Module Biocaml_math (.ml)

Numeric mathematics.

module Biocaml_math: 

Arithmetic Operations

val log : ?base:float -> float -> float
Logarithm. Default to natural logarithm if base not given.
val log10 : float -> float
Base 10 logarithm.
val log2 : float -> float
Base 2 logarithm.
val even : int -> bool
True if given integer is even.
val odd : int -> bool
True if given integer is odd.
val min : float array -> float
Return minimum value in given array. Behavior undefined if array length = 0.
val max : float array -> float
Return maximum value in given array. Behavior undefined if array length must = 0.
val range : float -> float -> float -> float array
range step first last returns array [|first; first +. step; ... |], where last element will be less than or equal to last. If first > last, step subtracted and last element must be greater than or equal to last. In either case, step must be positive.
val range_ints : int -> int -> int -> int list
val range_floats : float -> float -> float -> float list

Statistical Operations

val mean : float array -> float
Mean. Behavior undefined if array length = 0.
val variance : float array -> float
Variance. Behavior undefined if array length < 2.
val rms : float array -> float
Root mean square. Behavior undefined if array length = 0.
val stdv : float array -> float
Standard deviation. Behavior undefined if array length < 2.
val median : float array -> float
Median. Behavior undefined if array length = 0.
val pseudomedian : float array -> float
Pseudomedian is the median of all pairwise averages of values in given array (not including self-pairs). Behavior undefined if array length = 0.
val mad : float array -> float
Median absolute deviation (MAD). Behavior undefined if array length = 0.
val quantile_normalization : float array array -> float array array
Input matrix m should be arranged such that m.(i).(j) is the ith measurement in experiment j. Behavior undefined if m is not rectangular.
val histogram : ?cmp:('a -> 'a -> int) -> 'a array -> ('a * int) array
Return histogram of values using cmp (default = for comparison.
val prediction_values : int -> int -> int -> int -> float * float * float * float
prediction_values tp tn fp fn takes 4 arguments: the number of true-positives tp, true-negatives tn, false-positives fp, and false-negatives fn. It returns a quadruple of 4 measures of prediction accuracy: sensitivity, specificity, positive prediction accuracy, and negative prediction accuracy.
val pearson : float array -> float array -> float
pearson arr1 arr2 computes the Pearson product-moment correlation coefficient of two float arrays. See wikipedia for the formula. NB: everything is divided by n, not by n - 1.
val rank : float array -> float array
rank arr returns an array of ranked values, where ties are given the mean of what the rank would otherwise be. For example, rank [|2.;1.;2.|] returns |2.5.;1.;2.5|.
val spearman : float array -> float array -> float
spearman arr1 arr2 computes the Spearman rank correlation coefficient of two float arrays. See wikipedia for the formula. Essentially, it ranks the two arrays using rank, and then applies the pearson function.
val cnd : float -> float
Cumulative distribution function.
val ltqnorm : float -> float
Lower tail quantile for standard normal distribution function.

This function returns an approximation of the inverse cumulative standard normal distribution function. I.e., ltqnorm p returns an approximation to the X satisfying p = Pr where Z is a random variable from the standard normal distribution.

The algorithm uses a minimax approximation by rational functions and the result has a relative error whose absolute value is less than 1.15e-9.

val wilcoxon_rank_sum_to_z : float array -> float array -> float
As below, except returns a z value.
val wilcoxon_rank_sum_to_p : float array -> float array -> float
Performs the wilcoxon rank sum on two float arrays and returns the p-value. This assumes a two-tailed distribution.
val wilcoxon_rank_sum : ?alpha:float -> float array -> float array -> bool
wilcoxon_rank_sum ~alpha=(float) arr1 arr2 performs the Wilcoxon rank sum test on two arrays with an optional argument alpha, set to 0.05 by default. If the null hypothesis is rejected -- that is, there is no significant difference between the two arrays, wilcoxon_rank_sum returns false. NB: this is for two-tailed distributions.

Matrix Operations

val row : 'a array array -> int -> 'a array
row m i returns the ith row of matrix m. By convention this is m.(i), but a copy is returned. Raise Failure if m does not contain at least i+1 rows.
val column : 'a array array -> int -> 'a array
column m i extracts the ith column of matrix m. Raise Failure if every row of m does not have at least i+1 columns. See also Biocaml_math.row.
val transpose : 'a array array -> 'a array array
transpose m transpose the given matrix m. If the number of rows Array.length m ot the number of columns Array.length a.(0) is 0, return the empty matrix [| |]. Behavior undefined if m is not rectangular.

More Specialized Operations

val idxsort : ('a -> 'a -> int) -> 'a array -> int array
idxsort cmp a is like Array.sort but a is unaltered, and instead an array of the indices in sorted order is returned. E.g. idxsort compare [|'c'; 'd'; 'b'|] will return [|2; 0; 1|].
val find_regions : ?max_gap:int -> ('a -> bool) -> 'a array -> (int * int) array
find_regions ~max_gap pred a returns an array of (first,last) index pairs denoting boundaries (inclusive) of regions found in a. Each region is the longest contiguous sequence of values in a satisfying pred. A maximum of max_gap values within the region are allowed to fail pred but still get counted as if they had satisfied it. For example, find_regions ~max_gap:1 (fun k -> k >= 3) [|1; 3; 3; 2; 3; 1; 1; 3; 3|] will return [|(1,4); (7,8)|]. Default max_gap = 0, raise Failure if set to negative value.
val find_min_window : ?init_direction:string -> 'a array -> (int -> int -> bool) -> int -> 'a array
find_min_window a pred i finds the minimum sized window within a centered around index i that satisfies pred. Function pred is passed the window's start and end indices. Successively larger windows are created starting from [i, i] and the first one to satisfy pred is returned. An empty array is returned if the maximum window size, i.e. all of a, is reached and pred still fails. Raise Failure if i is not a valid index for a.

The first window tried is [i, i], by default the second is [i, i+1], the third [i-1, i+1], the fourth [i-1, i+2], and so on. The optional init_direction must be either "fwd" or "rev". If "fwd", which is the default, the window size is initially increased in the forward direction. If "rev", the second window tried will be [i-1, i]. If the array's boundary is reached on either side, the size continues to be increased by incrementing on the opposing side.

val factorial : int -> int
val epsilon : (int -> int -> float) -> int -> int -> float
epsilon f init fin applies f n fin to all numbers from init to fin and adds them up.
val shuffle : 'a array -> 'a array
shuffle arr takes an array and randomly shuffles it.