innmind / math
Library holding a set of math functions
Requires
- php: ~8.2
- innmind/immutable: ~4.15|~5.0
Requires (Dev)
- innmind/coding-standard: ~2.0
- phpunit/phpunit: ~9.0
- vimeo/psalm: ~5.15
README
Expose some math concepts as objects.
Note: all classes are immutable.
Algebra
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
By doing math like this you calculate the data that's really needed, so if you pass around a variable but never check it's content then it will never be calculated. The other advantage is that by casting to a string an operation you can see what the operation steps are (might be helpful for debugging a function operation).
Note: by calling collapse
on a Number
it will try to optimize some calculations such as squareRoot(square(x))
will directly return x
thus avoiding rounding errors.
Definition sets
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
Polynom
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
You also can call the derived
number for any point x
(as well as the tangent
). You can have access to the primitive
and derivative
of the polynom, the last one is notably used to calculate an Integral
.
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)
Regression
Polynomial Regression
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
Linear regression
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
Probabilities
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
Quantile
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