# fn()calculateCovarianceCalculates the covariance for the number of word occurrences for two words in a sequence of length n, given a background model.

Defined in ```void calculateCovariance(covariance, word1, word2, bgFrequencies, n); void calculateCovariance(covariance, word1, word2, bgModel, n); ```

## Parameters

 `covariance` Variance of the number of occurrences of the word in a sequence of length n given the model, double. String, usually of Dna. String, usually of Dna. String of double with the background frequencies representing MarkovModel to use. Length of the sequence where the occurrences of word are counted, int.

## Detailed Description

Calculates the covariance for the number of word occurrences for two words in a sequence of length n given a background model (Markov model or Bernoulli model). The covariance is influenced by the property of words to overlap, for example, the words ATAT and TATA have a high covariance since they are likely to overlap. The formula is based on (Robin et al., 2005).

### References

Robin, S., Rodolphe, F., and Schbath, S. (2005). DNA, Words and Models. Cambridge University Press. See Jonathan Goeke et al (to appear) for details on the implementation.

### Examples

Calculate the covariance for the number of occurrences of ATATAT and TATATA in a sequence of length 10000bp with p(A) = p(T) = 0.3 and p(C) = p(G) = 0.2.

```using namespace seqan;
double covar = 0.0;
int n = 10000;
DnaString word1 = "ATATAT";
DnaString word2 = "TATATA";
String<double> model;
resize(model, 4);
model[0] = 0.3;  // p(A)
model[1] = 0.2;  // p(C)
model[2] = 0.2;  // p(G)
model[3] = 0.3;  // p(T)
calculateCovariance(covar, word1, word2, model, n);  // covar = 4.74
```

Estimate a Markov model on a set of sequences and calculate the covariance for the number of occurrences of ATATAT and TATATA in a sequence of length 10000bp.

```using namespace seqan;
double covar = 0.0;
int n = 10000;
DnaString word1 = "ATATAT";
DnaString word2 = "TATATA";
StringSet<DnaString> sequences;
appendValue(sequences, "CAGCACTGATTAACAGGAATAAGCAGTTTACTTCTGTCAGAATATTGGGCATATATA"
"CTGGGACCCGTGTAATACTCTAATTTAATTAGGTGATCCCTGCGAAGTCTCCA");
MarkovModel<Dna, double> modelMM0(0);  // Bernoulli model
modelMM0.build(sequences);
calculateCovariance(covar, word1, word2, modelMM0, n);  // covar = 4.74
MarkovModel<Dna, double> modelMM1(1);  // First order Markov model
modelMM1.build(sequences);
calculateCovariance(covar, word1, word2, modelMM1, n);  // covar = 13.1541
```

## Data Races

If not stated otherwise, concurrent invocation is not guaranteed to be thread-safe.