Batteries user guide : BatComplex

# Module BatComplex

    module BatComplex: sig .. end

Additional and modified functions for complex numbers.

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 = Complex.t = {

`` | `re : `float`;`
`` | `im : `float`;`

}

    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.

    val operations : t BatNumber.numeric

    val inv : t -> t

`inv x` returns the value of `1/x`

    val succ : t -> t

Add `BatComplex.one` to this number.

    val pred : t -> t

Remove `BatComplex.one` from this number.

    val abs : t -> t

`abs c` returns the module of this complex number, i.e. `abs c = Float.sqrt((re c) *. (re c) +. (im c) *. (im c) )`

    val modulo : t -> t -> t

    val pow : t -> t -> t

    val compare : t -> t -> int

    val ord : t -> t -> BatOrd.order

    val equal : t -> t -> bool

    val of_int : int -> t

    val to_int : t -> int

`to_int c` is the integer part of the real part of `c`

    val of_string : string -> t

`of_string s` accepts strings with the following formats:

(<int>|<float>) (+|-) i ( * | . | ) (<int>|<float>)

where (a|b|c) is either a or b or c.

In addition the following degenerate formats are also accepted:

(+|-) i ( * | . | ) (<int>|<float>)

(<int>|<float>) (+|-) i

(<int>|<float>)

    val to_string : t -> string

    val (+) : t -> t -> t

    val (-) : t -> t -> t

    val ( * ) : t -> t -> t

    val (/) : t -> t -> t

    val ( ** ) : t -> t -> t

    val (--) : t -> t -> t BatEnum.t

    val (---) : t -> t -> t BatEnum.t

    val of_float : float -> t

`Complex.of_float x` returns the complex number `x+0i`

    val to_float : t -> float

`Complex.to_float (a+bi)` returns the float `a`

###### Submodules grouping all infix operators

    module Infix: BatNumber.Infix  with type bat__infix_t = t

    module Compare: BatNumber.Compare  with type bat__compare_t = t

###### Boilerplate code

    val print : 'a BatInnerIO.output -> t -> unit

Printing