Struct num::Complex [−] [src]

pub struct Complex<T> {
    pub re: T,
    pub im: T,
}

A complex number in Cartesian form.

Fields

re: T

Real portion of the complex number

im: T

Imaginary portion of the complex number

Methods

`impl<T> Complex<T> where T: Clone + Num`

`fn new(re: T, im: T) -> Complex<T>`

Create a new Complex

`fn i() -> Complex<T>`

Returns imaginary unit

`fn norm_sqr(&self) -> T`

Returns the square of the norm (since T doesn't necessarily have a sqrt function), i.e. re^2 + im^2.

`fn scale(&self, t: T) -> Complex<T>`

Multiplies self by the scalar t.

`fn unscale(&self, t: T) -> Complex<T>`

Divides self by the scalar t.

`impl<T> Complex<T> where T: Neg<Output=T> + Clone + Num`

`fn conj(&self) -> Complex<T>`

Returns the complex conjugate. i.e. re - i im

`fn inv(&self) -> Complex<T>`

Returns 1/self

`impl<T> Complex<T> where T: Clone + Float`

`fn norm(&self) -> T`

Calculate |self|

`fn arg(&self) -> T`

Calculate the principal Arg of self.

`fn to_polar(&self) -> (T, T)`

Convert to polar form (r, theta), such that self = r * exp(i * theta)

`fn from_polar(r: &T, theta: &T) -> Complex<T>`

Convert a polar representation into a complex number.

`fn exp(&self) -> Complex<T>`

Computes e^(self), where e is the base of the natural logarithm.

`fn ln(&self) -> Complex<T>`

Computes the principal value of natural logarithm of self.

This function has one branch cut:

(-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

`fn sqrt(&self) -> Complex<T>`

Computes the principal value of the square root of self.

This function has one branch cut:

(-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

`fn sin(&self) -> Complex<T>`

Computes the sine of self.

`fn cos(&self) -> Complex<T>`

Computes the cosine of self.

`fn tan(&self) -> Complex<T>`

Computes the tangent of self.

`fn asin(&self) -> Complex<T>`

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

(-∞, -1), continuous from above.
(1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

`fn acos(&self) -> Complex<T>`

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

(-∞, -1), continuous from above.
(1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

`fn atan(&self) -> Complex<T>`

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

(-∞i, -i], continuous from the left.
[i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

`fn sinh(&self) -> Complex<T>`

Computes the hyperbolic sine of self.

`fn cosh(&self) -> Complex<T>`

Computes the hyperbolic cosine of self.

`fn tanh(&self) -> Complex<T>`

Computes the hyperbolic tangent of self.

`fn asinh(&self) -> Complex<T>`

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

(-∞i, -i), continuous from the left.
(i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

`fn acosh(&self) -> Complex<T>`

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

(-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

`fn atanh(&self) -> Complex<T>`

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

(-∞, -1], continuous from above.
[1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

`fn is_nan(self) -> bool`

Checks if the given complex number is NaN

`fn is_infinite(self) -> bool`

Checks if the given complex number is infinite

`fn is_finite(self) -> bool`

Checks if the given complex number is finite

`fn is_normal(self) -> bool`

Checks if the given complex number is normal