README

将一些数学概念作为对象暴露。

注意：所有类都是不可变的。

代数

use Innmind\Math\Algebra\{
    Value,
    Integer,
};

$perimeter = Value::two->multiplyBy(Value::pi, $r = Integer::of(42)); // value still not calculated
echo $perimeter->toString(); // 2 x π x 42 (value still not calculated)
echo $perimeter->value(); // 263.89378290154

通过这种方式进行数学运算可以计算实际所需的数据，所以如果你传递一个变量但从未检查其内容，则它将永远不会被计算。另一个优点是，通过将操作转换为字符串，你可以看到操作的步骤（可能有助于调试函数操作）。

注意：在Number上调用collapse将尝试优化某些计算，例如squareRoot(square(x))将直接返回x，从而避免舍入误差。

定义集

use Innmind\Math\{
    DefinitionSet\Range,
    Algebra\Integer,
    Algebra\Value,
};

$set = Range::exlusive(Value::zero, Value::infinite);
echo $set->toString(); // ]0;+∞[
$set->contains(Integer::of(42)); // true
$set->contains(Integer::of(-42)); // false

$set = $set->union(
    Range::exclusive(Value::negativeInfinite, Value::zero),
);
echo $set; // ]-∞;0[∪]0;+∞[
$set->contains(Integer::of(-42)); // true
$set->contains(Integer::of(0)); // false

多项式

use Innmind\Math\Polynom\Polynom;

$p = Polynom::interceptAt($intercept = Integer::of(1))
    ->withDegree(Integer::of(1), new Number(0.5))
    ->withDegree(Integer::of(2), new Number(0.1));
$p(Integer::of(4))->value(); // 4.6
echo $p->toString(); // 0.1x^2 + 0.5x + 1

你也可以为任何点x调用derived数字（以及tangent）。你可以访问多项式的primitive和derivative，后者特别用于计算积分。

use Innmind\Math\Polynom\Integral;

$integral = Integral::of($somePolynom);
$area = $integral(Integer::of(0), new Integral(42)); // find the area beneath the curve between point 0 and 42
echo $integral->toString(); // ∫(-1x^2 + 4x)dx = [(-1 ÷ (2 + 1))x^3 + (4 ÷ (1 + 1))x^2] (if the polynom is -1x^2 + 4x)

回归

多项式回归

use Innmind\Math\{
    Regression\PolynomialRegression,
    Regression\Dataset,
    Algebra\Integer,
};

$regression = PolynomialRegression::of(
    Dataset::of([
        [-8, 64],
        [-4, 16],
        [0, 0],
        [2, 4],
        [4, 16],
        [8, 64],
    ]),
);
// so in essence it found x^2
$regression(Integer::of(9))->value(); // 81.0

线性回归

use Innmind\Math\{
    Regression\LinearRegression,
    Regression\Dataset,
    Algebra\Integer;
};

$r = LinearRegression::of(Dataset::of([
    [0, 0],
    [1, 1],
    [2, 0],
    [3, 2],
]));
$r->intercept()->value(); // 0.0
$r->slope()->value(); // 0.5
$r(Integer::of(4))->value(); // 2.0

概率

use Innmind\Math\{
    Regression\Dataset,
    Probabilities\Expectation,
    Probabilities\StandardDeviation,
    Probabilities\Variance,
};

$dataset = Dataset::of([
    [-1, 4/6], // 4 6th of a chance to obtain a -1
    [2, 1/6],
    [3, 1/6],
]);
echo Expectation::of($dataset)()->value(); //0,1666666667 (1 6th)
echo StandardDeviation::of($dataset)()->value(); //√(101/36)
echo Variance::of($dataset)()->value(); //101/36

分位数

use Innmind\Math\Quantile\Quantile;
use Innmind\Immutable\Sequence;

$q = Quantile::of(Sequence::of(...\range(1,12)));
$q->min()->value(); // 1
$q->max()->value(); // 12
$q->mean(); // 6.5
$q->median()->value(); // 6.5
$q->quartile(1)->value(); // 3.5 because 25% of values from the set are lower than 3.5
$q->quartile(3)->value(); // 9.5 because 75% of values from the set are lower than 9.5