Numeric mathematics.
module Biocaml_math: sigval log : ?base:float -> float -> floatbase not given.val log10 : float -> floatval log2 : float -> floatval even : int -> boolval odd : int -> boolval min : float array -> floatval max : float array -> floatval range : float -> float -> float -> float arrayrange 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 listval range_floats : float -> float -> float -> float listval mean : float array -> floatval variance : float array -> floatval rms : float array -> floatval stdv : float array -> floatval median : float array -> floatval pseudomedian : float array -> floatval mad : float array -> floatval quantile_normalization : float array array -> float array arraym 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) arraycmp (default = Pervasives.compare) for comparison.val prediction_values : int -> int -> int -> int -> float * float * float * floatprediction_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 -> floatpearson 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 arrayrank 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 -> floatspearman 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 -> floatval ltqnorm : float -> float
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 -> floatval wilcoxon_rank_sum_to_p : float array -> float array -> floatval wilcoxon_rank_sum : ?alpha:float -> float array -> float array -> boolwilcoxon_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.val row : 'a array array -> int -> 'a arrayrow 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 arraycolumn 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 arraytranspose 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.val idxsort : ('a -> 'a -> int) -> 'a array -> int arrayidxsort 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) arrayfind_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 arrayfind_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 -> intval epsilon : (int -> int -> float) -> int -> int -> floatepsilon f init fin applies f n fin to all numbers from init to fin and adds them up.val shuffle : 'a array -> 'a arrayshuffle arr takes an array and randomly shuffles it.end