biohazard-0.6.5: bioinformatics support library

Bio.Util.Numeric

Synopsis

# Documentation

wilson :: Double -> Int -> Int -> (Double, Double, Double) Source

Random useful stuff I didn't know where to put.

calculates the Wilson Score interval. If `(l,m,h) = wilson c x n`, then `m` is the binary proportion and `(l,h)` it's `c`-confidence interval for `x` positive examples out of `n` observations. `c` is typically something like 0.05.

invnormcdf :: (Ord a, Floating a) => a -> a Source

choose :: Integral a => a -> a -> a Source

Binomial coefficient: `n choose k == n! / ((n-k)! k!)`

estimateComplexity :: (Integral a, Floating b, Ord b) => a -> a -> Maybe b Source

Try to estimate complexity of a whole from a sample. Suppose we sampled `total` things and among those `singles` occured only once. How many different things are there?

Let the total number be `m`. The copy number follows a Poisson distribution with paramter `lambda`. Let `z := e^{lambda}`, then we have:

P( 0 ) = e^{-lambda} = 1/z P( 1 ) = lambda e^{-lambda} = ln z / z P(>=1) = 1 - e^{-lambda} = 1 - 1/z

singles = m ln z / z total = m (1 - 1/z)

D := totalsingles = (1 - 1z) * z / ln z f := z - 1 - D ln z = 0

To get `z`, we solve using Newton iteration and then substitute to get `m`:

dfdz = 1 - Dz z' := z - z (z - 1 - D ln z) / (z - D) m = singles * z /log z

It converges as long as the initial `z` is large enough, and `10D` (in the line for `zz` below) appears to work well.

showNum :: Show a => a -> String Source

log1p :: (Floating a, Ord a) => a -> a Source

Computes `log (1+x)` to a relative precision of `10^-8` even for very small `x`. Stolen from http://www.johndcook.com/cpp_log_one_plus_x.html

expm1 :: (Floating a, Ord a) => a -> a Source

Computes `exp x - 1` to a relative precision of `10^-10` even for very small `x`. Stolen from http://www.johndcook.com/cpp_expm1.html

(<#>) :: (Floating a, Ord a) => a -> a -> a infixl 5 Source

Computes `log (exp x + exp y)` without leaving the log domain and hence without losing precision.

lsum :: (Floating a, Ord a) => [a] -> a Source

Computes ( log ( sum_i e^{x_i} ) ) sensibly. The list must be sorted in descending(!) order.

llerp :: (Floating a, Ord a) => a -> a -> a -> a Source

Computes ( log left( c e^x + (1-c) e^y right) ).

sigmoid2 :: (Num a, Fractional a, Floating a) => a -> a Source

Kind-of sigmoid function that maps the reals to the interval `[0,1)`. Good to compute a probability without introducing boundary conditions.

isigmoid2 :: (Num a, Fractional a, Floating a) => a -> a Source

Inverse of `sigmoid2`.