hmean

Computes the harmonic mean of the input.

By default, if F is not floating point type or complex type, then the result will have a double type if F is implicitly convertible to a floating point type or a type for which isComplex!F is true.

template hmean(F, Summation summation = Summation.appropriate)
template hmean(Summation summation = Summation.appropriate)
template hmean(F, string summation)
template hmean(string summation)
template hmean (
string summation
)

Parameters

summation: algorithm for calculating sums (default: Summation.appropriate)

Return Value

harmonic mean of all the elements of the input, must be floating point or complex type

Examples

Harmonic mean of vector

import mir.math.common: approxEqual;
import mir.ndslice.slice: sliced;

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

assert(x.hmean.approxEqual(6.97269));

Harmonic mean of matrix

import mir.math.common: approxEqual;
import mir.ndslice.fuse: fuse;

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

assert(x.hmean.approxEqual(6.97269));

Column harmonic mean of matrix

import mir.algorithm.iteration: all;
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 y = [13.33333, 9.52381, 3.996004];

// Use byDim or alongDim with map to compute mean of row/column.
assert(x.byDim!1.map!hmean.all!approxEqual(y));
assert(x.alongDim!0.map!hmean.all!approxEqual(y));

Can also pass arguments to hmean

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

//Set sum algorithm or output type
auto x = [1, 1e-100, 1, -1e-100].sliced;

assert(x.hmean!"kb2".approxEqual(2));
assert(x.hmean!"precise".approxEqual(2));
assert(x.hmean!(double, "precise").approxEqual(2));

//Provide the summation type
assert(float.max.repeat(3).hmean!double.approxEqual(float.max));

For integral slices, pass output type as template parameter to ensure output type is correct.

import mir.math.common: approxEqual;
import mir.ndslice.slice: sliced;

auto x = [20, 100, 2000, 10, 5, 2].sliced;

auto y = x.hmean;

assert(y.approxEqual(6.97269));
static assert(is(typeof(y) == double));

assert(x.hmean!float.approxEqual(6.97269));

hmean works for complex numbers and other user-defined types (provided they can be converted to a floating point or complex type)

import mir.math.common: approxEqual;
import mir.ndslice.slice: sliced;

auto x = [1.0 + 2i, 2 + 3i, 3 + 4i, 4 + 5i].sliced;
assert(x.hmean.approxEqual(1.97110904 + 3.14849332i));

Arbitrary harmonic mean

import mir.math.common: approxEqual;
import mir.ndslice.slice: sliced;

auto x = hmean(20.0, 100, 2000, 10, 5, 2);
assert(x.approxEqual(6.97269));

auto y = hmean!float(20, 100, 2000, 10, 5, 2);
assert(y.approxEqual(6.97269));

hmean

Parameters

Return Value

Examples

See Also

Meta

Source