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.