seqan/graph_algorithms/graph_algorithm_hmm.h

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#ifndef SEQAN_HEADER_GRAPH_ALGORITHM_HMM_H
#define SEQAN_HEADER_GRAPH_ALGORITHM_HMM_H

namespace seqan
{

// ============================================================================
// Forwards
// ============================================================================

// ============================================================================
// Tags, Classes, Enums
// ============================================================================

// ============================================================================
// Metafunctions
// ============================================================================

// ============================================================================
// Functions
// ============================================================================

// --------------------------------------------------------------------------
// Function viterbiAlgorithm()
// --------------------------------------------------------------------------

/*!
 * @defgroup HmmAlgorithms HMM Algorithms
 * @brief Algorithms on @link HmmGraph @endlink objects.
 */

/*!
 * @fn HmmAlgorithms#viterbiAlgorithm
 * @headerfile <seqan/graph_algorithms.h>
 * @brief Implements the Viterbi algorithm for Hidden Markov Models.
 *
 * @signature TCargo viterbiAlgorithm(path, hmm, seq);
 *
 * @param[out] path The state path;  String of vertex descriptors.
 * @param[in]  hmm  The @link HmmGraph @endlink to use.
 * @param[in]  seq  Input sequence.
 *
 * @return TCargo Probability of the path, the type parameter <tt>TCargo</tt> from type of <tt>hmm</tt>.
 *
 * The Viterbi algorithm computes the most likely sequence of hidden states of the Hidden Markov Model <tt>hmm</tt>
 * given the sequence <tt>seq</tt> using dynamic programming.  The result is the most likely sequence of hidden states
 * and returned in <tt>path</tt>.
 *
 * @section Remarks
 *
 * See the <a href="http://wikipedia.org/wiki/Viterbi_algorithm"> Wikipedia article on the Viterbi algorithm</a> for an
 * introduction to the algorithm itself.
 *
 * @see HmmAlgorithms#forwardAlgorithm
 * @see HmmAlgorithms#backwardAlgorithm
 */
template<typename TAlphabet, typename TProbability, typename TSpec, typename TSequence, typename TPath>
inline TProbability
viterbiAlgorithm(TPath & path,
                 Graph<Hmm<TAlphabet, TProbability, TSpec> > const & hmm,
                 TSequence const & seq)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;

    // Initialization
    String<TProbability> vMat;
    String<TSize> traceback;
    TSize numCols = length(seq) + 2;
    TSize numRows = getIdUpperBound(_getVertexIdManager(hmm));
    resize(vMat, numCols * numRows, 0.0);
    resize(traceback, numCols * numRows);
    value(vMat, getBeginState(hmm)) = 1.0;
    TVertexDescriptor bState = getBeginState(hmm);
    TVertexDescriptor eState = getEndState(hmm);
    TVertexDescriptor nilVertex = getNil<TVertexDescriptor>();

    // Distinct between silent states and real states
    typedef String<TVertexDescriptor> TStateSet;
    typedef typename Iterator<TStateSet>::Type TStateIter;
    TStateSet silentStates;
    TStateSet realStates;
    TVertexIterator itVertex(hmm);
    for(;!atEnd(itVertex);goNext(itVertex)) {
        if (isSilent(hmm, value(itVertex))) {
            appendValue(silentStates, value(itVertex));
        } else {
            appendValue(realStates, value(itVertex));
        }
    }

    // Initialization for silent states connected to the begin state
    TStateIter itSilentStateEnd = end(silentStates);
    for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
        if ((value(itSilentState) == bState) || (value(itSilentState) == eState)) continue;
        TProbability maxValue = 0.0;
        TVertexDescriptor maxVertex = nilVertex;

        for(TStateIter itBelow = begin(silentStates); itBelow != itSilentState; goNext(itBelow)) {
            TProbability local = value(vMat, value(itBelow)) * getTransitionProbability(hmm, value(itBelow), value(itSilentState));
            if (local > maxValue) {
                maxValue = local;
                maxVertex = value(itBelow);
            }
        }

        // Set traceback vertex
        if (maxVertex != nilVertex) {
            value(vMat, value(itSilentState)) = maxValue;
            value(traceback, value(itSilentState)) = maxVertex;
        }
    }

    // Recurrence
    TSize len = length(seq);
    for(TSize i=1; i<=len; ++i) {
        // Iterate over real states
        TStateIter itRealStateEnd = end(realStates);
        for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
            // Find maximum
            TProbability maxValue = 0.0;
            TVertexDescriptor maxVertex = nilVertex;
            TVertexIterator itMax(hmm);
            for(;!atEnd(itMax);++itMax) {
                TProbability local = value(vMat, (i-1) * numRows + value(itMax)) * getTransitionProbability(hmm, value(itMax), value(itRealState));
                if (local > maxValue) {
                    maxValue = local;
                    maxVertex = *itMax;
                }
            }
            // Set traceback vertex
            if (maxVertex != nilVertex) {
                value(vMat, i * numRows + value(itRealState)) = maxValue * getEmissionProbability(hmm, value(itRealState), value(seq, i-1));
                value(traceback, i * numRows + value(itRealState)) = maxVertex;
            }
        }

        // Iterate over silent states
        for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
            if ((value(itSilentState) == bState) || (value(itSilentState) == eState)) continue;
            // Find maximum
            TProbability maxValue = 0.0;
            TVertexDescriptor maxVertex = nilVertex;

            // Iterate over real states
            for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
                TProbability local = value(vMat, i * numRows + value(itRealState)) * getTransitionProbability(hmm, value(itRealState), value(itSilentState));
                if (local > maxValue) {
                    maxValue = local;
                    maxVertex = value(itRealState);
                }
            }
            // Iterate over silent states in increasing order
            for(TStateIter itBelow = begin(silentStates); itBelow != itSilentState; goNext(itBelow)) {
                TProbability local = value(vMat, i * numRows + value(itBelow)) * getTransitionProbability(hmm, value(itBelow), value(itSilentState));
                if (local > maxValue) {
                    maxValue = local;
                    maxVertex = value(itBelow);
                }
            }
            // Set traceback vertex
            if (maxVertex != nilVertex) {
                value(traceback, i * numRows + value(itSilentState)) = maxVertex;
                value(vMat, i * numRows + value(itSilentState)) = maxValue;
            }
        }
    }

    // Termination
    TProbability maxValue = 0.0;
    TVertexDescriptor maxVertex = 0;
    TVertexIterator itMax(hmm);
    for(;!atEnd(itMax);++itMax) {
        TProbability local = value(vMat, len * numRows + *itMax) * getTransitionProbability(hmm, value(itMax), eState);
        if (local > maxValue) {
            maxValue = local;
            maxVertex = value(itMax);
        }
    }
    value(traceback, (len + 1) * numRows + eState) = maxVertex;
    if (maxVertex != nilVertex) value(vMat, (len+1) * numRows + eState) = maxValue;

    // Traceback
    if (maxValue > 0.0) {
        clear(path);
        TVertexDescriptor oldState = eState;
        appendValue(path, oldState);
        for(TSize i = len + 1; i>=1; --i) {
            do {
                if ((!isSilent(hmm, oldState)) || (oldState == eState)) oldState = value(traceback, i * numRows + oldState);
                else oldState = value(traceback, (i - 1) * numRows + oldState);
                appendValue(path, oldState);
            } while ((isSilent(hmm, oldState)) && (oldState != bState));
        }
        std::reverse(begin(path), end(path));
    }

    //// Debug code
    //for(TSize i = 0; i<numRows; ++i) {
    //  for(TSize j=0; j<numCols; ++j) {
    //      std::cout << value(vMat, j*numRows + i) << ',';
    //      //std::cout << value(traceback, j*numRows + i) << ',';
    //  }
    //  std::cout << std::endl;
    //}
    //for(TSize i = 0; i<length(path); ++i) {
    //  std::cout << path[i] << ',';
    //}
    //std::cout << std::endl;

    return value(vMat, (len+1) * numRows + eState);
}

// --------------------------------------------------------------------------
// Function forwardAlgorithm()
// --------------------------------------------------------------------------

template<typename TAlphabet, typename TProbability, typename TSpec, typename TSequence, typename TForwardMatrix>
inline TProbability
_forwardAlgorithm(Graph<Hmm<TAlphabet, TProbability, TSpec> > const& hmm,
                   TSequence const& seq,
                   TForwardMatrix& fMat)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;

    // Initialization
    TSize numCols = length(seq) + 2;
    TSize numRows = getIdUpperBound(_getVertexIdManager(hmm));
    resize(fMat, numCols * numRows, 0.0);
    value(fMat, getBeginState(hmm)) = 1.0;
    TVertexDescriptor bState = getBeginState(hmm);
    TVertexDescriptor eState = getEndState(hmm);

    // Distinct between silent states and real states
    typedef String<TVertexDescriptor> TStateSet;
    typedef typename Iterator<TStateSet>::Type TStateIter;
    TStateSet silentStates;
    TStateSet realStates;
    TVertexIterator itVertex(hmm);
    for(;!atEnd(itVertex);goNext(itVertex)) {
        if (isSilent(hmm, value(itVertex))) {
            appendValue(silentStates, value(itVertex));
        } else {
            appendValue(realStates, value(itVertex));
        }
    }

    // Initialization for silent states connected to the begin state
    TStateIter itSilentStateEnd = end(silentStates);
    for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
        if ((value(itSilentState) == bState) || (value(itSilentState) == eState)) continue;
        TProbability sumValue = 0.0;
        for(TStateIter itBelow = begin(silentStates); itBelow != itSilentState; goNext(itBelow)) {
            sumValue += value(fMat, value(itBelow)) * getTransitionProbability(hmm, value(itBelow), value(itSilentState));
        }
        value(fMat, value(itSilentState)) = sumValue;
    }

    // Recurrence
    TSize len = length(seq);
    for(TSize i=1; i<=len; ++i) {
        // Iterate over real states
        TStateIter itRealStateEnd = end(realStates);
        for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
            TProbability sum = 0.0;
            TVertexIterator itAll(hmm);
            for(;!atEnd(itAll);++itAll) sum += value(fMat, (i-1) * numRows + value(itAll)) * getTransitionProbability(hmm, value(itAll), value(itRealState));
            value(fMat, i * numRows + value(itRealState)) = getEmissionProbability(hmm, value(itRealState), seq[i-1]) * sum;
        }

        // Iterate over silent states
        for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
            if ((value(itSilentState) == bState) || (value(itSilentState) == eState)) continue;
            TProbability sumValue = 0.0;
            // Iterate over real states
            for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
                sumValue += value(fMat, i * numRows + value(itRealState)) * getTransitionProbability(hmm, value(itRealState), value(itSilentState));
            }
            // Iterate over silent states in increasing order
            for(TStateIter itBelow = begin(silentStates); itBelow != itSilentState; goNext(itBelow)) {
                sumValue += value(fMat, i * numRows + value(itBelow)) * getTransitionProbability(hmm, value(itBelow), value(itSilentState));
            }
            value(fMat, i * numRows + value(itSilentState)) = sumValue;
        }
    }

    // Termination
    TProbability sum = 0.0;
    TVertexIterator itAll(hmm);
    for(;!atEnd(itAll);++itAll) {
        sum += value(fMat, len * numRows + value(itAll)) * getTransitionProbability(hmm, value(itAll), eState);
    }
    value(fMat, (len+1) * numRows + eState) = sum;

    //// Debug code
    //for(TSize i = 0; i<numRows; ++i) {
    //  for(TSize j=0; j<numCols; ++j) {
    //      std::cout << value(fMat, j*numRows + i) << ',';
    //  }
    //  std::cout << std::endl;
    //}

    return value(fMat, (len+1) * numRows + eState);
}

/*!
 * @fn HmmAlgorithms#forwardAlgorithm
 * @headerfile <seqan/graph_algorithms.h>
 * @brief Given a Hidden Markov Model <tt>hmm</tt>, the forward algorithm computes the probability of the sequence
 *        <tt>seq</tt>.
 *
 * @signature TCargo forwardAlgorithm(hmm, seq);
 *
 * @param[in] hmm The @link HmmGraph @endlink with the HMM to use.
 * @param[in] seq Input sequence to use in the forward algorithm.
 *
 * @return TProbability The probability of the sequence <tt>seq</tt>.  <tt>TProbability</tt> is the type parameter
 *                      <tt>TCargo</tt> of the type of <tt>hmm</tt>.
 *
 * @section Remarks
 *
 * See the <a href="http://en.wikipedia.org/wiki/Forward_algorithm">Wikipedia article on the Forward algorithm</a> for
 * an introduction to the algorithm itself.
 *
 * @see HmmAlgorithms#viterbiAlgorithm
 * @see HmmAlgorithms#backwardAlgorithm
 */
template<typename TAlphabet, typename TProbability, typename TSpec, typename TSequence>
TProbability
forwardAlgorithm(Graph<Hmm<TAlphabet, TProbability, TSpec> > const & hmm,
                 TSequence const & seq)
{
    String<TProbability> fMat;
    return _forwardAlgorithm(hmm, seq, fMat);
}

// --------------------------------------------------------------------------
// Function backwardAlgorithm()
// --------------------------------------------------------------------------

template<typename TAlphabet, typename TProbability, typename TSpec, typename TSequence, typename TBackwardMatrix>
inline TProbability
_backwardAlgorithm(Graph<Hmm<TAlphabet, TProbability, TSpec> > const& hmm,
                    TSequence const& seq,
                    TBackwardMatrix& bMat)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;

    // Initialization
    TSize numCols = length(seq) + 2;
    TSize numRows = getIdUpperBound(_getVertexIdManager(hmm));
    resize(bMat, numCols * numRows, 0.0);
    TVertexDescriptor bState = getBeginState(hmm);
    TVertexDescriptor eState = getEndState(hmm);
    TSize len = length(seq);
    value(bMat, (len + 1) * numRows + eState) = 1.0;

    // Distinct between silent states and real states
    typedef String<TVertexDescriptor> TStateSet;
    typedef typename Iterator<TStateSet>::Type TStateIter;
    TStateSet silentStates;
    TStateSet realStates;
    TVertexIterator itVertex(hmm);
    for(;!atEnd(itVertex);goNext(itVertex)) {
        if (isSilent(hmm, value(itVertex))) {
            appendValue(silentStates, value(itVertex));
        } else {
            appendValue(realStates, value(itVertex));
        }
    }
    // Reverse the silent states order
    std::reverse(begin(silentStates), end(silentStates));

    // Initialization for silent states connected to the end state
    TStateIter itSilentStateEnd = end(silentStates);
    for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
        if (value(itSilentState) == eState) continue;
        TProbability sumValue = getTransitionProbability(hmm, value(itSilentState), eState);
        for(TStateIter itAbove = begin(silentStates); itAbove != itSilentState; goNext(itAbove)) {
            sumValue += value(bMat, len * numRows + value(itAbove)) * getTransitionProbability(hmm, value(itSilentState), value(itAbove));
        }
        value(bMat, len * numRows + value(itSilentState)) = sumValue;
    }

    // Initialization for real states
    TStateIter itRealStateEnd = end(realStates);
    for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
        TProbability sumValue = getTransitionProbability(hmm, value(itRealState), eState);
        for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
            sumValue += value(bMat, len * numRows + value(itSilentState)) * getTransitionProbability(hmm, value(itRealState), value(itSilentState));
        }
        value(bMat, len * numRows + value(itRealState)) = sumValue;
    }


    // Recurrence
    if (len > 0) {
        for(TSize i=len - 1; i>0; --i) {
            // Iterate over silent states
            for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
                if ((value(itSilentState) == bState) || (value(itSilentState) == eState)) continue;
                TProbability sumValue = 0.0;
                // Iterate over real states
                for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
                    sumValue += value(bMat, (i+1) * numRows + value(itRealState)) * getTransitionProbability(hmm, value(itSilentState), value(itRealState))* getEmissionProbability(hmm, value(itRealState), value(seq, i));
                }
                // Iterate over silent states in decreasing order
                for(TStateIter itAbove = begin(silentStates); itAbove != itSilentState; goNext(itAbove)) {
                    if ((value(itAbove) == bState) || (value(itAbove) == eState)) continue;
                    sumValue += value(bMat, i * numRows + value(itAbove)) * getTransitionProbability(hmm, value(itSilentState), value(itAbove));
                }
                value(bMat, i * numRows + value(itSilentState)) = sumValue;
            }

            // Iteration over real states
            for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
                TProbability sumValue = 0.0;
                // Iterate over silent states
                for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
                    if ((value(itSilentState) == bState) || (value(itSilentState) == eState)) continue;
                    sumValue += value(bMat, i * numRows + value(itSilentState)) * getTransitionProbability(hmm, value(itRealState), value(itSilentState));
                }
                // Iterate over real states
                for(TStateIter itR = begin(realStates); itR != itRealStateEnd; goNext(itR)) {
                    sumValue += value(bMat, (i+1) * numRows + value(itR)) * getTransitionProbability(hmm, value(itRealState), value(itR)) * getEmissionProbability(hmm, value(itR), value(seq, i));
                }
                value(bMat, i * numRows + value(itRealState)) =  sumValue;
            }
        }

        // Termination
        // Iterate over silent states
        for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
            if ((value(itSilentState) == bState) || (value(itSilentState) == eState)) continue;
            TProbability sumValue = 0.0;
            // Iterate over real states
            for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
                sumValue += value(bMat, 1 * numRows + value(itRealState)) * getTransitionProbability(hmm, value(itSilentState), value(itRealState))* getEmissionProbability(hmm, value(itRealState), value(seq, 0));
            }
            // Iterate over silent states in decreasing order
            for(TStateIter itAbove = begin(silentStates); itAbove != itSilentState; goNext(itAbove)) {
                if ((value(itAbove) == bState) || (value(itAbove) == eState)) continue;
                sumValue += value(bMat, value(itAbove)) * getTransitionProbability(hmm, value(itSilentState), value(itAbove));
            }
            value(bMat, value(itSilentState)) = sumValue;
        }
        // Sum up all values
        TProbability sumValue = 0.0;
        for(TStateIter itSilentState = begin(silentStates); itSilentState != itSilentStateEnd; goNext(itSilentState)) {
            if ((value(itSilentState) == bState) || (value(itSilentState) == eState)) continue;
            sumValue += value(bMat, value(itSilentState)) * getTransitionProbability(hmm, bState, value(itSilentState));
        }
        for(TStateIter itRealState = begin(realStates); itRealState != itRealStateEnd; goNext(itRealState)) {
            sumValue += value(bMat, 1 * numRows + value(itRealState)) * getTransitionProbability(hmm, bState, value(itRealState)) * getEmissionProbability(hmm, value(itRealState), value(seq, 0));
        }
        value(bMat, bState) = sumValue;
    }

    //// Debug code
    //for(TSize i = 0; i<numRows; ++i) {
    //  for(TSize j=0; j<numCols; ++j) {
    //      std::cout << value(bMat, j*numRows + i) << ',';
    //  }
    //  std::cout << std::endl;
    //}

    return value(bMat, bState);
}

/*!
 * @fn HmmAlgorithms#backwardAlgorithm
 * @headerfile <seqan/graph_algorithms.h>
 * @brief Given a Hidden Markov Model <tt>hmm</tt>, the backward algorithm computes the probability of the sequence
 *        <tt>seq</tt>.
 *
 * @signature TCargo backwardAlgorithm(hmm, seq);
 *
 * @param[in] hmm The @link HmmGraph @endlink with the HMM to use.
 * @param[in] seq Input sequence to use in the backward algorithm.
 *
 * @return TCargo The probability of the sequence <tt>seq</tt>.  <tt>TProbability</tt> is the type parameter
 *                <tt>TCargo</tt> of the type of <tt>hmm</tt>.
 *
 * See the <a href="http://en.wikipedia.org/wiki/Forward-backward_algorithm">Wikipedia article on the Forward-backward
 * algorithm</a> for an introduction to the algorithm itself.
 *
 * @see HmmAlgorithms#viterbiAlgorithm
 * @see HmmAlgorithms#forwardAlgorithm
 */
template<typename TAlphabet, typename TProbability, typename TSpec, typename TSequence>
TProbability
backwardAlgorithm(Graph<Hmm<TAlphabet, TProbability, TSpec> > const & hmm,
                  TSequence const & seq)
{
    String<TProbability> bMat;
    return _backwardAlgorithm(hmm, seq, bMat);
}

// --------------------------------------------------------------------------
// Function generateSequence()
// --------------------------------------------------------------------------

/*!
 * @fn HmmAlgorithms#generateSequence
 * @headerfile <seqan/graph_algorithms.h>
 * @brief Generates random state and alphabet sequence of a given HMM.
 *
 * @signature void generateSequence(hmm, seq, states, numSeq, maxLen);
 *
 * @param[out] seq    A @link StringSet @endlink of alphabet sequences.
 * @param[out] states A @link ContainerConcept @endlink object of state sequences.
 * @param[in]  hmm    The @link HmmGraph @endlink to use.
 * @param[in]  numSeq The number of sequences to generate.
 * @param[in]  maxLen The maximum length of the sequences.  The sequences might be shorter if the ends tate is reached
 *                    before maxLen.
 *
 * @section Remarks
 *
 * Because of silent states, generated alphabet and state sequences might have different lengths.
 */
template<typename TAlphabet, typename TProbability, typename TSpec,typename TSequenceSet, typename TStateSeqSet, typename TSize>
void generateSequence(TSequenceSet & sequences,
                      TStateSeqSet & states,
                      Graph<Hmm<TAlphabet, TProbability, TSpec> > const & hmm,
                      TSize numSeq,
                      TSize maxLength)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;
    typedef typename Value<TSequenceSet>::Type TSequence;
    typedef typename Value<TStateSeqSet>::Type TStateSeq;

    // TODO(holtgrew): It should be possible to use a per-call RNG.
    typedef typename GetDefaultRng<TGraph>::Type TRng;

    std::uniform_real_distribution<double> pdf(0.0, 1.0);
    TRng & rng = defaultRng(TGraph());

    // Initialization
    clear(sequences);
    clear(states);
    TSize alphSize = ValueSize<TAlphabet>::VALUE;

    // Simulate sequences
    TVertexDescriptor currentState;
    TVertexDescriptor endState = getEndState(hmm);
    for(TSize i=0;i<numSeq;++i){
        currentState = getBeginState(hmm);
        TSequence seq;
        TStateSeq stat;
        appendValue(stat, getBeginState(hmm));
        bool stop = false;
        TSize pos = 0;
        while (pos < maxLength) {
            TProbability prob = pdf(rng);
            TProbability compareProb = 0.0;
            TOutEdgeIterator itState(hmm, currentState);
            // Determine the next state
            for(;!atEnd(itState);++itState) {
                // Probability of the next transition
                compareProb += getTransitionProbability(hmm, value(itState));
                // Compare with random probability
                if (prob <= compareProb){
                    TVertexDescriptor nextState = targetVertex(hmm, value(itState));
                    if (nextState == endState) {
                        stop = true;
                        break;
                    }
                    appendValue(stat, nextState);
                    if (!isSilent(hmm, nextState)) {
                        compareProb =0.0;
                        prob = pdf(rng);
                        for (TSize c=0;c<alphSize;++c){
                            compareProb += getEmissionProbability(hmm,targetVertex(hmm, value(itState)), TAlphabet(c));
                            if (prob <= compareProb) {
                                appendValue(seq, TAlphabet(c));
                                ++pos;
                                break;
                            }
                        }
                    }
                    currentState = nextState;
                    break;
                }
            }
            if (stop==true) break;
        }
        appendValue(stat, getEndState(hmm));
        appendValue(sequences, seq);
        appendValue(states, stat);
    }
}

template<typename TAlphabet, typename TProbability, typename TSpec,typename TSequenceSet, typename TSize>
inline void
generateSequence(Graph<Hmm<TAlphabet, TProbability, TSpec> > const& hmm,
                 TSequenceSet& sequences,
                 TSize numSeq,
                 TSize maxLength)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    StringSet<String<TVertexDescriptor> > states;
    generateSequence(hmm, sequences, states, numSeq, maxLength);
}

// --------------------------------------------------------------------------
// Function estimationWithStates()
// --------------------------------------------------------------------------

template<typename TAlphabet, typename TProbability, typename TSpec,typename TEmissionCounter, typename TTransitionCounter>
inline void
_parameterEstimator(Graph<Hmm<TAlphabet, TProbability, TSpec> >& hmm,
                     TEmissionCounter const& emission,
                     TTransitionCounter const& transition)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;
    typedef typename Value<TTransitionCounter>::Type TCounterValue;

    // Initialization
    TSize alphSize = ValueSize<TAlphabet>::VALUE;
    TCounterValue pseudoCount = (TCounterValue) 1.0;

    // Estimate the parameters from the counter values
    TVertexIterator itAll(hmm);
    for(;!atEnd(itAll);++itAll){
        if (!isSilent(hmm, value(itAll))) {
            TCounterValue summedCount = (TCounterValue) (0.0);
            for(TSize i=0; i<alphSize;++i) summedCount += (pseudoCount + value(value(emission, value(itAll)),i));
            for(TSize i=0; i<alphSize;++i) emissionProbability(hmm,value(itAll),TAlphabet(i)) = (pseudoCount + value(value(emission, value(itAll)),i)) / summedCount;
        }
        TCounterValue summedCount = (TCounterValue) (0.0);
        TOutEdgeIterator itOutSum(hmm,value(itAll));
        for(;!atEnd(itOutSum);++itOutSum) summedCount += (pseudoCount + getProperty(transition, value(itOutSum)));
        TOutEdgeIterator itOut(hmm, value(itAll));
        for(;!atEnd(itOut);++itOut) transitionProbability(hmm, value(itOut)) = (pseudoCount + getProperty(transition, value(itOut))) / summedCount;
    }
}

///////////////////////////////////////////////////////////////////////////////////////

template<typename TAlphabet, typename TProbability, typename TSpec, typename TSequenceSet, typename TStateSeqSet>
inline void
estimationWithStates(Graph<Hmm<TAlphabet, TProbability, TSpec> >& hmm,
                     TSequenceSet& sequences,
                     TStateSeqSet& states)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    typedef typename Value<TStateSeqSet>::Type TStateSeq;
    typedef typename Value<TStateSeq>::Type TState;
    typedef typename EdgeDescriptor<TGraph>::Type TEdgeDescriptor;

    // Initialization
    TSize alphSize = ValueSize<TAlphabet>::VALUE;
    typedef String<TSize> TCountString;
    TCountString transitionCounter;
    resize(transitionCounter, getIdUpperBound(_getEdgeIdManager(hmm)), 0);
    StringSet<TCountString> emissionCounter;
    TSize numRows = getIdUpperBound(_getVertexIdManager(hmm));
    for(TSize i =0; i<numRows;++i) {
        TCountString emisCount;
        resize(emisCount,alphSize,0);
        appendValue(emissionCounter,emisCount);
    }

    // Iterate over all sequences
    for (TSize j=0;j<length(states);++j) {
        TSize posSeq = 0;
        for (TSize i = 0;i<length(value(states,j));++i) {
            TState s = value(value(states,j),i);
            if (!isSilent(hmm, s)) {
                TAlphabet c = value(value(sequences,j),posSeq);
                value(value(emissionCounter, s), ordValue(c)) += 1;
                ++posSeq;
            }
            if (i<(length(value(states,j))-1)) {
                TEdgeDescriptor currEdge = findEdge(hmm, s, value(value(states,j), (i+1)));
                property(transitionCounter, currEdge) += 1;
            }
        }
    }

    //// Debug Code
    //typedef typename Iterator<TGraph, EdgeIterator>::Type TEdgeIterator;
    //TEdgeIterator itE(hmm);
    //for(;!atEnd(itE);goNext(itE)) std::cout << sourceVertex(itE) << ',' << targetVertex(itE) << ':' << property(transitionCounter, value(itE)) << std::endl;
    //for(TSize j=0; j<length(emissionCounter); ++j) {
    //  for(TSize i=0;i<length(value(emissionCounter, j));++i) {
    //      std::cout << j << ":" << TAlphabet(i) << '=' << value(value(emissionCounter, j), i) << std::endl;
    //  }
    //}

    // Estimate Parameters
    _parameterEstimator(hmm,emissionCounter, transitionCounter);
}

// --------------------------------------------------------------------------
// Function baumWelchAlgorithm()
// --------------------------------------------------------------------------

template<typename TAlphabet, typename TProbability, typename TSpec>
inline void
_fillHmmUniform(Graph<Hmm<TAlphabet, TProbability, TSpec> >& hmm)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;

    // Initialization
    TSize alphSize = ValueSize<TAlphabet>::VALUE;

    // Iterate over all states
    TVertexIterator itState(hmm);
    for(;!atEnd(itState);goNext(itState)) {     //pass through the states of the hmm
        TSize oD = outDegree(hmm, value(itState));
        TOutEdgeIterator itOut(hmm, value(itState));
        for (;!atEnd(itOut);goNext(itOut)) transitionProbability(hmm, value(itOut)) = (TProbability) (1.0 / (double) (oD));
        if (!isSilent(hmm, value(itState))) {
            for(TSize i=0;i<alphSize;++i){
                emissionProbability(hmm,value(itState),TAlphabet(i)) = (TProbability) (1.0 / (double) (alphSize));
            }
        }
    }
}

template<typename TAlphabet, typename TProbability, typename TSpec, typename TRNG>
inline void
_fillHmmRandom(Graph<Hmm<TAlphabet, TProbability, TSpec> >& hmm,
                TRNG & rng)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;

    // Initialization
    std::uniform_int_distribution<TSize> pdf(20, 99);
    TSize alphSize = ValueSize<TAlphabet>::VALUE;

    // Iterate over all states
    TVertexIterator itState(hmm);
    for(;!atEnd(itState);goNext(itState)) {     //pass through the states of the hmm
        TSize oD = outDegree(hmm, value(itState));
        if (oD > 0) {
            String<TSize> counts;
            TSize sum = 0;
            for(TSize i = 0;i<oD;++i) {
                TSize rd = pdf(rng);
                sum += rd;
                appendValue(counts, rd);
            }
            TSize pos = 0;
            TOutEdgeIterator itOut(hmm, value(itState));
            for (;!atEnd(itOut);goNext(itOut), ++pos) transitionProbability(hmm, value(itOut)) = (TProbability) ((double) (value(counts, pos)) / (double) (sum));
        }
        if (!isSilent(hmm, value(itState))) {
            String<TSize> counts;
            TSize sum = 0;
            for(TSize i = 0;i<alphSize;++i) {
                TSize rd = pdf(rng);
                sum += rd;
                appendValue(counts, rd);
            }
            for(TSize i=0;i<alphSize;++i) emissionProbability(hmm,value(itState),TAlphabet(i)) = (TProbability) ((double) (value(counts, i)) / (double) (sum));
        }
    }
}

template<typename TAlphabet, typename TProbability, typename TSpec, typename TRNG>
inline void
randomizeHmm(Graph<Hmm<TAlphabet, TProbability, TSpec> >& hmm,
             TRNG & /*rng*/)
{
    // TODO(holtgrew): Why uniform and not random?
    //_fillHmmRandom(hmm, rng);
    _fillHmmUniform(hmm);
}

template <typename TAlphabet, typename TProbability, typename TSpec, typename TSequence, typename TSize>
inline TProbability
_baumWelchAlgorithm(Graph<Hmm<TAlphabet, TProbability, TSpec > >& hmm,
                     StringSet<TSequence> const& seqSet,
                     TSize maxIter,
                     TProbability epsilon)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;
    typedef String<TProbability> TCountString;

    // Initialization
    TSize alphSize = ValueSize<TAlphabet>::VALUE;
    TProbability lastTotalModelProb = 0.0;

    // Randomize current HMM so only topology is preserved
    randomizeHmm(hmm);

    // Iterative Optimization
    for(TSize iter=0; iter<maxIter; ++iter){
        std::cout << "Iteration: "<< iter << std::endl;
        std::cout << hmm << std::endl;
        TCountString transitionCounter;
        resize(transitionCounter, getIdUpperBound(_getEdgeIdManager(hmm)), 0.0);
        StringSet<TCountString> emissionCounter;
        TSize numRows = getIdUpperBound(_getVertexIdManager(hmm));
        for(TSize i =0; i<numRows;++i) {
            TCountString emisCount;
            resize(emisCount,alphSize, 0.0);
            appendValue(emissionCounter,emisCount);
        }

        // MaximationStep
        // Determine new contributions
        TProbability totalModelLogProb = 0.0;
        for (TSize i=0; i <length(seqSet);++i){     //sequences
            TSize len = length(value(seqSet,i));

            // Forward algorithm
            String<TProbability> fMat;
            TProbability modelLogProb = _forwardAlgorithm(hmm, value(seqSet,i), fMat);
            totalModelLogProb += modelLogProb;

            // Backward algorithm
            String<TProbability> bMat;
            _backwardAlgorithm(hmm, value(seqSet,i), bMat);

            // Use the posterior probabilities to estimate counter values
            for (TSize j=0;j<len;++j){
                TAlphabet c = value(value(seqSet,i),j);
                TAlphabet nextC = c;
                if (j < (len - 1))  nextC = value(value(seqSet,i),(j+1));

                // Iterate over all states
                TVertexIterator itAll(hmm);
                for(;!atEnd(itAll);++itAll) {
                    // Handle begin state
                    if (value(itAll) == beginState(hmm)) {
                        if (j == 0) {
                            TOutEdgeIterator itOut(hmm, value(itAll));
                            for(;!atEnd(itOut); goNext(itOut)) {
                                if (!isSilent(hmm, targetVertex(itOut))) {
                                    property(transitionCounter, value(itOut)) += (value(fMat, beginState(hmm)) * getTransitionProbability(hmm, value(itOut)) * getEmissionProbability(hmm, targetVertex(itOut), c) * value(bMat, numRows + targetVertex(itOut)) / modelLogProb);
                                } else {
                                    property(transitionCounter, value(itOut)) += (value(fMat, beginState(hmm)) * getTransitionProbability(hmm, value(itOut)) * value(bMat, targetVertex(itOut)) / modelLogProb);
                                }
                            }

                        }
                        continue;
                    }
                    // Ignore the end state
                    if (value(itAll) == endState(hmm)) continue;

                    // Determine emission expectation values
                    if (!isSilent(hmm, value(itAll))) value(value(emissionCounter, value(itAll)),ordValue(c)) += ((value(fMat, (j+1) * numRows + value(itAll)) * value(bMat, (j+1) * numRows + value(itAll))) / modelLogProb);

                    // Determine transition expectation values
                    TOutEdgeIterator itOut(hmm, value(itAll));
                    for(;!atEnd(itOut); goNext(itOut)) {
                        // Handle the end state
                        if ((j == (len - 1)) && (targetVertex(itOut)==endState(hmm))) {
                            property(transitionCounter, value(itOut)) += (value(fMat, (j+1) * numRows + value(itAll)) * getTransitionProbability(hmm, value(itAll),endState(hmm)) / modelLogProb);
                        } else {
                            if (!isSilent(hmm, targetVertex(itOut))) {
                                if (j < (len - 1)) property(transitionCounter, value(itOut)) += (value(fMat, (j+1) * numRows + value(itAll)) * getTransitionProbability(hmm, value(itOut)) * getEmissionProbability(hmm, targetVertex(itOut), nextC) * value(bMat, (j+2) * numRows + targetVertex(itOut)) / modelLogProb);
                            } else {
                                property(transitionCounter, value(itOut)) += (value(fMat, (j+1) * numRows + value(itAll)) * getTransitionProbability(hmm, value(itOut)) * value(bMat, (j+1) * numRows + targetVertex(itOut)) / modelLogProb);
                            }
                        }
                    }
                }
            }
        }
        // Expectation step
        _parameterEstimator(hmm,emissionCounter, transitionCounter);


        // Termination?
        if ((iter > 5) && ((totalModelLogProb - lastTotalModelProb) < epsilon)) {
            lastTotalModelProb = totalModelLogProb;
            break;
        } else {
            lastTotalModelProb = totalModelLogProb;
        }
    }
    return lastTotalModelProb;
}

template <typename TAlphabet, typename TProbability, typename TSpec, typename TSequence>
inline TProbability
baumWelchAlgorithm(Graph<Hmm<TAlphabet, TProbability, TSpec > >& hmm,
                   StringSet<TSequence> const& seqSet)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    TSize maxIter = 100;
    TProbability epsilon = 0.00001;
    return _baumWelchAlgorithm(hmm, seqSet, maxIter, epsilon);
}

/*
//////////////////////////////////////////////////////////////////////////////
// Profile HMMs
//////////////////////////////////////////////////////////////////////////////

//////////////////////////////////////////////////////////////////////////////


template < typename TAlphabet, typename TProbability, typename TSpec, typename TMat, typename TConsensus, typename TSize>
inline void
_profileHmmCounter(Graph<Hmm<TAlphabet, TProbability, TSpec> >& pHmm,
                    TMat const& matr,
                    TConsensus const& consensus,
                    TSize const& numRows,
                    TSize const& numCols)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    typedef typename EdgeDescriptor<TGraph>::Type TEdgeDescriptor;
    typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;
    typedef typename Value<TConsensus>::Type TValue;

    // Initialization
    TSize alphSize = ValueSize<TAlphabet>::VALUE;
    TValue gapChar = gapValue<TValue>();
    TVertexDescriptor begState = beginState(pHmm);
    TVertexDescriptor eState = endState(pHmm);
    TVertexDescriptor matchState = 1;
    TVertexDescriptor insertState = 2;
    TVertexDescriptor deleteState = 3;

    typedef String<TProbability> TCountString;
    TCountString transitionCounter;
    resize(transitionCounter, getIdUpperBound(_getEdgeIdManager(pHmm)), 0.0);
    StringSet<TCountString> emissionCounter;
    TSize nR = getIdUpperBound(_getVertexIdManager(pHmm));
    for(TSize i =0; i<nR;++i) {
        TCountString emisCount;
        resize(emisCount,alphSize, 0.0);
        appendValue(emissionCounter,emisCount);
    }


    String<TVertexDescriptor> oldCol;
    String<TVertexDescriptor> currCol;
    resize(oldCol, numRows, begState);
    resize(currCol, numRows, 0);
    TEdgeDescriptor currEdge;

    for(TSize i = 0; i<length(consensus); ++i) {
        //transitionvalues

        //being in insertState
        if (value(consensus, i)==gapChar){
            for(TSize j = 0; j<numRows; ++j){
                if ((value(matr, j * numCols + i)!=gapChar)){
                    value(currCol,j) = insertState;
                    currEdge = findEdge(pHmm, value(oldCol,j), value(currCol,j));
                    property(transitionCounter, currEdge) += 1;
                    value(oldCol,j) = value(currCol,j);
                }
                else if ((value(matr, j * numCols + i)==gapChar) ){
                    value(currCol,j) = value(oldCol,j);
                }
            }
        }
        //being in normal State
        else{
            for(TSize j = 0; j<numRows; ++j){
                if(value(matr, j * numCols + i)!=gapChar) value(currCol,j) = matchState;
                else value(currCol,j) = deleteState;
                currEdge = findEdge(pHmm, value(oldCol,j), value(currCol,j));
                property(transitionCounter, currEdge) += 1;
                value(oldCol,j)=value(currCol,j);
            }
        }
        //emissionvalues
        if (value(consensus, i)==gapChar) {
            for(TSize j = 0; j<numRows; ++j)
                if(value(matr, j * numCols + i)!=gapChar)
                    value(value(emissionCounter, insertState), ordValue( (TAlphabet)  value(matr, j * numCols + i) ) ) += 1;

            continue;
        }
        else
            for(TSize j = 0; j<numRows; ++j)
                if(value(matr, j * numCols + i)!=gapChar)
                    value(value(emissionCounter, matchState), ordValue( (TAlphabet)  value(matr, j * numCols + i) ) ) += 1;

        matchState+=3;
        if ((insertState+3)==eState) insertState+=2;
        else insertState+=3;
        deleteState+=3;
    }

    //transition in endState
    for(TSize j = 0; j<numRows; ++j){
        currEdge = findEdge(pHmm,value(currCol,j),eState);
        property(transitionCounter, currEdge) += 1;
    }

    _parameterEstimator(pHmm, emissionCounter, transitionCounter);
}


//////////////////////////////////////////////////////////////////////////////

template<typename TAlphabet, typename TCargo, typename TSpec, typename TConsensus>
inline void
_createProfileHmm(Graph<Hmm<TAlphabet, TCargo, TSpec> >& pHmm,
                   TConsensus const& consensus)
{
    typedef Graph<Hmm<TAlphabet, TCargo, TSpec> > TGraph;
    typedef typename Size<TGraph>::Type TSize;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    typedef typename EdgeDescriptor<TGraph>::Type TEdgeDescriptor;
    typedef typename Value<TConsensus>::Type TValue;

    // Initialization
    TSize alphSize = ValueSize<TAlphabet>::VALUE;
    TValue gapChar = gapValue<TValue>();
    clear(pHmm);

    // Add begin state
    TVertexDescriptor begState = addVertex(pHmm);
    assignBeginState(pHmm, begState);

    // Add for each consensus letter 3 states
    for (TSize i=0;i<length(consensus);++i){
        if (value(consensus,i) == gapChar) continue;
        addVertex(pHmm); addVertex(pHmm); addVertex(pHmm, true);
    }

    // Add last insertion state
    TVertexDescriptor lastIState = addVertex(pHmm);

    // Add end state
    TVertexDescriptor endState = addVertex(pHmm);
    assignEndState(pHmm, endState);

    // Is there no consensus letter?
    if (lastIState == 1) {
        clear(pHmm);
        return;
    }

    // Remember the kind of state
    TVertexDescriptor mState = 1;
    TVertexDescriptor iState = 2;
    TVertexDescriptor dState = 3;

    // Add tranistions from begin state
    addEdge(pHmm, begState, mState);
    addEdge(pHmm, begState, iState);
    addEdge(pHmm, begState, dState);

    // Add all remaining transitions
    for (TSize i=0;i<length(consensus);++i){
        if (value(consensus,i) == gapChar) continue;
        else if ((mState + 3) == lastIState) {
            addEdge(pHmm, iState, mState);
            addEdge(pHmm, iState, iState);
            addEdge(pHmm, iState, dState);
            break;
        }
        else{
            addEdge(pHmm, mState, (mState+3));
            addEdge(pHmm, iState, mState);
            addEdge(pHmm, dState, (mState+3));
            addEdge(pHmm, mState, (iState+3));
            addEdge(pHmm, iState, iState);
            addEdge(pHmm, dState, (iState+3));
            addEdge(pHmm, mState, (dState+3));
            addEdge(pHmm, iState, dState);
            addEdge(pHmm, dState, (dState+3));
            mState+=3;
            iState+=3;
            dState+=3;
        }
    }

    // Transitions to the endState and the last I-state
    addEdge(pHmm, mState, endState);
    addEdge(pHmm, mState, lastIState);
    addEdge(pHmm, lastIState, endState);
    addEdge(pHmm, lastIState, lastIState);
    addEdge(pHmm, dState, endState);
    addEdge(pHmm, dState, lastIState);
}

//////////////////////////////////////////////////////////////////////////////

//e.g.
//String<char> matr = "-AT---GAG-G-AG-CT-C--A--GT-G-CT---G";
//msaToProfileHmm(matr, hmm, 5);

template<typename TAlignmentChar, typename TAlphabet, typename TProbability, typename TSpec, typename TSize>
inline void
msaToProfileHmm(String<TAlignmentChar> const& matr,
                Graph<Hmm<TAlphabet, TProbability, TSpec> >& pHmm,
                TSize nSeq)
{
    typedef Graph<Hmm<TAlphabet, TProbability, TSpec> > THmm;

    // Consensus
    String<unsigned int> coverage;
    String<char> gappedConsensus;
    String<Dna> consensusSequence;
    consensusCalling(matr, consensusSequence, gappedConsensus, coverage, nSeq, MajorityVote() );

    // Build the HMM topology
    _createProfileHmm(pHmm,gappedConsensus);

    // Parameterize the pHmm
    TSize numCols = length(matr) / nSeq;
    _profileHmmCounter(pHmm, matr, gappedConsensus, nSeq, numCols);
}

*/


}  // namespace seqan

#endif //#ifndef SEQAN_HEADER_...