Safe Haskell | Safe |
---|---|

Language | Haskell98 |

- wilson :: Double -> Int -> Int -> (Double, Double, Double)
- invnormcdf :: (Ord a, Floating a) => a -> a
- choose :: Integral a => a -> a -> a
- estimateComplexity :: (Integral a, Floating b, Ord b) => a -> a -> Maybe b
- showNum :: Show a => a -> String
- showOOM :: Double -> String
- float2mini :: RealFloat a => a -> Word8
- mini2float :: Fractional a => Word8 -> a
- log1p :: (Floating a, Ord a) => a -> a
- expm1 :: (Floating a, Ord a) => a -> a
- phredplus :: Double -> Double -> Double
- phredminus :: Double -> Double -> Double
- phredsum :: [Double] -> Double
- (<#>) :: Double -> Double -> Double
- phredconverse :: Double -> Double

# 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

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

To get `z`

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

:

df*dz = 1 - D*z
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.

float2mini :: RealFloat a => a -> Word8 Source

Conversion to 0.4.4 format minifloat: This minifloat fits into a byte. It has no sign, four bits of precision, and the range is from 0 to 63488, initially in steps of 1/8. Nice to store quality scores with reasonable precision and range.

mini2float :: Fractional a => Word8 -> a Source

Conversion from 0.4.4 format minifloat, see `float2mini`

.

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

phredplus :: Double -> Double -> Double infixl 3 Source

Computes `-10 * log_10 (10 ** (-x/10) + 10 ** (-y/10))`

without
losing precision. Used to add numbers on "the Phred scale",
otherwise known as (deci-)bans.

phredminus :: Double -> Double -> Double infixl 3 Source

Computes `-10 * log_10 (10 ** (-x/10) - 10 ** (-y/10))`

without
losing precision. Used to subtract numbers on "the Phred scale",
otherwise known as (deci-)bans.

phredsum :: [Double] -> Double Source

Computes `-10 * log_10 (sum [10 ** (-x/10) | x <- xs])`

without losing
precision.

phredconverse :: Double -> Double Source

Computes `1-p`

without leaving the "Phred scale"