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Module Biocaml_math

module Biocaml_math: sig .. end

Numeric mathematics.

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 = Pervasives.compare) 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 given matrix m. Okay if number of rows (length m) is 0. If there are rows, they must not be empty; raise Failure if they are. 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

Self-explanatory.

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.