Complex numbers v0.1.0

Complex numbers at two precisions: arithmetic, polar form, and the elementary functions.

`Complex`

pub struct Complex {
    pub real: float64;
    pub imaginary: float64;
}

A complex number real + imaginary·i over float64. Copy.

Source

Fields

Name	Type	Description
`real`	`float64`	The real part.
`imaginary`	`float64`	The imaginary part.

Associated functions

`New`

pub func New(real: float64, imaginary: float64) -> Complex

The number real + imaginary·i.

Name	Type	Description
`real`	`float64`	the real part
`imaginary`	`float64`	the imaginary part

Returns: the number

Source

`FromPolar`

pub func FromPolar(
    magnitude: float64,
    angle: float64
) -> Complex

The number with magnitude magnitude at angle radians from the positive real axis.

Name	Type	Description
`magnitude`	`float64`	the distance from zero
`angle`	`float64`	the angle in radians

Returns: the number

Source

Methods

`Abs`

pub func Abs(self: &Complex) -> float64

The distance from zero, computed without overflow or underflow on the way.

Returns: the magnitude

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`Arg`

pub func Arg(self: &Complex) -> float64

The angle from the positive real axis, in (-π, π].

Returns: the argument in radians

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`Norm`

pub func Norm(self: &Complex) -> float64

The square of the magnitude, which needs no square root.

Returns: the squared magnitude

Source

`Conjugate`

pub func Conjugate(self: &Complex) -> Complex

The number reflected across the real axis.

Returns: the conjugate

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`Negate`

pub func Negate(self: &Complex) -> Complex

The number with both parts negated.

Returns: the negation

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`Scale`

pub func Scale(self: &Complex, factor: float64) -> Complex

The number with both parts multiplied by factor.

Name	Type	Description
`factor`	`float64`	the real factor

Returns: the scaled number

Source

`Exp`

pub func Exp(self: &Complex) -> Complex

e raised to this number.

Returns: the exponential

Source

`Log`

pub func Log(self: &Complex) -> Complex

The natural logarithm on the principal branch: the logarithm of the magnitude, and the argument.

Returns: the logarithm

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`Sqrt`

pub func Sqrt(self: &Complex) -> Complex

The principal square root, whose real part is never negative.

Returns: the square root

Source

`Pow`

pub func Pow(self: &Complex, exponent: Complex) -> Complex

This number raised to exponent, as e raised to exponent times the logarithm, so on the principal branch. Zero raised to anything is zero.

Name	Type	Description
`exponent`	`Complex`	the power

Returns: the power

Source

Operators

`+`

pub func +(self: &Complex, other: Complex) -> Complex

The sum.

Name	Type	Description
`other`	`Complex`	the number to add

Returns: the sum

Source

`-`

pub func -(self: &Complex, other: Complex) -> Complex

The difference.

Name	Type	Description
`other`	`Complex`	the number to subtract

Returns: the difference

Source

`*`

pub func *(self: &Complex, other: Complex) -> Complex

The product.

Name	Type	Description
`other`	`Complex`	the number to multiply by

Returns: the product

Source

`/`

pub func /(self: &Complex, other: Complex) -> Complex

The quotient, by Smith's method, so that a divisor with very large or very small parts keeps its precision. Dividing by zero gives infinities or NaN, as floating-point division does.

Name	Type	Description
`other`	`Complex`	the number to divide by

Returns: the quotient

Source

`Complex32`

pub struct Complex32 {
    pub real: float32;
    pub imaginary: float32;
}

A complex number real + imaginary·i over float32. Copy.

Source

Fields

Name	Type	Description
`real`	`float32`	The real part.
`imaginary`	`float32`	The imaginary part.

Associated functions

`New`

pub func New(real: float32, imaginary: float32) -> Complex32

The number real + imaginary·i.

Name	Type	Description
`real`	`float32`	the real part
`imaginary`	`float32`	the imaginary part

Returns: the number

Source

`FromPolar`

pub func FromPolar(
    magnitude: float32,
    angle: float32
) -> Complex32

The number with magnitude magnitude at angle radians from the positive real axis.

Name	Type	Description
`magnitude`	`float32`	the distance from zero
`angle`	`float32`	the angle in radians

Returns: the number

Source

Methods

`Abs`

pub func Abs(self: &Complex32) -> float32

The distance from zero, computed without overflow or underflow on the way.

Returns: the magnitude

Source

`Arg`

pub func Arg(self: &Complex32) -> float32

The angle from the positive real axis, in (-π, π].

Returns: the argument in radians

Source

`Norm`

pub func Norm(self: &Complex32) -> float32

The square of the magnitude, which needs no square root.

Returns: the squared magnitude

Source

`Conjugate`

pub func Conjugate(self: &Complex32) -> Complex32

The number reflected across the real axis.

Returns: the conjugate

Source

`Negate`

pub func Negate(self: &Complex32) -> Complex32

The number with both parts negated.

Returns: the negation

Source

`Scale`

pub func Scale(
    self: &Complex32,
    factor: float32
) -> Complex32

The number with both parts multiplied by factor.

Name	Type	Description
`factor`	`float32`	the real factor

Returns: the scaled number

Source

`Exp`

pub func Exp(self: &Complex32) -> Complex32

e raised to this number.

Returns: the exponential

Source

`Log`

pub func Log(self: &Complex32) -> Complex32

The natural logarithm on the principal branch: the logarithm of the magnitude, and the argument.

Returns: the logarithm

Source

`Sqrt`

pub func Sqrt(self: &Complex32) -> Complex32

The principal square root, whose real part is never negative.

Returns: the square root

Source

`Pow`

pub func Pow(
    self: &Complex32,
    exponent: Complex32
) -> Complex32

This number raised to exponent, as e raised to exponent times the logarithm, so on the principal branch. Zero raised to anything is zero.

Name	Type	Description
`exponent`	`Complex32`	the power

Returns: the power

Source

Operators

`+`

pub func +(self: &Complex32, other: Complex32) -> Complex32

The sum.

Name	Type	Description
`other`	`Complex32`	the number to add

Returns: the sum

Source

`-`

pub func -(self: &Complex32, other: Complex32) -> Complex32

The difference.

Name	Type	Description
`other`	`Complex32`	the number to subtract

Returns: the difference

Source

`*`

pub func *(self: &Complex32, other: Complex32) -> Complex32

The product.

Name	Type	Description
`other`	`Complex32`	the number to multiply by

Returns: the product

Source

`/`

pub func /(self: &Complex32, other: Complex32) -> Complex32

The quotient, by Smith's method, so that a divisor with very large or very small parts keeps its precision. Dividing by zero gives infinities or NaN, as floating-point division does.

Name	Type	Description
`other`	`Complex32`	the number to divide by

Returns: the quotient

Source

Overview

Mathematical constants and functions

Absolute value, minimum and maximum

The magnitude of a floating-point value and the smaller or larger of two.

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