center

Centers slice, which must be a finite iterable.

By default, slice is centered by the mean. A custom function may also be provided using centralTendency.

auto center(Slice!(Iterator, N, kind) slice)
template center(alias centralTendency = mean!(Summation.appropriate))
auto
center
(
Iterator
size_t N
SliceKind kind
)
(
Slice!(Iterator, N, kind) slice
)
auto center(T[] array)
auto center(T withAsSlice)

Members

Functions

center auto center(Slice!(Iterator, N, kind) slice)
auto center(T[] array)
auto center(T withAsSlice)

Return Value

The elements in the slice with the average subtracted from them.

Examples

Center 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.center.all!approxEqual([-2.5, -1.5, -0.5, 0.5, 1.5, 2.5]));

// Can center using different functions
assert(x.center!hmean.all!approxEqual([-1.44898, -0.44898, 0.55102, 1.55102, 2.55102, 3.55102]));
assert(x.center!gmean.all!approxEqual([-1.99379516, -0.99379516, 0.00620483, 1.00620483, 2.00620483, 3.00620483]));
assert(x.center!median.all!approxEqual([-2.5, -1.5, -0.5, 0.5, 1.5, 2.5]));

Center dynamic array

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

auto x = [1.0, 2, 3, 4, 5, 6];
assert(x.center.all!approxEqual([-2.5, -1.5, -0.5, 0.5, 1.5, 2.5]));

Center matrix

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

auto x = [
    [0.0, 1, 2], 
    [3.0, 4, 5]
].fuse;

auto y = [
    [-2.5, -1.5, -0.5], 
    [ 0.5,  1.5,  2.5]
].fuse;

assert(x.center.all!approxEqual(y));

Column center matrix

import mir.algorithm.iteration: all, equal;
import mir.math.common: approxEqual;
import mir.ndslice: 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 = [
    [ 5.0,  47.5,  999],
    [-5.0, -47.5, -999]
].fuse;

// Use byDim with map to compute average of row/column.
auto xCenterByDim = x.byDim!1.map!center;
auto resultByDim = result.byDim!1;
assert(xCenterByDim.equal!(equal!approxEqual)(resultByDim));

auto xCenterAlongDim = x.alongDim!0.map!center;
auto resultAlongDim = result.alongDim!0;
assert(xCenterByDim.equal!(equal!approxEqual)(resultAlongDim));

Can also pass arguments to average function used by center

import mir.ndslice.slice: sliced;

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

auto x = a.sliced * 10_000;

//Due to Floating Point precision, subtracting the mean from the second
//and fourth numbers in `x` does not change the value of the result
auto result = [5000, 1e104, 5000, -1e104].sliced;

assert(x.center!(mean!"kbn") == result);
assert(x.center!(mean!"kb2") == result);
assert(x.center!(mean!"precise") == result);

Passing a centered input to variance or standardDeviation with the assumeZeroMean algorithm is equivalent to calculating variance or standardDeviation on the original input.

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.center.variance!"assumeZeroMean".approxEqual(x.variance));
assert(x.center.standardDeviation!"assumeZeroMean".approxEqual(x.standardDeviation));

center

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