OCaml library : Complex (original) (raw)

Module Complex

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 = {

}

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

val zero : [t](Complex.html#TYPEt)

val one : [t](Complex.html#TYPEt)

val i : [t](Complex.html#TYPEt)

val neg : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

val conj : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

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

val add : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

val sub : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

val mul : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

val inv : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

Multiplicative inverse (1/z).

val div : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

val sqrt : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

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

val norm2 : [t](Complex.html#TYPEt) -> float

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

val norm : [t](Complex.html#TYPEt) -> float

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

val arg : [t](Complex.html#TYPEt) -> 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](Complex.html#TYPEt)

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

val exp : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

Exponentiation. exp z returns e to the z power.

val log : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

Natural logarithm (in base e).

val pow : [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt) -> [t](Complex.html#TYPEt)

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