Struct basic_dsp::numbers::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> where     T: Clone + Num,

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

Create a new Complex

pub fn i() -> Complex<T>

Returns imaginary unit

pub 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.

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

Multiplies self by the scalar t.

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

Divides self by the scalar t.

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

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

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

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

Returns 1/self

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

pub fn norm(&self) -> T

Calculate |self|

pub fn arg(&self) -> T

Calculate the principal Arg of self.

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

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

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

Convert a polar representation into a complex number.

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

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

pub 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.

pub 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.

pub fn powf(&self, exp: T) -> Complex<T>

Raises self to a floating point power.

pub fn log(&self, base: T) -> Complex<T>

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

pub fn powc(&self, exp: Complex<T>) -> Complex<T>

Raises self to a complex power.

pub fn expf(&self, base: T) -> Complex<T>

Raises a floating point number to the complex power self.

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

Computes the sine of self.

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

Computes the cosine of self.

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

Computes the tangent of self.

pub 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.

pub 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.

pub 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.

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

Computes the hyperbolic sine of self.

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

Computes the hyperbolic cosine of self.

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

Computes the hyperbolic tangent of self.

pub 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.

pub 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)) < ∞.

pub 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.

impl<T> Complex<T> where     T: Clone + FloatCore,

pub fn is_nan(self) -> bool

Checks if the given complex number is NaN

pub fn is_infinite(self) -> bool

Checks if the given complex number is infinite

pub fn is_finite(self) -> bool

Checks if the given complex number is finite

pub fn is_normal(self) -> bool

Checks if the given complex number is normal

Trait Implementations

impl<V, S, T> OffsetOps<Complex<T>> for Matrix2xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + OffsetOps<Complex<T>>,

fn offset(&mut self, offset: Complex<T>)

Adds a scalar to each vector element.

impl<V, S, T> OffsetOps<Complex<T>> for Matrix3xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + OffsetOps<Complex<T>>,

fn offset(&mut self, offset: Complex<T>)

Adds a scalar to each vector element.

impl<V, S, T> OffsetOps<Complex<T>> for MatrixMxN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + OffsetOps<Complex<T>>,

fn offset(&mut self, offset: Complex<T>)

Adds a scalar to each vector element.

impl<V, S, T> OffsetOps<Complex<T>> for Matrix4xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + OffsetOps<Complex<T>>,

fn offset(&mut self, offset: Complex<T>)

Adds a scalar to each vector element.

impl<V, S, T> ScaleOps<Complex<T>> for Matrix3xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + ScaleOps<Complex<T>>,

fn scale(&mut self, factor: Complex<T>)

Multiplies the vector element with a scalar.

impl<V, S, T> ScaleOps<Complex<T>> for MatrixMxN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + ScaleOps<Complex<T>>,

fn scale(&mut self, factor: Complex<T>)

Multiplies the vector element with a scalar.

impl<V, S, T> ScaleOps<Complex<T>> for Matrix4xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + ScaleOps<Complex<T>>,

fn scale(&mut self, factor: Complex<T>)

Multiplies the vector element with a scalar.

impl<V, S, T> ScaleOps<Complex<T>> for Matrix2xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + ScaleOps<Complex<T>>,

fn scale(&mut self, factor: Complex<T>)

Multiplies the vector element with a scalar.

impl<S, V, T> MapInplaceOps<Complex<T>> for MatrixMxN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + MapInplaceOps<Complex<T>>,

fn map_inplace<'a, A, F>(&mut self, argument: A, map: &F) where     A: Sync + Copy + Send,     F: Fn(Complex<T>, usize, A) -> Complex<T> + 'a + Sync,

Transforms all vector elements using the function map.

impl<S, V, T> MapInplaceOps<Complex<T>> for Matrix4xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + MapInplaceOps<Complex<T>>,

fn map_inplace<'a, A, F>(&mut self, argument: A, map: &F) where     A: Sync + Copy + Send,     F: Fn(Complex<T>, usize, A) -> Complex<T> + 'a + Sync,

Transforms all vector elements using the function map.

impl<S, V, T> MapInplaceOps<Complex<T>> for Matrix2xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + MapInplaceOps<Complex<T>>,

fn map_inplace<'a, A, F>(&mut self, argument: A, map: &F) where     A: Sync + Copy + Send,     F: Fn(Complex<T>, usize, A) -> Complex<T> + 'a + Sync,

Transforms all vector elements using the function map.

impl<S, V, T> MapInplaceOps<Complex<T>> for Matrix3xN<V, S, T> where     S: ToSlice<T>,     T: RealNumber,     V: Vector<T> + MapInplaceOps<Complex<T>>,

fn map_inplace<'a, A, F>(&mut self, argument: A, map: &F) where     A: Sync + Copy + Send,     F: Fn(Complex<T>, usize, A) -> Complex<T> + 'a + Sync,

Transforms all vector elements using the function map.

impl<T> Stats<Complex<T>> for Statistics<Complex<T>> where     T: RealNumber,

fn empty() -> Statistics<Complex<T>>

Creates an empty statistics struct.

fn invalid() -> Statistics<Complex<T>>

Creates a statistics struct which resembles an invalid result.

fn merge(stats: &[Statistics<Complex<T>>]) -> Statistics<Complex<T>>

Merges several statistics into one.

fn merge_cols(     stats: &[ArrayVec<[Statistics<Complex<T>>; 16]>] ) -> ArrayVec<[Statistics<Complex<T>>; 16]>

Merges several vectors of statistics into one vector.

fn empty_vec(len: usize) -> ArrayVec<[Statistics<Complex<T>>; 16]>

Creates a vector of empty statistics structs.

fn add(&mut self, elem: Complex<T>, index: usize)

Adds a new value to the statistics, all statistic fields get updated.

impl<S, T, N, D> SumOps<Complex<T>> for DspVec<S, T, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<T>,     T: RealNumber,

fn sum(&self) -> Complex<T>

Calculates the sum of the data contained in the vector. # Example

fn sum_sq(&self) -> Complex<T>

Calculates the sum of the squared data contained in the vector. # Example

impl<S, T, N, D> StatisticsSplitOps<Complex<T>> for DspVec<S, T, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<T>,     T: RealNumber,

type Result = ArrayVec<[Statistics<Complex<T>>; 16]>

fn statistics_split(     &self,     len: usize ) -> Result<ArrayVec<[Statistics<Complex<T>>; 16]>, ErrorReason>

Calculates the statistics of the data contained in the vector as if the vector would have been split into len pieces. self.len should be dividable by len without a remainder, but this isn't enforced by the implementation. For implementation reasons len <= 16 must be true.

impl<S, T, N, D> StatisticsOps<Complex<T>> for DspVec<S, T, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<T>,     T: RealNumber,

type Result = Statistics<Complex<T>>

fn statistics(&self) -> Statistics<Complex<T>>

Calculates the statistics of the data.

impl<S, T, D, N> ScaleOps<Complex<T>> for DspVec<S, T, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSliceMut<T>,     T: RealNumber,

fn scale(&mut self, factor: Complex<T>)

Multiplies the vector element with a scalar.

impl<T> Zero for Complex<T> where     T: DspNumber,

fn zero() -> Complex<T>

impl<S, O, T, N, D, NO, DO> PreciseDotProductOps<O, Complex<T>, T, NO, DO> for DspVec<S, T, N, D> where     D: Domain,     DO: PosEq<D> + Domain,     N: ComplexNumberSpace,     NO: PosEq<N> + NumberSpace,     O: Vector<T> + GetMetaData<T, NO, DO> + Index<RangeFull, Output = [T]>,     S: ToSlice<T>,     T: RealNumber,

type Output = Result<Complex<T>, ErrorReason>

fn dot_product_prec(&self, factor: &O) -> Result<Complex<T>, ErrorReason>

Calculates the dot product of self and factor using a more precise but slower algorithm. Self and factor remain unchanged.

impl<S, O, T, N, D, NO, DO> DotProductOps<O, Complex<T>, T, NO, DO> for DspVec<S, T, N, D> where     D: Domain,     DO: PosEq<D> + Domain,     N: ComplexNumberSpace,     NO: PosEq<N> + NumberSpace,     O: Vector<T> + GetMetaData<T, NO, DO> + Index<RangeFull, Output = [T]>,     S: ToSlice<T>,     T: RealNumber,

type Output = Result<Complex<T>, ErrorReason>

fn dot_product(&self, factor: &O) -> Result<Complex<T>, ErrorReason>

Calculates the dot product of self and factor. Self and factor remain unchanged.

impl<S, T, N, D, R> MapAggregateOps<Complex<T>, R> for DspVec<S, T, N, D> where     D: Domain,     N: ComplexNumberSpace,     R: Send,     S: ToSlice<T>,     T: RealNumber,

type Output = Result<R, ErrorReason>

fn map_aggregate<'a, A, FMap, FAggr>(     &self,     argument: A,     map: &FMap,     aggregate: &FAggr ) -> Result<R, ErrorReason> where     A: Sync + Copy + Send,     FAggr: Fn(R, R) -> R + 'a + Sync + Send,     FMap: Fn(Complex<T>, usize, A) -> R + 'a + Sync,

Transforms all vector elements using the function map and then aggregates all the results with aggregate. aggregate must be a commutativity and associativity; that's because there is no guarantee that the numbers will be aggregated in any deterministic order.

impl<T> PreciseStats<Complex<T>> for Statistics<Complex<T>> where     T: RealNumber,

fn add_prec(     &mut self,     elem: Complex<T>,     index: usize,     sumc: &mut Complex<T>,     rmsc: &mut Complex<T> )

Adds a new values to the statistics using the Kahan summation algorithm described here: https://en.wikipedia.org/wiki/Kahan_summation_algorithm

impl<S, N, D> PreciseSumOps<Complex<f64>> for DspVec<S, f32, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<f32>,

fn sum_prec(&self) -> Complex<f64>

Calculates the sum of the data contained in the vector using a more precise but slower algorithm. # Example

fn sum_sq_prec(&self) -> Complex<f64>

Calculates the sum of the squared data contained in the vector using a more precise but slower algorithm. # Example

impl<S, N, D> PreciseSumOps<Complex<f64>> for DspVec<S, f64, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<f64>,

fn sum_prec(&self) -> Complex<f64>

Calculates the sum of the data contained in the vector using a more precise but slower algorithm. # Example

fn sum_sq_prec(&self) -> Complex<f64>

Calculates the sum of the squared data contained in the vector using a more precise but slower algorithm. # Example

impl<S, N, D> PreciseStatisticsSplitOps<Complex<f64>> for DspVec<S, f32, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<f32>,

type Result = ArrayVec<[Statistics<Complex<f64>>; 16]>

fn statistics_split_prec(     &self,     len: usize ) -> Result<ArrayVec<[Statistics<Complex<f64>>; 16]>, ErrorReason>

Calculates the statistics of the data contained in the vector as if the vector would have been split into len pieces using a more precise but slower algorithm. self.len should be dividable by len without a remainder, but this isn't enforced by the implementation. For implementation reasons len <= 16 must be true.

impl<S, N, D> PreciseStatisticsSplitOps<Complex<f64>> for DspVec<S, f64, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<f64>,

type Result = ArrayVec<[Statistics<Complex<f64>>; 16]>

fn statistics_split_prec(     &self,     len: usize ) -> Result<ArrayVec<[Statistics<Complex<f64>>; 16]>, ErrorReason>

Calculates the statistics of the data contained in the vector as if the vector would have been split into len pieces using a more precise but slower algorithm. self.len should be dividable by len without a remainder, but this isn't enforced by the implementation. For implementation reasons len <= 16 must be true.

impl<S, N, D> PreciseStatisticsOps<Complex<f64>> for DspVec<S, f32, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<f32>,

type Result = Statistics<Complex<f64>>

fn statistics_prec(&self) -> Statistics<Complex<f64>>

Calculates the statistics of the data contained in the vector using a more precise but slower algorithm.

impl<S, N, D> PreciseStatisticsOps<Complex<f64>> for DspVec<S, f64, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSlice<f64>,

type Result = Statistics<Complex<f64>>

fn statistics_prec(&self) -> Statistics<Complex<f64>>

Calculates the statistics of the data contained in the vector using a more precise but slower algorithm.

impl<S, T, N, D> OffsetOps<Complex<T>> for DspVec<S, T, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSliceMut<T>,     T: RealNumber,

fn offset(&mut self, offset: Complex<T>)

Adds a scalar to each vector element.

impl<S, T, N, D> MapInplaceOps<Complex<T>> for DspVec<S, T, N, D> where     D: Domain,     N: ComplexNumberSpace,     S: ToSliceMut<T>,     T: RealNumber,

fn map_inplace<'a, A, F>(&mut self, argument: A, map: &F) where     A: Sync + Copy + Send,     F: Fn(Complex<T>, usize, A) -> Complex<T> + 'a + Sync,

Transforms all vector elements using the function map.

impl<'a, 'b, T> Rem<&'b Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<T>) -> Complex<T>

Performs the % operation.

impl<T> Rem<T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: T) -> Complex<T>

Performs the % operation.

impl<'a, T> Rem<T> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: T) -> Complex<T>

Performs the % operation.

impl<'a, T> Rem<&'a Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &Complex<T>) -> Complex<T>

Performs the % operation.

impl<'a, 'b, T> Rem<&'a T> for &'b Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &T) -> Complex<T>

Performs the % operation.

impl<T> Rem<Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, modulus: Complex<T>) -> Complex<T>

Performs the % operation.

impl<'a, T> Rem<Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: Complex<T>) -> Complex<T>

Performs the % operation.

impl<'a, T> Rem<&'a T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the % operator.

fn rem(self, other: &T) -> Complex<T>

Performs the % operation.

impl<T> NumCast for Complex<T> where     T: NumCast + Num,

fn from<U>(n: U) -> Option<Complex<T>> where     U: ToPrimitive,

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait.

impl<T> LowerHex for Complex<T> where     T: LowerHex + Num + PartialOrd<T> + Clone,

fn fmt(&self, f: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<'a, 'b, T> Sub<&'a T> for &'b Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &T) -> Complex<T>

Performs the - operation.

impl<'a, T> Sub<Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: Complex<T>) -> Complex<T>

Performs the - operation.

impl<'a, T> Sub<&'a Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<T>) -> Complex<T>

Performs the - operation.

impl<T> Sub<Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: Complex<T>) -> Complex<T>

Performs the - operation.

impl<'a, T> Sub<&'a T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &T) -> Complex<T>

Performs the - operation.

impl<'a, 'b, T> Sub<&'b Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: &Complex<T>) -> Complex<T>

Performs the - operation.

impl<T> Sub<T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: T) -> Complex<T>

Performs the - operation.

impl<'a, T> Sub<T> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn sub(self, other: T) -> Complex<T>

Performs the - operation.

impl<T> Eq for Complex<T> where     T: Eq,

impl<T> Display for Complex<T> where     T: Display + Num + PartialOrd<T> + Clone,

fn fmt(&self, f: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<T> Num for Complex<T> where     T: Clone + Num,

type FromStrRadixErr = ParseComplexError<<T as Num>::FromStrRadixErr>

fn from_str_radix(     s: &str,     radix: u32 ) -> Result<Complex<T>, <Complex<T> as Num>::FromStrRadixErr>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

impl<T> Add<T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: T) -> Complex<T>

Performs the + operation.

impl<'a, T> Add<T> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: T) -> Complex<T>

Performs the + operation.

impl<'a, T> Add<&'a Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &Complex<T>) -> Complex<T>

Performs the + operation.

impl<'a, T> Add<&'a T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &T) -> Complex<T>

Performs the + operation.

impl<'a, 'b, T> Add<&'b Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &Complex<T>) -> Complex<T>

Performs the + operation.

impl<'a, T> Add<Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: Complex<T>) -> Complex<T>

Performs the + operation.

impl<'a, 'b, T> Add<&'a T> for &'b Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: &T) -> Complex<T>

Performs the + operation.

impl<T> Add<Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the + operator.

fn add(self, other: Complex<T>) -> Complex<T>

Performs the + operation.

impl<T> Inv for Complex<T> where     T: Neg<Output = T> + Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> Complex<T>

Returns the multiplicative inverse of self.

impl<'a, T> Inv for &'a Complex<T> where     T: Neg<Output = T> + Clone + Num,

type Output = Complex<T>

The result after applying the operator.

fn inv(self) -> Complex<T>

Returns the multiplicative inverse of self.

impl<T> Octal for Complex<T> where     T: Octal + Num + PartialOrd<T> + Clone,

fn fmt(&self, f: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<'a, T> Sum<&'a Complex<T>> for Complex<T> where     T: 'a + Clone + Num,

fn sum<I>(iter: I) -> Complex<T> where     I: Iterator<Item = &'a Complex<T>>,

Method which takes an iterator and generates Self from the elements by "summing up" the items.

impl<T> Sum<Complex<T>> for Complex<T> where     T: Clone + Num,

fn sum<I>(iter: I) -> Complex<T> where     I: Iterator<Item = Complex<T>>,

Method which takes an iterator and generates Self from the elements by "summing up" the items.

impl<T> Clone for Complex<T> where     T: Clone,

fn clone(&self) -> Complex<T>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T> Product<Complex<T>> for Complex<T> where     T: Clone + Num,

fn product<I>(iter: I) -> Complex<T> where     I: Iterator<Item = Complex<T>>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<'a, T> Product<&'a Complex<T>> for Complex<T> where     T: 'a + Clone + Num,

fn product<I>(iter: I) -> Complex<T> where     I: Iterator<Item = &'a Complex<T>>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<T> FromPrimitive for Complex<T> where     T: FromPrimitive + Num,

fn from_usize(n: usize) -> Option<Complex<T>>

Convert a usize to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_isize(n: isize) -> Option<Complex<T>>

Convert an isize to return an optional value of this type. If the value cannot be represented by this value, then None is returned.

fn from_u8(n: u8) -> Option<Complex<T>>

Convert an u8 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u16(n: u16) -> Option<Complex<T>>

Convert an u16 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u32(n: u32) -> Option<Complex<T>>

Convert an u32 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u64(n: u64) -> Option<Complex<T>>

Convert an u64 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i8(n: i8) -> Option<Complex<T>>

Convert an i8 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i16(n: i16) -> Option<Complex<T>>

Convert an i16 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i32(n: i32) -> Option<Complex<T>>

Convert an i32 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i64(n: i64) -> Option<Complex<T>>

Convert an i64 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_u128(n: u128) -> Option<Complex<T>>

Convert an u128 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_i128(n: i128) -> Option<Complex<T>>

Convert an i128 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_f32(n: f32) -> Option<Complex<T>>

Convert a f32 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

fn from_f64(n: f64) -> Option<Complex<T>>

Convert a f64 to return an optional value of this type. If the type cannot be represented by this value, then None is returned.

impl<T> UpperExp for Complex<T> where     T: UpperExp + Num + PartialOrd<T> + Clone,

fn fmt(&self, f: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<T> Div<Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: Complex<T>) -> Complex<T>

Performs the / operation.

impl<T> Div<T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: T) -> Complex<T>

Performs the / operation.

impl<'a, T> Div<Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: Complex<T>) -> Complex<T>

Performs the / operation.

impl<'a, 'b, T> Div<&'a T> for &'b Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &T) -> Complex<T>

Performs the / operation.

impl<'a, T> Div<T> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: T) -> Complex<T>

Performs the / operation.

impl<'a, T> Div<&'a Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &Complex<T>) -> Complex<T>

Performs the / operation.

impl<'a, 'b, T> Div<&'b Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &Complex<T>) -> Complex<T>

Performs the / operation.

impl<'a, T> Div<&'a T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the / operator.

fn div(self, other: &T) -> Complex<T>

Performs the / operation.

impl<T> FromStr for Complex<T> where     T: FromStr + Num + Clone,

type Err = ParseComplexError<<T as FromStr>::Err>

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Complex<T>, <Complex<T> as FromStr>::Err>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

impl<T> UpperHex for Complex<T> where     T: UpperHex + Num + PartialOrd<T> + Clone,

fn fmt(&self, f: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<'a, T> DivAssign<&'a T> for Complex<T> where     T: Clone + NumAssign,

fn div_assign(&mut self, other: &T)

Performs the /= operation.

impl<T> DivAssign<Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn div_assign(&mut self, other: Complex<T>)

Performs the /= operation.

impl<T> DivAssign<T> for Complex<T> where     T: Clone + NumAssign,

fn div_assign(&mut self, other: T)

Performs the /= operation.

impl<'a, T> DivAssign<&'a Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn div_assign(&mut self, other: &Complex<T>)

Performs the /= operation.

impl<T> RemAssign<Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn rem_assign(&mut self, other: Complex<T>)

Performs the %= operation.

impl<'a, T> RemAssign<&'a Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn rem_assign(&mut self, other: &Complex<T>)

Performs the %= operation.

impl<'a, T> RemAssign<&'a T> for Complex<T> where     T: Clone + NumAssign,

fn rem_assign(&mut self, other: &T)

Performs the %= operation.

impl<T> RemAssign<T> for Complex<T> where     T: Clone + NumAssign,

fn rem_assign(&mut self, other: T)

Performs the %= operation.

impl<'a, 'b, T> Mul<&'a T> for &'b Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &T) -> Complex<T>

Performs the * operation.

impl<T> Mul<T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Complex<T>

Performs the * operation.

impl<'a, 'b, T> Mul<&'b Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<T>) -> Complex<T>

Performs the * operation.

impl<'a, T> Mul<T> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Complex<T>

Performs the * operation.

impl<'a, T> Mul<Complex<T>> for &'a Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: Complex<T>) -> Complex<T>

Performs the * operation.

impl<'a, T> Mul<&'a Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &Complex<T>) -> Complex<T>

Performs the * operation.

impl<T> Mul<Complex<T>> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: Complex<T>) -> Complex<T>

Performs the * operation.

impl<'a, T> Mul<&'a T> for Complex<T> where     T: Clone + Num,

type Output = Complex<T>

The resulting type after applying the * operator.

fn mul(self, other: &T) -> Complex<T>

Performs the * operation.

impl<'a, T> SubAssign<&'a T> for Complex<T> where     T: Clone + NumAssign,

fn sub_assign(&mut self, other: &T)

Performs the -= operation.

impl<T> SubAssign<Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn sub_assign(&mut self, other: Complex<T>)

Performs the -= operation.

impl<'a, T> SubAssign<&'a Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn sub_assign(&mut self, other: &Complex<T>)

Performs the -= operation.

impl<T> SubAssign<T> for Complex<T> where     T: Clone + NumAssign,

fn sub_assign(&mut self, other: T)

Performs the -= operation.

impl<'a, T> MulAssign<&'a T> for Complex<T> where     T: Clone + NumAssign,

fn mul_assign(&mut self, other: &T)

Performs the *= operation.

impl<T> MulAssign<Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn mul_assign(&mut self, other: Complex<T>)

Performs the *= operation.

impl<T> MulAssign<T> for Complex<T> where     T: Clone + NumAssign,

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<'a, T> MulAssign<&'a Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn mul_assign(&mut self, other: &Complex<T>)

Performs the *= operation.

impl<T> Binary for Complex<T> where     T: Binary + Num + PartialOrd<T> + Clone,

fn fmt(&self, f: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<T> PartialEq<Complex<T>> for Complex<T> where     T: PartialEq<T>,

fn eq(&self, other: &Complex<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Complex<T>) -> bool

This method tests for !=.

impl<T> Zero for Complex<T> where     T: Clone + Num,

fn zero() -> Complex<T>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

impl<T> One for Complex<T> where     T: Clone + Num,

fn one() -> Complex<T>

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

impl<T> Default for Complex<T> where     T: Default,

fn default() -> Complex<T>

Returns the "default value" for a type.

impl<T> LowerExp for Complex<T> where     T: LowerExp + Num + PartialOrd<T> + Clone,

fn fmt(&self, f: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<T> Debug for Complex<T> where     T: Debug,

fn fmt(&self, f: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<'a, T> AddAssign<&'a Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn add_assign(&mut self, other: &Complex<T>)

Performs the += operation.

impl<T> AddAssign<Complex<T>> for Complex<T> where     T: Clone + NumAssign,

fn add_assign(&mut self, other: Complex<T>)

Performs the += operation.

impl<'a, T> AddAssign<&'a T> for Complex<T> where     T: Clone + NumAssign,

fn add_assign(&mut self, other: &T)

Performs the += operation.

impl<T> AddAssign<T> for Complex<T> where     T: Clone + NumAssign,

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<T> Hash for Complex<T> where     T: Hash,

fn hash<__HT>(&self, state: &mut __HT) where     __HT: Hasher,

Feeds this value into the given [Hasher].

fn hash_slice<H>(data: &[Self], state: &mut H) where     H: Hasher,

Feeds a slice of this type into the given [Hasher].

impl<T> Copy for Complex<T> where     T: Copy,

impl<T, U> AsPrimitive<U> for Complex<T> where     T: AsPrimitive<U>,     U: 'static + Copy,

fn as_(self) -> U

Convert a value to another, using the as operator.

impl<T> ToPrimitive for Complex<T> where     T: ToPrimitive + Num,

fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize.

fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize.

fn to_u8(&self) -> Option<u8>

Converts the value of self to an u8.

fn to_u16(&self) -> Option<u16>

Converts the value of self to an u16.

fn to_u32(&self) -> Option<u32>

Converts the value of self to an u32.

fn to_u64(&self) -> Option<u64>

Converts the value of self to an u64.

fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8.

fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16.

fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32.

fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64.

fn to_u128(&self) -> Option<u128>

Converts the value of self to an u128.

fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128.

fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32.

fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64.

impl<'a, T> Neg for &'a Complex<T> where     T: Neg<Output = T> + Clone + Num,

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Complex<T>

Performs the unary - operation.

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

type Output = Complex<T>

The resulting type after applying the - operator.

fn neg(self) -> Complex<T>

Performs the unary - operation.

impl<'a, T> From<&'a T> for Complex<T> where     T: Clone + Num,

fn from(re: &T) -> Complex<T>

Performs the conversion.

impl<T> From<T> for Complex<T> where     T: Clone + Num,

fn from(re: T) -> Complex<T>

Performs the conversion.