Math extended

(add m a)

Add `a` to matrix `m` where it can be matrix or scalar.
Matrix `m` is mutated.

(add-to-mean m n v)

Adds new value `v` to mean `m` from `n` values.

(approx-eq a e &opt t)

Approximate equality between actual number `a`
and expected number `e`. Default tolerance `t`
is `epsilon`.

(bernoulli-distribution p)

Creates Bernoulli distribution from probability `p` in the tuple.

(binominal-coeficient n k)

Computes binominal coefficient from set of size `n`
and sample size `k`.

(binominal-distribution t p)

Creates binominal distribution from trials `t`
and probability `p` in the tuple.

(check-probability p)

Asserts that probability is in the [0 1] range.

Chi Squared distribution table.

(cols m)

Returns number of columns of matrix `m`.

(copy xs)

Deep copy an array or view `xs`.

(cumulative-std-normal-probability z)

Computes standard normal probability for `y`.

(det m)

Computes determinant of matrix `m`.

(dot v1 v2)

Dot product between two row vectors.

(dot-fast v1 v2)

Fast dot product between two row vectors of equal size.

Epsilon constant

(expand-m n m)

Embeds a matrix `m` inside an identity matrix of size n.

(extent xs)

Returns the minimum & maximum number in an `xs` as tuple.

(factor n)

Returns an array containing the prime factors of `n`.

(factorial n)

Returns factorial of `n`.

(fliplr m)

Flip a matrix leftside-right.

(flipud m)

Flip a matrix upside-down.

(geometric-mean xs)

Gets the geometric mean from `xs`.

(get-only-el m)

Convenience macro for geting first element
from first row of the two dimensional array `m`.

(harmonic-mean xs)

Gets the harmonic mean from `xs`.

(ident c)

Creates identity matrix with `c` x `c` size.

(interquartile-range xs)

Gets the interquartile range from `xs`.

(math/invmod a m)

Modular multiplicative inverse of `a` mod `m`. Both arguments must be integer. The return value has the same type as `m`. If no inverse exists, returns `math/nan` instead.

(math/jacobi a m)

Computes the Jacobi Symbol (a|m).

(join-cols m1 m2)

Stack horizontally columns of two matrices.

(join-rows m1 m2)

Stack vertically rows of two matrices.

(linear-regression coords)

Computes the slope `:m` and y-intercept `:b`
of the function in the struct from set of coordinates.

(linear-regression-line {:b b :m m})

Constructs function from struct returned by linear regression.

(m-approx= m1 m2 &opt tolerance)

Compares two matrices of equal size for equivalence within epsilon.

(matmul ma mb)

Matrix multiplication between matrices `ma` and `mb`. Does not mutate.

(median xs)

Gets the median value from `xs`

(median-absolute-deviation xs)

Gets median absolute deviation from `xs`.

(minor m x y)

Computes minor matrix of matrix `m` and `x`, `y`.

(mode xs)

Gets the mode value from `xs`.

(mop m op a)

Mutates every cell of the matrix `m` with `op`
and corresponding cell from matrix arg `a`.

(mul m a)

Multiply matrix `m` with `a` which can be matrix or a list.
Mutates `m`. A list `a` will be converted to column vector
then multiplifed from the right as `x * a`.

(math/mulmod a b m)

Modular multiplication of `a` and `b` mod `m`. All arguments must be integer. The return value has the same type as `m`.

(next-prime n)

Returns the next prime number strictly larger than `n`.

(normalize-v xs)

Returns normalized vector of `xs` by Euclidian (L2) norm.

(outer v1 v2)

Outer product of vectors `v1` and `v2`.

(perm m)

Computes permanent of the matrix `m`.

(permutation-test xs ys &opt a k)

Conducts a permutation test to determine if two data sets
`xs` and `ys` are *significantly* different from each other.
You can use alternative hypothesis `a`, which defaults to `:two-side`,
with `:greater` and `:lesser` being the other two options.
The last optional argument is `k` number of values
in permutation distribution

(permutations s &opt k)

Returns permutations of length `k` from members of `s`

(poisson-distribution lambda)

Creates Poisson distribution from `lambda` in tuple.

(math/powmod a b m)

Modular exponentiation of `a` to the power of `b` mod `m`. All arguments must be integer. The return value has the same type as `m`.

(prime? n)

A primality test, deterministic for all `n` less than 2^63.

(primes)

A boundless prime number generator.

(qr m)

Stable and robust QR decomposition of a matrix. 
Decompose a matrix using Householder transformations. O(n^3).

(qr1 m)

Transform using Householder reflections by one step.

(quantile xs p)

Gets the quantile value from `xs` at `p` from unsorted population.

(quantile-rank xs p)

Gets the quantile rank of value `v` from unsorted `xs`.

(quantile-rank-sorted xs v)

Gets the quantile rank of value `v` from sorted `xs`.

(quantile-sorted xs p)

Gets the quantile value from `xs` at `p` from sorted population.

(quickselect arr k &opt left right)

Rearrange items in `arr` so that all items in `[left, k]` range
are the smallest.
The `k`-th element will have the `(k - left + 1)`-th smallest value
in `[left, right]`.
Mutates `arr`.

(relative-err a e)

Gets the relative err between actual number `a`
and expected number `e`.

(root-mean-square xs)

Gets the root mean square from `xs`.

(row->col xs)

Transposes a row vector `xs` to col vector. Returns `xs` if it has higher dimensions.

(rows m)

Returns number of rows of matrix `m`.

(sample-correlation xs ys)

Gets the sample correlation between `xs` and `ys`.

(sample-covariance xs ys)

Gets the sample covariance between `xs` and `ys`.

(sample-skewness xs)

Gets the sample skeweness from the `xs`.

(sample-standard-deviation xs)

Gets sample standard deviation from `xs`.

(sample-variance xs)

Get the sample variance from `xs`.

(scalar c s)

Creates scalar `s` matrix with `c` x `c` size.

(scale v k)

Scale a vector `v` by a number `k`.

(shuffle-in-place xs)

Generate random permutation of the array `xs`
which is shuffled in place.

(sign x)

Sign function.

(size m)

Returns tuple with the matrix `m` size [rows cols].

(slice-m m rslice cslice)

Slice a matrix `m` by rows and columns.

(sop m op & a)

Mutates every cell of the matrix `m` with `op`
and variadic args `a`.

(squeeze m)

Concatenate a list of rows into a single row. Does not mutate `m`.

(standard-deviation xs)

Gets the standard deviation from `ds`.

Computed standard normal table.

(subtract v1 v2)

Elementwise subtract vector `v2` from `v1`.

(sum-compensated xs)

Returns sum of the members of `xs` with Kahan-Babushka algorithm.

(sum-nth-power-deviations xs n)

Get the sum of deviations to the n power.

(svd m &opt n-iter)

Simple Singular-Value-Decomposition based on repeated QR decomposition. The algorithm converges at O(n^3).

(swap arr i j)

Swaps members with indices `i` and `j` of arr.
Noop when `i` equals `j`.

(t-test xs expv)

Computes one sample t-test comparing the mean of `xs`
to known value `expv`.

(t-test-2 xs ys &opt d)

Computes two sample t-test of two samples `xs` and `ys`
with difference optional `d` which defaults to 0.

(trans m)

Tansposes a list of row vectors.

(unit-e n k)

Unit vector of `n` dimensions along dimension `k`.

(variance xs)

Get the variance from the `xs`.

(z-score x m d)

Gets the standard score for number `x` from mean `m`
and standard deviation `d`.

(zero c &opt r)

Creates vector of length `c`, or matrix if `r`
is provided, and fills it with zeros.