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[−][src]Struct num_complex::Complex

#[repr(C)]
pub struct Complex<T> {
    pub re: T,
    pub im: T,
}

A complex number in Cartesian form.

Representation and Foreign Function Interface Compatibility

Complex<T> is memory layout compatible with an array [T; 2].

Note that Complex<F> where F is a floating point type is only memory layout compatible with C's complex types, not necessarily calling convention compatible. This means that for FFI you can only pass Complex<F> behind a pointer, not as a value.

Examples

Example of extern function declaration.

use num_complex::Complex;
use std::os::raw::c_int;

extern "C" {
    fn zaxpy_(n: *const c_int, alpha: *const Complex<f64>,
              x: *const Complex<f64>, incx: *const c_int,
              y: *mut Complex<f64>, incy: *const c_int);
}

Fields

re: T

Real portion of the complex number

im: T

Imaginary portion of the complex number

Methods

`impl<T> Complex<T>`[src]

`pub const fn new(re: T, im: T) -> Self`[src]

Create a new Complex

`impl<T: Clone + Num> Complex<T>`[src]

`pub fn i() -> Self`[src]

Returns imaginary unit

`pub fn norm_sqr(&self) -> T`[src]

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

`pub fn scale(&self, t: T) -> Self`[src]

Multiplies self by the scalar t.

`pub fn unscale(&self, t: T) -> Self`[src]

Divides self by the scalar t.

`pub fn powu(&self, exp: u32) -> Self`[src]

Raises self to an unsigned integer power.

`impl<T: Clone + Num + Neg<Output = T>> Complex<T>`[src]

`pub fn conj(&self) -> Self`[src]

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

`pub fn inv(&self) -> Self`[src]

Returns 1/self

`pub fn powi(&self, exp: i32) -> Self`[src]

Raises self to a signed integer power.

`impl<T: Clone + Signed> Complex<T>`[src]

`pub fn l1_norm(&self) -> T`[src]

Returns the L1 norm |re| + |im| -- the Manhattan distance from the origin.

`impl<T: Clone + Float> Complex<T>`[src]

`pub fn norm(&self) -> T`[src]

Calculate |self|

`pub fn arg(&self) -> T`[src]

Calculate the principal Arg of self.

`pub fn to_polar(&self) -> (T, T)`[src]

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

`pub fn from_polar(r: &T, theta: &T) -> Self`[src]

Convert a polar representation into a complex number.

`pub fn exp(&self) -> Self`[src]

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

`pub fn ln(&self) -> Self`[src]

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.

`pub fn sqrt(&self) -> Self`[src]

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.

`pub fn cbrt(&self) -> Self`[src]

Computes the principal value of the cube root of self.

This function has one branch cut:

(-∞, 0), continuous from above.

The branch satisfies -π/3 ≤ arg(cbrt(z)) ≤ π/3.

Note that this does not match the usual result for the cube root of negative real numbers. For example, the real cube root of -8 is -2, but the principal complex cube root of -8 is 1 + i√3.

`pub fn powf(&self, exp: T) -> Self`[src]

Raises self to a floating point power.

`pub fn log(&self, base: T) -> Self`[src]

Returns the logarithm of self with respect to an arbitrary base.

`pub fn powc(&self, exp: Self) -> Self`[src]

Raises self to a complex power.

`pub fn expf(&self, base: T) -> Self`[src]

Raises a floating point number to the complex power self.

`pub fn sin(&self) -> Self`[src]

Computes the sine of self.

`pub fn cos(&self) -> Self`[src]

Computes the cosine of self.

`pub fn tan(&self) -> Self`[src]

Computes the tangent of self.

`pub fn asin(&self) -> Self`[src]

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.

`pub fn acos(&self) -> Self`[src]

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.

`pub fn atan(&self) -> Self`[src]

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.

`pub fn sinh(&self) -> Self`[src]

Computes the hyperbolic sine of self.

`pub fn cosh(&self) -> Self`[src]

Computes the hyperbolic cosine of self.

`pub fn tanh(&self) -> Self`[src]

Computes the hyperbolic tangent of self.

`pub fn asinh(&self) -> Self`[src]

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.

`pub fn acosh(&self) -> Self`[src]

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)) < ∞.

`pub fn atanh(&self) -> Self`[src]

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.

`pub fn finv(&self) -> Complex<T>`[src]

Returns 1/self using floating-point operations.

This may be more accurate than the generic self.inv() in cases where self.norm_sqr() would overflow to ∞ or underflow to 0.

Examples

use num_complex::Complex64;
let c = Complex64::new(1e300, 1e300);

// The generic `inv()` will overflow.
assert!(!c.inv().is_normal());

// But we can do better for `Float` types.
let inv = c.finv();
assert!(inv.is_normal());
println!("{:e}", inv);

let expected = Complex64::new(5e-301, -5e-301);
assert!((inv - expected).norm() < 1e-315);

`pub fn fdiv(&self, other: Complex<T>) -> Complex<T>`[src]

Returns self/other using floating-point operations.

This may be more accurate than the generic Div implementation in cases where other.norm_sqr() would overflow to ∞ or underflow to 0.

Examples

use num_complex::Complex64;
let a = Complex64::new(2.0, 3.0);
let b = Complex64::new(1e300, 1e300);

// Generic division will overflow.
assert!(!(a / b).is_normal());

// But we can do better for `Float` types.
let quotient = a.fdiv(b);
assert!(quotient.is_normal());
println!("{:e}", quotient);

let expected = Complex64::new(2.5e-300, 5e-301);
assert!((quotient - expected).norm() < 1e-315);

`impl<T: Clone + FloatCore> Complex<T>`[src]

`pub fn is_nan(self) -> bool`[src]

Checks if the given complex number is NaN

`pub fn is_infinite(self) -> bool`[src]

Checks if the given complex number is infinite

`pub fn is_finite(self) -> bool`[src]

Checks if the given complex number is finite

`pub fn is_normal(self) -> bool`[src]

Checks if the given complex number is normal