+        0.2360774301,
+        0.0746274607,
+        0.0012172579,
+        0.0034825786,
+        0.0459225422,
+    ],
+    [
+        0.0402295888,
+        0.0735203003,
+        0.1036647193,
+        0.0365523994,
+        0.0124782975,
+        0.0826558132,
+        0.0372197283,
+        0.0233618081,
+        0.2108307125,
+        0.0093478727,
+        0.0360561493,
+        0.0482410586,
+        0.0100289536,
+        0.0459094917,
+        0.0098503973,
+        0.0533383445,
+        0.0310209005,
+        0.0140076639,
+        0.1064377821,
+        0.0152480184,
+    ],
+    [
+        0.0323453034,
+        0.0236282995,
+        0.2520448083,
+        0.2431495959,
+        0.0035976296,
+        0.0330831153,
+        0.0710274499,
+        0.1016074562,
+        0.0366225082,
+        0.0031410809,
+        0.0051980542,
+        0.0470129351,
+        0.0024028744,
+        0.0024429276,
+        0.0094837826,
+        0.0848355278,
+        0.0359083275,
+        0.0008730928,
+        0.0067247672,
+        0.0048704638,
+    ],
+    [
+        0.1476256642,
+        0.0334506604,
+        0.0211972524,
+        0.0403051550,
+        0.0032327194,
+        0.0371554480,
+        0.0576893391,
+        0.0330850942,
+        0.0146392559,
+        0.0108267008,
+        0.0256200793,
+        0.0451350877,
+        0.0058651400,
+        0.0047177179,
+        0.3473710507,
+        0.0892065279,
+        0.0485899446,
+        0.0016358749,
+        0.0044177191,
+        0.0282335685,
+    ],
+    [
+        0.1031448143,
+        0.0717747663,
+        0.0435172139,
+        0.0386401502,
+        0.0061762467,
+        0.0786603123,
+        0.0923369140,
+        0.0202338419,
+        0.0246761899,
+        0.0376904275,
+        0.0376283678,
+        0.0921698920,
+        0.0161883318,
+        0.0067666433,
+        0.0128302120,
+        0.0951450188,
+        0.1378566702,
+        0.0022144738,
+        0.0083041573,
+        0.0740453560,
+    ],
+    [
+        0.0837542823,
+        0.0899383244,
+        0.0518811417,
+        0.0804870571,
+        0.0020735078,
+        0.1456497470,
+        0.1947759184,
+        0.0229030361,
+        0.0268458796,
+        0.0074079756,
+        0.0190249576,
+        0.1459287407,
+        0.0067395241,
+        0.0023063393,
+        0.0085616014,
+        0.0455739585,
+        0.0451080843,
+        0.0010771349,
+        0.0049325333,
+        0.0150302559,
+    ],
+    [
+        0.0578735570,
+        0.0138313604,
+        0.0491421636,
+        0.2946738942,
+        0.0011130839,
+        0.0598250358,
+        0.3402102668,
+        0.0293911435,
+        0.0139817004,
+        0.0030525663,
+        0.0062611922,
+        0.0363365043,
+        0.0027295976,
+        0.0017034884,
+        0.0156106390,
+        0.0358044639,
+        0.0249941878,
+        0.0008664342,
+        0.0038312977,
+        0.0087674229,
+    ],
+];
+
+pub const C20_WEIGHTS: &'static [f64] = &[
+    0.0559910600,
+    0.0514824870,
+    0.0812922124,
+    0.0721976867,
+    0.0556718858,
+    0.0331003080,
+    0.0589501763,
+    0.0263756889,
+    0.0307584220,
+    0.0376701125,
+    0.0303058290,
+    0.0808775576,
+    0.0263349134,
+    0.0579101455,
+    0.0371248064,
+    0.0586867766,
+    0.0561479138,
+    0.0349810886,
+    0.0544937394,
+    0.0596471901,
+];
+
+pub const C60: &'static [[f64; 20]] = &[
+    [
+        0.1534363248,
+        0.0444389067,
+        0.0796726990,
+        0.0546757288,
+        0.0047306596,
+        0.0514333025,
+        0.0529324359,
+        0.1103775749,
+        0.0174480218,
+        0.0050343887,
+        0.0130294160,
+        0.0603928711,
+        0.0075550589,
+        0.0035554315,
+        0.0249523704,
+        0.2029625968,
+        0.0957668473,
+        0.0014444483,
+        0.0059800307,
+        0.0101808864,
+    ],
+    [
+        0.0281984692,
+        0.3031055487,
+        0.0312954609,
+        0.0091549350,
+        0.0019503463,
+        0.0939884393,
+        0.0388530140,
+        0.0084028325,
+        0.0155384715,
+        0.0107872879,
+        0.0217786594,
+        0.3476042929,
+        0.0109904917,
+        0.0015919288,
+        0.0071539896,
+        0.0197479052,
+        0.0328352333,
+        0.0009209994,
+        0.0025714024,
+        0.0135302919,
+    ],
+    [
+        0.0083680740,
+        0.0007319768,
+        0.0006123446,
+        0.0002228366,
+        0.0020433870,
+        0.0009498685,
+        0.0004731544,
+        0.0004825748,
+        0.0005189995,
+        0.3768453098,
+        0.2608334606,
+        0.0006296168,
+        0.0315700586,
+        0.0123984358,
+        0.0009595916,
+        0.0009746383,
+        0.0049990761,
+        0.0008657759,
+        0.0017132332,
+        0.2938075872,
+    ],
+    [
+        0.2227229348,
+        0.0064846074,
+        0.0061206496,
+        0.0007997588,
+        0.1640285908,
+        0.0051051888,
+        0.0027280806,
+        0.0202702520,
+        0.0037183875,
+        0.0455406072,
+        0.0883350071,
+        0.0022832871,
+        0.0348094559,
+        0.0228667054,
+        0.0035471579,
+        0.0850040072,
+        0.1012848285,
+        0.0048424833,
+        0.0096500033,
+        0.1698580069,
+    ],
+    [
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+        0.0051067690,
+        0.0017434391,
+        0.0204715649,
+        0.0057538477,
+        0.0037263409,
+        0.0069107492,
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+        0.1154281623,
+        0.1693562458,
+        0.0042900270,
+        0.0414066566,
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+        0.0058416410,
+        0.0149106129,
+        0.0239548406,
+        0.0332237129,
+        0.1379349474,
+        0.1200342049,
+    ],
+    [
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+        0.0747676701,
+        0.1855184661,
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+        0.0872162350,
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+        0.0277340828,
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+        0.0439680761,
+        0.0324588883,
+        0.0034665720,
+        0.0387499964,
+        0.0181769181,
+    ],
+    [
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+        0.0056903327,
+        0.0037091821,
+        0.0598639097,
+        0.3185565304,
+        0.0152753744,
+    ],
+    [
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+        0.0098310464,
+        0.0006474254,
+        0.0041611385,
+        0.0068976432,
+        0.0038767247,
+        0.1864537050,
+        0.0687189855,
+        0.0027083549,
+        0.0061033012,
+        0.0345742379,
+    ],
+    [
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+        0.0134869242,
+        0.0170572285,
+        0.0070719770,
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+        0.0343564471,
+        0.0305859029,
+        0.0204571345,
+        0.0994551128,
+        0.0212367087,
+        0.0318165939,
+        0.1140907926,
+        0.0297628218,
+        0.0505792699,
+        0.0339368402,
+        0.2312808862,
+        0.1192491702,
+        0.0217421638,
+    ],
+    [
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+        0.0416822304,
+        0.0324482918,
+        0.0131641265,
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+        0.1282255556,
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+        0.0390362930,
+        0.0594359563,
+        0.0135608209,
+        0.0551343199,
+        0.0642260358,
+        0.0137118382,
+        0.0673934289,
+        0.0789609573,
+    ],
+    [
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+        0.0076332888,
+        0.0303081645,
+        0.3430234188,
+        0.0007199837,
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+        0.0016999627,
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+        0.0019734329,
+        0.0009814186,
+        0.0174791407,
+        0.0337831940,
+        0.0203426591,
+        0.0006130268,
+        0.0017102752,
+        0.0058992300,
+    ],
+    [
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+        0.1042068314,
+        0.0286980872,
+        0.0164385240,
+        0.0044450330,
+        0.1393690851,
+        0.0531949072,
+        0.0134711207,
+        0.0177764997,
+        0.0267727728,
+        0.1967237776,
+        0.1323735242,
+        0.1182827521,
+        0.0086728324,
+        0.0051837880,
+        0.0255852718,
+        0.0333292020,
+        0.0045852327,
+        0.0070281498,
+        0.0217066546,
+    ],
+    [
+        0.2814809927,
+        0.0100367066,
+        0.0172867775,
+        0.0064385734,
+        0.0258337508,
+        0.0133101925,
+        0.0115046410,
+        0.0270054934,
+        0.0054629657,
+        0.0188216093,
+        0.0190993462,
+        0.0098712843,
+        0.0158719589,
+        0.0050481705,
+        0.0129510033,
+        0.1886808600,
+        0.2427104979,
+        0.0012274627,
+        0.0036052922,
+        0.0837524211,
+    ],
+    [
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+        0.0017226995,
+        0.0021315271,
+        0.0011672545,
+        0.0318292645,
+        0.0018216251,
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+        0.0005170863,
+        0.0983109006,
+        0.0489264326,
+        0.0016232163,
+        0.0173414948,
+        0.0070843906,
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+        0.0336348952,
+        0.0814141404,
+        0.0007118144,
+        0.0032942319,
+        0.3620922883,
+    ],
+    [
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+        0.0053318076,
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+        0.0533809635,
+        0.0029171632,
+        0.0156225571,
+        0.0782148712,
+        0.0045758969,
+        0.0025047816,
+        0.0067077844,
+        0.0929310045,
+        0.0393122597,
+        0.0028575821,
+        0.0077590269,
+        0.0085040899,
+    ],
+    [
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+        0.0020993577,
+        0.0056191259,
+        0.0750172075,
+        0.0021871739,
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+        0.0726449461,
+        0.0380238271,
+        0.0007346460,
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+        0.0042669729,
+    ],
+    [
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+        0.0046842467,
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+    [
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+        0.0067612939,
+        0.0038937184,
+        0.0074911765,
+        0.1290478057,
+    ],
+    [
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+    ],
+    [
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+    [
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+    [
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+    [
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+    [
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+    [
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+        0.0362876891,
+        0.0032887534,
+        0.0015223902,
+        0.0008537454,
+        0.0020289624,
+    ],
+    [
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+    [
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+        0.0106565111,
+        0.0281012433,
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+    [
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+        0.1064984500,
+        0.0438053705,
+        0.0006333959,
+        0.0056197958,
+        0.0040302013,
+    ],
+    [
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+        0.0686820704,
+        0.0081981143,
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+        0.0073954898,
+        0.0017471177,
+        0.0039653113,
+        0.0129342146,
+        0.0019557975,
+        0.0024132583,
+        0.0355924232,
+        0.3115606483,
+        0.2113368612,
+        0.0016329034,
+        0.0017991083,
+        0.0047138579,
+    ],
+    [
+        0.0181409133,
+        0.4129662563,
+        0.0233205154,
+        0.0033333547,
+        0.0085143598,
+        0.0526694251,
+        0.0096531879,
+        0.0224552642,
+        0.0375238929,
+        0.0035090482,
+        0.0149146621,
+        0.3208065790,
+        0.0046098856,
+        0.0035426859,
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+        0.0262309419,
+        0.0131791136,
+        0.0034766995,
+        0.0079588201,
+        0.0044746474,
+    ],
+    [
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+        0.0228501981,
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+        0.0451065029,
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+        0.0204556127,
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+        0.0686403544,
+        0.0889295672,
+        0.0986017356,
+        0.0028603862,
+        0.0061938477,
+        0.1672519917,
+    ],
+    [
+        0.1419737638,
+        0.0373945961,
+        0.0576296888,
+        0.0537452477,
+        0.0068856658,
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+        0.0040286132,
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+        0.1123731997,
+        0.0242478202,
+        0.0025909098,
+        0.0049054208,
+        0.0048462908,
+    ],
+    [
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+        0.0009938415,
+        0.0181675536,
+        0.0186260222,
+        0.2260554691,
+        0.0859787232,
+        0.0113864962,
+    ],
+    [
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+        0.0420979067,
+        0.0400419720,
+        0.1294249748,
+        0.0014186329,
+        0.0906469055,
+        0.2471353458,
+        0.0319650773,
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+        0.0058525371,
+        0.0123593139,
+        0.0818154090,
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+        0.0656688174,
+        0.0511289472,
+        0.0007731441,
+        0.0029258438,
+        0.0169400635,
+    ],
+    [
+        0.0169799462,
+        0.0242346701,
+        0.1318047919,
+        0.1043655101,
+        0.0022087215,
+        0.0269349684,
+        0.0376379591,
+        0.5404470183,
+        0.0181137053,
+        0.0007459679,
+        0.0021146994,
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+        0.0006780593,
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+        0.0297030159,
+        0.0045836180,
+        0.0006031889,
+        0.0015704090,
+        0.0015891728,
+    ],
+    [
+        0.0402646249,
+        0.1152022601,
+        0.0323829165,
+        0.0293968352,
+        0.0039388655,
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+        0.0041153375,
+        0.0043374229,
+        0.0243246958,
+        0.0305645368,
+        0.0026676598,
+        0.0097227847,
+        0.0156026694,
+    ],
+    [
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+        0.0523417493,
+        0.0244308734,
+        0.0637125217,
+        0.0043390149,
+        0.0578159236,
+        0.1154830640,
+        0.0867335173,
+        0.0131066949,
+        0.0085086217,
+        0.0193314218,
+        0.0660468804,
+        0.0064877206,
+        0.0027440054,
+        0.0611149102,
+        0.1070877179,
+        0.0507677144,
+        0.0013695913,
+        0.0028982948,
+        0.0299883012,
+    ],
+    [
+        0.0033164209,
+        0.0015310773,
+        0.0030830171,
+        0.0008266472,
+        0.0051890730,
+        0.0011024889,
+        0.0005134130,
+        0.0010432830,
+        0.0278451262,
+        0.0041895268,
+        0.0111212494,
+        0.0007149922,
+        0.0023621780,
+        0.3801761447,
+        0.0008365077,
+        0.0035876698,
+        0.0023608948,
+        0.0333346985,
+        0.5107889643,
+        0.0060766272,
+    ],
+    [
+        0.1995014012,
+        0.0236078675,
+        0.0392254543,
+        0.0094955104,
+        0.0584590451,
+        0.0254265363,
+        0.0125535371,
+        0.0939787338,
+        0.0341857201,
+        0.0140209879,
+        0.0449387571,
+        0.0118723304,
+        0.0246990633,
+        0.0634433944,
+        0.0145385320,
+        0.1663920640,
+        0.0533159207,
+        0.0129802666,
+        0.0606346163,
+        0.0367302614,
+    ],
+    [
+        0.0319448994,
+        0.1011667268,
+        0.2084709220,
+        0.0378074649,
+        0.0066040348,
+        0.0766372935,
+        0.0279488190,
+        0.0365541130,
+        0.2088643258,
+        0.0047542347,
+        0.0156545731,
+        0.0868664783,
+        0.0043253317,
+        0.0108915768,
+        0.0060899575,
+        0.0577656939,
+        0.0302051160,
+        0.0026001883,
+        0.0387897304,
+        0.0060585202,
+    ],
+    [
+        0.0776799515,
+        0.0142518583,
+        0.0403216692,
+        0.0080651725,
+        0.0140092962,
+        0.0179995517,
+        0.0112622427,
+        0.0136868237,
+        0.0133729897,
+        0.1239635380,
+        0.0724670993,
+        0.0129144967,
+        0.0420745442,
+        0.0173584908,
+        0.0117084432,
+        0.0922723571,
+        0.2316899445,
+        0.0028153633,
+        0.0141726542,
+        0.1679135132,
+    ],
+    [
+        0.1183662657,
+        0.0805192606,
+        0.0259524932,
+        0.0495595439,
+        0.0035624835,
+        0.1204924917,
+        0.1537589210,
+        0.0194993426,
+        0.0229373171,
+        0.0302661211,
+        0.0571250629,
+        0.0982304112,
+        0.0171727472,
+        0.0068665705,
+        0.0175153030,
+        0.0486588400,
+        0.0635796210,
+        0.0023008307,
+        0.0083027431,
+        0.0553336300,
+    ],
+    [
+        0.0528559899,
+        0.0193569043,
+        0.0264743774,
+        0.2092761515,
+        0.0008625883,
+        0.1212409715,
+        0.4024189781,
+        0.0155838458,
+        0.0124148798,
+        0.0054864832,
+        0.0090256472,
+        0.0497017031,
+        0.0042357114,
+        0.0012650715,
+        0.0063185636,
+        0.0197262901,
+        0.0235463735,
+        0.0008381610,
+        0.0033948741,
+        0.0159764347,
+    ],
+    [
+        0.0344366215,
+        0.0426221820,
+        0.1636716191,
+        0.1139007491,
+        0.0020985982,
+        0.0605413987,
+        0.0541780220,
+        0.3361639671,
+        0.0461776737,
+        0.0003463416,
+        0.0048355678,
+        0.0667552967,
+        0.0019704509,
+        0.0031557619,
+        0.0040369775,
+        0.0481173332,
+        0.0089148085,
+        0.0006510101,
+        0.0054145649,
+        0.0020110555,
+    ],
+    [
+        0.1153088951,
+        0.0151278638,
+        0.0458476603,
+        0.1755516676,
+        0.0014962362,
+        0.0366731222,
+        0.1749410045,
+        0.0394181311,
+        0.0132401530,
+        0.0056912974,
+        0.0101409559,
+        0.0433118387,
+        0.0030332064,
+        0.0015700232,
+        0.1665802563,
+        0.0871536033,
+        0.0468260603,
+        0.0007515702,
+        0.0031432715,
+        0.0141931831,
+    ],
+    [
+        0.3865149348,
+        0.0037579334,
+        0.0030420497,
+        0.0022366810,
+        0.0218928357,
+        0.0021464743,
+        0.0031387843,
+        0.3694353983,
+        0.0014672902,
+        0.0085376076,
+        0.0127257242,
+        0.0018840458,
+        0.0080581695,
+        0.0039281367,
+        0.0158688291,
+        0.0808877279,
+        0.0305195935,
+        0.0009922880,
+        0.0019020345,
+        0.0410634615,
+    ],
+    [
+        0.0146570745,
+        0.0028841333,
+        0.0012998335,
+        0.0005210575,
+        0.0024317913,
+        0.0049362750,
+        0.0014874369,
+        0.0020953252,
+        0.0010181940,
+        0.1913901476,
+        0.4432797758,
+        0.0022898369,
+        0.2217427062,
+        0.0091637503,
+        0.0007685153,
+        0.0027251487,
+        0.0170997497,
+        0.0008779380,
+        0.0014756028,
+        0.0778557075,
+    ],
+];
+
+pub const C60_WEIGHTS: &'static [f64] = &[
+    0.0169698865,
+    0.0211683374,
+    0.0276589079,
+    0.0065675964,
+    0.0141221416,
+    0.0068774834,
+    0.0146909701,
+    0.0067225777,
+    0.0018396660,
+    0.0102547197,
+    0.0230896163,
+    0.0057941033,
+    0.0125394534,
+    0.0204526478,
+    0.0070629602,
+    0.0117982741,
+    0.0068334668,
+    0.0433775839,
+    0.0318278731,
+    0.0222546108,
+    0.0102264969,
+    0.0150545891,
+    0.0134159878,
+    0.0148552065,
+    0.0239111516,
+    0.0128776278,
+    0.0222318842,
+    0.0247444742,
+    0.0214274810,
+    0.0115001882,
+    0.0076017389,
+    0.0130258568,
+    0.0093701965,
+    0.0467194264,
+    0.0441940314,
+    0.0322263154,
+    0.0402999891,
+    0.0150234227,
+    0.0104589903,
+    0.0214742395,
+    0.0154957836,
+    0.0101789953,
+    0.0227980379,
+    0.0123204539,
+    0.0066777583,
+    0.0004150083,
+    0.0344385130,
+    0.0113663379,
+    0.0127143049,
+    0.0124323741,
+    0.0262124415,
+    0.0064994957,
+    0.0103203293,
+    0.0142463512,
+    0.0215600067,
+    0.0199150700,
+    0.0038964200,
+    0.0113448855,
+    0.0128595846,
+    0.0117656776,
+];
+
+pub const UDM256: &'static [[f64; 20]] = &[
+    [
+        0.0688549572,
+        0.0605280252,
+        0.0519105389,
+        0.0568524289,
+        0.0179942803,
+        0.0511728262,
+        0.0658138717,
+        0.0600029876,
+        0.0268497187,
+        0.0604142440,
+        0.0836442548,
+        0.0615695503,
+        0.0211388645,
+        0.0434461283,
+        0.0336523401,
+        0.0674385272,
+        0.0599848094,
+        0.0100780344,
+        0.0321211264,
+        0.0665324858,
+    ],
+    [
+        0.0685883410,
+        0.0564612276,
+        0.0579724100,
+        0.0589588467,
+        0.0049634517,
+        0.0520377286,
+        0.0610470807,
+        0.0629374349,
+        0.0219954724,
+        0.0553418912,
+        0.0752534655,
+        0.0602870546,
+        0.0187252694,
+        0.0461336563,
+        0.0406348213,
+        0.0661970974,
+        0.0625965074,
+        0.0157536981,
+        0.0496627633,
+        0.0644517819,
+    ],
+    [
+        0.0708934510,
+        0.0550727429,
+        0.0328216828,
+        0.0452519149,
+        0.0110356391,
+        0.0479888222,
+        0.0561397354,
+        0.0522772330,
+        0.0218666396,
+        0.0670372737,
+        0.1635707641,
+        0.0526801158,
+        0.0254959777,
+        0.0500481615,
+        0.0246598831,
+        0.0580524554,
+        0.0547437711,
+        0.0092108952,
+        0.0300737966,
+        0.0710790450,
+    ],
+    [
+        0.1451294666,
+        0.0607528498,
+        0.0415699288,
+        0.0562841368,
+        0.0107150695,
+        0.0536019344,
+        0.0642001739,
+        0.0632952380,
+        0.0222271210,
+        0.0498107323,
+        0.0786148687,
+        0.0516857964,
+        0.0175619515,
+        0.0257073910,
+        0.0305997557,
+        0.0714727315,
+        0.0607610975,
+        0.0087103704,
+        0.0224887433,
+        0.0648106430,
+    ],
+    [
+        0.0764076115,
+        0.0570897984,
+        0.0478245773,
+        0.0728070552,
+        0.0076652285,
+        0.0606986267,
+        0.1559860156,
+        0.0502441425,
+        0.0208387421,
+        0.0474075818,
+        0.0691069716,
+        0.0703170610,
+        0.0162169681,
+        0.0209063460,
+        0.0236375318,
+        0.0616871407,
+        0.0576490625,
+        0.0058736284,
+        0.0204305715,
+        0.0572053389,
+    ],
+    [
+        0.0778825403,
+        0.0536629900,
+        0.0540623977,
+        0.0605374118,
+        0.0086576713,
+        0.0423324409,
+        0.0567371107,
+        0.1688078518,
+        0.0207784101,
+        0.0496236658,
+        0.0710674985,
+        0.0542699207,
+        0.0166720416,
+        0.0263842723,
+        0.0277160875,
+        0.0664600111,
+        0.0537731894,
+        0.0085066825,
+        0.0239509531,
+        0.0581168530,
+    ],
+    [
+        0.0852326898,
+        0.0530472345,
+        0.0638550979,
+        0.0541358563,
+        0.0118137257,
+        0.0508622214,
+        0.0569893969,
+        0.0621563786,
+        0.0227013217,
+        0.0381978782,
+        0.0633874597,
+        0.0555457222,
+        0.0164021745,
+        0.0218127459,
+        0.0259020761,
+        0.1566772936,
+        0.0785229434,
+        0.0065053595,
+        0.0218239971,
+        0.0544284270,
+    ],
+    [
+        0.0812294559,
+        0.0524145867,
+        0.0296834708,
+        0.0442272346,
+        0.0108407450,
+        0.0381126562,
+        0.0546607148,
+        0.0518297867,
+        0.0199090830,
+        0.0778124273,
+        0.0865766981,
+        0.0516412266,
+        0.0208324777,
+        0.0332835264,
+        0.0251127599,
+        0.0580122011,
+        0.0660765407,
+        0.0086067972,
+        0.0259016764,
+        0.1632359349,
+    ],
+    [
+        0.0695341703,
+        0.0704509985,
+        0.0570255062,
+        0.0543701642,
+        0.0072581759,
+        0.0617017280,
+        0.0721340096,
+        0.0501406316,
+        0.0217333405,
+        0.0500644745,
+        0.0684328046,
+        0.1482371427,
+        0.0169956734,
+        0.0212651915,
+        0.0210331580,
+        0.0645445704,
+        0.0609951706,
+        0.0055179400,
+        0.0221228836,
+        0.0564422658,
+    ],
+    [
+        0.0802600904,
+        0.1551614284,
+        0.0437069808,
+        0.0455750297,
+        0.0090845344,
+        0.0670680421,
+        0.0635415202,
+        0.0496003969,
+        0.0398983751,
+        0.0377116648,
+        0.0711609122,
+        0.0789071567,
+        0.0160131376,
+        0.0189416393,
+        0.0190198164,
+        0.0624606638,
+        0.0598552722,
+        0.0072250517,
+        0.0193671790,
+        0.0554411082,
+    ],
+    [
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+        0.0360659724,
+        0.0186143820,
+        0.0186042975,
+        0.0101037228,
+        0.0231954844,
+        0.0277784176,
+        0.0279494467,
+        0.0150825562,
+        0.1404190636,
+        0.1852042048,
+        0.0266742762,
+        0.0491661528,
+        0.0546650191,
+        0.0160861006,
+        0.0446907069,
+        0.0549665236,
+        0.0071085651,
+        0.0256461017,
+        0.1503812624,
+    ],
+    [
+        0.0628794938,
+        0.0486145538,
+        0.0232133958,
+        0.0254697443,
+        0.0085820307,
+        0.0423824997,
+        0.0441765969,
+        0.0428880528,
+        0.0174220067,
+        0.0728234511,
+        0.2559336703,
+        0.0405507455,
+        0.0499531233,
+        0.0495419184,
+        0.0166893140,
+        0.0471810582,
+        0.0479827057,
+        0.0074597416,
+        0.0253289752,
+        0.0709269222,
+    ],
+    [
+        0.2308791155,
+        0.0523222188,
+        0.0290220311,
+        0.0457437624,
+        0.0098150511,
+        0.0427394316,
+        0.0508581488,
+        0.0651797747,
+        0.0181948157,
+        0.0475386837,
+        0.0681444051,
+        0.0487005728,
+        0.0166663599,
+        0.0234542292,
+        0.0231113417,
+        0.0723034371,
+        0.0610007086,
+        0.0073221231,
+        0.0202485425,
+        0.0667552468,
+    ],
+    [
+        0.0829939350,
+        0.0527752660,
+        0.0382497354,
+        0.0530745719,
+        0.0079155737,
+        0.0449048440,
+        0.0611312249,
+        0.0557605998,
+        0.0198851844,
+        0.0486477692,
+        0.0726094546,
+        0.0540290548,
+        0.0159502616,
+        0.0247673211,
+        0.1534801239,
+        0.0660682329,
+        0.0565784048,
+        0.0079017295,
+        0.0215220067,
+        0.0617547060,
+    ],
+    [
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+        0.0503375261,
+        0.0642835982,
+        0.1542924263,
+        0.0073999165,
+        0.0461513491,
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+        0.0623312653,
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+        0.0577022604,
+        0.0156861168,
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+        0.0642877417,
+        0.0562904430,
+        0.0083112947,
+        0.0235940746,
+        0.0558288068,
+    ],
+    [
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+        0.0500243695,
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+        0.0804366625,
+        0.1697086517,
+        0.0071239696,
+        0.0205775867,
+        0.0681380375,
+    ],
+    [
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+        0.0436294286,
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+        0.0550426265,
+        0.0077528541,
+        0.0292674575,
+        0.0961956262,
+    ],
+    [
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+        0.0094543772,
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+        0.0288673755,
+        0.0997070517,
+        0.0691914775,
+        0.0026862674,
+        0.0116684629,
+        0.0241930949,
+    ],
+    [
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+        0.0109845999,
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+        0.0155657342,
+        0.0802193267,
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+    ],
+    [
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+    ],
+    [
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+    [
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+    ],
+    [
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+        0.0016269670,
+        0.0014528256,
+        0.0010446558,
+        0.9594298690,
+        0.0011497890,
+        0.0012814363,
+        0.0024187614,
+        0.0011095944,
+        0.0021494695,
+        0.0035929840,
+        0.0014281970,
+        0.0009839080,
+        0.0014107050,
+        0.0008977366,
+        0.0067809464,
+        0.0035670450,
+        0.0004489576,
+        0.0017018361,
+        0.0033878865,
+    ],
+    [
+        0.0113674874,
+        0.0005811409,
+        0.0015300667,
+        0.0016392583,
+        0.0003004493,
+        0.0004056006,
+        0.0011648055,
+        0.9740978959,
+        0.0003272178,
+        0.0003373238,
+        0.0005062548,
+        0.0004139458,
+        0.0002847896,
+        0.0002311786,
+        0.0002465138,
+        0.0048714108,
+        0.0010201338,
+        0.0000646212,
+        0.0001868573,
+        0.0004230482,
+    ],
+    [
+        0.0105115962,
+        0.0039179025,
+        0.8481729277,
+        0.0219909682,
+        0.0023250409,
+        0.0078855196,
+        0.0032942022,
+        0.0096057230,
+        0.0179422022,
+        0.0027572428,
+        0.0034394540,
+        0.0105505296,
+        0.0021348281,
+        0.0017144742,
+        0.0012277814,
+        0.0300811551,
+        0.0153898155,
+        0.0005389121,
+        0.0027886278,
+        0.0037310968,
+    ],
+    [
+        0.0025467281,
+        0.0011093608,
+        0.0020292716,
+        0.0008704391,
+        0.0014814879,
+        0.0012697132,
+        0.0010799089,
+        0.0010171417,
+        0.0185818664,
+        0.0023336860,
+        0.0065445550,
+        0.0009625246,
+        0.0015133713,
+        0.1219302869,
+        0.0005246140,
+        0.0023750971,
+        0.0021929386,
+        0.0109595547,
+        0.8176793358,
+        0.0029981182,
+    ],
+    [
+        0.0053463120,
+        0.0009509803,
+        0.0013962723,
+        0.0006563455,
+        0.0011000771,
+        0.0010846615,
+        0.0009204072,
+        0.0009580447,
+        0.0058156117,
+        0.0049568468,
+        0.0181859952,
+        0.0010380012,
+        0.0047316621,
+        0.6669446035,
+        0.0005373062,
+        0.0041734593,
+        0.0020339017,
+        0.0068238890,
+        0.2672901433,
+        0.0050554795,
+    ],
+    [
+        0.0090906821,
+        0.0083891088,
+        0.0268772067,
+        0.0028942681,
+        0.0018495551,
+        0.0276441596,
+        0.0033195709,
+        0.0027637786,
+        0.8477445332,
+        0.0035946234,
+        0.0098165405,
+        0.0031403564,
+        0.0029324886,
+        0.0084603197,
+        0.0016721287,
+        0.0106976471,
+        0.0090486674,
+        0.0009511879,
+        0.0143804222,
+        0.0047327550,
+    ],
+    [
+        0.0149451132,
+        0.0018735398,
+        0.0088071718,
+        0.0019735801,
+        0.0057629865,
+        0.0017260572,
+        0.0013698343,
+        0.0037408219,
+        0.0012288701,
+        0.0046842343,
+        0.0049796913,
+        0.0076200061,
+        0.0051778323,
+        0.0011713586,
+        0.0018949880,
+        0.0808031232,
+        0.8424393924,
+        0.0003502773,
+        0.0011664607,
+        0.0082846609,
+    ],
+    [
+        0.0040518988,
+        0.9362062008,
+        0.0035497378,
+        0.0009039109,
+        0.0011937131,
+        0.0053010850,
+        0.0012781108,
+        0.0019757996,
+        0.0049499985,
+        0.0012879297,
+        0.0037915593,
+        0.0193284213,
+        0.0012819075,
+        0.0008969649,
+        0.0006577212,
+        0.0053342455,
+        0.0049861730,
+        0.0003837759,
+        0.0008622330,
+        0.0017786134,
+    ],
+    [
+        0.0032144162,
+        0.0006886313,
+        0.0132532373,
+        0.9452545555,
+        0.0003822369,
+        0.0025362867,
+        0.0165697248,
+        0.0022918808,
+        0.0022640542,
+        0.0005651621,
+        0.0009349163,
+        0.0008945372,
+        0.0005155701,
+        0.0003969504,
+        0.0004426615,
+        0.0053234500,
+        0.0030288409,
+        0.0001360466,
+        0.0004642849,
+        0.0008425563,
+    ],
+    [
+        0.0040153469,
+        0.0014812403,
+        0.0012978828,
+        0.0009085945,
+        0.0015236063,
+        0.0015518352,
+        0.0012113905,
+        0.0018771734,
+        0.0011386515,
+        0.0014521824,
+        0.0063163517,
+        0.0010967489,
+        0.0015912681,
+        0.0146119399,
+        0.0007342342,
+        0.0044180974,
+        0.0025329750,
+        0.9362725549,
+        0.0141257395,
+        0.0018421867,
+    ],
+    [
+        0.0106642685,
+        0.0093245549,
+        0.0079063737,
+        0.0034749195,
+        0.0015221501,
+        0.8257471230,
+        0.0279456584,
+        0.0061751225,
+        0.0230313789,
+        0.0031976776,
+        0.0153997545,
+        0.0186618224,
+        0.0128243564,
+        0.0017570364,
+        0.0023360342,
+        0.0124292387,
+        0.0102632162,
+        0.0007356825,
+        0.0018198961,
+        0.0047837355,
+    ],
+    [
+        0.0047970679,
+        0.0032841520,
+        0.0015733529,
+        0.0105186354,
+        0.0003555544,
+        0.0148087895,
+        0.9438427420,
+        0.0009855191,
+        0.0008123537,
+        0.0007379429,
+        0.0012059557,
+        0.0074570243,
+        0.0008019033,
+        0.0004051340,
+        0.0004904064,
+        0.0037152586,
+        0.0013594786,
+        0.0001602349,
+        0.0006169570,
+        0.0020715372,
+    ],
+];
+
+pub const UDM256_WEIGHTS: &'static [f64] = &[
+    0.0762326617,
+    0.0331562190,
+    0.0324804617,
+    0.0257352390,
+    0.0185489214,
+    0.0179772624,
+    0.0175405785,
+    0.0175052909,
+    0.0167889529,
+    0.0140859235,
+    0.0131534490,
+    0.0131269833,
+    0.0131261011,
+    0.0129390769,
+    0.0129293728,
+    0.0127988087,
+    0.0126479542,
+    0.0126241351,
+    0.0095664655,
+    0.0094967725,
+    0.0094411946,
+    0.0092753429,
+    0.0092479950,
+    0.0091438966,
+    0.0090609708,
+    0.0089974531,
+    0.0085942924,
+    0.0084390270,
+    0.0080349841,
+    0.0071713204,
+    0.0069631236,
+    0.0069128388,
+    0.0066552394,
+    0.0065132068,
+    0.0061268077,
+    0.0060474106,
+    0.0058586220,
+    0.0058462714,
+    0.0058392139,
+    0.0057448196,
+    0.0056751266,
+    0.0056283705,
+    0.0056054336,
+    0.0055666172,
+    0.0055286831,
+    0.0053213685,
+    0.0052163879,
+    0.0052040373,
+    0.0051793359,
+    0.0051696319,
+    0.0051211114,
+    0.0050161308,
+    0.0050073089,
+    0.0049437913,
+    0.0046720768,
+    0.0046226742,
+    0.0044232993,
+    0.0043721323,
+    0.0043650748,
+    0.0043244941,
+    0.0042892065,
+    0.0042706805,
+    0.0042195135,
+    0.0042186313,
+    0.0041965766,
+    0.0041745218,
+    0.0041595246,
+    0.0040951248,
+    0.0039725004,
+    0.0039380950,
+    0.0038922211,
+    0.0038833992,
+    0.0037987090,
+    0.0037863583,
+    0.0037290160,
+    0.0036999038,
+    0.0036954928,
+    0.0036919640,
+    0.0036646162,
+    0.0035561068,
+    0.0035349343,
+    0.0035049398,
+    0.0033443813,
+    0.0033346772,
+    0.0031291270,
+    0.0030973682,
+    0.0030841353,
+    0.0030744312,
+    0.0030576696,
+    0.0030303217,
+    0.0029544534,
+    0.0029421028,
+    0.0029412206,
+    0.0029182836,
+    0.0028671166,
+    0.0027771333,
+    0.0027427279,
+    0.0027400813,
+    0.0027136156,
+    0.0027021472,
+    0.0027021472,
+    0.0026571555,
+    0.0026492158,
+    0.0026456870,
+    0.0026086350,
+    0.0025945200,
+    0.0025786406,
+    0.0025724653,
+    0.0025583502,
+    0.0025477640,
+    0.0025327667,
+    0.0025265914,
+    0.0025239448,
+    0.0025160051,
+    0.0025089476,
+    0.0025010079,
+    0.0024948326,
+    0.0024648381,
+    0.0024586628,
+    0.0024577806,
+    0.0024348437,
+    0.0024074958,
+    0.0023836767,
+    0.0023219234,
+    0.0023192768,
+    0.0022381154,
+    0.0021816552,
+    0.0021446032,
+    0.0021234307,
+    0.0021234307,
+    0.0021181376,
+    0.0021128444,
+    0.0020934362,
+    0.0020828500,
+    0.0020343295,
+    0.0020290364,
+    0.0019743406,
+    0.0019602256,
+    0.0019125873,
+    0.0019002367,
+    0.0018764176,
+    0.0018305437,
+    0.0018146643,
+    0.0018102533,
+    0.0018067246,
+    0.0018058424,
+    0.0017952561,
+    0.0017661439,
+    0.0017582041,
+    0.0017529110,
+    0.0017220344,
+    0.0017211522,
+    0.0017061549,
+    0.0017017440,
+    0.0016858646,
+    0.0016426373,
+    0.0016382263,
+    0.0016338154,
+    0.0016188182,
+    0.0015923525,
+    0.0015702977,
+    0.0015667690,
+    0.0015632402,
+    0.0015579471,
+    0.0015500074,
+    0.0015447142,
+    0.0015244239,
+    0.0014953116,
+    0.0014944294,
+    0.0014909007,
+    0.0014794322,
+    0.0014741390,
+    0.0014723747,
+    0.0014706103,
+    0.0014635528,
+    0.0014538487,
+    0.0014062104,
+    0.0013770982,
+    0.0013391640,
+    0.0013382818,
+    0.0013162271,
+    0.0013003477,
+    0.0012968189,
+    0.0012941723,
+    0.0012721176,
+    0.0012527094,
+    0.0012315369,
+    0.0012315369,
+    0.0012059534,
+    0.0012015424,
+    0.0012006602,
+    0.0011988959,
+    0.0011803699,
+    0.0011627261,
+    0.0011106769,
+    0.0011106769,
+    0.0010798002,
+    0.0010736249,
+    0.0010736249,
+    0.0010498058,
+    0.0010462770,
+    0.0010233401,
+    0.0009942278,
+    0.0009854059,
+    0.0009845237,
+    0.0009836416,
+    0.0009783484,
+    0.0009642334,
+    0.0009404143,
+    0.0009386499,
+    0.0008601350,
+    0.0008451378,
+    0.0008380802,
+    0.0008151433,
+    0.0008001461,
+    0.0007930886,
+    0.0007763270,
+    0.0007675051,
+    0.0007586832,
+    0.0007454503,
+    0.0007286887,
+    0.0007269243,
+    0.0007260422,
+    0.0007066340,
+    0.0007022230,
+    0.0006828149,
+    0.0006713464,
+    0.0006686998,
+    0.0006678176,
+    0.0006660533,
+    0.0006492916,
+    0.0006484095,
+    0.0006175328,
+    0.0006060643,
+    0.0005813630,
+    0.0005451933,
+    0.0005363714,
+    0.0005187276,
+    0.0005178454,
+    0.0005143166,
+    0.0005002016,
+    0.0004975550,
+    0.0004243333,
+    0.0003758128,
+    0.0003458184,
+    0.0003369965,
+    0.0003070020,
+    0.0002778898,
+    0.0002637747,
+    0.0002514241,
+    0.0002408378,
+    0.0002099612,
+    0.0001517366,
+    0.0001455613,
+    0.0001402682,
+    0.0000961587,
+];
diff --git a/mutsel_rust/src/felsenstein.rs b/mutsel_rust/src/felsenstein.rs
new file mode 100644
index 000000000..261321bb2
--- /dev/null
+++ b/mutsel_rust/src/felsenstein.rs
@@ -0,0 +1,377 @@
+use std::sync::{Arc, Mutex};
+
+use candle_core::CpuStorage;
+
+pub struct FelsensteinOp {
+    felsenstein : Arc<Mutex<phylo_grad::FelsensteinTree<20>>>,
+    result_storage: Mutex<Option<phylo_grad::FelsensteinResult<20>>>,
+}
+pub struct FelsensteinWithEdgeOp {
+    felsenstein : Arc<Mutex<phylo_grad::FelsensteinTree<20>>>,
+    result_storage: Mutex<Option<phylo_grad::FelsensteinResultWithTree<20>>>,
+}
+
+#[derive(Clone, Debug)]
+pub struct FelsensteinWithEdgeFwdOp {
+    felsenstein : Arc<Mutex<phylo_grad::FelsensteinTree<20>>>,
+}
+
+#[derive(Clone, Debug)]
+pub struct FelsensteinFwdOp {
+    felsenstein: Arc<Mutex<phylo_grad::FelsensteinTree<20>>>,
+}
+
+impl Clone for FelsensteinOp {
+    fn clone(&self) -> Self {
+        Self {
+            felsenstein: Arc::clone(&self.felsenstein),
+            result_storage: Mutex::new(None),
+        }
+    }
+}
+
+impl Clone for FelsensteinWithEdgeOp {
+    fn clone(&self) -> Self {
+        Self {
+            felsenstein: Arc::clone(&self.felsenstein),
+            result_storage: Mutex::new(None),
+        }
+    }
+}
+
+fn tensor2nalgebra2d(s: &candle_core::CpuStorage, l: &candle_core::Layout) -> Vec<phylo_grad::nalgebra::SMatrix<f64, 20, 20>> {
+    let dims = l.shape().dims();
+    let stride = l.stride();
+    assert!(dims.len() == 3);
+    let batch_size = dims[0];
+    let mut result = Vec::with_capacity(batch_size);
+    match s {
+        CpuStorage::F64(data) => {
+            let mut offset = l.start_offset();
+            for _ in 0..batch_size {
+                let mut mat = phylo_grad::nalgebra::SMatrix::<f64, 20, 20>::zeros();
+                for i in 0..20 {
+                    for j in 0..20 {
+                        mat[(i, j)] = data[offset + i * stride[1] + j * stride[2]];
+                    }
+                }
+                result.push(mat);
+                offset += stride[0];
+            }
+        }
+        _ => panic!("Expected f64 storage."),
+    }
+    result
+}
+
+fn tensor2nalgebra1d(s: &candle_core::CpuStorage, l: &candle_core::Layout) -> Vec<phylo_grad::nalgebra::SVector<f64, 20>> {
+    let dims = l.shape().dims();
+    let stride = l.stride();
+    assert!(dims.len() == 2);
+    let batch_size = dims[0];
+    let mut result = Vec::with_capacity(batch_size);
+    match s {
+        CpuStorage::F64(data) => {
+            let mut offset = l.start_offset();
+            for _ in 0..batch_size {
+                let mut vec = phylo_grad::nalgebra::SVector::<f64, 20>::zeros();
+                for i in 0..20 {
+                    vec[i] = data[offset + i * stride[1]];
+                }
+                result.push(vec);
+                offset += stride[0];
+            }
+        }
+        _ => panic!("Expected f64 storage."),
+    }
+    result
+}
+
+fn tensor2vec(s: &candle_core::CpuStorage, l: &candle_core::Layout) -> Vec<f64> {
+    let dims = l.shape().dims();
+    let stride = l.stride();
+    assert!(dims.len() == 1);
+    let batch_size = dims[0];
+    let mut result = Vec::with_capacity(batch_size);
+    match s {
+        CpuStorage::F64(data) => {
+            let mut offset = l.start_offset();
+            for _ in 0..batch_size {
+                result.push(data[offset]);
+                offset += stride[0];
+            }
+        }
+        _ => panic!("Expected f64 storage."),
+    }
+    result
+}
+
+fn nalgebra2tensor1d(vec: &Vec<phylo_grad::nalgebra::SVector<f64, 20>>) -> candle_core::Tensor {
+    let batch_size = vec.len();
+    let mut data = vec![0f64; batch_size * 20];
+    for (b, v) in vec.iter().enumerate() {
+        for i in 0..20 {
+            data[b * 20 + i] = v[i];
+        }
+    }
+    candle_core::Tensor::from_vec(data, &candle_core::Shape::from(&[batch_size, 20]), &candle_core::Device::Cpu).unwrap()
+}
+
+fn nalgebra2tensor2d(mats: &Vec<phylo_grad::nalgebra::SMatrix<f64, 20, 20>>) -> candle_core::Tensor {
+    let batch_size = mats.len();
+    let mut data = vec![0f64; batch_size * 20 * 20];
+    for (b, m) in mats.iter().enumerate() {
+        for i in 0..20 {
+            for j in 0..20 {
+                data[b * 20 * 20 + i * 20 + j] = m[(i, j)];
+            }
+        }
+    }
+    candle_core::Tensor::from_vec(data, &candle_core::Shape::from(&[batch_size, 20, 20]), &candle_core::Device::Cpu).unwrap()
+}
+
+impl FelsensteinFwdOp {
+    pub fn new(felsenstein: Arc<Mutex<phylo_grad::FelsensteinTree<20>>>) -> Self {
+        Self {
+            felsenstein,
+        }
+    }
+}
+
+impl FelsensteinWithEdgeOp {
+    pub fn new(felsenstein: Arc<Mutex<phylo_grad::FelsensteinTree<20>>>) -> Self {
+        Self {
+            felsenstein,
+            result_storage: Mutex::new(None),
+        }
+    }
+    pub fn into_fwd_op(&self) -> FelsensteinWithEdgeFwdOp {
+        FelsensteinWithEdgeFwdOp {
+            felsenstein: Arc::clone(&self.felsenstein),
+        }
+    }
+}
+
+impl candle_core::CustomOp2 for FelsensteinFwdOp {
+
+    fn name(&self) -> &'static str {
+        "FelsensteinFwdOp"
+    }
+
+    /// S, sqrt
+    fn cpu_fwd(
+            &self,
+            s1: &candle_core::CpuStorage,
+            l1: &candle_core::Layout,
+            s2: &candle_core::CpuStorage,
+            l2: &candle_core::Layout,
+        ) -> candle_core::Result<(candle_core::CpuStorage, candle_core::Shape)> {
+        
+        let s = tensor2nalgebra2d(s1, l1);
+        let sqrt_pi = tensor2nalgebra1d(s2, l2);
+
+        let mut felsenstein = self.felsenstein.lock().unwrap();
+        let result = felsenstein.calculate_likelihoods(&s, &sqrt_pi);
+
+        let shape = candle_core::Shape::from(&[result.len()]);
+        let cpu_storage = candle_core::CpuStorage::F64(result);
+        return Ok((cpu_storage, shape))
+    }
+}
+
+impl FelsensteinOp {
+    pub fn new(felsenstein: Arc<Mutex<phylo_grad::FelsensteinTree<20>>>) -> Self {
+        Self {
+            felsenstein,
+            result_storage: Mutex::new(None),
+        }
+    }
+
+    pub fn into_fwd_op(&self) -> FelsensteinFwdOp {
+        FelsensteinFwdOp {
+            felsenstein: Arc::clone(&self.felsenstein),
+        }
+    }
+
+    pub fn into_with_edge_op(&self) -> FelsensteinWithEdgeOp {
+        FelsensteinWithEdgeOp {
+            felsenstein: Arc::clone(&self.felsenstein),
+            result_storage: Mutex::new(None),
+        }
+    }
+
+    pub fn into_with_edge_fwd_op(&self) -> FelsensteinWithEdgeFwdOp {
+        FelsensteinWithEdgeFwdOp {
+            felsenstein: Arc::clone(&self.felsenstein),
+        }
+    }
+}
+
+impl candle_core::CustomOp2 for FelsensteinOp {
+
+    fn name(&self) -> &'static str {
+        "FelsensteinOp"
+    }
+
+    /// S, sqrt
+    fn cpu_fwd(
+            &self,
+            s1: &candle_core::CpuStorage,
+            l1: &candle_core::Layout,
+            s2: &candle_core::CpuStorage,
+            l2: &candle_core::Layout,
+        ) -> candle_core::Result<(candle_core::CpuStorage, candle_core::Shape)> {
+        
+        let s = tensor2nalgebra2d(s1, l1);
+        let sqrt_pi = tensor2nalgebra1d(s2, l2);
+
+        let mut felsenstein = self.felsenstein.lock().unwrap();
+        let mut result = felsenstein.calculate_gradients(&s, &sqrt_pi);
+
+        let likelihood = std::mem::take(&mut result.log_likelihood);
+
+        let mut storage = self.result_storage.lock().unwrap();
+        *storage = Some(result);
+
+        let shape = candle_core::Shape::from(&[likelihood.len()]);
+        let cpu_storage = candle_core::CpuStorage::F64(likelihood);
+        return Ok((cpu_storage, shape))
+    }
+
+    fn bwd(
+            &self,
+            _arg1: &candle_core::Tensor,
+            _arg2: &candle_core::Tensor,
+            _res: &candle_core::Tensor,
+            _grad_res: &candle_core::Tensor,
+        ) -> candle_core::Result<(Option<candle_core::Tensor>, Option<candle_core::Tensor>)> {
+        let mut result = self.result_storage.lock().unwrap();
+        
+
+        let grad_s = std::mem::take(&mut result.as_mut().unwrap().grad_s);
+        let grad_s_tensor = nalgebra2tensor2d(&grad_s);
+        let grad_sqrt_pi = std::mem::take(&mut result.as_mut().unwrap().grad_sqrt_pi);
+        let grad_sqrt_pi_tensor = nalgebra2tensor1d(&grad_sqrt_pi);
+
+        let grad_2 = _grad_res.unsqueeze(1).unwrap().unsqueeze(2).unwrap();
+        let grad_1 = _grad_res.unsqueeze(1).unwrap();
+
+        Ok((
+            Some(grad_2.broadcast_mul(&grad_s_tensor).unwrap()),
+            Some(grad_1.broadcast_mul(&grad_sqrt_pi_tensor).unwrap()),
+        ))
+
+    }
+}
+
+
+impl candle_core::CustomOp3 for FelsensteinWithEdgeOp {
+
+    fn name(&self) -> &'static str {
+        "FelsensteinWithEdgeOp"
+    }
+
+    /// S, sqrt
+    fn cpu_fwd(
+            &self,
+            s1: &candle_core::CpuStorage,
+            l1: &candle_core::Layout,
+            s2: &candle_core::CpuStorage,
+            l2: &candle_core::Layout,
+            s3: &candle_core::CpuStorage,
+            l3: &candle_core::Layout,
+        ) -> candle_core::Result<(candle_core::CpuStorage, candle_core::Shape)> {
+        
+        let s = tensor2nalgebra2d(s1, l1);
+        let sqrt_pi = tensor2nalgebra1d(s2, l2);
+        let branch_lengths = tensor2vec(s3, l3);
+
+        let mut felsenstein = self.felsenstein.lock().unwrap();
+        let mut result = felsenstein.calculate_gradients_with_branch_lengths(&s, &sqrt_pi, &branch_lengths);
+
+        let likelihood = std::mem::take(&mut result.log_likelihood);
+
+        let mut storage = self.result_storage.lock().unwrap();
+        *storage = Some(result);
+
+        let shape = candle_core::Shape::from(&[likelihood.len()]);
+        let cpu_storage = candle_core::CpuStorage::F64(likelihood);
+        return Ok((cpu_storage, shape))
+    }
+
+    fn bwd(
+            &self,
+            _arg1: &candle_core::Tensor,
+            _arg2: &candle_core::Tensor,
+            _arg3: &candle_core::Tensor,
+            _res: &candle_core::Tensor,
+            grad_res: &candle_core::Tensor,
+        ) -> candle_core::Result<(Option<candle_core::Tensor>, Option<candle_core::Tensor>, Option<candle_core::Tensor>)> {
+        let mut result = self.result_storage.lock().unwrap();
+        
+
+        let grad_s = std::mem::take(&mut result.as_mut().unwrap().grad_s);
+        let grad_s_tensor = nalgebra2tensor2d(&grad_s);
+        let grad_sqrt_pi = std::mem::take(&mut result.as_mut().unwrap().grad_sqrt_pi);
+        let grad_sqrt_pi_tensor = nalgebra2tensor1d(&grad_sqrt_pi);
+        let grad_branch_lengths = std::mem::take(&mut result.as_mut().unwrap().grad_tree);
+        let L = grad_branch_lengths.len();
+        let num_branch = grad_branch_lengths[0].len();
+        let grad_branch_lengths_flat: Vec<f64> = grad_branch_lengths.into_iter().flatten().collect();
+
+        let grad_branch_lengths_tensor = candle_core::Tensor::from_vec(grad_branch_lengths_flat, &candle_core::Shape::from(&[L, num_branch]), &candle_core::Device::Cpu).unwrap();
+
+
+        let grad_2 = grad_res.unsqueeze(1).unwrap().unsqueeze(2).unwrap();
+        let grad_1 = grad_res.unsqueeze(1).unwrap();
+
+
+        Ok((
+            Some(grad_2.broadcast_mul(&grad_s_tensor).unwrap()),
+            Some(grad_1.broadcast_mul(&grad_sqrt_pi_tensor).unwrap()),
+            Some(grad_1.broadcast_mul(&grad_branch_lengths_tensor).unwrap().sum(0).unwrap()),
+        ))
+
+    }
+}
+
+impl candle_core::CustomOp3 for FelsensteinWithEdgeFwdOp {
+
+    fn name(&self) -> &'static str {
+        "FelsensteinWithEdgeFwdOp"
+    }
+
+    /// S, sqrt
+    fn cpu_fwd(
+            &self,
+            s1: &candle_core::CpuStorage,
+            l1: &candle_core::Layout,
+            s2: &candle_core::CpuStorage,
+            l2: &candle_core::Layout,
+            s3: &candle_core::CpuStorage,
+            l3: &candle_core::Layout,
+        ) -> candle_core::Result<(candle_core::CpuStorage, candle_core::Shape)> {
+        
+        let s = tensor2nalgebra2d(s1, l1);
+        let sqrt_pi = tensor2nalgebra1d(s2, l2);
+        let branch_lengths = tensor2vec(s3, l3);
+
+        let mut felsenstein = self.felsenstein.lock().unwrap();
+        let likelihood = felsenstein.calculate_likelihoods_with_branch_lengths(&s, &sqrt_pi, &branch_lengths);
+
+        let shape = candle_core::Shape::from(&[likelihood.len()]);
+        let cpu_storage = candle_core::CpuStorage::F64(likelihood);
+        return Ok((cpu_storage, shape))
+    }
+
+    fn bwd(
+            &self,
+            _arg1: &candle_core::Tensor,
+            _arg2: &candle_core::Tensor,
+            _arg3: &candle_core::Tensor,
+            _res: &candle_core::Tensor,
+            _grad_res: &candle_core::Tensor,
+        ) -> candle_core::Result<(Option<candle_core::Tensor>, Option<candle_core::Tensor>, Option<candle_core::Tensor>)> {
+        panic!("FelsensteinWithEdgeFwdOp does not support backward pass");
+    }
+}
\ No newline at end of file
diff --git a/mutsel_rust/src/gamma.rs b/mutsel_rust/src/gamma.rs
new file mode 100644
index 000000000..ea97bd9d5
--- /dev/null
+++ b/mutsel_rust/src/gamma.rs
@@ -0,0 +1,136 @@
+use std::ops::Deref;
+
+use candle_core::{CpuStorage, CustomOp1, Storage, Tensor};
+
+
+pub fn log_gamma_pdf(x: &Tensor, alpha: &Tensor) -> Tensor {
+    let lgamma_alpha = alpha.apply_op1(LgammaOp).unwrap();
+
+    let lgamma_alpha_b = lgamma_alpha.broadcast_as(x.shape()).unwrap();
+    let alpha_b = alpha.broadcast_as(x.shape()).unwrap();
+
+    let log_pdf = ((&alpha_b * &alpha_b.log().unwrap() - lgamma_alpha_b).unwrap() + (&alpha_b - 1.0) * x.log().unwrap()).unwrap() - &alpha_b * x;
+    log_pdf.unwrap()
+}
+
+/// Custom op that computes lgamma(x) elementwise.
+/// Backward uses the digamma function (derivative of lgamma).
+#[derive(Debug, Clone)]
+pub struct LgammaOp;
+
+impl CustomOp1 for LgammaOp {
+    fn name(&self) -> &'static str {
+        "LgammaOp"
+    }
+
+    fn cpu_fwd(
+        &self,
+        storage: &CpuStorage,
+        layout: &candle_core::Layout,
+    ) -> candle_core::Result<(CpuStorage, candle_core::Shape)> {
+        let data = match storage {
+            CpuStorage::F64(data) => data,
+            _ => panic!("LgammaOp: expected f64 storage"),
+        };
+
+        let output = candle_core::cpu_backend::unary_map(data, layout, spec_math::cephes64::lgam);
+        Ok((CpuStorage::F64(output), layout.shape().clone()))
+    }
+
+    fn bwd(
+        &self,
+        arg: &Tensor,
+        _res: &candle_core::Tensor,
+        grad_res: &Tensor,
+    ) -> candle_core::Result<Option<Tensor>> {
+        let (storage, layout) = arg.storage_and_layout();
+
+        let data = match storage.deref() {
+            Storage::Cpu(CpuStorage::F64(data)) => data,
+            _ => panic!("LgammaOp: expected cpu f64 storage in bwd"),
+        };
+
+        let grads = candle_core::cpu_backend::unary_map(data, &layout, spec_math::cephes64::psi);
+        let grad_tensor = Tensor::from_vec(grads, arg.shape(), &candle_core::Device::Cpu)?;
+
+        Ok(Some(grad_tensor.mul(grad_res)?))
+    }
+}
+
+#[derive(Debug, Clone)]
+pub struct GammaOp {
+    categories: usize,
+}
+
+impl GammaOp {
+    pub fn new(categories: usize) -> Self {
+        Self { categories }
+    }
+}
+
+impl candle_core::CustomOp1 for GammaOp {
+    fn name(&self) -> &'static str {
+        "GammaOp"
+    }
+    
+    fn cpu_fwd(&self, storage: &candle_core::CpuStorage, layout: &candle_core::Layout) -> candle_core::Result<(candle_core::CpuStorage, candle_core::Shape)> {
+        let alpha = match storage {
+            candle_core::CpuStorage::F64(v) => v[layout.start_offset()],
+            _ => panic!("Expected f64 storage for GammaOp"),
+        };
+
+        let bounds = (0..=self.categories).map(|k| {
+            //gamma.inverse_cdf(k as f64 / self.categories as f64)
+            spec_math::cephes64::gdtri(alpha, alpha, k as f64 / self.categories as f64)
+        }).collect::<Vec<f64>>();
+
+        let categories = bounds.iter().zip(bounds.iter().skip(1)).map(|(a, b)| {
+            //let mean = gamma_alpha1.cdf(*b) - gamma_alpha1.cdf(*a);
+            // a and b seems to be swapped here.
+            let mean = spec_math::cephes64::gdtr(alpha, alpha + 1.0, *b) - spec_math::cephes64::gdtr(alpha, alpha + 1.0, *a);
+            mean * self.categories as f64
+        }).collect::<Vec<f64>>();
+
+        let output = CpuStorage::F64(categories);
+        let shape = candle_core::Shape::from(&[self.categories]);
+
+        Ok((output, shape))
+    }
+
+    fn bwd(&self, _arg: &candle_core::Tensor, _res: &candle_core::Tensor, _grad_res: &candle_core::Tensor) -> candle_core::Result<Option<candle_core::Tensor>> {
+        
+        let h = 1e-5;
+
+        let h_plus = _arg + candle_core::Tensor::full(h, &[], _arg.device())?;
+        let h_minus = _arg - candle_core::Tensor::full(h, &[], _arg.device())?;
+
+        let derivative = (h_plus?.apply_op1(self.clone())? - h_minus?.apply_op1(self.clone())?)? / (2.0 * h);
+
+        let grad = (_grad_res * derivative?)?.sum_all()?;
+        Ok(Some(grad))
+    }
+}
+
+
+#[cfg(test)]
+mod test {
+    use candle_core::{Tensor, Var};
+
+    use super::*;
+    #[test]
+    fn test_gamma_op() {
+        let op = GammaOp::new(4);
+        let alpha = 0.08;
+        
+        let alpha = Tensor::from_vec(vec![alpha], &[], &candle_core::Device::Cpu).unwrap();
+        let alpha = Var::from_tensor(&alpha).unwrap();
+
+        let categories = alpha.apply_op1(op).unwrap();
+
+        println!("{:?}", categories);
+
+        
+
+        println!("{:?}", categories.get(0).unwrap().backward().unwrap());
+    }
+}
\ No newline at end of file
diff --git a/mutsel_rust/src/io.rs b/mutsel_rust/src/io.rs
new file mode 100644
index 000000000..5daa94582
--- /dev/null
+++ b/mutsel_rust/src/io.rs
@@ -0,0 +1,411 @@
+use candle_core::Tensor;
+use lazy_static::lazy_static;
+use seq_io::fasta::Record;
+use std::{collections::HashMap, io::Read, path::Path, vec};
+
+use anyhow::{Context, Result};
+
+lazy_static! {
+    static ref AMINO_MAPPING: HashMap<u8, u8> = {
+        let mut m = HashMap::new();
+        m.insert(b'A', 0);
+        m.insert(b'R', 1);
+        m.insert(b'N', 2);
+        m.insert(b'D', 3);
+        m.insert(b'C', 4);
+        m.insert(b'Q', 5);
+        m.insert(b'E', 6);
+        m.insert(b'G', 7);
+        m.insert(b'H', 8);
+        m.insert(b'I', 9);
+        m.insert(b'L', 10);
+        m.insert(b'K', 11);
+        m.insert(b'M', 12);
+        m.insert(b'F', 13);
+        m.insert(b'P', 14);
+        m.insert(b'S', 15);
+        m.insert(b'T', 16);
+        m.insert(b'W', 17);
+        m.insert(b'Y', 18);
+        m.insert(b'V', 19);
+        m.insert(b'-', 20);
+        m.insert(b'X', 20);
+        m.insert(b'?', 20);
+        m.insert(b'.', 20);
+        m
+    };
+}
+
+fn normalize_residue(residue: u8) -> u8 {
+    residue.to_ascii_uppercase()
+}
+
+fn seq2pll(
+    seq: impl Iterator<Item = u8>,
+) -> Vec<phylo_grad::nalgebra::SVector<f64, 20>> {
+    seq.map(|c| *AMINO_MAPPING.get(&normalize_residue(c)).unwrap_or(&20))
+        .map(|idx| {
+            let mut v = phylo_grad::nalgebra::SVector::<f64, 20>::zeros();
+                
+            if idx < 20 {
+                v[idx as usize] = 1.0;
+            } else {
+                for i in 0..20 {
+                    v[i] = 1.0;
+                }
+            }
+            v
+        })
+        .collect()
+}
+
+pub fn read_alignment(fasta_file: &Path) -> HashMap<String, Vec<u8>> {
+    let mut alignment = seq_io::fasta::Reader::new(
+        std::fs::File::open(fasta_file).expect("Could not open fasta file"),
+    );
+    let mut sequences = HashMap::new();
+    while let Some(result) = alignment.next() {
+        let record = result.expect("Error reading fasta record");
+        let seq: Vec<u8> = record.seq().iter().copied().collect();
+        sequences.insert(record.id().unwrap().to_string(), seq);
+    }
+    sequences
+}
+
+pub fn get_site_specific_aa_distribution(sequences: &HashMap<String, Vec<u8>>) -> Tensor {
+    let num_sites = sequences.values().next().unwrap().len();
+
+    let mut data = vec![0f64; num_sites * 20];
+
+    for seq in sequences.values() {
+        for (site_idx, &residue) in seq.iter().enumerate() {
+            let aa_idx = *AMINO_MAPPING.get(&normalize_residue(residue)).unwrap_or(&20);
+            if aa_idx == 20 {
+                continue;
+            }
+            data[site_idx * 20 + aa_idx as usize] += 1.0;
+        }
+    }
+
+    Tensor::from_vec(data, &[num_sites, 20], &candle_core::Device::Cpu).unwrap()
+}
+
+pub fn get_site_specific_aa_distribution_iqtree(alignment: &[u8], L: usize, N: usize) -> Tensor {
+    let mut data = vec![0f64; L * 20];
+
+    for site_idx in 0..L {
+        for seq_idx in 0..N {
+            let residue = alignment[site_idx * N + seq_idx];
+            if residue == 20 {
+                continue;
+            }
+            data[site_idx * 20 + residue as usize] += 1.0;
+        }
+    }
+
+    Tensor::from_vec(data, &[L, 20], &candle_core::Device::Cpu).unwrap()
+}
+
+pub fn create_felsenstein_tree(
+    parents: &[i32],
+    distances: &[f64],
+    alignment: &[u8],
+    L : usize,
+    N : usize,
+) -> phylo_grad::FelsensteinTree<20> {
+    let mut felsenstein = phylo_grad::FelsensteinTree::<20>::new(parents, distances);
+
+    let mut sites = vec![];
+    sites.resize(L, vec![]);
+    for site_idx in 0..L {
+        sites[site_idx].resize(N, phylo_grad::nalgebra::SVector::<f64, 20>::zeros());
+        for seq_idx in 0..N {
+            let residue = alignment[site_idx * N + seq_idx];
+            if residue < 20 {
+                sites[site_idx][seq_idx][residue as usize] = 1.0;
+            } else {
+                for i in 0..20 {
+                    sites[site_idx][seq_idx][i] = 1.0;
+                }
+            }
+        }
+    }
+    felsenstein.bind_leaf_pl(sites);
+    felsenstein
+}
+
+pub fn process_newick_alignment(
+    newick: &str,
+    sequences: &HashMap<String, Vec<u8>>,
+) -> (phylo_grad::FelsensteinTree<20>, Vec<f64>) {
+    let tree = phylotree::tree::Tree::from_newick(newick).unwrap();
+
+    let num_sides = sequences.values().next().unwrap().len();
+    let level_order = tree.levelorder(&tree.get_root().unwrap()).unwrap();
+
+    let mut parents = vec![i32::MAX; level_order.len()];
+    let mut distances = vec![f64::NAN; level_order.len()];
+
+    let num_leaves = tree.n_leaves();
+
+    // idx_mapping[tree_idx] = new_idx
+    let mut idx_mapping = vec![i32::MAX; level_order.len()];
+
+    let mut leaf_idx = 0usize;
+    let mut internal_idx = level_order.len() - 1;
+
+    for node_idx in &level_order {
+        let node = tree.get(node_idx).unwrap();
+        if node.is_tip() {
+            idx_mapping[*node_idx] = leaf_idx as i32;
+            parents[leaf_idx] = idx_mapping[node.parent.unwrap()];
+            distances[leaf_idx] = node.parent_edge.unwrap();
+            leaf_idx += 1;
+        } else {
+            idx_mapping[*node_idx] = internal_idx as i32;
+            if let Some(parent_idx) = node.parent {
+                parents[internal_idx] = idx_mapping[parent_idx];
+                distances[internal_idx] = node.parent_edge.unwrap();
+            } else {
+                parents[internal_idx] = -1;
+            }
+            internal_idx -= 1;
+        }
+    }
+
+    let mut leaf_pll = vec![];
+
+    for i in 0..num_sides {
+        let mut column_seq = vec![b'x'; num_leaves];
+
+        for node_idx in level_order.iter() {
+            let node = tree.get(&node_idx).unwrap();
+            if node.is_tip() {
+                let new_idx = idx_mapping[*node_idx];
+                assert!(new_idx < num_leaves as i32);
+                let seq = sequences.get(node.name.as_ref().unwrap()).unwrap();
+                column_seq[new_idx as usize] = seq[i];
+            }
+        }
+        leaf_pll.push(seq2pll(column_seq.into_iter()));
+    }
+
+    let mut felsenstein = phylo_grad::FelsensteinTree::<20>::new(&parents, &distances);
+    felsenstein.bind_leaf_pl(leaf_pll);
+    (felsenstein, distances)
+}
+
+pub fn write_sitefreq_file(pi: &Tensor, path: &Path) {
+    use std::io::Write;
+    let pi_data: Vec<Vec<f64>> = pi.to_vec2().unwrap();
+    let mut file = std::fs::File::create(path).expect("Could not create sitefreq file");
+    for (idx, chunk) in pi_data.iter().enumerate() {
+        let line = chunk
+            .iter()
+            .map(|v| v.to_string())
+            .collect::<Vec<String>>()
+            .join("\t");
+        writeln!(file, "{}\t{}", idx + 1, line).expect("Could not write to sitefreq file");
+    }
+}
+
+pub fn write_pam_file(R: &Tensor, path: &Path) {
+    use std::io::Write;
+    let R_data: Vec<Vec<f64>> = R.to_vec2().unwrap();
+    let mut file = std::fs::File::create(path).expect("Could not create pam file");
+    for i in 1..20 {
+        for j in 0..i {
+            write!(file, "{}\t", R_data[i][j]).expect("Could not write to pam file");
+        }
+        write!(file, "\n").expect("Could not write to pam file");
+    }
+    let equi: Vec<&str> = vec!["0.05"; 20];
+    writeln!(file, "{}", equi.join("\t")).expect("Could not write to pam file");
+}
+
+/// Ignores the first column (site index)
+pub fn read_sitefreq_file(path: &Path) -> Tensor {
+    use std::io::BufRead;
+    let file = std::fs::File::open(path).expect("Could not open sitefreq file");
+    let reader = std::io::BufReader::new(file);
+    let mut data = vec![];
+    for line in reader.lines() {
+        let line = line.expect("Could not read line from sitefreq file");
+        line.split_whitespace().skip(1).for_each(|v| {
+            data.push(
+                v.parse::<f64>()
+                    .expect("Could not parse float from sitefreq file"),
+            )
+        });
+    }
+    let L = data.len() / 20;
+    return Tensor::from_vec(data, &[L, 20], &candle_core::Device::Cpu).unwrap();
+}
+
+pub fn read_pam_file(path: &Path) -> Tensor {
+    let file_content = std::fs::read_to_string(path).expect("Could not read pam file");
+    return crate::data::load_lower_R(&file_content);
+}
+
+pub fn write_nexus_file(S: &Tensor, sqrt_pi: &Tensor, alpha : &Tensor, path: &Path) {
+    use std::io::Write;
+    let mut file = std::fs::File::create(path).expect("Could not create nexus file");
+
+    file.write(b"#nexus\n")
+        .expect("Could not write to nexus file");
+    file.write(b"begin sets;\n")
+        .expect("Could not write to nexus file");
+
+    let (R, pi) = crate::model::phylograd2iqtree_parametrization(S, sqrt_pi).unwrap();
+
+    let L = R.dims()[0];
+
+    for i in 0..L {
+        file.write(format!("    charset p{} = AA, {}-{};\n", i + 1, i + 1, i + 1).as_bytes())
+            .expect("Could not write to nexus file");
+    }
+
+    file.write(b"charpartition mine = ").expect("Could not write to nexus file");
+
+    let mut charpart_elems = vec![];
+
+    let alpha : f64 = alpha.to_scalar().unwrap();
+
+    for i in 0..L {
+        let freq_str = pi
+            .get(i)
+            .unwrap()
+            .to_vec1::<f64>()
+            .unwrap()
+            .iter()
+            .map(|v| format!("{:.6}", v))
+            .collect::<Vec<String>>()
+            .join("/");
+
+        let R_data: Vec<Vec<f64>> = R.get(i).unwrap().to_vec2().unwrap();
+
+        let mut rate_elems = vec![];
+        for a in 1..20 {
+            for b in 0..a {
+                rate_elems.push(format!("{:.6}", R_data[a][b]));
+            }
+        }
+
+        let rate_str = rate_elems.join("/");
+
+        charpart_elems.push(format!(
+            "GTR{{{}}}+F{{{}}}+G4{{{}}} : p{}",
+            rate_str,
+            freq_str,
+            format!("{:.6}", alpha),
+            i + 1
+        ));
+    }
+
+    file.write(charpart_elems.join(", ").as_bytes())
+        .expect("Could not write to nexus file");
+    file.write(b";\nend;\n").expect("Could not write to nexus file");
+}
+
+pub struct BinarySiteModelData {
+    pub rate_model_string: String,
+    pub site_freq: Tensor,
+    pub rate_matrices: Tensor,
+}
+
+fn read_u64_le(reader: &mut impl Read, field_name: &str) -> Result<u64> {
+    let mut buf = [0u8; 8];
+    reader
+        .read_exact(&mut buf)
+        .with_context(|| format!("Failed to read {} from binary site model file", field_name))?;
+    Ok(u64::from_le_bytes(buf))
+}
+
+fn read_f64_vec_le(reader: &mut impl Read, len: usize, field_name: &str) -> Result<Vec<f64>> {
+    let byte_len = len
+        .checked_mul(8)
+        .context("Binary site model file field is too large")?;
+    let mut bytes = vec![0u8; byte_len];
+    reader
+        .read_exact(&mut bytes)
+        .with_context(|| format!("Failed to read {} from binary site model file", field_name))?;
+
+    let mut out = Vec::with_capacity(len);
+    for chunk in bytes.chunks_exact(8) {
+        out.push(f64::from_le_bytes(chunk.try_into().unwrap()));
+    }
+    Ok(out)
+}
+
+/// Read IQ-TREE binary site model format.
+///
+/// Format:
+/// - uint64 little-endian: byte length of rate-model string
+/// - [len] bytes: rate-model string
+/// - uint64 little-endian: number of sites
+/// - num_sites * 20 little-endian f64: per-site frequencies
+/// - num_sites * 190 little-endian f64: per-site upper-triangular rates
+pub fn read_binary_site_model_file(path: &Path) -> Result<BinarySiteModelData> {
+    if cfg!(target_endian = "big") {
+        anyhow::bail!("Only little-endian machine is supported for reading binary site model file");
+    }
+
+    let file = std::fs::File::open(path)
+        .with_context(|| format!("Failed to open binary site model file: {}", path.display()))?;
+    let mut reader = std::io::BufReader::new(file);
+
+    let rate_model_string_len = usize::try_from(read_u64_le(&mut reader, "rate model string length")?)
+        .context("Rate model string length does not fit in usize")?;
+    let mut rate_model_string_buf = vec![0u8; rate_model_string_len];
+    if rate_model_string_len > 0 {
+        reader
+            .read_exact(&mut rate_model_string_buf)
+            .context("Failed to read rate model string from binary site model file")?;
+    }
+    let rate_model_string = String::from_utf8(rate_model_string_buf)
+        .context("Rate model string is not valid UTF-8")?;
+
+    let num_sites = usize::try_from(read_u64_le(&mut reader, "number of sites")?)
+        .context("Number of sites does not fit in usize")?;
+
+    let freq_len = num_sites
+        .checked_mul(20)
+        .context("Number of frequency values overflows usize")?;
+    let site_freq_data = read_f64_vec_le(&mut reader, freq_len, "site frequencies")?;
+
+    let rate_len = num_sites
+        .checked_mul(190)
+        .context("Number of rate values overflows usize")?;
+    let rate_matrices_data = read_f64_vec_le(&mut reader, rate_len, "rate matrices")?;
+
+    let site_freq = Tensor::from_vec(site_freq_data, &[num_sites, 20], &candle_core::Device::Cpu)
+        .context("Failed to create site frequency tensor")?;
+
+    let mut rate_matrices = Vec::with_capacity(num_sites * 20 * 20);
+
+    for i in 0..num_sites {
+        let mut full_matrix = vec![0f64; 20 * 20];
+        let mut idx = 0;
+        for a in 0..20 {
+            for b in (a+1)..20 {
+                let rate = rate_matrices_data[i * 190 + idx];
+                full_matrix[a * 20 + b] = rate;
+                full_matrix[b * 20 + a] = rate;
+                idx += 1;
+            }
+        }
+        rate_matrices.extend(full_matrix);
+    }
+
+    let rate_matrices = Tensor::from_vec(rate_matrices, &[num_sites, 20, 20], &candle_core::Device::Cpu)
+        .context("Failed to create rate matrices tensor")?;
+
+    // Convert the upper diagonal rate matrices to full R matrices
+    
+
+    Ok(BinarySiteModelData {
+        rate_model_string,
+        site_freq,
+        rate_matrices,
+    })
+}
\ No newline at end of file
diff --git a/mutsel_rust/src/lib.rs b/mutsel_rust/src/lib.rs
new file mode 100644
index 000000000..fcc500355
--- /dev/null
+++ b/mutsel_rust/src/lib.rs
@@ -0,0 +1,593 @@
+#![allow(non_snake_case)]
+
+pub mod data;
+pub mod felsenstein;
+pub mod gamma;
+pub mod io;
+pub mod model;
+mod optimization;
+mod utils;
+
+use std::{
+    io::Write,
+    mem::MaybeUninit,
+    path::Path,
+};
+
+use candle_core::{IndexOp, Tensor};
+use candle_nn::ops::sigmoid;
+
+use crate::{gamma::log_gamma_pdf, utils::tensor_full};
+
+#[unsafe(no_mangle)]
+pub extern "C" fn rust_set_rayon_threads(num_threads: u32) {
+    rayon::ThreadPoolBuilder::new()
+        .num_threads(num_threads as usize)
+        .build_global()
+        .unwrap_or_else(|_| println!("Rust Threadnumber has already been set. Ignoring."));
+}
+
+const STDOUT_FD: libc::c_int = 1;
+const STDERR_FD: libc::c_int = 2;
+
+unsafe fn os_dup(fd: libc::c_int) -> libc::c_int {
+    unsafe { libc::dup(fd) }
+}
+
+unsafe fn os_dup2(src: libc::c_int, dst: libc::c_int) -> libc::c_int {
+    unsafe { libc::dup2(src, dst) }
+}
+
+
+unsafe fn os_close(fd: libc::c_int) -> libc::c_int {
+    unsafe { libc::close(fd) }
+}
+
+#[cfg(unix)]
+unsafe fn os_read(fd: libc::c_int, buf: &mut [u8]) -> isize {
+    unsafe { libc::read(fd, buf.as_mut_ptr() as *mut libc::c_void, buf.len()) as isize }
+}
+
+#[cfg(windows)]
+unsafe fn os_read(fd: libc::c_int, buf: &mut [u8]) -> isize {
+    unsafe { libc::read(fd, buf.as_mut_ptr() as *mut libc::c_void, buf.len() as libc::c_uint) as isize }
+}
+
+#[cfg(unix)]
+unsafe fn os_write(fd: libc::c_int, buf: &[u8]) -> isize {
+    unsafe { libc::write(fd, buf.as_ptr() as *const libc::c_void, buf.len()) as isize }
+}
+
+#[cfg(windows)]
+unsafe fn os_write(fd: libc::c_int, buf: &[u8]) -> isize {
+    unsafe { libc::write(fd, buf.as_ptr() as *const libc::c_void, buf.len() as libc::c_uint) as isize }
+}
+
+#[cfg(unix)]
+fn create_pipe() -> std::io::Result<[libc::c_int; 2]> {
+    let mut fds = [0; 2];
+    let ret = unsafe { libc::pipe(fds.as_mut_ptr()) };
+    if ret != 0 {
+        Err(std::io::Error::last_os_error())
+    } else {
+        Ok(fds)
+    }
+}
+
+#[cfg(windows)]
+fn create_pipe() -> std::io::Result<[libc::c_int; 2]> {
+    let mut fds = [0; 2];
+    // libc::pipe on Windows maps to the CRT signature (fds, psize, textmode).
+    let ret = unsafe { libc::pipe(fds.as_mut_ptr(), 4096, 0) };
+    if ret != 0 {
+        Err(std::io::Error::last_os_error())
+    } else {
+        Ok(fds)
+    }
+}
+
+fn write_all_fd(fd: libc::c_int, mut buf: &[u8]) -> std::io::Result<()> {
+    while !buf.is_empty() {
+        let n = unsafe { os_write(fd, buf) };
+        if n < 0 {
+            let err = std::io::Error::last_os_error();
+            if err.kind() == std::io::ErrorKind::Interrupted {
+                continue;
+            }
+            return Err(err);
+        }
+        let n = n as usize;
+        if n == 0 {
+            return Err(std::io::Error::new(
+                std::io::ErrorKind::WriteZero,
+                "write to redirected stdout returned 0",
+            ));
+        }
+        buf = &buf[n..];
+    }
+    Ok(())
+}
+
+fn tee_to_file(path: &str) -> (i32, i32, std::thread::JoinHandle<()>) {
+    let fds = create_pipe().unwrap_or_else(|e| panic!("tee_to_file: pipe() failed: {}", e));
+
+    // Save original stdout
+    let saved_stdout = unsafe { os_dup(STDOUT_FD) };
+    if saved_stdout < 0 {
+        panic!(
+            "tee_to_file: dup(STDOUT_FILENO) failed: {}",
+            std::io::Error::last_os_error()
+        );
+    }
+    let saved_stderr = unsafe { os_dup(STDERR_FD) };
+    if saved_stderr < 0 {
+        panic!(
+            "tee_to_file: dup(STDERR_FILENO) failed: {}",
+            std::io::Error::last_os_error()
+        );
+    }
+
+    // Dedicated copy for tee thread so saved_stdout can be restored/closed independently.
+    let tee_stdout = unsafe { os_dup(saved_stdout) };
+    if tee_stdout < 0 {
+        panic!(
+            "tee_to_file: dup(saved_stdout) failed: {}",
+            std::io::Error::last_os_error()
+        );
+    }
+
+    // Redirect stdout to pipe write end
+    let ret = unsafe { os_dup2(fds[1], STDOUT_FD) };
+    if ret < 0 {
+        panic!(
+            "tee_to_file: dup2(STDOUT_FILENO) failed: {}",
+            std::io::Error::last_os_error()
+        );
+    }
+    let ret = unsafe { os_dup2(fds[1], STDERR_FD) };
+    if ret < 0 {
+        panic!(
+            "tee_to_file: dup2(STDERR_FILENO) failed: {}",
+            std::io::Error::last_os_error()
+        );
+    }
+
+    // Close the original write end — stdout/stderr now hold the only references
+    let ret = unsafe { os_close(fds[1]) };
+    if ret != 0 {
+        panic!(
+            "tee_to_file: close(pipe write end) failed: {}",
+            std::io::Error::last_os_error()
+        );
+    }
+
+    // Open log file
+    let mut file = std::fs::OpenOptions::new()
+        .append(true)
+        .open(path)
+        .unwrap_or_else(|e| panic!("tee_to_file: failed to open '{}': {}", path, e));
+
+    // Spawn thread to read from pipe and write to both
+    let handle = std::thread::spawn(move || {
+        let mut buffer = [0u8; 1024];
+
+        loop {
+            let n = unsafe { os_read(fds[0], &mut buffer) };
+            if n == 0 {
+                break; // EOF
+            }
+            if n < 0 {
+                let err = std::io::Error::last_os_error();
+                if err.kind() == std::io::ErrorKind::Interrupted {
+                    continue;
+                }
+                panic!("tee_to_file: read from pipe failed: {}", err);
+            }
+
+            let n = n as usize;
+            // Write to original stdout
+            write_all_fd(tee_stdout, &buffer[..n])
+                .unwrap_or_else(|e| panic!("tee_to_file: write to stdout failed: {}", e));
+            // Write to file
+            file.write_all(&buffer[..n])
+                .unwrap_or_else(|e| panic!("tee_to_file: write to log file failed: {}", e));
+        }
+
+        let ret = unsafe { os_close(fds[0]) };
+        if ret != 0 {
+            panic!(
+                "tee_to_file: close(pipe read end) failed: {}",
+                std::io::Error::last_os_error()
+            );
+        }
+        let ret = unsafe { os_close(tee_stdout) };
+        if ret != 0 {
+            panic!(
+                "tee_to_file: close(tee stdout) failed: {}",
+                std::io::Error::last_os_error()
+            );
+        }
+
+        file.flush()
+            .unwrap_or_else(|e| panic!("tee_to_file: flush log file failed: {}", e));
+    });
+
+    (saved_stdout, saved_stderr, handle)
+}
+
+fn restore_stdout_stderr(
+    saved_stdout: i32,
+    saved_stderr: i32,
+    handle: std::thread::JoinHandle<()>,
+) {
+    unsafe {
+        // Restoring stdout/stderr drops the last write-end references to the pipe,
+        // causing EOF on the read end so the tee thread can exit cleanly.
+        os_dup2(saved_stdout, STDOUT_FD);
+        os_dup2(saved_stderr, STDERR_FD);
+    }
+    // Wait for the tee thread to drain and flush all remaining output.
+    handle
+        .join()
+        .unwrap_or_else(|_| panic!("restore_stdout_stderr: tee thread panicked"));
+    unsafe {
+        os_close(saved_stdout);
+        os_close(saved_stderr);
+    }
+}
+
+pub struct MutselParams {
+    pi_reg: f64,
+    Mu_reg: f64,
+    branch_reg: f64,
+}
+
+fn parse_mustel_str(model_str: &str) -> MutselParams {
+    let model_str = model_str.trim();
+    let model_upper = model_str.to_ascii_uppercase();
+
+    let (pi_reg, Mu_reg, branch_reg) = if model_upper == "MUTSEL" {
+        (0.65, 1.05, 1.86)
+    } else if model_upper.starts_with("MUTSEL{") && model_str.ends_with('}') {
+        let params_str = &model_str[7..model_str.len() - 1];
+        let values = params_str
+            .split('/')
+            .map(|value| value.trim().parse::<f64>().unwrap())
+            .collect::<Vec<_>>();
+        assert!(
+            values.len() == 3,
+            "Invalid MUTSEL format: expected MUTSEL{{pi_reg/Mu_reg/branch_reg}}, got {}",
+            model_str
+        );
+        (values[0], values[1], values[2])
+    } else {
+        panic!(
+            "Invalid MUTSEL format: expected MUTSEL or MUTSEL{{pi_reg/Mu_reg/branch_reg}}, got {}",
+            model_str
+        );
+    };
+
+    MutselParams {
+        pi_reg,
+        Mu_reg,
+        branch_reg,
+    }
+}
+
+/// parents: [num_nodes]
+/// branch_lengths: [num_nodes]
+/// alignment: [num_sites * num_leaves] (row-major)
+/// out_site_freq: [num_sites * 20] (row-major)
+/// out_rate_matrix: [num_sites * 190] (row-major)
+/// out_rate_para: [num_para] from the rate model 1 for gamma, 2 * num_cat for free rate
+/// out variables do not need to be initialized
+/// prior_R_file and prior_pi_file can be null pointers
+#[unsafe(no_mangle)]
+pub unsafe extern "C" fn rust_mutsel(
+    parents: *const i32,
+    branch_lengths: *const f64,
+    alignment: *const u8,
+    num_sites: u32,
+    num_leaves: u32,
+    num_nodes: u32,
+    model_str: *const std::os::raw::c_char,
+    prior_R_file: *const std::os::raw::c_char,
+    prior_pi_file: *const std::os::raw::c_char,
+    verbose: u8,
+    out_site_freq: *mut f64,
+    out_rate_matrix: *mut f64,
+    output_prefix: *const std::os::raw::c_char,
+) {
+    let out_prefix = unsafe { std::ffi::CStr::from_ptr(output_prefix) }
+        .to_str()
+        .unwrap();
+    let (saved_stdout, saved_stderr, tee_handle) = tee_to_file(&format!("{}.log", out_prefix));
+
+    let parents = unsafe { std::slice::from_raw_parts(parents, num_nodes as usize) };
+    let branch_lengths = unsafe { std::slice::from_raw_parts(branch_lengths, num_nodes as usize) };
+    let alignment =
+        unsafe { std::slice::from_raw_parts(alignment, (num_sites * num_leaves) as usize) };
+
+    let out_site_freq = unsafe {
+        std::slice::from_raw_parts_mut(
+            out_site_freq as *mut MaybeUninit<f64>,
+            (num_sites * 20) as usize,
+        )
+    };
+
+    let out_rate_matrix = unsafe {
+        std::slice::from_raw_parts_mut(
+            out_rate_matrix as *mut MaybeUninit<f64>,
+            (num_sites * 190) as usize,
+        )
+    };
+
+    let model_cstr = unsafe { std::ffi::CStr::from_ptr(model_str) };
+    let model_str = model_cstr.to_str().unwrap();
+
+    println!("Starting mutsel optimization with {}", model_str);
+
+    let mutsel_params = parse_mustel_str(model_str);
+
+    let felsenstein = io::create_felsenstein_tree(
+        parents,
+        branch_lengths,
+        alignment,
+        num_sites as usize,
+        num_leaves as usize,
+    );
+
+    let prior_R_file = if prior_R_file.is_null() {
+        None
+    } else {
+        let cstr = unsafe { std::ffi::CStr::from_ptr(prior_R_file) };
+        Some(Path::new(cstr.to_str().unwrap()))
+    };
+
+    let prior_pi_file = if prior_pi_file.is_null() {
+        None
+    } else {
+        let cstr = unsafe { std::ffi::CStr::from_ptr(prior_pi_file) };
+        Some(Path::new(cstr.to_str().unwrap()))
+    };
+
+    let substitution_model = SubstitutionModel::MutSel;
+
+    let aa_dist = io::get_site_specific_aa_distribution_iqtree(
+        alignment,
+        num_sites as usize,
+        num_leaves as usize,
+    );
+
+    let (S, sqrt_pi, _rate_para, _substitution_rates) = optimization::optimize_internal(
+        felsenstein,
+        branch_lengths,
+        aa_dist,
+        mutsel_params,
+        RateModel::R(1),
+        prior_R_file,
+        prior_pi_file,
+        substitution_model,
+        crate::Verbosity::from_u8(verbose),
+        out_prefix,
+    )
+    .unwrap();
+
+    let (R, pi) = model::phylograd2iqtree_parametrization(&S, &sqrt_pi).unwrap();
+    let site_freq = pi.to_vec2().unwrap();
+
+    for site_index in 0..num_sites as usize {
+        for aa_index in 0..20 {
+            let value = site_freq[site_index][aa_index];
+            out_site_freq[site_index * 20 + aa_index].write(value);
+        }
+    }
+
+    for site_index in 0..num_sites as usize {
+        let mut idx = 0;
+        // Upper diagonal
+        for i in 0..20 {
+            for j in (i + 1)..20 {
+                out_rate_matrix[site_index * 190 + idx]
+                    .write(R.i((site_index, i, j)).unwrap().to_scalar().unwrap());
+                idx += 1;
+            }
+        }
+    }
+    std::io::stdout().flush().unwrap();
+    restore_stdout_stderr(saved_stdout, saved_stderr, tee_handle);
+}
+
+#[derive(Debug, Clone, Copy)]
+enum RateModel {
+    G(usize),
+    R(usize),
+    X(f64, SiteSpecificRateModel), // this is the strength of the prior
+}
+
+#[derive(Debug, Clone, Copy)]
+enum SiteSpecificRateModel {
+    Triangle,
+    Uniform,
+    Gamma(f64),     // alpha parameter
+    LogNormal(f64), // Mean
+}
+
+impl SiteSpecificRateModel {
+    fn from_str(s: &str) -> SiteSpecificRateModel {
+        let s = s.trim().to_ascii_lowercase();
+        if s == "triangle" {
+            SiteSpecificRateModel::Triangle
+        } else if s == "uniform" {
+            SiteSpecificRateModel::Uniform
+        } else if let Some(alpha_str) = s.strip_prefix("gamma{").and_then(|s| s.strip_suffix('}')) {
+            let alpha: f64 = alpha_str.parse().unwrap();
+            SiteSpecificRateModel::Gamma(alpha)
+        } else if let Some(mean_str) = s
+            .strip_prefix("lognormal{")
+            .and_then(|s| s.strip_suffix('}'))
+        {
+            let mean: f64 = mean_str.parse().unwrap();
+            SiteSpecificRateModel::LogNormal(mean)
+        } else {
+            panic!("Unknown site-specific rate model: {}", s);
+        }
+    }
+
+    fn penalty(&self, rate_para: &Tensor) -> Tensor {
+        match self {
+            SiteSpecificRateModel::Triangle => (1.0 - rate_para).unwrap().sum_all().unwrap(),
+            SiteSpecificRateModel::Uniform => {
+                return tensor_full(1.0, &[]);
+            }
+            SiteSpecificRateModel::Gamma(alpha) => {
+                return log_gamma_pdf(rate_para, &tensor_full(*alpha, &[]))
+                    .neg()
+                    .unwrap();
+            }
+            SiteSpecificRateModel::LogNormal(mean) => {
+                return (rate_para.log().unwrap() - mean.ln())
+                    .unwrap()
+                    .powf(2.0)
+                    .unwrap();
+            }
+        }
+    }
+
+    fn rates_from_parameters(&self, rate_para: &Tensor) -> Tensor {
+        match self {
+            SiteSpecificRateModel::Triangle | SiteSpecificRateModel::Uniform => {
+                sigmoid(rate_para).unwrap()
+            }
+            SiteSpecificRateModel::Gamma(_) => {
+                rate_para.exp().unwrap() // this will be transformed to rates in the penalty function
+            }
+            SiteSpecificRateModel::LogNormal(_) => {
+                rate_para.exp().unwrap() // this will be transformed to rates in the penalty function
+            }
+        }
+    }
+
+    fn init(&self, num_sites: usize) -> Tensor {
+        match self {
+            SiteSpecificRateModel::Triangle | SiteSpecificRateModel::Uniform => {
+                tensor_full(0.0, &[num_sites])
+            }
+            SiteSpecificRateModel::Gamma(_) => tensor_full(0.0, &[num_sites]),
+            SiteSpecificRateModel::LogNormal(mean) => tensor_full(mean.ln(), &[num_sites]),
+        }
+    }
+}
+
+fn parse_rate_model(rate_model: &str) -> RateModel {
+    let mut chars = rate_model.chars();
+    let model_type = chars.next().unwrap();
+    match model_type {
+        'G' => {
+            let num_categories: usize = chars.collect::<String>().parse().unwrap();
+            RateModel::G(num_categories)
+        }
+        'R' => {
+            let num_categories: usize = chars.collect::<String>().parse().unwrap();
+            RateModel::R(num_categories)
+        }
+        'X' => {
+            // X{strength, site_specific_model}
+            let params_str = chars.collect::<String>();
+            let params_str = params_str.trim();
+            assert!(
+                params_str.starts_with('{') && params_str.ends_with('}'),
+                "Invalid X model format: {}",
+                params_str
+            );
+            let params_str = &params_str[1..params_str.len() - 1]; // remove { and }
+            let mut params = params_str.splitn(2, '/');
+            let strength: f64 = params.next().unwrap().trim().parse().unwrap();
+            let site_specific_model_str = params.next().unwrap().trim();
+            let site_specific_model = SiteSpecificRateModel::from_str(site_specific_model_str);
+            RateModel::X(strength, site_specific_model)
+        }
+        _ => panic!("Unknown rate model"),
+    }
+}
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum SubstitutionModel {
+    MutSel,
+    MutSelApprox,
+    RelaxPMSF,
+}
+
+#[derive(Debug, Clone, Copy)]
+enum Verbosity {
+    Quiet,
+    Min,
+    Med,
+    Max,
+    Debug,
+}
+
+impl Verbosity {
+    fn from_u8(value: u8) -> Verbosity {
+        match value {
+            0 => Verbosity::Quiet,
+            1 => Verbosity::Min,
+            2 => Verbosity::Med,
+            3 => Verbosity::Max,
+            4 => Verbosity::Debug,
+            _ => panic!("Invalid verbosity level"),
+        }
+    }
+
+    fn should_print(&self, level: Verbosity) -> bool {
+        match (self, level) {
+            (Verbosity::Quiet, _) => false,
+            (
+                Verbosity::Min,
+                Verbosity::Min | Verbosity::Med | Verbosity::Max | Verbosity::Debug,
+            ) => true,
+            (Verbosity::Med, Verbosity::Med | Verbosity::Max | Verbosity::Debug) => true,
+            (Verbosity::Max, Verbosity::Max | Verbosity::Debug) => true,
+            (Verbosity::Debug, _) => true,
+            _ => false,
+        }
+    }
+}
+
+// optimize function called from the rust binary
+pub fn optimize_rust_binary(
+    newick: &Path,
+    fasta: &Path,
+    pi_reg: f64,
+    R_reg: f64,
+    rate_mode: &str,
+    prior_R_file: Option<&Path>,
+    prior_pi_file: Option<&Path>,
+    substitution_model: SubstitutionModel,
+) -> Result<(Tensor, Tensor, Tensor, Vec<f64>), candle_core::Error> {
+    let sequences = io::read_alignment(fasta);
+
+    let (felsenstein, distances) =
+        io::process_newick_alignment(&std::fs::read_to_string(&newick).unwrap(), &sequences);
+
+    let aa_dist = io::get_site_specific_aa_distribution(&sequences);
+
+    let rate_model = parse_rate_model(rate_mode);
+
+    optimization::optimize_internal(
+        felsenstein,
+        &distances,
+        aa_dist,
+        MutselParams {
+            pi_reg,
+            Mu_reg: R_reg,
+            branch_reg: 10.0, // default value
+        },
+        rate_model,
+        prior_R_file,
+        prior_pi_file,
+        substitution_model,
+        Verbosity::Debug,
+        "./mutsel"
+    )
+}
diff --git a/mutsel_rust/src/main.rs b/mutsel_rust/src/main.rs
new file mode 100644
index 000000000..b5415c720
--- /dev/null
+++ b/mutsel_rust/src/main.rs
@@ -0,0 +1,229 @@
+#![allow(non_snake_case)]
+
+use candle_core::Tensor;
+use mutsel_rust::gamma::GammaOp;
+
+fn run(args : &[String]) {
+    let newick = args[0].clone();
+    let fasta = args[1].clone();
+    let pi_reg = args[2].parse::<f64>().unwrap();
+    let R_reg = args[3].parse::<f64>().unwrap();
+    let rate_model = args[4].clone();
+    let mutsel = args[5].clone();
+
+
+    let substitution_model = match mutsel.as_str() {
+        "mutselapprox" => mutsel_rust::SubstitutionModel::MutSelApprox,
+        "relaxpmsf" => mutsel_rust::SubstitutionModel::RelaxPMSF,
+        "mutsel" => mutsel_rust::SubstitutionModel::MutSel,
+        _ => panic!("Unknown substitution model"),
+    };
+
+    let (S, sqrt_pi, rate_para, _substitution_rates) = mutsel_rust::optimize_rust_binary(
+        &std::path::Path::new(&newick),
+        &std::path::Path::new(&fasta),
+        pi_reg,
+        R_reg,
+        &rate_model,
+        None,
+        None,
+        substitution_model
+    )
+    .unwrap();
+
+    if substitution_model == mutsel_rust::SubstitutionModel::RelaxPMSF {
+        let (R, pi) = mutsel_rust::model::phylograd2iqtree_parametrization(&S, &sqrt_pi).unwrap();
+        mutsel_rust::io::write_sitefreq_file(&pi, &std::path::Path::new(args[6].as_str()));
+        // R should be the same for all sites
+        mutsel_rust::io::write_pam_file(&R.get(0).unwrap(), &std::path::Path::new(args[7].as_str()));
+    } else {
+        mutsel_rust::io::write_nexus_file(&S, &sqrt_pi, &rate_para, &std::path::Path::new(args[6].as_str()));
+    }
+}
+
+fn phylo_grad_param(args : &[String]) {
+    let model_file = args[0].clone();
+    let parsed = mutsel_rust::io::read_binary_site_model_file(std::path::Path::new(&model_file))
+        .unwrap_or_else(|e| panic!("Error reading site model file '{}': {e}", model_file));
+
+    let rate_model =  parse_rate_model(&parsed.rate_model_string).unwrap();
+
+    println!("Parsed rate model: {:?}\n", rate_model);
+
+    let (weights, rates) = if let ParsedRateModel::Gamma { categories, alpha } = rate_model {
+        (Tensor::full(1.0 / categories as f64, &[categories], &candle_core::Device::Cpu).unwrap(), Tensor::full(alpha.unwrap(), &[categories], &candle_core::Device::Cpu).unwrap().apply_op1(GammaOp::new(categories)).unwrap())
+    } else if let ParsedRateModel::FreeRate { categories, weights, rates } = rate_model {
+        (Tensor::from_vec(weights.unwrap(), &[categories], &candle_core::Device::Cpu).unwrap(), Tensor::from_vec(rates.unwrap(), &[categories], &candle_core::Device::Cpu).unwrap())
+    } else if let ParsedRateModel::X = rate_model {
+        (Tensor::full(1.0, &[1], &candle_core::Device::Cpu).unwrap(), Tensor::full(1.0, &[1], &candle_core::Device::Cpu).unwrap())
+    } else {
+        panic!("Unexpected rate model variant");
+    };
+
+    println!("Weights: {:?}", weights);
+    println!("Rates: {:?}", rates);
+
+
+    let (S, sqrt_pi) = mutsel_rust::model::iqtree2phylograd_parametrization(&parsed.rate_matrices, &parsed.site_freq).unwrap();
+
+    Tensor::write_npz(&[("weights", weights), ("rates", rates), ("S", S), ("sqrt_pi", sqrt_pi)], args[1].as_str()).unwrap();
+}
+
+#[derive(Debug, Clone, PartialEq)]
+enum ParsedRateModel {
+    Gamma {
+        categories: usize,
+        alpha: Option<f64>,
+    },
+    FreeRate {
+        categories: usize,
+        weights: Option<Vec<f64>>,
+        rates: Option<Vec<f64>>,
+    },
+    X
+}
+
+fn parse_rate_model(rate_model: &str) -> Result<ParsedRateModel, String> {
+    let model = rate_model.trim();
+    if model.is_empty() {
+        return Err("Rate model string is empty".to_string());
+    }
+
+    if model.starts_with("R1") {
+        return Ok(ParsedRateModel::X);
+    }
+
+    let first_brace = model.find('{');
+    let (head, body) = match first_brace {
+        Some(pos) => {
+            if !model.ends_with('}') {
+                return Err(format!("Missing closing '}}' in rate model '{model}'"));
+            }
+            (&model[..pos], Some(&model[pos + 1..model.len() - 1]))
+        }
+        None => (model, None),
+    };
+
+    let mut chars = head.chars();
+    let model_type = chars
+        .next()
+        .ok_or_else(|| "Missing rate model type".to_string())?
+        .to_ascii_uppercase();
+    let categories_str = chars.as_str().trim();
+    let categories = categories_str
+        .parse::<usize>()
+        .map_err(|_| format!("Invalid category count '{categories_str}' in '{model}'"))?;
+    if categories == 0 {
+        return Err("Category count must be greater than 0".to_string());
+    }
+
+    let params = if let Some(inner) = body {
+        let values = inner
+            .split(',')
+            .map(|v| {
+                let token = v.trim();
+                token
+                    .parse::<f64>()
+                    .map_err(|_| format!("Invalid numeric value '{token}' in '{model}'"))
+            })
+            .collect::<Result<Vec<_>, _>>()?;
+        Some(values)
+    } else {
+        None
+    };
+
+    match model_type {
+        'G' => {
+            if let Some(values) = params {
+                if values.len() != 1 {
+                    return Err(format!(
+                        "Gamma model expects exactly 1 parameter (alpha), got {}",
+                        values.len()
+                    ));
+                }
+                Ok(ParsedRateModel::Gamma {
+                    categories,
+                    alpha: Some(values[0]),
+                })
+            } else {
+                Ok(ParsedRateModel::Gamma {
+                    categories,
+                    alpha: None,
+                })
+            }
+        }
+        'R' => {
+            if let Some(values) = params {
+                if values.len() != 2 * categories {
+                    return Err(format!(
+                        "FreeRate model expects {} parameters ({} weights + {} rates), got {}",
+                        2 * categories,
+                        categories,
+                        categories,
+                        values.len()
+                    ));
+                }
+                let weights = values[..categories].to_vec();
+                let rates = values[categories..].to_vec();
+                Ok(ParsedRateModel::FreeRate {
+                    categories,
+                    weights: Some(weights),
+                    rates: Some(rates),
+                })
+            } else {
+                Ok(ParsedRateModel::FreeRate {
+                    categories,
+                    weights: None,
+                    rates: None,
+                })
+            }
+        },
+        'X' => Ok(ParsedRateModel::X),
+        _ => Err(format!(
+            "Unknown rate model type '{}', expected 'G' or 'R'",
+            model_type
+        )),
+    }
+}
+
+fn main() {
+    let args: Vec<String> = std::env::args().collect();
+    if args[1] == "run" {
+        run(&args[2..].to_vec());
+    } else if args[1] == "phylograd-param" {
+        phylo_grad_param(&args[2..].to_vec());
+    } 
+    else {
+        panic!("Unknown command");
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn parses_gamma_with_alpha() {
+        let parsed = parse_rate_model("G4{0.456}").unwrap();
+        assert_eq!(
+            parsed,
+            ParsedRateModel::Gamma {
+                categories: 4,
+                alpha: Some(0.456),
+            }
+        );
+    }
+
+    #[test]
+    fn parses_freerate_with_weights_and_rates() {
+        let parsed = parse_rate_model("R2{0.5,1.0, 0.5, 3.5}").unwrap();
+        assert_eq!(
+            parsed,
+            ParsedRateModel::FreeRate {
+                categories: 2,
+                weights: Some(vec![0.5, 1.0]),
+                rates: Some(vec![0.5, 3.5]),
+            }
+        );
+    }
+}
diff --git a/mutsel_rust/src/model.rs b/mutsel_rust/src/model.rs
new file mode 100644
index 000000000..fde3959ef
--- /dev/null
+++ b/mutsel_rust/src/model.rs
@@ -0,0 +1,268 @@
+use std::ops::Deref;
+
+use candle_core::{CpuStorage, CustomOp1, Storage, Tensor};
+
+use crate::SubstitutionModel;
+
+fn g_scalar(x: f64) -> f64 {
+    if x.abs() < 1e-6 {
+        return 1.0 + x / 2.0 + x * x / 12.0;
+    } else {
+        return x / (1.0 - (-x).exp());
+    }
+}
+
+fn dx_g_scalar(x: f64) -> f64 {
+    if x.abs() < 1e-6 {
+        return 0.5 + x / 6.0 - x * x * x / 180.0;
+    } else {
+        let exp_x = x.exp();
+        return exp_x * (-1.0 + exp_x - x) / (exp_x - 1.0).powi(2);
+    }
+}
+
+#[derive(Debug, Clone)]
+pub struct GOp {}
+
+impl CustomOp1 for GOp {
+    fn name(&self) -> &'static str {
+        "g_op"
+    }
+
+    fn cpu_fwd(
+        &self,
+        storage: &candle_core::CpuStorage,
+        layout: &candle_core::Layout,
+    ) -> candle_core::Result<(candle_core::CpuStorage, candle_core::Shape)> {
+        let data = match storage {
+            CpuStorage::F64(data) => data,
+            _ => panic!("Expected f64 storage."),
+        };
+
+        let output = candle_core::cpu_backend::unary_map(&data, layout, g_scalar);
+
+        Ok((CpuStorage::F64(output), layout.shape().clone()))
+    }
+
+    fn bwd(
+        &self,
+        _arg: &Tensor,
+        _res: &Tensor,
+        _grad_res: &Tensor,
+    ) -> candle_core::Result<Option<Tensor>> {
+        let (storage, layout) = _arg.storage_and_layout();
+
+        let data = match storage.deref() {
+            Storage::Cpu(CpuStorage::F64(data)) => data,
+            _ => panic!("Expected f64 storage."),
+        };
+
+        let grads = candle_core::cpu_backend::unary_map(&data, &layout, dx_g_scalar);
+
+        let grad_tensor = Tensor::from_vec(grads, _arg.shape(), &candle_core::Device::Cpu)?;
+
+        Ok(Some(grad_tensor.mul(_grad_res)?))
+    }
+}
+
+pub fn calc_rate_matrix(
+    R: &Tensor,
+    log_pi: &Tensor,
+    global_scaling: &Tensor,
+    substitution_model: SubstitutionModel,
+) -> (Tensor, Tensor) {
+    match substitution_model {
+        SubstitutionModel::MutSelApprox => {
+            calc_rate_matrix_mutselapprox(R, log_pi, global_scaling).unwrap()
+        }
+        SubstitutionModel::RelaxPMSF => calc_rate_matrix_relaxpmsf(R, log_pi, global_scaling),
+        SubstitutionModel::MutSel => calc_rate_matrix_mutsel(R, log_pi, global_scaling),
+    }
+}
+
+/// RelaxPMSF rate matrix. We do normalize to 1 PAM per column here.
+pub fn calc_rate_matrix_relaxpmsf(R: &Tensor, log_pi: &Tensor, rate: &Tensor) -> (Tensor, Tensor) {
+    let pi = candle_nn::ops::softmax(log_pi, 1).unwrap();
+    let pi_sqrt = pi.sqrt().unwrap();
+
+    let R = R.unsqueeze(0).unwrap();
+
+    let Q = R.broadcast_mul(&pi.unsqueeze(1).unwrap()).unwrap();
+
+    let eye = Tensor::eye(20, candle_core::DType::F64, &candle_core::Device::Cpu).unwrap();
+
+    // Make sure diagonal of Q is correct, i.e. Q_ii = -sum_{j!=i} Q_ij
+    let Q = (Q.broadcast_sub(
+        &(&Q.sum_keepdim(2).unwrap().broadcast_as(Q.dims()).unwrap() * &eye.unsqueeze(0).unwrap())
+            .unwrap(),
+    ))
+    .unwrap();
+
+    // normalize to 1 PAM per column, i.e. -sum_i pi_i Q_ii = 1
+    let q_diag = Q
+        .broadcast_mul(&eye.unsqueeze(0).unwrap())
+        .unwrap()
+        .sum(2)
+        .unwrap();
+    let normalization = pi.mul(&q_diag).unwrap().sum(1).unwrap().neg().unwrap();
+
+    let Q = Q
+        .broadcast_div(&normalization.unsqueeze(1).unwrap().unsqueeze(2).unwrap())
+        .unwrap();
+
+    // Diagonal of S and therefore Q does not get used
+
+    let sqrt_pi_Q = pi_sqrt.unsqueeze(2).unwrap().broadcast_mul(&Q).unwrap();
+    let S = (sqrt_pi_Q.broadcast_div(&pi_sqrt.unsqueeze(1).unwrap())).unwrap();
+
+    let S = S.broadcast_mul(&rate).unwrap();
+    (S, pi_sqrt)
+}
+
+pub fn calc_rate_matrix_mutselapprox(
+    R: &Tensor,
+    log_pi: &Tensor,
+    rate: &Tensor,
+) -> Result<(Tensor, Tensor), candle_core::Error> {
+    let L = log_pi.dims()[0];
+    let pi = candle_nn::ops::softmax(log_pi, 1)?;
+    let pi_sqrt = pi.sqrt()?;
+
+    let S = R
+        .broadcast_mul(rate)?
+        .unsqueeze(0)?
+        .broadcast_as(&[L, 20, 20])?;
+
+    Ok((S, pi_sqrt))
+}
+
+/// We assume a mutation process Mu is the rate matrix of the mutation process with its equlibirium in the diagonal.
+/// It should be the output of the Mu function.
+pub fn calc_rate_matrix_mutsel(
+    Mu: &Tensor,
+    log_pi: &Tensor,
+    rate: &Tensor,
+) -> (Tensor, Tensor) {
+    let L = log_pi.dims()[0];
+
+    let equi_mutation = (Mu * Tensor::eye(20, candle_core::DType::F64, &candle_core::Device::Cpu).unwrap()).unwrap();
+    let equi_mutation = equi_mutation.sum(1).unwrap();
+    let log_equi_mutation = equi_mutation.log().unwrap();
+
+    // This is a correction because of the equilibirum of the mutation process.
+    let fitness = log_pi.broadcast_sub(&log_equi_mutation.unsqueeze(0).unwrap()).unwrap();
+
+    let log_pi_diff = fitness.unsqueeze(1).unwrap().broadcast_sub(&fitness.unsqueeze(2).unwrap()).unwrap();
+
+    let fixation = log_pi_diff.apply_op1(GOp {}).unwrap();
+
+    let R = Mu.unsqueeze(0).unwrap().broadcast_as(&[L, 20, 20]).unwrap();
+
+    let Q = R.mul(&fixation).unwrap();
+
+    let pi = candle_nn::ops::softmax(&log_pi, 1).unwrap();
+    let pi_sqrt = pi.sqrt().unwrap();
+
+    let sqrt_pi_Q = pi_sqrt.unsqueeze(2).unwrap().broadcast_mul(&Q).unwrap();
+    let S = sqrt_pi_Q.broadcast_div(&pi_sqrt.unsqueeze(1).unwrap()).unwrap();
+
+    let S = S.broadcast_mul(&rate).unwrap();
+    (S, pi_sqrt)
+}
+
+// From S, sqrt_pi to R, pi
+pub fn phylograd2iqtree_parametrization(
+    S: &Tensor,
+    sqrt_pi: &Tensor,
+) -> Result<(Tensor, Tensor), candle_core::Error> {
+    let S_sqrt_pi_inv = S.broadcast_div(&sqrt_pi.unsqueeze(1)?)?;
+    let R = S_sqrt_pi_inv.broadcast_div(&sqrt_pi.unsqueeze(2)?)?;
+
+    let pi = sqrt_pi.mul(sqrt_pi)?;
+
+    Ok((R, pi))
+}
+
+// From R, pi to S, sqrt_pi
+pub fn iqtree2phylograd_parametrization(
+    R: &Tensor,
+    pi: &Tensor,
+) -> Result<(Tensor, Tensor), candle_core::Error> {
+    let pi_sqrt = pi.sqrt()?;
+
+    let sqrt_pi_R = R.broadcast_mul(&pi_sqrt.unsqueeze(2)?)?;
+    let S = sqrt_pi_R.broadcast_mul(&pi_sqrt.unsqueeze(1)?)?;
+
+    Ok((S, pi_sqrt))
+}
+
+pub fn substitution_rates(S: &Tensor, sqrt_pi: &Tensor) -> Vec<f64> {
+    // Q_ij = S_ij * sqrt_pi_j / sqrt_pi_i
+
+    let S = S.to_vec3::<f64>().unwrap();
+    let sqrt_pi = sqrt_pi.to_vec2::<f64>().unwrap();
+
+    assert_eq!(S.len(), sqrt_pi.len(), "Batch dimensions do not match.");
+
+    let mut rates = Vec::with_capacity(S.len());
+    for site in 0..S.len() {
+        let mut total_rate = 0.0;
+        for i in 0..20 {
+            for j in 0..20 {
+                if i != j {
+                    total_rate += S[site][i][j] * sqrt_pi[site][j] * sqrt_pi[site][i];
+                }
+            }
+        }
+        rates.push(total_rate);
+    }
+    rates
+}
+
+pub fn average_substitution_rate(S: &Tensor, sqrt_pi: &Tensor) -> f64 {
+    // Q_ij = S_ij * sqrt_pi_j / sqrt_pi_i
+
+    let S = S.to_vec3::<f64>().unwrap();
+    let sqrt_pi = sqrt_pi.to_vec2::<f64>().unwrap();
+
+    assert_eq!(S.len(), sqrt_pi.len(), "Batch dimensions do not match.");
+
+    let mut total_rate = 0.0;
+    for site in 0..S.len() {
+        for i in 0..20 {
+            for j in 0..20 {
+                if i != j {
+                    total_rate += S[site][i][j] * sqrt_pi[site][j] * sqrt_pi[site][i];
+                }
+            }
+        }
+    }
+
+    total_rate / S.len() as f64
+}
+
+// Tests
+#[cfg(test)]
+mod tests {
+    use crate::{optimization::Mu, utils::tensor_full};
+
+use super::*;
+    #[test]
+    fn test_mutsel() {
+        let L = 2;
+        let log_pi = Tensor::rand(-1.0, 1.0, &[L, 20], &candle_core::Device::Cpu).unwrap();
+
+        let R = Tensor::rand(0.1, 2.0, &[20, 20], &candle_core::Device::Cpu).unwrap();
+
+        let R = Mu(&R);
+
+        let (S, sqrt_pi) = calc_rate_matrix_mutsel(&R, &log_pi, &tensor_full(1.0, &[]));
+
+        println!("S: {}", S);
+        println!("sqrt_pi: {}", (&sqrt_pi * &sqrt_pi).unwrap());
+
+        println!("S - S.T: {}", (&S - &S.transpose(1, 2).unwrap()).unwrap());
+
+        assert!((&S - &S.transpose(1, 2).unwrap()).unwrap().abs().unwrap().max_all().unwrap().to_scalar::<f64>().unwrap() < 1e-12);
+    }
+}
\ No newline at end of file
diff --git a/mutsel_rust/src/optimization.rs b/mutsel_rust/src/optimization.rs
new file mode 100644
index 000000000..d0793e3d1
--- /dev/null
+++ b/mutsel_rust/src/optimization.rs
@@ -0,0 +1,837 @@
+use std::{
+    iter,
+    path::Path,
+    sync::{Arc, Mutex},
+};
+
+use candle_core::{Tensor, Var};
+use candle_nn::{Optimizer, ops::softmax};
+use phylo_grad::FelsensteinTree;
+
+use crate::{
+    RateModel, SiteSpecificRateModel, SubstitutionModel, Verbosity,
+    felsenstein::{self, FelsensteinOp, FelsensteinWithEdgeOp},
+    gamma::GammaOp,
+    model,
+    utils::{histogram, tensor_full},
+};
+
+trait Optimizable {
+    fn variables(&self) -> Vec<Var>;
+    fn likelihood(&self) -> Tensor;
+    fn penalty(&self) -> Tensor;
+    fn print_state(&self) {}
+}
+
+pub enum RateParameters {
+    G(usize, Var),                      // alpha for gamma distribution
+    R(Var, Var),                        // log_rate_cat and log_rate_weights for free rate model
+    X(Var, f64, SiteSpecificRateModel), // site-specific rates paramter, strength of penalty, and the type of penalty
+}
+
+impl RateParameters {
+    fn gamma(n: usize, alpha: f64) -> RateParameters {
+        // Alpha is unconstrained, but there is a very strong barrier approaching 0. So this is not a problem.
+        RateParameters::G(n, Var::from_tensor(&tensor_full(alpha, &[])).unwrap())
+    }
+
+    fn init(num_sites: usize, rate_model: RateModel, alpha: f64) -> RateParameters {
+        match rate_model {
+            RateModel::G(num_cat) => RateParameters::gamma(num_cat, alpha),
+            RateModel::R(num_cat) => {
+                let gamma_op = GammaOp::new(num_cat);
+                let alpha = Var::from_tensor(&tensor_full(alpha, &[])).unwrap();
+                let log_rate_cat =
+                    Var::from_tensor(&alpha.apply_op1(gamma_op).unwrap().log().unwrap()).unwrap();
+                let log_rate_weights = Var::from_tensor(&tensor_full(0.0, &[num_cat])).unwrap();
+                RateParameters::R(log_rate_cat, log_rate_weights)
+            }
+            RateModel::X(strength, site_specific_rate_model) => RateParameters::X(
+                Var::from_tensor(&site_specific_rate_model.init(num_sites)).unwrap(),
+                strength,
+                site_specific_rate_model,
+            ),
+        }
+    }
+
+    fn parameters_for_iqtree(&self) -> Tensor {
+        match self {
+            RateParameters::G(_, alpha) => alpha.as_detached_tensor().unsqueeze(0).unwrap(),
+            RateParameters::R(log_rate_cat, log_rate_weights) => {
+                let (categories, log_weights) = normalize_rate_cat(
+                    &log_rate_cat.as_detached_tensor(),
+                    &log_rate_weights.as_detached_tensor(),
+                );
+                Tensor::cat(&[log_weights.exp().unwrap(), categories], 0).unwrap()
+            }
+            RateParameters::X(_, _, _) => {
+                // Dummy value, want to make sure this allocates, so there is a valid pointer to return
+                tensor_full(0.0, &[1])
+            }
+        }
+    }
+
+    fn variables(&self) -> Vec<Var> {
+        match self {
+            RateParameters::G(_, alpha) => vec![alpha.clone()],
+            RateParameters::R(log_rate_cat, log_rate_weights) => {
+                vec![log_rate_cat.clone(), log_rate_weights.clone()]
+            }
+            RateParameters::X(site_rate_var, _, _) => vec![site_rate_var.clone()],
+        }
+    }
+
+    fn rates(&self) -> (Tensor, Tensor) {
+        match self {
+            RateParameters::G(num_cat, alpha) => {
+                let gamma_op = GammaOp::new(*num_cat);
+                let categories = alpha.apply_op1(gamma_op.clone()).unwrap();
+                let log_weights = tensor_full(f64::ln(1.0 / *num_cat as f64), &[*num_cat]);
+                (categories, log_weights)
+            }
+            RateParameters::R(log_rate_cat, log_rate_weights) => {
+                normalize_rate_cat(log_rate_cat, log_rate_weights)
+            }
+            RateParameters::X(_, _, _) => {
+                panic!(
+                    "Rates for site-specific model should be calculated separately using the site-specific model and parameters."
+                )
+            }
+        }
+    }
+
+    fn site_specific_rates(&self) -> Tensor {
+        match self {
+            RateParameters::X(site_rate_var, _, site_model) => {
+                site_model.rates_from_parameters(site_rate_var)
+            }
+            _ => {
+                panic!("Site-specific rates should only be calculated for the site-specific model.")
+            }
+        }
+    }
+
+    fn penalty(&self) -> Tensor {
+        match self {
+            RateParameters::X(_, strength, site_model) => {
+                (site_model.penalty(&self.site_specific_rates()) * *strength).unwrap()
+            }
+            _ => tensor_full(0.0, &[]),
+        }
+    }
+
+    fn calc_rate_matrix(
+        &self,
+        R: &Tensor,
+        log_pi: &Tensor,
+        global_scaling: &Tensor,
+        substitution_model: SubstitutionModel,
+    ) -> (Tensor, Tensor) {
+        let (S, sqrt_pi) = model::calc_rate_matrix(R, log_pi, global_scaling, substitution_model);
+        let S = if let RateParameters::X(_, _, _) = self {
+            S.broadcast_mul(
+                &self
+                    .site_specific_rates()
+                    .unsqueeze(1)
+                    .unwrap()
+                    .unsqueeze(2)
+                    .unwrap(),
+            )
+            .unwrap()
+        } else {
+            S
+        };
+        (S, sqrt_pi)
+    }
+
+    fn likelihood(
+        &self,
+        felsenstein_op: FelsensteinWithEdgeOp,
+        R: &Tensor,
+        log_pi: &Tensor,
+        substitution_model: SubstitutionModel,
+        calc_gradients: bool,
+        log_branch_lengths: &Tensor,
+    ) -> Tensor {
+        self.likelihood_per_site(
+            felsenstein_op,
+            R,
+            log_pi,
+            substitution_model,
+            calc_gradients,
+            log_branch_lengths,
+        )
+        .sum_all()
+        .unwrap()
+    }
+
+    fn likelihood_per_site(
+        &self,
+        felsenstein_op: FelsensteinWithEdgeOp,
+        R: &Tensor,
+        log_pi: &Tensor,
+        substitution_model: SubstitutionModel,
+        calc_gradients: bool,
+        log_branch_lengths: &Tensor,
+    ) -> Tensor {
+        let (S, sqrt_pi) =
+            self.calc_rate_matrix(R, log_pi, &tensor_full(1.0, &[]), substitution_model);
+        let branch_lengths = log_branch_lengths.exp().unwrap();
+        let likelihood = match self {
+            RateParameters::G(_, _) | RateParameters::R(_, _) => {
+                let mut all_likelihoods = vec![];
+                let (rate_categories, log_weights) = self.rates();
+                for r_cat_index in 0..rate_categories.dims()[0] {
+                    let rate_tensor = rate_categories.get(r_cat_index).unwrap();
+                    let S = S
+                        .broadcast_mul(&rate_tensor.reshape(&[1, 1, 1]).unwrap())
+                        .unwrap();
+                    let likelihoods = if calc_gradients {
+                        S.apply_op3(&sqrt_pi, &branch_lengths, felsenstein_op.clone())
+                            .unwrap()
+                    } else {
+                        S.apply_op3(&sqrt_pi, &branch_lengths, felsenstein_op.into_fwd_op())
+                            .unwrap()
+                    };
+                    let weighted_likelihoods = likelihoods
+                        .broadcast_add(&log_weights.get(r_cat_index).unwrap())
+                        .unwrap();
+                    all_likelihoods.push(weighted_likelihoods);
+                }
+                let all_likelihoods = Tensor::stack(&all_likelihoods, 0).unwrap();
+                let final_likelihoods = all_likelihoods.log_sum_exp(0).unwrap();
+                final_likelihoods
+            }
+            RateParameters::X(_, _, _) => {
+                if calc_gradients {
+                    S.apply_op3(&sqrt_pi, &branch_lengths, felsenstein_op.clone())
+                        .unwrap()
+                } else {
+                    S.apply_op3(&sqrt_pi, &branch_lengths, felsenstein_op.into_fwd_op())
+                        .unwrap()
+                }
+            }
+        };
+
+        likelihood
+    }
+}
+
+pub struct AlphaAndScalingParameters {
+    pub felsenstein_op: FelsensteinWithEdgeOp,
+    pub log_global_scaling: Var,
+    pub log_branch_length_scaling: Var,
+    pub init_log_branch_lengths: Tensor,
+    pub R: Tensor,
+    pub log_pi: Tensor,
+    pub rate_model: RateParameters,
+    pub branch_length_penalty: f64,
+}
+
+impl Optimizable for AlphaAndScalingParameters {
+    fn variables(&self) -> Vec<Var> {
+        let mut vars = vec![
+            self.log_global_scaling.clone(),
+            self.log_branch_length_scaling.clone(),
+        ];
+        vars.extend(self.rate_model.variables());
+        vars
+    }
+
+    fn likelihood(&self) -> Tensor {
+        let log_branch_length_scaling = self
+            .log_branch_length_scaling
+            .broadcast_sub(&self.log_branch_length_scaling.mean(0).unwrap())
+            .unwrap();
+
+        let log_branch_lengths = (&self.init_log_branch_lengths + log_branch_length_scaling)
+            .unwrap()
+            .broadcast_add(&self.log_global_scaling)
+            .unwrap();
+
+        self.rate_model.likelihood(
+            self.felsenstein_op.clone(),
+            &self.R,
+            &self.log_pi,
+            SubstitutionModel::MutSel,
+            true,
+            &log_branch_lengths,
+        )
+    }
+
+    fn penalty(&self) -> Tensor {
+        let branch_penalty = self
+            .log_branch_length_scaling
+            .powf(2.0)
+            .unwrap()
+            .sum_all()
+            .unwrap()
+            * self.branch_length_penalty;
+        (self.rate_model.penalty() + branch_penalty.unwrap()).unwrap()
+    }
+
+    fn print_state(&self) {
+        println!(
+            "global_scaling: {}",
+            self.log_global_scaling
+                .exp()
+                .unwrap()
+                .to_scalar::<f64>()
+                .unwrap()
+        );
+        match &self.rate_model {
+            RateParameters::G(num_cat, alpha) if *num_cat > 1 => {
+                println!("alpha: {}", alpha.to_scalar::<f64>().unwrap())
+            }
+            _ => {}
+        }
+    }
+}
+
+pub struct ModelParameters {
+    pub felsenstein_op: FelsensteinWithEdgeOp,
+    pub log_R: Var,
+    pub log_pi: Var,
+    pub log_global_scaling: Var,
+    pub log_branch_length_scaling: Var,
+    pub init_log_branch_lengths: Tensor,
+    pub rate_parameters: RateParameters,
+    pub pi_reg: f64,
+    pub R_reg: f64,
+    pub branch_length_penalty: f64,
+    pub init_log_R: Tensor,
+    pub init_log_pi: Tensor,
+    pub substitution_model: SubstitutionModel,
+}
+
+impl ModelParameters {
+    pub fn calc_rate_matrix(&self) -> (Tensor, Tensor) {
+        self.rate_parameters.calc_rate_matrix(
+            &Mu(&self.log_R.as_detached_tensor()),
+            &self.log_pi.as_detached_tensor(),
+            &self.log_global_scaling.as_detached_tensor().exp().unwrap(),
+            self.substitution_model,
+        )
+    }
+
+    pub fn save_npz(&self, path: &Path) {
+        let Mu = Mu(&self.log_R.as_detached_tensor());
+        let pi = softmax(&self.log_pi.as_detached_tensor(), 1).unwrap();
+
+        Tensor::write_npz(
+            &[
+                ("Mu", &Mu),
+                ("pi", &pi),
+                (
+                    "global_scaling",
+                    &self.log_global_scaling.as_detached_tensor(),
+                ),
+                ("init_log_pi", &self.init_log_pi),
+                ("init_log_R", &self.init_log_R),
+                (
+                    "log_branch_length_scaling",
+                    &self.log_branch_length_scaling.as_detached_tensor(),
+                ),
+            ],
+            path,
+        )
+        .unwrap();
+    }
+}
+
+impl Optimizable for ModelParameters {
+    fn variables(&self) -> Vec<Var> {
+        let mut vars = vec![
+            self.log_R.clone(),
+            self.log_pi.clone(),
+            self.log_global_scaling.clone(),
+            self.log_branch_length_scaling.clone(),
+        ];
+        vars.extend(self.rate_parameters.variables());
+        vars
+    }
+
+    fn likelihood(&self) -> Tensor {
+        let Mu = Mu(&self.log_R);
+
+        let log_branch_length_scaling = self
+            .log_branch_length_scaling
+            .broadcast_sub(&self.log_branch_length_scaling.mean(0).unwrap())
+            .unwrap();
+
+        let log_branch_lengths = (&self.init_log_branch_lengths + log_branch_length_scaling)
+            .unwrap()
+            .broadcast_add(&self.log_global_scaling)
+            .unwrap();
+
+        self.rate_parameters.likelihood(
+            self.felsenstein_op.clone(),
+            &Mu,
+            &self.log_pi,
+            self.substitution_model,
+            true,
+            &log_branch_lengths,
+        )
+    }
+
+    fn penalty(&self) -> Tensor {
+        let pi_penalty = self
+            .init_log_pi
+            .sub(&self.log_pi)
+            .unwrap()
+            .powf(2.0)
+            .unwrap()
+            .sum_all()
+            .unwrap();
+        let pi_penalty = (pi_penalty * self.pi_reg).unwrap();
+
+        fn log_Mu(log_R: &Tensor) -> Tensor {
+            let Mu = Mu(log_R);
+
+            // One out the diagonal, since we only want to penalize the off-diagonal elements
+            let Mu = (&Mu
+                - (&Mu - 1.0).unwrap()
+                    * Tensor::eye(20, candle_core::DType::F64, &candle_core::Device::Cpu).unwrap())
+            .unwrap();
+
+            return Mu.log().unwrap();
+        }
+
+        let Mu = log_Mu(&self.log_R)
+            .sub(&log_Mu(&self.init_log_R))
+            .unwrap()
+            .powf(2.0)
+            .unwrap()
+            .sum_all()
+            .unwrap();
+        let R_penalty = (Mu * self.R_reg).unwrap();
+
+        let branch_penalty = self
+            .log_branch_length_scaling
+            .powf(2.0)
+            .unwrap()
+            .sum_all()
+            .unwrap()
+            * self.branch_length_penalty;
+
+        (pi_penalty + R_penalty + branch_penalty.unwrap() + self.rate_parameters.penalty()).unwrap()
+    }
+
+    fn print_state(&self) {
+        println!(
+            "global_scaling: {}",
+            self.log_global_scaling
+                .exp()
+                .unwrap()
+                .to_scalar::<f64>()
+                .unwrap()
+        );
+        match &self.rate_parameters {
+            RateParameters::G(num_cat, alpha) if *num_cat > 1 => {
+                println!("alpha: {}", alpha.to_scalar::<f64>().unwrap())
+            }
+            RateParameters::G(_, _) => {}
+            RateParameters::R(log_rate_cat, log_rate_weights) => {
+                let (categories, log_weights) = normalize_rate_cat(
+                    &log_rate_cat.as_detached_tensor(),
+                    &log_rate_weights.as_detached_tensor(),
+                );
+                let weights = log_weights.exp().unwrap();
+                println!("Rate categories: {}", categories);
+                println!("Rate category weights: {}", weights);
+            }
+            RateParameters::X(site_rate_var, _, site_model) => {
+                let rates = site_model.rates_from_parameters(site_rate_var);
+                let histogram = histogram(&rates, 10);
+                println!("Site rate bounds: {}", histogram.0);
+                println!("Site rate counts: {}", histogram.1);
+            }
+        }
+    }
+}
+
+fn optimize(
+    model: &impl Optimizable,
+    min_iterations: usize,
+    max_iterations: usize,
+    min_rel_improvement: f64,
+    no_improve_patience: usize,
+    verbosity: Verbosity,
+) {
+    let variables = model.variables();
+    let mut opt = candle_nn::optim::AdamW::new_lr(variables, 0.05).unwrap();
+    let parameter = candle_nn::optim::ParamsAdamW {
+        lr: 0.05,
+        weight_decay: 0.0,
+        ..Default::default()
+    };
+    opt.set_params(parameter);
+
+    let mut prev_opt = f64::INFINITY;
+    let mut no_improve_count = 0;
+
+    for iteration in 0.. {
+        let neg_likelihood = model.likelihood().neg().unwrap();
+        let penalty = model.penalty();
+        let opt_fn = (&neg_likelihood + &penalty).unwrap();
+
+        let current_opt = opt_fn.to_scalar::<f64>().unwrap();
+        if verbosity.should_print(Verbosity::Med) {
+            println!(
+                "Iteration {}: neg Loglikelihood {:.3}, Optfn {:.3}",
+                iteration,
+                neg_likelihood.to_scalar::<f64>().unwrap(),
+                current_opt
+            );
+        }
+
+        model.print_state();
+        let grads = opt_fn.backward().unwrap();
+        opt.step(&grads).unwrap();
+
+        if iteration > min_iterations {
+            let rel_improvement = (prev_opt - current_opt) / prev_opt.abs().max(1e-12);
+            if rel_improvement > min_rel_improvement {
+                no_improve_count = 0;
+            } else {
+                no_improve_count += 1;
+            }
+            if no_improve_count >= no_improve_patience {
+                println!(
+                    "Stopping at iteration {} (relative loss improvement {:.2e} <= {:.2e} for {} consecutive iterations)",
+                    iteration, rel_improvement, min_rel_improvement, no_improve_patience
+                );
+                break;
+            }
+        }
+
+        if iteration > max_iterations {
+            println!("Reached maximum iterations ({})", max_iterations);
+            break;
+        }
+
+        prev_opt = current_opt;
+    }
+}
+
+pub fn optimize_global_scaling_alpha(
+    felsenstein_op: FelsensteinWithEdgeOp,
+    log_pi: &Tensor,
+    R: &Tensor,
+    log_branch_lengths: &Tensor,
+    branch_length_penalty: f64,
+    verbosity: Verbosity,
+) -> (Tensor, Tensor, Tensor) {
+    let var_log_global_scaling = Var::from_tensor(&tensor_full(0.0, &[])).unwrap();
+    let var_alpha = Var::from_tensor(&tensor_full(1.0, &[])).unwrap();
+    let var_log_branch_length_scaling =
+        Var::from_tensor(&tensor_full(0.0, log_branch_lengths.dims())).unwrap();
+
+    let model = AlphaAndScalingParameters {
+        felsenstein_op,
+        log_global_scaling: var_log_global_scaling,
+        R: R.detach(),
+        log_pi: log_pi.detach(),
+        init_log_branch_lengths: log_branch_lengths.detach(),
+        log_branch_length_scaling: var_log_branch_length_scaling,
+        rate_model: RateParameters::G(1, var_alpha),
+        branch_length_penalty,
+    };
+
+    optimize(&model, 10, 100, 1e-5, 5, verbosity);
+
+    let alpha = if let RateParameters::G(_, alpha) = model.rate_model {
+        alpha
+    } else {
+        panic!("Expected gamma rate model.");
+    };
+
+    return (
+        model.log_global_scaling.as_detached_tensor(),
+        alpha.as_detached_tensor(),
+        model.log_branch_length_scaling.as_detached_tensor(),
+    );
+}
+
+pub fn two_step_light_pmsf(
+    felsenstein_op: FelsensteinOp,
+    categories: &[[f64; 20]],
+    weights: &[f64],
+    f_class: &[f64; 20],
+    log_branch_lengths: &Tensor,
+    mutsel_params: &super::MutselParams,
+    verbosity: Verbosity,
+) -> (Tensor, f64, f64, Tensor) {
+    let step1_site_freq = light_pmsf(
+        felsenstein_op.into_with_edge_op(),
+        categories,
+        weights,
+        1.0,
+        log_branch_lengths,
+        f_class,
+    );
+
+    let Mu = loadMu();
+
+    let log_pi = step1_site_freq.log().unwrap();
+
+    let (step2_log_global_scaling, step2_alpha, step2_log_branch_length_scaling) =
+        optimize_global_scaling_alpha(
+            felsenstein_op.into_with_edge_op(),
+            &log_pi,
+            &Mu,
+            log_branch_lengths,
+            mutsel_params.branch_reg,
+            verbosity,
+        );
+
+    let final_site_freq = light_pmsf(
+        felsenstein_op.into_with_edge_op(),
+        categories,
+        weights,
+        step2_alpha.to_scalar::<f64>().unwrap(),
+        &(log_branch_lengths + &step2_log_branch_length_scaling)
+            .unwrap()
+            .broadcast_add(&step2_log_global_scaling)
+            .unwrap(),
+        f_class,
+    );
+
+    (
+        final_site_freq,
+        step2_log_global_scaling.to_scalar::<f64>().unwrap(),
+        step2_alpha.to_scalar::<f64>().unwrap(),
+        step2_log_branch_length_scaling,
+    )
+}
+
+pub fn light_pmsf(
+    felsenstein_op: FelsensteinWithEdgeOp,
+    categories: &[[f64; 20]],
+    weights: &[f64],
+    alpha: f64,
+    log_branch_lengths: &Tensor,
+    f_class: &[f64; 20],
+) -> Tensor {
+    let mut likelihoods = vec![];
+
+    let Mu = loadMu();
+
+    let rate_model = RateParameters::gamma(1, alpha);
+
+    for category in iter::once(f_class).chain(categories.iter()) {
+        let category_tensor =
+            Tensor::from_vec(category.to_vec(), &[20], &candle_core::Device::Cpu).unwrap();
+        let log_pi = category_tensor.log().unwrap().unsqueeze(0).unwrap();
+
+        likelihoods.push(rate_model.likelihood_per_site(
+            felsenstein_op.clone(),
+            &Mu,
+            &log_pi,
+            SubstitutionModel::MutSel,
+            false,
+            log_branch_lengths,
+        ));
+    }
+
+    let likelihoods = Tensor::stack(&likelihoods, 0).unwrap();
+    let weights_tensor =
+        Tensor::from_slice(&weights, &[weights.len()], &candle_core::Device::Cpu).unwrap();
+    let log_weights_tensor = weights_tensor.log().unwrap().unsqueeze(1).unwrap();
+
+    let weighted_likelihoods = (likelihoods.broadcast_add(&log_weights_tensor)).unwrap();
+
+    let posteriors = candle_nn::ops::softmax(&weighted_likelihoods, 0).unwrap();
+
+    let category_tensor = Tensor::from_vec(
+        iter::once(f_class)
+            .chain(categories.iter())
+            .flatten()
+            .copied()
+            .collect(),
+        &[categories.len() + 1, 20],
+        &candle_core::Device::Cpu,
+    )
+    .unwrap();
+
+    let site_freq = posteriors.t().unwrap().matmul(&category_tensor).unwrap();
+
+    site_freq
+}
+
+/// Calculates the mutation rate matrix from the log_R variable. This is a lower triangular matrix with the exchanabilities and the equilibirum in the diagonal. Both as in log space.
+/// Returns Mut and the equilibrium frequencies in the diagonal. (not log space)
+pub fn Mu(log_parameter: &Tensor) -> Tensor {
+    let parameter = log_parameter.exp().unwrap();
+    let diagonal = (&parameter
+        * Tensor::eye(20, candle_core::DType::F64, &candle_core::Device::Cpu).unwrap())
+    .unwrap();
+    let off_diagonal = (parameter - &diagonal).unwrap();
+
+    let pi = diagonal
+        .broadcast_div(&diagonal.sum_all().unwrap())
+        .unwrap();
+
+    let R = (&off_diagonal + off_diagonal.t().unwrap()).unwrap();
+
+    let Q = R.matmul(&pi).unwrap();
+
+    let Q = (&Q
+        - &Q * Tensor::eye(20, candle_core::DType::F64, &candle_core::Device::Cpu).unwrap())
+    .unwrap();
+
+    let row_sum = Q.sum(1).unwrap();
+    let pi_vec = pi.sum(1).unwrap();
+    let sum = row_sum.dot(&pi_vec).unwrap();
+    let Q = Q.broadcast_div(&sum).unwrap();
+
+    // This has one expected mutation per unit time. The guide tree will be more in the regime of 1 substitution.
+    // So we mutlpiphy with 20. Exact factor is fitted later. We also divide with 8 which is emprically close to the optimum.
+    // (This does depend on the protein and how many columns are under strong selection)
+
+    let Q = (Q * (20.0 / 12.0)).unwrap();
+
+    // diagonal is zero here, but they are not used anyway
+    (Q + pi).unwrap()
+}
+
+// Used with the MutSel model.
+fn loadMu() -> Tensor {
+    let R_lower = crate::data::load_lower_R_with_equi(crate::data::CODON2_TXT);
+    let log_R = R_lower.log().unwrap();
+    Mu(&log_R)
+}
+
+/// Returns the optimal S, sqrt_pi and rate parameters.
+/// S: [L, 20, 20], sqrt_pi: [L, 20]
+/// rate parameters is either alpha shape: [1] or [2 * num_cat] for free rate model (first num_cat weights, second num_cat are rates)
+pub fn optimize_internal(
+    felsenstein: FelsensteinTree<20>,
+    distances: &[f64],
+    aa_dist: Tensor,
+    mutsel_params: super::MutselParams,
+    rate_model: RateModel,
+    prior_R_file: Option<&Path>,
+    prior_pi_file: Option<&Path>,
+    substitution_model: SubstitutionModel,
+    verbosity: Verbosity,
+    out_prefix: &str,
+) -> Result<(Tensor, Tensor, Tensor, Vec<f64>), candle_core::Error> {
+    let op = felsenstein::FelsensteinOp::new(Arc::new(Mutex::new(felsenstein)));
+
+    // 0.5 psuedo counts
+    let aa_dist = (aa_dist + 0.5).unwrap();
+
+    // Lower triangular matrix with zeros everywhere else
+    let init_R = if let Some(prior_R_file) = prior_R_file {
+        let file_content = std::fs::read_to_string(prior_R_file)?;
+        crate::data::load_lower_R_with_equi(&file_content)
+    } else {
+        crate::data::load_lower_R_with_equi(crate::data::CODON2_TXT)
+    };
+
+    let log_branch_lengths =
+        Tensor::from_slice(distances, &[distances.len()], &candle_core::Device::Cpu)?.log()?;
+
+    let mut var_log_global_scaling = 0.0;
+    let mut var_alpha = 1.0;
+    let var_log_branch_length_scaling =
+        Var::from_tensor(&tensor_full(0.0, log_branch_lengths.dims())).unwrap();
+
+    let site_freq = if let Some(prior_pi_file) = prior_pi_file {
+        println!(
+            "Using prior site frequencies from file: {:?}",
+            prior_pi_file
+        );
+        crate::io::read_sitefreq_file(prior_pi_file)
+    } else {
+        // Do our lightweight PMSF procedure for the site_freq prior:
+        let f_class_weight = 0.1;
+
+        let weights = iter::once(f_class_weight)
+            .chain(
+                crate::data::UDM256_WEIGHTS
+                    .iter()
+                    .map(|w| w * (1.0 - f_class_weight)),
+            )
+            .collect::<Vec<f64>>();
+
+        let f_class = aa_dist
+            .sum(0)?
+            .broadcast_div(&aa_dist.sum_all()?.unsqueeze(0)?)?;
+        let f_class: [f64; 20] = f_class.to_vec1()?.try_into().unwrap();
+
+        let (site_freq, global_scaling, alpha, log_branch_length_scaling) = two_step_light_pmsf(
+            op.clone(),
+            crate::data::UDM256,
+            &weights,
+            &f_class,
+            &log_branch_lengths,
+            &mutsel_params,
+            verbosity
+        );
+        var_log_global_scaling = global_scaling;
+        var_alpha = alpha;
+        var_log_branch_length_scaling
+            .set(&log_branch_length_scaling)
+            .unwrap();
+
+        site_freq
+    };
+
+    // Variable which gets optimized
+    let log_R = Var::from_tensor(&init_R.log()?)?;
+    let init_log_pi = site_freq.log()?;
+    let log_pi = Var::from_tensor(&init_log_pi)?;
+    let num_sites = site_freq.dims()[0];
+
+    let init_log_R = log_R.detach().copy().unwrap();
+    let init_log_pi = log_pi.detach().copy().unwrap();
+
+    let model = ModelParameters {
+        felsenstein_op: op.into_with_edge_op(),
+        log_R,
+        log_pi,
+        log_global_scaling: Var::from_tensor(&tensor_full(var_log_global_scaling, &[]))?,
+        log_branch_length_scaling: var_log_branch_length_scaling,
+        init_log_branch_lengths: log_branch_lengths.detach(),
+        rate_parameters: RateParameters::init(num_sites, rate_model, var_alpha),
+        pi_reg: mutsel_params.pi_reg,
+        R_reg: mutsel_params.Mu_reg,
+        branch_length_penalty: mutsel_params.branch_reg,
+        init_log_R,
+        init_log_pi,
+        substitution_model,
+    };
+
+    optimize(&model, 100, 500, 1e-5, 5, verbosity);
+
+    let (S, sqrt_pi) = model.calc_rate_matrix();
+    let rate_para = model.rate_parameters.parameters_for_iqtree();
+
+    let substitution_rates = model::substitution_rates(&S, &sqrt_pi);
+
+    let average_rate = substitution_rates.iter().sum::<f64>() / substitution_rates.len() as f64;
+    if verbosity.should_print(Verbosity::Min) {
+        println!("Average substitution rate: {:.3}", average_rate);
+        model.save_npz(Path::new(&format!("{}.mutsel.npz", out_prefix)));
+    }
+
+    let S = S.broadcast_div(&tensor_full(average_rate, &[])).unwrap();
+
+    Ok((S, sqrt_pi, rate_para, substitution_rates))
+}
+
+// Outputs categories and log_weights
+fn normalize_rate_cat(log_rate_cat: &Tensor, log_rate_weights: &Tensor) -> (Tensor, Tensor) {
+    let log_weights = candle_nn::ops::log_softmax(&log_rate_weights, 0).unwrap();
+    let log_sum = (log_weights.add(&log_rate_cat))
+        .unwrap()
+        .log_sum_exp(0)
+        .unwrap();
+    let categories = (log_rate_cat.broadcast_sub(&log_sum))
+        .unwrap()
+        .exp()
+        .unwrap();
+    (categories, log_weights)
+}
diff --git a/mutsel_rust/src/utils.rs b/mutsel_rust/src/utils.rs
new file mode 100644
index 000000000..1339b4515
--- /dev/null
+++ b/mutsel_rust/src/utils.rs
@@ -0,0 +1,138 @@
+use candle_core::Tensor;
+
+pub fn tensor_full(value: f64, dims: &[usize]) -> Tensor {
+    Tensor::full(value, dims, &candle_core::Device::Cpu).unwrap()
+}
+
+fn histogram_with_edges(values: &[f64], bin_edges: Vec<f64>) -> (Tensor, Tensor) {
+    let num_bins = bin_edges.len() - 1;
+    let device = &candle_core::Device::Cpu;
+    let mut counts = vec![0i64; num_bins];
+
+    for &value in values {
+        // Binary search for the bin: right-inclusive on the last bin
+        let idx = bin_edges.partition_point(|&e| e <= value).saturating_sub(1);
+        let idx = idx.min(num_bins - 1);
+        counts[idx] += 1;
+    }
+
+    let bin_edges = Tensor::from_vec(bin_edges, &[num_bins + 1], device).unwrap();
+    let counts = Tensor::from_vec(counts, &[num_bins], device).unwrap();
+    (bin_edges, counts)
+}
+
+/// Linear-spaced histogram.
+pub fn histogram(data: &Tensor, num_bins: usize) -> (Tensor, Tensor) {
+    assert!(num_bins > 0, "histogram requires at least one bin");
+
+    let values = data.flatten_all().unwrap().to_vec1::<f64>().unwrap();
+    assert!(!values.is_empty(), "histogram requires at least one value");
+
+    let min = values.iter().copied().fold(f64::INFINITY, f64::min);
+    let max = values.iter().copied().fold(f64::NEG_INFINITY, f64::max);
+
+    if min == max {
+        let device = &candle_core::Device::Cpu;
+        let mut counts = vec![0i64; num_bins];
+        counts[0] = values.len() as i64;
+        let edges = Tensor::from_vec(vec![min; num_bins + 1], &[num_bins + 1], device).unwrap();
+        let counts = Tensor::from_vec(counts, &[num_bins], device).unwrap();
+        return (edges, counts);
+    }
+
+    let width = (max - min) / num_bins as f64;
+    let bin_edges = (0..=num_bins)
+        .map(|i| min + i as f64 * width)
+        .collect::<Vec<f64>>();
+
+    histogram_with_edges(&values, bin_edges)
+}
+
+/// Log-spaced histogram. All values must be positive.
+pub fn _histogram_log(data: &Tensor, num_bins: usize) -> (Tensor, Tensor) {
+    assert!(num_bins > 0, "histogram_log requires at least one bin");
+
+    let values = data.flatten_all().unwrap().to_vec1::<f64>().unwrap();
+    assert!(
+        !values.is_empty(),
+        "histogram_log requires at least one value"
+    );
+    assert!(
+        values.iter().all(|&v| v > 0.0),
+        "histogram_log requires all values to be positive"
+    );
+
+    let log_min = values
+        .iter()
+        .copied()
+        .map(f64::ln)
+        .fold(f64::INFINITY, f64::min);
+    let log_max = values
+        .iter()
+        .copied()
+        .map(f64::ln)
+        .fold(f64::NEG_INFINITY, f64::max);
+
+    if log_min == log_max {
+        let device = &candle_core::Device::Cpu;
+        let mut counts = vec![0i64; num_bins];
+        counts[0] = values.len() as i64;
+        let v = log_min.exp();
+        let edges = Tensor::from_vec(vec![v; num_bins + 1], &[num_bins + 1], device).unwrap();
+        let counts = Tensor::from_vec(counts, &[num_bins], device).unwrap();
+        return (edges, counts);
+    }
+
+    let log_width = (log_max - log_min) / num_bins as f64;
+    let bin_edges = (0..=num_bins)
+        .map(|i| (log_min + i as f64 * log_width).exp())
+        .collect::<Vec<f64>>();
+
+    histogram_with_edges(&values, bin_edges)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn histogram_counts_values_in_expected_bins() {
+        let data =
+            Tensor::from_vec(vec![0.0, 0.2, 0.8, 1.0], &[4], &candle_core::Device::Cpu).unwrap();
+
+        let (edges, counts) = histogram(&data, 2);
+
+        assert_eq!(edges.to_vec1::<f64>().unwrap(), vec![0.0, 0.5, 1.0]);
+        assert_eq!(counts.to_vec1::<i64>().unwrap(), vec![2, 2]);
+    }
+
+    #[test]
+    fn histogram_handles_constant_input() {
+        let data = Tensor::from_vec(vec![3.0, 3.0, 3.0], &[3], &candle_core::Device::Cpu).unwrap();
+
+        let (edges, counts) = histogram(&data, 3);
+
+        assert_eq!(edges.to_vec1::<f64>().unwrap(), vec![3.0, 3.0, 3.0, 3.0]);
+        assert_eq!(counts.to_vec1::<i64>().unwrap(), vec![3, 0, 0]);
+    }
+
+    #[test]
+    fn histogram_log_spans_decades() {
+        // Values spanning 3 decades: 0.1, 1, 10, 100
+        let data =
+            Tensor::from_vec(vec![0.1, 1.0, 10.0, 100.0], &[4], &candle_core::Device::Cpu).unwrap();
+
+        let (edges, counts) = _histogram_log(&data, 3);
+
+        let edges_v = edges.to_vec1::<f64>().unwrap();
+        let counts_v = counts.to_vec1::<i64>().unwrap();
+
+        // 4 edges spanning [0.1, 100] in 3 log-equal steps
+        assert_eq!(edges_v.len(), 4);
+        assert!((edges_v[0] - 0.1).abs() < 1e-10);
+        assert!((edges_v[3] - 100.0).abs() < 1e-10);
+
+        // All 4 values should be counted
+        assert_eq!(counts_v.iter().sum::<i64>(), 4);
+    }
+}
diff --git a/pll/pllInternal.h b/pll/pllInternal.h
index a32d5c832..811f70734 100644
--- a/pll/pllInternal.h
+++ b/pll/pllInternal.h
@@ -147,7 +147,6 @@ extern void initRateMatrix(pllInstance *tr, partitionList *pr);
 extern void bitVectorInitravSpecial(unsigned int **bitVectors, nodeptr p, int numsp, unsigned int vectorLength, pllHashTable *h, int treeNumber, int function, branchInfo *bInf,
                                     int *countBranches, int treeVectorLength, pllBoolean traverseOnly, pllBoolean computeWRF, int processID);
 extern  unsigned int bitcount_32_bit(unsigned int i);
-extern __inline unsigned int bitcount_64_bit(uint64_t i);
 extern void perSiteLogLikelihoods(pllInstance *tr, partitionList *pr, double *logLikelihoods);
 extern void updatePerSiteRates(pllInstance *tr, partitionList *pr, pllBoolean scaleRates);
 extern void restart(pllInstance *tr, partitionList *pr);
diff --git a/test_scripts/test_data/expect_ans.txt b/test_scripts/test_data/expect_ans.txt
index 0a3c8d70a..9a88ea0bb 100644
--- a/test_scripts/test_data/expect_ans.txt
+++ b/test_scripts/test_data/expect_ans.txt
@@ -19,4 +19,5 @@ turtle_aa.nex.constr2.iqtree	Log-likelihood of the tree	-5029.4460	1
 turtle_aa.nex.iqtree	Log-likelihood of the tree	-5027.9688	1
 turtle_aa.test.iqtree	Log-likelihood of the tree	-5039.6498	1
 turtle_aa.wpl.iqtree	Log-likelihood of the tree	-5030.7986	1
-turtle_aa.mix.iqtree	Log-likelihood of the tree	-5212.5728	1
\ No newline at end of file
+turtle_aa.mix.iqtree	Log-likelihood of the tree	-5212.5728	1
+turtle_aa.mutsel.iqtree	Log-likelihood of the tree	-3547.550	1
\ No newline at end of file
diff --git a/test_scripts/test_data/turtle_aa.newick b/test_scripts/test_data/turtle_aa.newick
new file mode 100644
index 000000000..9bbc881bc
--- /dev/null
+++ b/test_scripts/test_data/turtle_aa.newick
@@ -0,0 +1 @@
+(Anolis:0.0543205734,(((((Gallus:0.0014359175,Taeniopygia:0.0133014847):0.0142834569,(((caretta:0.0161674188,chelonoidis_nigra:0.0052946560):0.0022096696,emys_orbicularis:0.0034233568):0.0083672035,phrynops:0.0209840768):0.0154702718):0.0043509501,(alligator:0.0000010000,caiman:0.0000010000):0.0161212459):0.0071034575,(((Homo:0.0322675822,Monodelphis:0.0143707730):0.0161409179,Ornithorhynchus:0.0739073357):0.0290482411,(Xenopus:0.1314721565,protopterus:0.1210330699):0.0354509879):0.0125965752):0.0171189889,python:0.0329330642):0.0052979455,podarcis:0.0112010029);
diff --git a/test_scripts/test_iqtree.ps1 b/test_scripts/test_iqtree.ps1
index 78f58e0fb..6e7f2fa70 100755
--- a/test_scripts/test_iqtree.ps1
+++ b/test_scripts/test_iqtree.ps1
@@ -122,3 +122,5 @@ Measure-IQTree "$IQTreeBin -s $WD/turtle_aa.fasta -m `"MIX{LG+F,WAG+F}`" --prefi
 Measure-IQTree "$IQTreeBin -s $WD/turtle_aa.fasta -p $WD/turtle_aa.nex -g $WD/turtle.constr.tree --prefix $OutDir/turtle_aa.nex.constr -T 1 -seed $SEED"
 
 Measure-IQTree "$IQTreeBin -s $WD/turtle_aa.fasta -p $WD/turtle_aa.nex -g $WD/turtle.constr.tree2 -B 1000 -alrt 1000 --prefix $OutDir/turtle_aa.nex.constr2 -T 1 -seed $SEED"
+
+Measure-IQTree "$IQTreeBin -s $WD/turtle_aa.fasta -m MUTSEL -ft AUTO --prefix $OutDir/turtle_aa.mutsel -T 1 -seed $SEED"
diff --git a/test_scripts/test_iqtree.sh b/test_scripts/test_iqtree.sh
index d87057d71..1d9a11d09 100755
--- a/test_scripts/test_iqtree.sh
+++ b/test_scripts/test_iqtree.sh
@@ -118,3 +118,5 @@ run_timed ${IQTREE_BIN} -s $AA_FASTA -m "MIX{LG+F,WAG+F}" --prefix ${OUT_DIR}/tu
 run_timed ${IQTREE_BIN} -s $AA_FASTA -p $AA_NEX -g ${WD}/turtle.constr.tree --prefix ${OUT_DIR}/turtle_aa.nex.constr -T 1 -seed $SEED
 
 run_timed ${IQTREE_BIN} -s $AA_FASTA -p $AA_NEX -g ${WD}/turtle.constr.tree2 -B 1000 -alrt 1000 --prefix ${OUT_DIR}/turtle_aa.nex.constr2 -T 1 -seed $SEED
+
+run_timed ${IQTREE_BIN} -s $AA_FASTA -m "MUTSEL" -ft AUTO --prefix ${OUT_DIR}/turtle_aa.mutsel -T 1 -seed $SEED
\ No newline at end of file
diff --git a/utils/CMakeLists.txt b/utils/CMakeLists.txt
index 46d922b9c..75888b3ae 100644
--- a/utils/CMakeLists.txt
+++ b/utils/CMakeLists.txt
@@ -13,8 +13,18 @@ progress.cpp progress.h
 timeutil.h hammingdistance.h
 operatingsystem.cpp operatingsystem.h
 heapsort.h
+mutsel_wrapper.cpp mutsel_wrapper.h
+self_process.h
 )
 
+if (USE_MUTSEL STREQUAL "ON")
+    add_dependencies(utils mutsel)
+    target_link_libraries(utils "${MUTSEL_RUST_LIB_PATH}")
+    if (WIN32)
+        target_link_libraries(utils ntdll userenv bcrypt ws2_32)
+    endif()
+endif()
+
 if(ZLIB_FOUND)
   target_link_libraries(utils ${ZLIB_LIBRARIES})
 else(ZLIB_FOUND)
diff --git a/utils/mutsel_wrapper.cpp b/utils/mutsel_wrapper.cpp
new file mode 100644
index 000000000..29aa07bf9
--- /dev/null
+++ b/utils/mutsel_wrapper.cpp
@@ -0,0 +1,487 @@
+// C++ wrapper for the mutsel rust library
+
+#include "mutsel_wrapper.h"
+
+#if !defined(USE_MUTSEL)
+void rust_mutsel(int32_t *parents,
+                 double *branch_lengths,
+                 uint8_t *alignment,
+                 uint32_t site_num,
+                 uint32_t leave_num,
+                 uint32_t node_num,
+                 const char *model_string,
+                 const char *priorMuFile,
+                 const char *priorPiFile,
+                 uint8_t verbose,
+                 double *out_site_freq,
+                 double *out_R_matrices,
+                 const char *output_prefix)
+{
+    std::cout << "Mutsel support not compiled in!" << std::endl;
+    exit(1);
+}
+void rust_set_rayon_threads(int32_t num_threads)
+{
+    return;
+}
+#endif
+
+std::pair<std::vector<double>, std::vector<int32_t>> prepare_mutsel_tree(MTree *orig_tree)
+{
+    // Copy tree
+
+    MTree *tree = new MTree(*orig_tree);
+
+    if (tree->rooted)
+    {
+        tree->convertToUnrooted();
+    }
+
+    std::vector<double> branch_lengths;
+    std::vector<int32_t> parent_indices;
+
+    auto num_nodes = tree->nodeNum;
+
+    branch_lengths.resize(num_nodes);
+    parent_indices.resize(num_nodes);
+
+    auto orig_root = tree->root;
+    ASSERT(orig_root->isLeaf());
+
+    auto root = orig_root->neighbors[0]->node;
+
+    std::vector<std::pair<Node *, Node *>> stack;
+    stack.push_back({root, nullptr});
+
+    branch_lengths.at(root->id) = 0.0; // root branch length
+    parent_indices.at(root->id) = -1;  // root has no parent
+
+    while (!stack.empty())
+    {
+        Node *node = stack.back().first;
+        Node *dad = stack.back().second;
+        stack.pop_back();
+
+        for (auto nei : node->neighbors)
+        {
+            if (dad != nullptr && nei->node->id == dad->id)
+            {
+                continue;
+            }
+            Node *child = nei->node;
+
+            if (nei->length < 0.0)
+            {
+                throw std::runtime_error("The guide Tree for MUTSEL needs to have branchlengths. Please provide a tree with branch lengths.");
+            }
+
+            branch_lengths.at(child->id) = nei->length;
+            parent_indices.at(child->id) = node->id;
+
+            stack.push_back({child, node});
+        }
+    }
+
+    delete tree;
+
+    return {std::move(branch_lengths), std::move(parent_indices)};
+}
+
+// Returns the alignment in the format required by mutsel library as dense [L, N] matrix and returns L the sequence length
+std::tuple<std::vector<uint8_t>, int32_t, int32_t> prepare_mutsel_alignment(Alignment *alignment)
+{
+    // [L, N] matrix where L is sequence length and N is number of sequences
+    std::vector<uint8_t> sequences;
+    size_t L = alignment->getNSite();
+    size_t N = alignment->getNSeq();
+
+    std::cout << "Preparing alignment for mutsel inference: " << N << " sequences, " << L << " sites" << std::endl;
+
+    sequences.resize(L * N);
+
+    for (size_t site = 0; site < L; ++site)
+    {
+        Pattern &pat = alignment->at(alignment->getPatternID(site));
+        for (size_t seq_idx = 0; seq_idx < N; ++seq_idx)
+        {
+            auto state = static_cast<uint8_t>(pat.at(seq_idx));
+            if (!(state < 20))
+            {
+                // map unknown states to gaps (state 20)
+                state = 20;
+            }
+            sequences[site * N + seq_idx] = state;
+        }
+    }
+
+    return std::make_tuple(std::move(sequences), static_cast<int32_t>(L), static_cast<int32_t>(N));
+}
+
+std::string read_binary_site_model_file_internal(std::string &filename, std::vector<double> &site_freq, std::vector<double> &rate_matrices, std::vector<int> &site_model)
+{
+    cout << endl
+         << "Reading site-specific model file " << filename << " ..." << endl;
+
+    site_freq.clear();
+    site_model.clear();
+    rate_matrices.clear();
+
+    std::ifstream in;
+    std::string rate_model_string;
+
+    // assert little-endian
+    uint16_t num = 1;
+    if (*((uint8_t *)&num) != 1)
+    {
+        throw std::runtime_error("Only little-endian machine is supported for reading binary site model file");
+    }
+
+    try
+    {
+        in.open(filename, std::ios::binary);
+        if (!in.is_open())
+        {
+            throw std::runtime_error("Failed to open binary site model file");
+        }
+
+        auto read_exact = [&](char *buffer, std::streamsize size, const char *field_name)
+        {
+            in.read(buffer, size);
+            if (!in || in.gcount() != size)
+            {
+                throw std::runtime_error(std::string("Failed to read ") + field_name + " from binary site model file");
+            }
+        };
+
+        // Read in the model string. First 8 bytes little endian length of the string, followed by the string itself.
+        uint64_t rate_model_string_length;
+        read_exact(reinterpret_cast<char *>(&rate_model_string_length), sizeof(uint64_t), "rate model string length");
+
+        std::vector<char> rate_model_string_buf(rate_model_string_length);
+        if (rate_model_string_length > 0)
+        {
+            read_exact(rate_model_string_buf.data(), static_cast<std::streamsize>(rate_model_string_length), "rate model string");
+        }
+        rate_model_string = std::string(rate_model_string_buf.data(), rate_model_string_length);
+
+        // Read number of sites. 8 bytes
+
+        uint64_t num_sites;
+        read_exact(reinterpret_cast<char *>(&num_sites), sizeof(uint64_t), "number of sites");
+
+        // num_sites * 20 doubles for site frequencies
+        site_freq.resize(num_sites * 20);
+        read_exact(reinterpret_cast<char *>(site_freq.data()),
+                   static_cast<std::streamsize>(num_sites * 20 * sizeof(double)),
+                   "site frequencies");
+
+        // num_sites * 190 doubles for rate matrices
+        rate_matrices.resize(num_sites * 190);
+        read_exact(reinterpret_cast<char *>(rate_matrices.data()),
+                   static_cast<std::streamsize>(num_sites * 190 * sizeof(double)),
+                   "rate matrices");
+
+        for (size_t i = 0; i < num_sites; ++i)
+        {
+            site_model.push_back(i);
+            for (int j = 0; j < 20; ++j)
+            {
+                if (site_freq[i * 20 + j] <= 1e-10)
+                    throw std::runtime_error("Frequencies must be strictly bigger than 1e-10");
+            }
+            double sum = 0;
+            for (int j = 0; j < 20; ++j)
+            {
+                sum += site_freq[i * 20 + j];
+            }
+            if (std::abs(sum - 1.0) > 1e-4)
+            {
+                std::cout << "Warning: frequencies for site " << i + 1 << " do not sum to 1, normalizing..." << std::endl;
+                for (int j = 0; j < 20; ++j)
+                {
+                    site_freq[i * 20 + j] /= sum;
+                }
+            }
+            for (int j = 0; j < 190; ++j)
+            {
+                if (rate_matrices[i * 190 + j] <= 0.0)
+                    throw "Rate parameters must be positive";
+            }
+        }
+    }
+    catch (const std::exception &e)
+    {
+        throw std::runtime_error("Error reading site model file: " + std::string(e.what()));
+    }
+
+    return rate_model_string;
+}
+
+void write_site_models_to_alignment(Alignment &alignment, const double *site_freq, const double *rate_matrices, int len)
+{
+    alignment.ptn_state_freq.clear();
+    alignment.site_rate_matrices.clear();
+
+    size_t nsite = alignment.getNSite();
+    if (len != static_cast<int>(nsite))
+    {
+        throw std::runtime_error("Site model file site count does not match alignment length");
+    }
+
+    IntVector site_model(nsite, -1); // map each site to a model
+    IntVector pattern_first_site(alignment.getNPattern(), -1);
+    for (size_t site = 0; site < nsite; ++site)
+    {
+        if (pattern_first_site[alignment.getPatternID(site)] == -1)
+        {
+            pattern_first_site[alignment.getPatternID(site)] = static_cast<int>(site);
+        }
+    }
+
+    bool aln_changed = false;
+    ASSERT(alignment.num_states == 20); // currently we only support 20 states for mutsel model, so this function should only be called for protein alignments
+
+    vector<double *> models_freq;
+    vector<DoubleVector> models_rate;
+    for (size_t site = 0; site < nsite; ++site)
+    {
+        site_model[site] = models_freq.size();
+
+        const double *freq = site_freq + site * 20;
+        const double *rate_para = rate_matrices + site * 190;
+
+        bool add = true;
+        int first_site = pattern_first_site[alignment.getPatternID(site)];
+        if (first_site < static_cast<int>(site) && site_model[first_site] != -1)
+        {
+            int first_model = site_model[first_site];
+            bool matched_freq_and_rate = true;
+            for (int i = 0; i < 20; ++i)
+            {
+                if (freq[i] != models_freq[first_model][i])
+                {
+                    matched_freq_and_rate = false;
+                    break;
+                }
+            }
+            if (matched_freq_and_rate)
+            {
+                for (int i = 0; i < 190; ++i)
+                {
+                    if (rate_para[i] != models_rate[first_model][i])
+                    {
+                        matched_freq_and_rate = false;
+                        break;
+                    }
+                }
+            }
+
+            if (matched_freq_and_rate)
+            {
+                site_model[site] = first_model;
+                add = false;
+            }
+            else
+            {
+                aln_changed = true;
+            }
+        }
+
+        if (add)
+        {
+            double *site_freq_entry = new double[20];
+            memcpy(site_freq_entry, freq, sizeof(double) * 20);
+            models_freq.push_back(site_freq_entry);
+            models_rate.emplace_back(rate_para, rate_para + 190);
+        }
+    }
+
+    if (aln_changed)
+    {
+        cout << "Regrouping alignment sites..." << endl;
+        alignment.regroupSitePattern(site_model);
+        pattern_first_site = IntVector(alignment.getNPattern(), -1);
+        for (size_t site = 0; site < nsite; ++site)
+        {
+            if (pattern_first_site[alignment.getPatternID(site)] == -1)
+            {
+                pattern_first_site[alignment.getPatternID(site)] = static_cast<int>(site);
+            }
+        }
+    }
+
+    vector<bool> used_model(models_freq.size(), false);
+    for (size_t ptn = 0; ptn < alignment.getNPattern(); ++ptn)
+    {
+        int first_site = pattern_first_site[ptn];
+        int model_id = site_model[first_site];
+        used_model[model_id] = true;
+        alignment.ptn_state_freq.push_back(models_freq[model_id]);
+        alignment.site_rate_matrices.insert(
+            alignment.site_rate_matrices.end(),
+            models_rate[model_id].begin(),
+            models_rate[model_id].end());
+    }
+
+    for (size_t model_id = 0; model_id < models_freq.size(); ++model_id)
+    {
+        if (!used_model[model_id])
+        {
+            delete[] models_freq[model_id];
+        }
+    }
+
+    cout << models_freq.size() << " distinct per-site state frequency vectors detected" << endl;
+}
+
+void read_site_model_file(const std::string &filename, Alignment &alignment)
+{
+    auto site_freq = std::vector<double>();
+    auto rate_matrices = std::vector<double>();
+    auto site_model = std::vector<int>();
+    auto _custom_str = read_binary_site_model_file_internal(const_cast<std::string &>(filename), site_freq, rate_matrices, site_model);
+    write_site_models_to_alignment(alignment, site_freq.data(), rate_matrices.data(), site_model.size());
+    return;
+}
+
+void write_binary_site_model_file(const std::string &filename, Alignment &alignment)
+{
+    size_t nsites = alignment.getNSite();
+    size_t nstates = alignment.num_states;
+    ASSERT(nstates == 20);
+
+    try
+    {
+        ofstream out;
+        out.exceptions(ios::failbit | ios::badbit);
+        out.open(filename, std::ios::binary);
+        IntVector pattern_index;
+        alignment.getSitePatternIndex(pattern_index);
+
+        uint64_t custom_string_length = 6; // length of "UNUSED"
+        out.write(reinterpret_cast<const char *>(&custom_string_length), sizeof(uint64_t));
+        out.write("UNUSED", custom_string_length);
+
+        uint64_t num_sites = nsites;
+        out.write(reinterpret_cast<const char *>(&num_sites), sizeof(uint64_t));
+
+        for (size_t i = 0; i < nsites; ++i)
+        {
+            double *state_freq = alignment.ptn_state_freq[pattern_index[i]];
+            out.write(reinterpret_cast<const char *>(state_freq), 20 * sizeof(double));
+        }
+
+        for (size_t i = 0; i < nsites; ++i)
+        {
+            double *rate_para_ptr = alignment.site_rate_matrices.data() + pattern_index[i] * 190;
+            out.write(reinterpret_cast<const char *>(rate_para_ptr), 190 * sizeof(double));
+        }
+
+        cout << "Site mutsel model printed to " << filename << endl;
+    }
+    catch (ios::failure)
+    {
+        outError(ERR_WRITE_OUTPUT, filename);
+    }
+}
+
+DoubleVector computeMutselSiteRates(Alignment &alignment)
+{
+    ASSERT(alignment.num_states == 20);
+    ASSERT(alignment.ptn_state_freq.size() == alignment.getNPattern());
+    ASSERT(alignment.site_rate_matrices.size() == alignment.getNPattern() * 190);
+
+    size_t npattern = alignment.getNPattern();
+    DoubleVector pattern_rates(npattern);
+    for (size_t ptn = 0; ptn < npattern; ++ptn)
+    {
+        double *pi = alignment.ptn_state_freq[ptn];
+        double *R = alignment.site_rate_matrices.data() + ptn * 190;
+        double rate = 0.0;
+        int idx = 0;
+        for (int i = 0; i < 20; ++i)
+        {
+            for (int j = i + 1; j < 20; ++j)
+            {
+                rate += R[idx] * pi[i] * pi[j];
+                idx++;
+            }
+        }
+        pattern_rates[ptn] = 2.0 * rate;
+    }
+
+    size_t nsite = alignment.getNSite();
+    DoubleVector site_rates(nsite);
+    for (size_t site = 0; site < nsite; ++site)
+    {
+        site_rates[site] = pattern_rates[alignment.getPatternID(site)];
+    }
+    return site_rates;
+}
+
+void computeMutselSiteFrequencyModel(Params &params, Alignment *alignment)
+{
+    ASSERT(params.tree_freq_file);
+    cout << endl
+         << "===> COMPUTING MUTSEL MODEL BASED ON TREE FILE " << params.tree_freq_file << endl;
+    PhyloTree *tree = new PhyloTree(alignment);
+    tree->setParams(&params);
+    bool myrooted = params.is_rooted;
+    tree->readTree(params.tree_freq_file, myrooted);
+    tree->setAlignment(alignment);
+    tree->setRootNode(params.root);
+
+    tree->setNumThreads(params.num_threads);
+
+    tree->ensureNumberOfThreadsIsSet(nullptr);
+
+    auto [branch_lengths, parent_indices] = prepare_mutsel_tree(tree);
+    auto [sequences, L, N] = prepare_mutsel_alignment(alignment);
+
+    double *site_freq = new double[L * 20];
+
+    double *site_rate = new double[L * 190];
+
+    // Close log file, so we can append in the mutsel library without messing up the order of log messages from IQ-TREE and mutsel library
+    std::cout << std::flush;
+    auto outstream = dynamic_cast<outstreambuf *>(std::cout.rdbuf());
+    if (outstream)
+    {
+        outstream->close();
+    }
+    else
+    {
+        throw std::runtime_error("IQTREE-Logging seems to be uninitialized");
+    }
+
+    // Calls into the Rust code
+    rust_set_rayon_threads(params.num_threads);
+    rust_mutsel(parent_indices.data(),
+                branch_lengths.data(),
+                sequences.data(),
+                L,
+                N,
+                parent_indices.size(),
+                params.model_name.c_str(),
+                params.mutsel_prior_rate_file.empty() ? nullptr : params.mutsel_prior_rate_file.c_str(),
+                params.mutsel_prior_freq_file.empty() ? nullptr : params.mutsel_prior_freq_file.c_str(),
+                verbose_mode,
+                site_freq,
+                site_rate,
+                ((string)params.out_prefix).c_str());
+
+    outstream->open(((string)params.out_prefix + ".log").c_str(), std::ios::app); // reopen log file
+
+    write_site_models_to_alignment(*alignment, site_freq, site_rate, L);
+
+    write_binary_site_model_file(((string)params.out_prefix + ".sitemodel").c_str(), *alignment);
+
+    params.print_site_state_freq = WSF_NONE;
+
+    delete[] site_freq;
+    delete[] site_rate;
+    delete tree;
+
+    cout << endl
+         << "===> CONTINUE ANALYSIS USING THE INFERRED MUTSEL MODEL" << endl;
+}
\ No newline at end of file
diff --git a/utils/mutsel_wrapper.h b/utils/mutsel_wrapper.h
new file mode 100644
index 000000000..c94cd1864
--- /dev/null
+++ b/utils/mutsel_wrapper.h
@@ -0,0 +1,94 @@
+// C++ wrapper for the mutsel rust library
+
+#ifndef IQTREE_UTILS_MUTSEL_WRAPPER_H
+#define IQTREE_UTILS_MUTSEL_WRAPPER_H
+
+#include <vector>
+#include <cstdint>
+#include <string>
+#include <tuple>
+#include <utility>
+#include "tree/mtree.h"
+#include "alignment/alignment.h"
+#include "tree/phylotree.h"
+#include "main/outstreambuf.h"
+
+/**
+ * Convert a IQ-TREE tree into the format required by the mutsel library.
+ */
+std::pair<std::vector<double>, std::vector<int32_t>> prepare_mutsel_tree(MTree *tree);
+
+/**
+ * Returns the alignment in the format required by mutsel library as dense [L, N] matrix and returns L the sequence length and N the number of sequences.
+ */
+std::tuple<std::vector<uint8_t>, int32_t, int32_t> prepare_mutsel_alignment(Alignment *alignment);
+
+// Mutsel internals, if not compiled in we provide dummy implementations here, otherwise these functions need to be linked.
+#if defined(USE_MUTSEL)
+extern "C" void rust_mutsel(int32_t *parents,
+                            double *branch_lengths,
+                            uint8_t *alignment,
+                            uint32_t site_num,
+                            uint32_t leave_num,
+                            uint32_t node_num,
+                            const char *model_string,
+                            const char *priorMuFile,
+                            const char *priorPiFile,
+                            uint8_t verbose,
+                            double *out_site_freq,
+                            double *out_R_matrices,
+                            const char *output_prefix);
+
+extern "C" void rust_set_rayon_threads(int32_t num_threads);
+#else
+void rust_mutsel(int32_t *parents,
+                 double *branch_lengths,
+                 uint8_t *alignment,
+                 uint32_t site_num,
+                 uint32_t leave_num,
+                 uint32_t node_num,
+                 const char *model_string,
+                 const char *priorMuFile,
+                 const char *priorPiFile,
+                 uint8_t verbose,
+                 double *out_site_freq,
+                 double *out_R_matrices,
+                 const char *output_prefix);
+
+void rust_set_rayon_threads(int32_t num_threads);
+#endif
+
+/**
+ * Simple read function which just puts the binary file into vectors. frequences get normalized, rates are checked to be positive. It returns the rate model string of the file.
+ * Format is documented in the body of the function.
+ */
+std::string read_binary_site_model_file_internal(std::string &filename, std::vector<double> &site_freq, std::vector<double> &rate_matrices, std::vector<int> &site_model);
+
+/**
+ * Takes the data from the file (or the rust_mutsel function) and updates the alignment object.
+ * This deals with duplicated pattern and stuff.
+ */
+void write_site_models_to_alignment(Alignment &alignment, const double *site_freq, const double *rate_matrices, int len);
+
+/**
+ * Read a site model file and update the alignment object.
+ * This is a simple wrapper function around read_binary_site_model_file_internal and write_site_models_to_alignment.
+ */
+void read_site_model_file(const std::string &filename, Alignment &alignment);
+
+/**
+ * Print a site model from the alignment to binary file.
+ */
+void write_binary_site_model_file(const std::string &filename, Alignment &alignment);
+
+/**
+ * Compute the site frequency model using the mutsel library. It writes a site model file with the inferred parameters and also updates the alignment object with the inferred site frequency and rate parameters. It returns a string representing the rate model, e.g., "G4{0.5}" or "R5{0.1/0.2/0.3/0.4/0.5/0.6/0.7/0.8/0.9/1.0}".
+ */
+void computeMutselSiteFrequencyModel(Params &params, Alignment *alignment);
+
+/**
+ * Per-site substitution rate implied by the fitted MUTSEL model
+ */
+DoubleVector computeMutselSiteRates(Alignment &alignment);
+
+#endif // IQTREE_UTILS_MUTSEL_WRAPPER_H
\ No newline at end of file
diff --git a/utils/self_process.h b/utils/self_process.h
new file mode 100644
index 000000000..37cb25f6d
--- /dev/null
+++ b/utils/self_process.h
@@ -0,0 +1,197 @@
+// self_process.hpp — spawn a copy of the currently running executable, portably.
+#pragma once
+
+#include <string>
+#include <vector>
+#include <filesystem>
+#include <stdexcept>
+#include <cstdlib>
+#include <cstring>
+
+#if defined(_WIN32)
+  #define WIN32_LEAN_AND_MEAN
+  #include <windows.h>
+#elif defined(__APPLE__)
+  #include <libproc.h>
+  #include <unistd.h>
+  #include <sys/wait.h>
+  #include <spawn.h>
+  extern char **environ;
+#else // Linux / other POSIX
+  #include <unistd.h>
+  #include <sys/wait.h>
+  #include <spawn.h>
+  #include <climits>
+  extern char **environ;
+  #if defined(__FreeBSD__)
+    #include <sys/types.h>
+    #include <sys/sysctl.h>
+  #endif
+#endif
+
+namespace selfproc {
+
+// Returns the absolute, resolved path to the currently running executable.
+inline std::filesystem::path executable_path() {
+#if defined(_WIN32)
+    std::wstring buf(MAX_PATH, L'\0');
+    for (;;) {
+        DWORD len = GetModuleFileNameW(nullptr, buf.data(), (DWORD)buf.size());
+        if (len == 0) throw std::runtime_error("GetModuleFileNameW failed");
+        if (len < buf.size() - 1) { buf.resize(len); break; }
+        buf.resize(buf.size() * 2);
+    }
+    return std::filesystem::path(buf);
+
+#elif defined(__APPLE__)
+    std::array<char, PROC_PIDPATHINFO_MAXSIZE> buffer{};
+    pid_t pid = getpid();
+    
+    int bytes = proc_pidpath(pid, buffer.data(), buffer.size());
+    if (bytes > 0) {
+        return std::filesystem::path(buffer.data());
+    }
+    
+    return {}; // Return empty path on failure
+#elif defined(__linux__)
+    std::error_code ec;
+    auto p = std::filesystem::read_symlink("/proc/self/exe", ec);
+    if (ec) throw std::runtime_error("reading /proc/self/exe failed: " + ec.message());
+    return p;
+
+#elif defined(__FreeBSD__)
+    int mib[4] = {CTL_KERN, KERN_PROC, KERN_PROC_PATHNAME, -1};
+    char buf[PATH_MAX];
+    size_t len = sizeof(buf);
+    if (sysctl(mib, 4, buf, &len, nullptr, 0) != 0)
+        throw std::runtime_error("sysctl KERN_PROC_PATHNAME failed");
+    return std::filesystem::path(std::string(buf, len ? len - 1 : 0));
+
+#else
+    #error "executable_path() not implemented for this platform"
+#endif
+}
+
+#if defined(_WIN32)
+
+struct Process {
+    PROCESS_INFORMATION pi{};
+
+    int wait() {
+        WaitForSingleObject(pi.hProcess, INFINITE);
+        DWORD code = 0;
+        GetExitCodeProcess(pi.hProcess, &code);
+        CloseHandle(pi.hProcess);
+        CloseHandle(pi.hThread);
+        return static_cast<int>(code);
+    }
+};
+
+namespace detail {
+inline std::wstring to_wide(const std::string& s) {
+    if (s.empty()) return {};
+    int n = MultiByteToWideChar(CP_UTF8, 0, s.c_str(), (int)s.size(), nullptr, 0);
+    std::wstring w(n, L'\0');
+    MultiByteToWideChar(CP_UTF8, 0, s.c_str(), (int)s.size(), w.data(), n);
+    return w;
+}
+
+// Correct Win32 argv-style quoting (handles embedded quotes/backslashes).
+inline std::wstring quote_arg(const std::wstring& a) {
+    if (!a.empty() && a.find_first_of(L" \t\"") == std::wstring::npos)
+        return a;
+    std::wstring out = L"\"";
+    for (auto it = a.begin(); ; ++it) {
+        size_t backslashes = 0;
+        while (it != a.end() && *it == L'\\') { ++backslashes; ++it; }
+        if (it == a.end()) {
+            out.append(backslashes * 2, L'\\');
+            break;
+        } else if (*it == L'"') {
+            out.append(backslashes * 2 + 1, L'\\');
+            out.push_back(L'"');
+        } else {
+            out.append(backslashes, L'\\');
+            out.push_back(*it);
+        }
+    }
+    out.push_back(L'"');
+    return out;
+}
+} // namespace detail
+
+inline Process spawn(const std::filesystem::path& exe,
+                      const std::vector<std::string>& args) {
+    std::wstring cmdline = detail::quote_arg(exe.wstring());
+    for (auto& a : args) {
+        cmdline.push_back(L' ');
+        cmdline += detail::quote_arg(detail::to_wide(a));
+    }
+
+    STARTUPINFOW si{};
+    si.cb = sizeof(si);
+    PROCESS_INFORMATION pi{};
+
+    std::vector<wchar_t> mutable_cmd(cmdline.begin(), cmdline.end());
+    mutable_cmd.push_back(L'\0');
+
+    BOOL ok = CreateProcessW(
+        exe.wstring().c_str(),   // application name (avoids PATH search ambiguity)
+        mutable_cmd.data(),      // command line, must be a mutable buffer
+        nullptr, nullptr,
+        TRUE,
+        0, nullptr, nullptr,
+        &si, &pi);
+
+    if (!ok)
+        throw std::runtime_error("CreateProcessW failed, error " + std::to_string(GetLastError()));
+
+    Process p;
+    p.pi = pi;
+    return p;
+}
+
+#else // POSIX (Linux, macOS, FreeBSD, ...)
+
+struct Process {
+    pid_t pid = -1;
+
+    int wait() {
+        int status = 0;
+        if (waitpid(pid, &status, 0) < 0)
+            throw std::runtime_error("waitpid failed");
+        if (WIFEXITED(status)) return WEXITSTATUS(status);
+        if (WIFSIGNALED(status)) return 128 + WTERMSIG(status);
+        return -1;
+    }
+};
+
+inline Process spawn(const std::filesystem::path& exe,
+                      const std::vector<std::string>& args) {
+
+    std::vector<std::string> argv_storage;
+    argv_storage.push_back(exe.string());
+    for (auto& a : args) argv_storage.push_back(a);
+
+    std::vector<char*> argv;
+    for (auto& s : argv_storage) argv.push_back(s.data());
+    argv.push_back(nullptr);
+
+    pid_t pid;
+    int rc = posix_spawn(&pid, exe.c_str(), nullptr, nullptr, argv.data(), environ);
+    if (rc != 0)
+        throw std::runtime_error(std::string("posix_spawn failed: ") + std::strerror(rc));
+
+    Process p;
+    p.pid = pid;
+    return p;
+}
+
+#endif
+
+// Convenience: spawn a fresh copy of the currently running executable with the given args.
+inline Process spawn_self(const std::vector<std::string>& args) {
+    return spawn(executable_path(), args);
+}
+
+} // namespace selfproc
\ No newline at end of file
diff --git a/utils/tools.cpp b/utils/tools.cpp
index 5096ca343..09eaa919d 100644
--- a/utils/tools.cpp
+++ b/utils/tools.cpp
@@ -4623,6 +4623,29 @@ void parseArg(int argc, char *argv[], Params &params) {
                 continue;
             }
 
+            if (strcmp(argv[cnt], "--site-model-file") == 0 || strcmp(argv[cnt], "-site-model-file") == 0) {
+                cnt++;
+                if (cnt >= argc)
+                    throw "Use --site-model-file <site_model_file>";
+                params.site_model_file = argv[cnt];
+                continue;
+            }
+
+            if (strcmp(argv[cnt], "--mutsel-prior-freq-file") == 0 || strcmp(argv[cnt], "-mutsel-prior-freq-file") == 0) {
+                cnt++;
+                if (cnt >= argc)
+                    throw "Use --mutsel-prior-freq-file <mutsel_prior_freq_file>";
+                params.mutsel_prior_freq_file = argv[cnt];
+                continue;
+            }
+
+            if (strcmp(argv[cnt], "--mutsel-prior-rate-file") == 0 || strcmp(argv[cnt], "-mutsel-prior-rate-file") == 0) {
+                cnt++;
+                if (cnt >= argc)
+                    throw "Use --mutsel-prior-rate-file <mutsel_prior_rate_file>";
+                params.mutsel_prior_rate_file = argv[cnt];
+                continue;
+            }
 //			if (strcmp(argv[cnt], "-rootstate") == 0) {
 //                cnt++;
 //                if (cnt >= argc)
diff --git a/utils/tools.h b/utils/tools.h
index 58473002e..28834f538 100644
--- a/utils/tools.h
+++ b/utils/tools.h
@@ -2925,6 +2925,27 @@ class Params {
      *  input tree string (instead of a file)
      */
     string intree_str;
+
+    // MUTSEL parameters
+
+    /**
+     *  the file containing the site-specific model parameters.
+     *  it uses a simple binary format and will be output by a MUTSEL run.
+     *  The file is not intended to be human-readable.
+     */
+    std::string site_model_file;
+
+    /**
+     *  the file containing the prior state frequencies for the mutsel model, in the format of "site_ID state1_freq state2_freq ... state20_freq"
+     *  by default MUTSEL will calculate these priors by an approximated PMSF method.
+     */
+    std::string mutsel_prior_freq_file;
+
+    /**
+     *  the prior for the shared rates in PAML format.
+     *  by default MUTSEL will use the CODON model (A matrix derived for this purpose, for more information see the paper).
+     */
+    std::string mutsel_prior_rate_file;
 };
 
 /**