Module `BatComplex`

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).

author Xavier Leroy (base module)

author Gabriel Scherer

author David Teller

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 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 operations : t BatNumber.numeric

val inv : t -> t

inv x returns the value of 1/x

val succ : t -> t

Add one to this number.

val pred : t -> t

Remove 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

Install

dune-project
Dependency

Authors

Maintainers

Sources

doc/batteries/BatComplex/index.html

Module `BatComplex`

Submodules grouping all infix operators

Boilerplate code

package batteries

Install

dune-project Dependency

Authors

Maintainers

Sources

doc/batteries/BatComplex/index.html

Module BatComplex

Submodules grouping all infix operators

Boilerplate code

dune-project
Dependency

Module `BatComplex`