Module

Documentation

Module Complex
 :  sig end

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 ;
 }

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

val zero : t

The complex number 0 .

val one : t

The complex number 1 .

val i : t

The complex number i .

val neg : t -> t

Unary negation.

val conj : t -> t

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

val add : t -> t -> t

Addition

val sub : t -> t -> t

Subtraction

val mul : t -> t -> t

Multiplication

val inv : t -> t

Multiplicative inverse ( 1/z ).

val div : t -> t -> t

Division

val 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

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

val norm : t -> float

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

val 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

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

val exp : t -> t

Exponentiation. exp z returns e to the z power.

val log : t -> t

Natural logarithm (in base e ).

val pow : t -> t -> t

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