Module Stdlib.Complex

Complex numbers.

This module provides arithmetic operations on complex numbers. Complex numbers are represented by their real and imaginary parts (cartesian representation). Each part is represented by a double-precision floating-point number (type float).

type t = {
  re : float;
  im : float;
}

type t = {
  re: float,
  im: float,
};

The type of complex numbers. re is the real part and im the imaginary part.

val zero : t

let zero: t;

The complex number 0.

val one : t

let one: t;

The complex number 1.

val i : t

let i: t;

The complex number i.

val neg : t -> t

let neg: t => t;

Unary negation.

val conj : t -> t

let conj: t => t;

Conjugate: given the complex x + i.y, returns x - i.y.

val add : t -> t -> t

let add: t => t => t;

Addition

val sub : t -> t -> t

let sub: t => t => t;

Subtraction

val mul : t -> t -> t

let mul: t => t => t;

Multiplication

val inv : t -> t

let inv: t => t;

Multiplicative inverse (1/z).

val div : t -> t -> t

let div: t => t => t;

Division

val sqrt : t -> t

let sqrt: t => t;

Square root. The result x + i.y is such that x > 0 or x = 0 and y >= 0. This function has a discontinuity along the negative real axis.

val norm2 : t -> float

let norm2: t => float;

Norm squared: given x + i.y, returns x^2 + y^2.

val norm : t -> float

let norm: t => float;

Norm: given x + i.y, returns sqrt(x^2 + y^2).

val arg : t -> float

let arg: t => float;

Argument. The argument of a complex number is the angle in the complex plane between the positive real axis and a line passing through zero and the number. This angle ranges from -pi to pi. This function has a discontinuity along the negative real axis.

val polar : float -> float -> t

let polar: float => float => t;

polar norm arg returns the complex having norm norm and argument arg.

val exp : t -> t

let exp: t => t;

Exponentiation. exp z returns e to the z power.

val log : t -> t

let log: t => t;

Natural logarithm (in base e).

val pow : t -> t -> t

let pow: t => t => t;

Power function. pow z1 z2 returns z1 to the z2 power.