Struct rug_maths::Complex

pub struct Complex {
    pub val: Complex,
}

Fields

val: Complex

Implementations

impl Complex

pub fn with_val<P, T>(prec: P, val: T) -> Self where
    Complex: Assign<T>,
    P: Prec, 

impl Complex

pub fn real(&self) -> Float

Returns the real part

pub fn imag(&self) -> Float

Returns the imaginary part

Trait Implementations

impl<'a> Add<&'a Complex> for Complex

type Output = Complex

The resulting type after applying the + operator.

fn add(self, rhs: &Self) -> Self::Output

Performs the + operation.

impl<'a> Add<&'a Complex> for &'a Complex

type Output = Complex

The resulting type after applying the + operator.

fn add(self, rhs: &'a Complex) -> Self::Output

Performs the + operation.

impl<B> Add<B> for Complex where
    Complex: Add<B, Output = Complex>, 

type Output = Complex

The resulting type after applying the + operator.

fn add(self, rhs: B) -> Self::Output

Performs the + operation.

impl<'a, B> Add<B> for &'a Complex where
    Complex: Add<B, Output = Complex>, 

type Output = Complex

The resulting type after applying the + operator.

fn add(self, rhs: B) -> Self::Output

Performs the + operation.

impl Add<Complex> for Complex

type Output = Complex

The resulting type after applying the + operator.

fn add(self, rhs: Complex) -> Self::Output

Performs the + operation.

impl<'a> Add<Complex> for &'a Complex

type Output = Complex

The resulting type after applying the + operator.

fn add(self, rhs: Complex) -> Self::Output

Performs the + operation.

impl<'a> AddAssign<&'a Complex> for Complex

fn add_assign(&mut self, rhs: &Self)

Performs the += operation.

impl<B> AddAssign<B> for Complex where
    Complex: AddAssign<B>, 

fn add_assign(&mut self, rhs: B)

Performs the += operation.

impl AddAssign<Complex> for Complex

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl AddAssociative for Complex

impl AddCommutative for Complex

impl CheckedAdd for Complex

fn checked_add(&self, v: &Self) -> Option<Self>

Adds two numbers, checking for overflow. If overflow happens, None is returned.

impl CheckedDiv for Complex

fn checked_div(&self, v: &Self) -> Option<Self>

Divides two numbers, checking for underflow, overflow and division by zero. If any of that happens, None is returned.

impl CheckedMul for Complex

fn checked_mul(&self, v: &Self) -> Option<Self>

Multiplies two numbers, checking for underflow or overflow. If underflow or overflow happens, None is returned.

impl CheckedNeg for Complex

fn checked_neg(&self) -> Option<Self>

Negates a number, returning None for results that can’t be represented, like signed MIN values that can’t be positive, or non-zero unsigned values that can’t be negative.

impl CheckedSub for Complex

fn checked_sub(&self, v: &Self) -> Option<Self>

Subtracts two numbers, checking for underflow. If underflow happens, None is returned.

impl Clone for Complex

fn clone(&self) -> Complex

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ComplexSubset for Complex

type Real = Float

type Natural = Integer

type Integer = Integer

fn as_real(self) -> Self::Real

Converts self to a real number, discarding any imaginary component, if complex.

fn as_natural(self) -> Self::Natural

Converts self to a natural number, truncating when necessary.

fn as_integer(self) -> Self::Integer

Converts self to an integer, truncating when necessary.

fn floor(self) -> Self

Rounds the real and imaginary components of self to the closest integer downward

fn ceil(self) -> Self

Rounds the real and imaginary components of self to the closest integer upward

fn round(self) -> Self

Rounds the real and imaginary components of self to the closest integer

fn trunc(self) -> Self

Rounds the real and imaginary components of self by removing the factional parts

fn fract(self) -> Self

Removes the integral parts of the real and imaginary components of self

fn im(self) -> Self

Sets the real component of self to 0

fn re(self) -> Self

Sets the imaginary component of self to 0

fn conj(self) -> Self

The complex conjugate of self

pub fn modulus_sqrd(self) -> Self

The square of the complex absolute value of self

pub fn modulus(self) -> Self::Real

The complex absolute value of self

impl Debug for Complex

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

Formats the value using the given formatter.

impl Display for Complex

fn fmt(&self, f: &mut Formatter<'_>) -> FmtResult

Formats the value using the given formatter.

impl Distributive<Complex> for Complex

impl<'a> Div<&'a Complex> for Complex

type Output = Complex

The resulting type after applying the / operator.

fn div(self, rhs: &Self) -> Self::Output

Performs the / operation.

impl<'a> Div<&'a Complex> for &'a Complex

type Output = Complex

The resulting type after applying the / operator.

fn div(self, rhs: &'a Complex) -> Self::Output

Performs the / operation.

impl<B> Div<B> for Complex where
    Complex: Div<B, Output = Complex>, 

type Output = Complex

The resulting type after applying the / operator.

fn div(self, rhs: B) -> Self::Output

Performs the / operation.

impl<'a, B> Div<B> for &'a Complex where
    Complex: Div<B, Output = Complex>, 

type Output = Complex

The resulting type after applying the / operator.

fn div(self, rhs: B) -> Self::Output

Performs the / operation.

impl Div<Complex> for Complex

type Output = Complex

The resulting type after applying the / operator.

fn div(self, rhs: Complex) -> Self::Output

Performs the / operation.

impl<'a> Div<Complex> for &'a Complex

type Output = Complex

The resulting type after applying the / operator.

fn div(self, rhs: Complex) -> Self::Output

Performs the / operation.

impl<'a> DivAssign<&'a Complex> for Complex

fn div_assign(&mut self, rhs: &Self)

Performs the /= operation.

impl<B> DivAssign<B> for Complex where
    Complex: DivAssign<B>, 

fn div_assign(&mut self, rhs: B)

Performs the /= operation.

impl DivAssign<Complex> for Complex

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl Divisibility for Complex

fn divides(self, rhs: Self) -> bool

Determines if there exists an element x such that self*x = rhs

fn divide(self, rhs: Self) -> Option<Self>

Finds an element x such that self*x = rhs if such an element exists

fn unit(&self) -> bool

Determines if this element has a multiplicative inverse

fn inverse(self) -> Option<Self>

Finds this element’s multiplicative inverse if it exists

impl Exponential for Complex

fn exp(self) -> Self

The exponential of this ring element

fn try_ln(self) -> Option<Self>

An inverse of exp(x) where ln(1) = 0

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

fn from(src: T) -> Self

Performs the conversion.

impl Inv for Complex

type Output = Complex

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<'a> Mul<&'a Complex> for Complex

type Output = Complex

The resulting type after applying the * operator.

fn mul(self, rhs: &Self) -> Self::Output

Performs the * operation.

impl<'a> Mul<&'a Complex> for &'a Complex

type Output = Complex

The resulting type after applying the * operator.

fn mul(self, rhs: &'a Complex) -> Self::Output

Performs the * operation.

impl<B> Mul<B> for Complex where
    Complex: Mul<B, Output = Complex>, 

type Output = Complex

The resulting type after applying the * operator.

fn mul(self, rhs: B) -> Self::Output

Performs the * operation.

impl<'a, B> Mul<B> for &'a Complex where
    Complex: Mul<B, Output = Complex>, 

type Output = Complex

The resulting type after applying the * operator.

fn mul(self, rhs: B) -> Self::Output

Performs the * operation.

impl Mul<Complex> for Complex

type Output = Complex

The resulting type after applying the * operator.

fn mul(self, rhs: Complex) -> Self::Output

Performs the * operation.

impl<'a> Mul<Complex> for &'a Complex

type Output = Complex

The resulting type after applying the * operator.

fn mul(self, rhs: Complex) -> Self::Output

Performs the * operation.

impl<'a> MulAssign<&'a Complex> for Complex

fn mul_assign(&mut self, rhs: &Self)

Performs the *= operation.

impl<B> MulAssign<B> for Complex where
    Complex: MulAssign<B>, 

fn mul_assign(&mut self, rhs: B)

Performs the *= operation.

impl MulAssign<Complex> for Complex

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl MulAssociative for Complex

impl MulCommutative for Complex

impl Neg for Complex

type Output = Complex

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl NoZeroDivisors for Complex

impl One for Complex

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl PartialEq<Complex> for Complex

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

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

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

This method tests for !=.

impl RealExponential for Complex

pub fn try_pow(self, power: Self) -> Option<Self>

This element raised to the given power as defined by x^y = exp(ln(x)*y), if ln(x) exists

pub fn try_root(self, index: Self) -> Option<Self>

This element taken to the given root as defined as root(x, y) = x^(1/y), if ln(x) and 1/y exist

pub fn try_log(self, base: Self) -> Option<Self>

The inverse of pow(), if it exists

pub fn ln(self) -> Self

The natural logarithm of self

pub fn log(self, base: Self) -> Self

The logarithm of self over a specific base

pub fn pow(self, p: Self) -> Self

The power of self over a specific exponent

pub fn root(self, r: Self) -> Self

The root of self over a specific index

pub fn exp2(self) -> Self

Raises 2 to the power of self

pub fn exp10(self) -> Self

Raises 10 to the power of self

pub fn log2(self) -> Self

The logarithm of base 2

pub fn log10(self) -> Self

The logarithm of base 10

pub fn sqrt(self) -> Self

pub fn cbrt(self) -> Self

pub fn ln_1p(self) -> Self

The natural logarithm of self plus 1.

pub fn exp_m1(self) -> Self

The exponential of self minus 1.

pub fn e() -> Self

The exponential of 1. Mirrors ::core::f32::consts::E

pub fn ln_2() -> Self

The natural logarithm of 2. Mirrors ::core::f32::consts::LN_2

pub fn ln_10() -> Self

The natural logarithm of 10. Mirrors ::core::f32::consts::LN_10

pub fn log2_e() -> Self

The logarithm base 2 of e. Mirrors ::core::f32::consts::LOG2_E

pub fn log10_e() -> Self

The logarithm base 10 of e. Mirrors ::core::f32::consts::LOG10_E

pub fn log2_10() -> Self

The logarithm base 2 of 10. Mirrors ::core::f32::consts::LOG2_10

pub fn log10_2() -> Self

The logarithm base 10 of 2. Mirrors ::core::f32::consts::LOG10_2

pub fn sqrt_2() -> Self

The square root of 2. Mirrors ::core::f32::consts::SQRT_2

pub fn frac_1_sqrt_2() -> Self

One over the square root of 2. Mirrors ::core::f32::consts::FRAC_1_SQRT_2

impl StructuralPartialEq for Complex

impl<'a> Sub<&'a Complex> for Complex

type Output = Complex

The resulting type after applying the - operator.

fn sub(self, rhs: &Self) -> Self::Output

Performs the - operation.

impl<'a> Sub<&'a Complex> for &'a Complex

type Output = Complex

The resulting type after applying the - operator.

fn sub(self, rhs: &'a Complex) -> Self::Output

Performs the - operation.

impl<B> Sub<B> for Complex where
    Complex: Sub<B, Output = Complex>, 

type Output = Complex

The resulting type after applying the - operator.

fn sub(self, rhs: B) -> Self::Output

Performs the - operation.

impl<'a, B> Sub<B> for &'a Complex where
    Complex: Sub<B, Output = Complex>, 

type Output = Complex

The resulting type after applying the - operator.

fn sub(self, rhs: B) -> Self::Output

Performs the - operation.

impl Sub<Complex> for Complex

type Output = Complex

The resulting type after applying the - operator.

fn sub(self, rhs: Complex) -> Self::Output

Performs the - operation.

impl<'a> Sub<Complex> for &'a Complex

type Output = Complex

The resulting type after applying the - operator.

fn sub(self, rhs: Complex) -> Self::Output

Performs the - operation.

impl<'a> SubAssign<&'a Complex> for Complex

fn sub_assign(&mut self, rhs: &Self)

Performs the -= operation.

impl<B> SubAssign<B> for Complex where
    Complex: SubAssign<B>, 

fn sub_assign(&mut self, rhs: B)

Performs the -= operation.

impl SubAssign<Complex> for Complex

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl Trig for Complex

fn sin(self) -> Self

Finds the Sine of the given value

fn cos(self) -> Self

Finds the Cosine of the given value

fn tan(self) -> Self

Finds the Tangent of the given value

fn sinh(self) -> Self

Finds the Hyperbolic Sine of the given value

fn cosh(self) -> Self

Finds the Hyperbolic Cosine of the given value

fn tanh(self) -> Self

Finds the Hyperbolic Tangent of the given value

fn asin(self) -> Self

A continuous inverse function of Sine such that asin(1) = π/2 and asin(-1) = -π/2

fn acos(self) -> Self

A continuous inverse function of Cosine such that acos(1) = 0 and asin(-1) = π

fn atan(self) -> Self

A continuous inverse function of Tangent such that atan(0) = 0 and atan(1) = π/4

fn asinh(self) -> Self

A continuous inverse function of Hyperbolic Sine such that asinh(0)=0

fn acosh(self) -> Self

A continuous inverse function of Hyperbolic Cosine such that acosh(0)=1

fn atanh(self) -> Self

A continuous inverse function of Hyperbolic Tangent such that atanh(0)=0

fn try_asin(self) -> Option<Self>

A continuous inverse function of Sine such that asin(1) = π/2 and asin(-1) = -π/2

fn try_acos(self) -> Option<Self>

A continuous inverse function of Cosine such that acos(1) = 0 and asin(-1) = π

fn try_asinh(self) -> Option<Self>

A continuous inverse function of Hyperbolic Sine such that asinh(0)=0

fn try_acosh(self) -> Option<Self>

A continuous inverse function of Hyperbolic Cosine such that acosh(0)=1

fn try_atanh(self) -> Option<Self>

A continuous inverse function of Hyperbolic Tangent such that atanh(0)=0

fn atan2(_y: Self, _x: Self) -> Self

A continuous function of two variables where tan(atan2(y,x)) = y/x for y!=0 and atan2(0,1) = 0

fn pi() -> Self

The classic cicle constant

pub fn sin_cos(self) -> (Self, Self)

Finds both the Sine and Cosine as a tuple

pub fn frac_2_pi() -> Self

2/π. Mirrors FRAC_2_PI

pub fn frac_pi_2() -> Self

π/2. Mirrors FRAC_PI_2

pub fn frac_pi_3() -> Self

π/3. Mirrors FRAC_PI_3

pub fn frac_pi_4() -> Self

π/4. Mirrors FRAC_PI_4

pub fn frac_pi_6() -> Self

π/6. Mirrors FRAC_PI_6

pub fn frac_pi_8() -> Self

π/8. Mirrors FRAC_PI_8

pub fn pythag_const() -> Self

The length of the hypotenuse of a unit right-triangle. Mirrors SQRT_2

pub fn pythag_const_inv() -> Self

The sine of π/4. Mirrors FRAC_1_SQRT_2

pub fn to_degrees(self) -> Self

pub fn to_radians(self) -> Self

impl Zero for Complex

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.