zscore

Computes the Z-score of the input.

The Z-score is computed by first calculating the mean and standard deviation of the input, by default in one pass, and then scaling the input using those values.

auto zscore(Slice!(Iterator, N, kind) slice, bool isPopulation)
template zscore(F, VarianceAlgo varianceAlgo = VarianceAlgo.hybrid, Summation summation = Summation.appropriate)
@fmamath
auto
zscore
(
Iterator
size_t N
SliceKind kind
)
(
Slice!(Iterator, N, kind) slice
,
bool isPopulation = false
)
auto zscore(SliceLike x, bool isPopulation)
template zscore(VarianceAlgo varianceAlgo = VarianceAlgo.hybrid, Summation summation = Summation.appropriate)
template zscore(F, string varianceAlgo, string summation = "appropriate")
template zscore(string varianceAlgo, string summation = "appropriate")

Members

Functions

zscore auto zscore(Slice!(Iterator, N, kind) slice, bool isPopulation)
auto zscore(SliceLike x, bool isPopulation)

Parameters

F: controls type of output
varianceAlgo: algorithm for calculating variance (default: VarianceAlgo.hybrid)
summation: algorithm for calculating sums (default: Summation.appropriate)

Return Value

The z-score of the input

Examples

zscore vector

import mir.algorithm.iteration: all;
import mir.math.common: approxEqual;
import mir.ndslice.slice: sliced;

auto x = [1.0, 2, 3, 4, 5, 6].sliced;

assert(x.zscore.all!approxEqual([-1.336306, -0.801784, -0.267261, 0.267261, 0.801784, 1.336306]));
assert(x.zscore(true).all!approxEqual([-1.46385, -0.87831, -0.29277, 0.29277, 0.87831, 1.46385]));

zscore dynamic array

import mir.algorithm.iteration: all;
import mir.math.common: approxEqual;

auto x = [1.0, 2, 3, 4, 5, 6];
assert(x.zscore.all!approxEqual([-1.336306, -0.801784, -0.267261, 0.267261, 0.801784, 1.336306]));
assert(x.zscore(true).all!approxEqual([-1.46385, -0.87831, -0.29277, 0.29277, 0.87831, 1.46385]));

zscore matrix

import mir.algorithm.iteration: all;
import mir.math.common: approxEqual;
import mir.ndslice.fuse: fuse;

auto x = [
    [1.0, 2, 3], 
    [4.0, 5, 6]
].fuse;

assert(x.zscore.all!approxEqual([[-1.336306, -0.801784, -0.267261], [0.267261, 0.801784, 1.336306]]));
assert(x.zscore(true).all!approxEqual([[-1.46385, -0.87831, -0.29277], [0.29277, 0.87831, 1.46385]]));

Column zscore matrix

import mir.algorithm.iteration: all, equal;
import mir.math.common: approxEqual;
import mir.ndslice.fuse: fuse;
import mir.ndslice.topology: alongDim, byDim, map;

auto x = [
    [20.0, 100.0, 2000.0],
    [10.0,   5.0,    2.0]
].fuse;

auto result = [
    [ 0.707107,  0.707107,  0.707107],
    [-0.707107, -0.707107, -0.707107]
].fuse;

// Use byDim with map to scale by row/column.
auto xZScoreByDim = x.byDim!1.map!zscore;
auto resultByDim = result.byDim!1;
assert(xZScoreByDim.equal!(equal!approxEqual)(resultByDim));

auto xZScoreAlongDim = x.alongDim!0.map!zscore;
auto resultAlongDim = result.alongDim!0;
assert(xZScoreAlongDim.equal!(equal!approxEqual)(resultAlongDim));

Can control how mean and standardDeviation are calculated and output type

import mir.algorithm.iteration: all;
import mir.math.common: approxEqual;
import mir.ndslice.slice: sliced;
import mir.ndslice.topology: repeat;

//Set sum algorithm or output type
auto a = [1, 1e100, 1, -1e100];

auto x = a.sliced * 10_000;

auto result = [6.123724e-101, 1.224745, 6.123724e-101, -1.224745].sliced;

assert(x.zscore!("online", "kbn").all!approxEqual(result));
assert(x.zscore!("online", "kb2").all!approxEqual(result));
assert(x.zscore!("online", "precise").all!approxEqual(result));
assert(x.zscore!(double, "online", "precise").all!approxEqual(result));

auto y = [uint.max, uint.max / 2, uint.max / 3].sliced;
assert(y.zscore!ulong.all!approxEqual([1.120897, -0.320256, -0.800641]));

The OpenD Programming Language

zscore

Members

Functions

Parameters

Return Value

Examples

See Also

Meta

Source