ppALIGN API documentation

BoltzmannWeight Class Reference

#include <weights.hpp>

Inheritance diagram for BoltzmannWeight:
Weight

List of all members.

Public Member Functions

 BoltzmannWeight (const ScoreMatrix &s, double _scale, double temperature, double gap_open, double gap_extension, AlignmentType t, bool allow_DI=true, bool allow_ID=false)
 BoltzmannWeight (const Alphabet &alphabet1, const Alphabet &alphabet2, const std::string &matrix_name, double temperature, double gap_open, double gap_extension, AlignmentType t, bool allow_DI=true, bool allow_ID=false)
virtual ~BoltzmannWeight ()
xdouble Average (const Frequencies &freq1, const Frequencies &freq2) const
double Temperature () const
virtual bool IsBoltzmann () const

Public Attributes

double temper
double alpha
double beta
xdouble exp_alpha
xdouble exp_beta

Detailed Description

Boltzmannweights of the score matrix. Each pair of letters a and b is assigned a weight $w[a][b] = \exp ( s[a][b] / T / \lambda)$ where s is a score matrix and T the temperature. The relationship between the log-likelihood ratio and the score is given by $s[a][b] = \lambda * \log \frac{p(a,b)}{q(a)q(b)}$. $\lambda$ is stored in the field Weight::scale.

  • BoltzmannWeight::BoltzmannWeight(const ScoreMatrix & s,double,double, double,AlignmentType,bool,bool) Constructor from a integer valued score matrix with scale $ \lambda = 1$.
  • BoltzmannWeight::BoltzmannWeight(const Alphabet &, const Alphabet &, const std::string &, double,double, double,AlignmentType,bool,bool). Construcotr from a matrix name. The scale $ \lambda $ is set accordingly, e.g. $ 2 / \log(2)$ for the blosum matrix. In this case the canonical temperature where finite temperature alignment approximates the pair HMM is 1.

The free score is defined as

\[ F_T = T \lambda \log Z_T \]

and the expected score as

\[ \langle S \rangle_T = \frac{1}{Z_T}\sum_A S(A) \exp\left( \frac{S(A)}{T\lambda} \right) \]

with

\[ Z_T = \sum_A \exp\left(\frac{S(A)}{T \lambda}\right) \]

. The image below shows how the free score and the expected score variies with temperature. In the limit $ T \rightarrow 0$ both values approach the value of the optimal score.

freescore.png
Examples:

alternative_alignments.cpp, freescore.cpp, and pairprobmap.cpp.

Definition at line 232 of file weights.hpp.

Constructor & Destructor Documentation

BoltzmannWeight::BoltzmannWeight ( const ScoreMatrix &  s,
double  _scale,
double  temperature,
double  gap_open,
double  gap_extension,
AlignmentType  t,
bool  allow_DI = true,
bool  allow_ID = false 
)

Construct the weights from the score matrix and temperature.

Assume that the score matrix is given by the integer values stored in s[a][b]. The weights are given by $ w[a][b] = \exp(s[a][b] / temperature / lambda) $. If the scale is not known use the method ScoreMatrix::GetScale(). It is stored in Weight::scale. Gaps are given the weight $\exp(-\frac{\alpha}{ \lambda T })$ and $\exp(-\frac{\beta}{ \lambda T})$, where

  • $\alpha$ = gap_open + gap_extension.
  • $\beta$ = gap_extension.
    Parameters:
    s score matrix (integer valued)
    scale scale of the matrix
    temperature temperature
    gap_open gap open penalty
    gap_extension gap extension penalty
    t type of the alignment
    allow_DI transitions from deletion to insertion possible
    allow_ID transitions from insertion to deletion possible
BoltzmannWeight::BoltzmannWeight ( const Alphabet &  alphabet1,
const Alphabet &  alphabet2,
const std::string &  matrix_name,
double  temperature,
double  gap_open,
double  gap_extension,
AlignmentType  t,
bool  allow_DI = true,
bool  allow_ID = false 
)

Construct the weights from the score matrix and temperature. Assume that the name of the score matrix is known and supported by ppalign. The score matrix is scaled by $\exp[ p(a,b)/q(a)/q(b)/T ]$ The scale of the corresponding matrix is stored in Weight::scale. Gaps are given the weight $\exp(-\frac{\alpha}{\lambda T})$ and $\exp(-\frac{\beta}{\lambda T})$, where

  • $\alpha$ = gap_open + gap_extension.
  • $\beta$ = gap_extension.
    Parameters:
    alphabet1 alphabet of the first sequence
    alphabet2 alphabet of the second sequence
    matrix_name name of the scoring matrix
    temperature temperature T
    gap_open gap open penalty
    gap_extension gap extension penalty
    t alignment type
    allow_DI transitions from deletion to insertion possible
    allow_ID transitions from insertion to deletion possible
virtual BoltzmannWeight::~BoltzmannWeight (  )  [inline, virtual]

Destructor.

Definition at line 329 of file weights.hpp.

Member Function Documentation

xdouble BoltzmannWeight::Average ( const Frequencies &  freq1,
const Frequencies &  freq2 
) const

Average the weights with respect to frequencies freq1 and freq2.

Parameters:
freq1 Frequencies for the first letter
freq2 Frequencies for the second letter
Returns:
$[ \sum_{a,b} p(a) p(b) w[a][b]$ where p=freq1 and q=freq2
Remarks:
ensure that freq1 and freq2 are normalized
virtual bool BoltzmannWeight::IsBoltzmann (  )  const [inline, virtual]
Returns:
true

Reimplemented from Weight.

Definition at line 349 of file weights.hpp.

double BoltzmannWeight::Temperature (  )  const [inline]

Temperature

Returns:
temperature

Definition at line 343 of file weights.hpp.

Member Data Documentation

double BoltzmannWeight::alpha

gap open penality

Definition at line 243 of file weights.hpp.

double BoltzmannWeight::beta

gap extension penality

Definition at line 245 of file weights.hpp.

xdouble BoltzmannWeight::exp_alpha

Weights for gap open $\exp(-frac{\alpha}{T \lambda})$. see different constructor for the definition of the scale $\lambda$.

Definition at line 255 of file weights.hpp.

xdouble BoltzmannWeight::exp_beta

Weights for gap extension $ \exp(-frac{\alpha}{T \lambda})$. See different constructor for the definition of the scale

Definition at line 265 of file weights.hpp.

double BoltzmannWeight::temper

temperature value.

Definition at line 241 of file weights.hpp.

The documentation for this class was generated from the following file: