Struct num_dual::Dual2

pub struct Dual2<T: DualNum<F>, F> {
    pub re: T,
    pub v1: T,
    pub v2: T,
    /* private fields */
}

A scalar second order dual number for the calculation of second derivatives.

Fields

re: T

Real part of the second order dual number

v1: T

First derivative part of the second order dual number

v2: T

Second derivative part of the second order dual number

Implementations

impl<T: DualNum<F>, F> Dual2<T, F>

pub fn new(re: T, v1: T, v2: T) -> Self

Create a new second order dual number from its fields.

impl<T: DualNum<F>, F> Dual2<T, F>

pub fn derivative(self) -> Self

Set the derivative part to 1.

let x = Dual2::from_re(5.0).derivative().powi(2);
assert_eq!(x.re, 25.0);             // x²
assert_eq!(x.v1, 10.0);    // 2x
assert_eq!(x.v2, 2.0);     // 2

Can also be used for higher order derivatives.

let x = Dual2::from_re(Dual64::from_re(5.0).derivative())
    .derivative()
    .powi(2);
assert_eq!(x.re.re, 25.0);      // x²
assert_eq!(x.re.eps, 10.0);     // 2x
assert_eq!(x.v1.re, 10.0);      // 2x
assert_eq!(x.v1.eps, 2.0);      // 2
assert_eq!(x.v2.re, 2.0);       // 2

impl<T: DualNum<F>, F> Dual2<T, F>

pub fn from_re(re: T) -> Self

Create a new second order dual number from the real part.

Trait Implementations

impl<'a, 'b, T: DualNum<F>, F: Float> Add<&'a Dual2<T, F>> for &'b Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the + operator.

fn add(self, other: &Dual2<T, F>) -> Dual2<T, F>

Performs the + operation.

impl<T: DualNum<F>, F: Float> Add<&Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the + operator.

fn add(self, rhs: &Dual2<T, F>) -> Self::Output

Performs the + operation.

impl<T: DualNum<F>, F: Float> Add<Dual2<T, F>> for &Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the + operator.

fn add(self, rhs: Dual2<T, F>) -> Self::Output

Performs the + operation.

impl<T: DualNum<F>, F: Float> Add<Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the + operator.

fn add(self, rhs: Dual2<T, F>) -> Self::Output

Performs the + operation.

impl<T: DualNum<F>, F> Add<F> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the + operator.

fn add(self, other: F) -> Self

Performs the + operation.

impl<T: DualNum<F>, F> AddAssign<Dual2<T, F>> for Dual2<T, F>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<T: DualNum<F>, F> AddAssign<F> for Dual2<T, F>

fn add_assign(&mut self, other: F)

Performs the += operation.

impl<T: Clone + DualNum<F>, F: Clone> Clone for Dual2<T, F>

fn clone(&self) -> Dual2<T, F>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug + DualNum<F>, F: Debug> Debug for Dual2<T, F>

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

Formats the value using the given formatter.

impl<T: DualNum<F>, F: Display> Display for Dual2<T, F>

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

Formats the value using the given formatter.

impl<'a, 'b, T: DualNum<F>, F: Float> Div<&'a Dual2<T, F>> for &'b Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the / operator.

fn div(self, other: &Dual2<T, F>) -> Dual2<T, F>

Performs the / operation.

impl<T: DualNum<F>, F: Float> Div<&Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the / operator.

fn div(self, rhs: &Dual2<T, F>) -> Self::Output

Performs the / operation.

impl<T: DualNum<F>, F: Float> Div<Dual2<T, F>> for &Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the / operator.

fn div(self, rhs: Dual2<T, F>) -> Self::Output

Performs the / operation.

impl<T: DualNum<F>, F: Float> Div<Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the / operator.

fn div(self, rhs: Dual2<T, F>) -> Self::Output

Performs the / operation.

impl<T: DualNum<F>, F: DualNumFloat> Div<F> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the / operator.

fn div(self, other: F) -> Self

Performs the / operation.

impl<T: DualNum<F>, F: Float> DivAssign<Dual2<T, F>> for Dual2<T, F>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<T: DualNum<F>, F: DualNumFloat> DivAssign<F> for Dual2<T, F>

fn div_assign(&mut self, other: F)

Performs the /= operation.

impl<T: DualNum<F>, F: DualNumFloat> DualNum<F> for Dual2<T, F>

const NDERIV: usize = _

Highest derivative that can be calculated with this struct

fn re(&self) -> F

Real part (0th derivative) of the number

fn recip(&self) -> Self

Reciprocal (inverse) of a number 1/x.

fn powi(&self, exp: i32) -> Self

Power with integer exponent x^n

fn powf(&self, n: F) -> Self

Power with real exponent x^n

fn sqrt(&self) -> Self

Square root

fn cbrt(&self) -> Self

Cubic root

fn exp(&self) -> Self

Exponential e^x

fn exp2(&self) -> Self

Exponential with base 2 2^x

fn exp_m1(&self) -> Self

Exponential minus 1 e^x-1

fn ln(&self) -> Self

Natural logarithm

fn log(&self, base: F) -> Self

Logarithm with arbitrary base

fn log2(&self) -> Self

Logarithm with base 2

fn log10(&self) -> Self

Logarithm with base 10

fn ln_1p(&self) -> Self

Logarithm on x plus one ln(1+x)

fn sin(&self) -> Self

Sine

fn cos(&self) -> Self

Cosine

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

Calculate sine and cosine simultaneously

fn tan(&self) -> Self

Tangent

fn asin(&self) -> Self

Arcsine

fn acos(&self) -> Self

Arccosine

fn atan(&self) -> Self

Arctangent

fn sinh(&self) -> Self

Hyperbolic sine

fn cosh(&self) -> Self

Hyperbolic cosine

fn tanh(&self) -> Self

Hyperbolic tangent

fn asinh(&self) -> Self

Area hyperbolic sine

fn acosh(&self) -> Self

Area hyperbolic cosine

fn atanh(&self) -> Self

Area hyperbolic tangent

fn sph_j0(&self) -> Self

0th order spherical Bessel function of the first kind

fn sph_j1(&self) -> Self

1st order spherical Bessel function of the first kind

fn sph_j2(&self) -> Self

2nd order spherical Bessel function of the first kind

fn mul_add(&self, a: Self, b: Self) -> Self

Fused multiply-add

fn powd(&self, exp: Self) -> Self

Power with dual exponent x^n

impl<T: DualNum<F>, F: Float + FloatConst> FloatConst for Dual2<T, F>

fn E() -> Self

Return Euler’s number.

fn FRAC_1_PI() -> Self

Return 1.0 / π.

fn FRAC_1_SQRT_2() -> Self

Return 1.0 / sqrt(2.0).

fn FRAC_2_PI() -> Self

Return 2.0 / π.

fn FRAC_2_SQRT_PI() -> Self

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> Self

Return π / 2.0.

fn FRAC_PI_3() -> Self

Return π / 3.0.

fn FRAC_PI_4() -> Self

Return π / 4.0.

fn FRAC_PI_6() -> Self

Return π / 6.0.

fn FRAC_PI_8() -> Self

Return π / 8.0.

fn LN_10() -> Self

Return ln(10.0).

fn LN_2() -> Self

Return ln(2.0).

fn LOG10_E() -> Self

Return log10(e).

fn LOG2_E() -> Self

Return log2(e).

fn PI() -> Self

Return Archimedes’ constant π.

fn SQRT_2() -> Self

Return sqrt(2.0).

fn TAU() -> Selfwhere Self: Sized + Add<Self, Output = Self>,

Return the full circle constant τ.

fn LOG10_2() -> Selfwhere Self: Sized + Div<Self, Output = Self>,

Return log10(2.0).

fn LOG2_10() -> Selfwhere Self: Sized + Div<Self, Output = Self>,

Return log2(10.0).

impl<T: DualNum<F>, F> From<F> for Dual2<T, F>

fn from(float: F) -> Self

Converts to this type from the input type.

impl<T: DualNum<F>, F: Float + FromPrimitive> FromPrimitive for Dual2<T, F>

fn from_isize(n: isize) -> Option<Self>

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

fn from_i8(n: i8) -> Option<Self>

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

fn from_i16(n: i16) -> Option<Self>

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

fn from_i32(n: i32) -> Option<Self>

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

fn from_i64(n: i64) -> Option<Self>

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

fn from_i128(n: i128) -> Option<Self>

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

fn from_usize(n: usize) -> Option<Self>

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

fn from_u8(n: u8) -> Option<Self>

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

fn from_u16(n: u16) -> Option<Self>

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

fn from_u32(n: u32) -> Option<Self>

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

fn from_u64(n: u64) -> Option<Self>

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

fn from_u128(n: u128) -> Option<Self>

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

fn from_f32(n: f32) -> Option<Self>

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

fn from_f64(n: f64) -> Option<Self>

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

impl<T: DualNum<F>, F: DualNumFloat> Inv for Dual2<T, F>

type Output = Dual2<T, F>

The result after applying the operator.

fn inv(self) -> Self

Returns the multiplicative inverse of self.

impl<'a, 'b, T: DualNum<F>, F: Float> Mul<&'a Dual2<T, F>> for &'b Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the * operator.

fn mul(self, other: &Dual2<T, F>) -> Dual2<T, F>

Performs the * operation.

impl<T: DualNum<F>, F: Float> Mul<&Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the * operator.

fn mul(self, rhs: &Dual2<T, F>) -> Self::Output

Performs the * operation.

impl<T: DualNum<F>, F: Float> Mul<Dual2<T, F>> for &Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the * operator.

fn mul(self, rhs: Dual2<T, F>) -> Self::Output

Performs the * operation.

impl<T: DualNum<F>, F: Float> Mul<Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the * operator.

fn mul(self, rhs: Dual2<T, F>) -> Self::Output

Performs the * operation.

impl<T: DualNum<F>, F: DualNumFloat> Mul<F> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the * operator.

fn mul(self, other: F) -> Self

Performs the * operation.

impl<T: DualNum<F>, F: Float> MulAssign<Dual2<T, F>> for Dual2<T, F>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<T: DualNum<F>, F: DualNumFloat> MulAssign<F> for Dual2<T, F>

fn mul_assign(&mut self, other: F)

Performs the *= operation.

impl<T: DualNum<F>, F: Float> Neg for &Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: DualNum<F>, F: Float> Neg for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<T: DualNum<F> + Signed, F: Float> Num for Dual2<T, F>

type FromStrRadixErr = <F as Num>::FromStrRadixErr

fn from_str_radix( _str: &str, _radix: u32 ) -> Result<Self, Self::FromStrRadixErr>

Convert from a string and radix (typically 2..=36).

impl<T: DualNum<F>, F: Float> One for Dual2<T, F>

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<T: PartialEq + DualNum<F>, F: PartialEq> PartialEq<Dual2<T, F>> for Dual2<T, F>

fn eq(&self, other: &Dual2<T, F>) -> bool

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

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, T: DualNum<F>, F: Float> Product<&'a Dual2<T, F>> for Dual2<T, F>

fn product<I>(iter: I) -> Selfwhere I: Iterator<Item = &'a Dual2<T, F>>,

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

impl<T: DualNum<F>, F: Float> Product<Dual2<T, F>> for Dual2<T, F>

fn product<I>(iter: I) -> Selfwhere I: Iterator<Item = Self>,

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

impl<'a, 'b, T: DualNum<F>, F> Rem<&'a Dual2<T, F>> for &'b Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the % operator.

fn rem(self, _other: &Dual2<T, F>) -> Dual2<T, F>

Performs the % operation.

impl<T: DualNum<F>, F: Float> Rem<&Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the % operator.

fn rem(self, rhs: &Dual2<T, F>) -> Self::Output

Performs the % operation.

impl<T: DualNum<F>, F: Float> Rem<Dual2<T, F>> for &Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the % operator.

fn rem(self, rhs: Dual2<T, F>) -> Self::Output

Performs the % operation.

impl<T: DualNum<F>, F: Float> Rem<Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the % operator.

fn rem(self, rhs: Dual2<T, F>) -> Self::Output

Performs the % operation.

impl<T: DualNum<F>, F> Rem<F> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the % operator.

fn rem(self, _other: F) -> Self

Performs the % operation.

impl<T: DualNum<F>, F> RemAssign<Dual2<T, F>> for Dual2<T, F>

fn rem_assign(&mut self, _other: Self)

Performs the %= operation.

impl<T: DualNum<F>, F> RemAssign<F> for Dual2<T, F>

fn rem_assign(&mut self, _other: F)

Performs the %= operation.

impl<T: DualNum<F>, F: DualNumFloat> Signed for Dual2<T, F>

fn abs(&self) -> Self

Computes the absolute value.

fn abs_sub(&self, other: &Self) -> Self

The positive difference of two numbers.

fn signum(&self) -> Self

Returns the sign of the number.

fn is_positive(&self) -> bool

Returns true if the number is positive and false if the number is zero or negative.

fn is_negative(&self) -> bool

Returns true if the number is negative and false if the number is zero or positive.

impl<'a, 'b, T: DualNum<F>, F: Float> Sub<&'a Dual2<T, F>> for &'b Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the - operator.

fn sub(self, other: &Dual2<T, F>) -> Dual2<T, F>

Performs the - operation.

impl<T: DualNum<F>, F: Float> Sub<&Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the - operator.

fn sub(self, rhs: &Dual2<T, F>) -> Self::Output

Performs the - operation.

impl<T: DualNum<F>, F: Float> Sub<Dual2<T, F>> for &Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the - operator.

fn sub(self, rhs: Dual2<T, F>) -> Self::Output

Performs the - operation.

impl<T: DualNum<F>, F: Float> Sub<Dual2<T, F>> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the - operator.

fn sub(self, rhs: Dual2<T, F>) -> Self::Output

Performs the - operation.

impl<T: DualNum<F>, F> Sub<F> for Dual2<T, F>

type Output = Dual2<T, F>

The resulting type after applying the - operator.

fn sub(self, other: F) -> Self

Performs the - operation.

impl<T: DualNum<F>, F> SubAssign<Dual2<T, F>> for Dual2<T, F>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<T: DualNum<F>, F> SubAssign<F> for Dual2<T, F>

fn sub_assign(&mut self, other: F)

Performs the -= operation.

impl<'a, T: DualNum<F>, F: Float> Sum<&'a Dual2<T, F>> for Dual2<T, F>

fn sum<I>(iter: I) -> Selfwhere I: Iterator<Item = &'a Dual2<T, F>>,

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

impl<T: DualNum<F>, F: Float> Sum<Dual2<T, F>> for Dual2<T, F>

fn sum<I>(iter: I) -> Selfwhere I: Iterator<Item = Self>,

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

impl<T: DualNum<F>, F: Float> Zero for Dual2<T, F>

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.

impl<T: Copy + DualNum<F>, F: Copy> Copy for Dual2<T, F>

impl<T: Eq + DualNum<F>, F: Eq> Eq for Dual2<T, F>

impl<T: DualNum<F>, F> StructuralEq for Dual2<T, F>

impl<T: DualNum<F>, F> StructuralPartialEq for Dual2<T, F>