Struct 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<T: DualNum<F> + AbsDiffEq<Epsilon = T>, F: Float> AbsDiffEq for Dual2<T, F>

Like PartialEq, comparisons are only made based on the real part. This allows the code to follow the same execution path as real-valued code would.

type Epsilon = Dual2<T, F>

Used for specifying relative comparisons.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

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> 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: Float> Add 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> AddAssign<F> for Dual2<T, F>

fn add_assign(&mut self, other: F)

Performs the += operation.

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

fn add_assign(&mut self, other: Self)

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> ComplexField for Dual2<T, T::Element>

where T: DualNum<T::Element> + SupersetOf<T> + AbsDiffEq<Epsilon = T> + Sync + Send + SupersetOf<T::Element> + SupersetOf<f32> + SupersetOf<f64> + SimdPartialOrd + PartialOrd + SimdValue<Element = T, SimdBool = bool> + RelativeEq + UlpsEq + AbsDiffEq, T::Element: DualNum<T::Element> + Scalar + DualNumFloat + Sync + Send,

type RealField = Dual2<T, <T as SimdValue>::Element>

fn from_real(re: Self::RealField) -> Self

Builds a pure-real complex number from the given value.

fn real(self) -> Self::RealField

The real part of this complex number.

fn imaginary(self) -> Self::RealField

The imaginary part of this complex number.

fn modulus(self) -> Self::RealField

The modulus of this complex number.

fn modulus_squared(self) -> Self::RealField

The squared modulus of this complex number.

fn argument(self) -> Self::RealField

The argument of this complex number.

fn norm1(self) -> Self::RealField

The sum of the absolute value of this complex number’s real and imaginary part.

fn scale(self, factor: Self::RealField) -> Self

Multiplies this complex number by factor.

fn unscale(self, factor: Self::RealField) -> Self

Divides this complex number by factor.

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

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

fn abs(self) -> Self::RealField

The absolute value of this complex number: self / self.signum().

fn hypot(self, other: Self) -> Self::RealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

fn recip(self) -> Self

fn conjugate(self) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

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

fn tan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn atan(self) -> Self

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

fn asinh(self) -> Self

fn acosh(self) -> Self

fn atanh(self) -> Self

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

fn log2(self) -> Self

fn log10(self) -> Self

fn ln(self) -> Self

fn ln_1p(self) -> Self

fn sqrt(self) -> Self

fn exp(self) -> Self

fn exp2(self) -> Self

fn exp_m1(self) -> Self

fn powi(self, n: i32) -> Self

fn powf(self, n: Self::RealField) -> Self

fn powc(self, n: Self) -> Self

fn cbrt(self) -> Self

fn is_finite(&self) -> bool

fn try_sqrt(self) -> Option<Self>

fn to_polar(self) -> (Self::RealField, Self::RealField)

The polar form of this complex number: (modulus, arg)

fn to_exp(self) -> (Self::RealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})

fn signum(self) -> Self

The exponential part of this complex number: self / self.modulus()

fn sinh_cosh(self) -> (Self, Self)

fn sinc(self) -> Self

Cardinal sine

fn sinhc(self) -> Self

fn cosc(self) -> Self

Cardinal cos

fn coshc(self) -> Self

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<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, 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: 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> Div 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> DivAssign<F> for Dual2<T, F>

fn div_assign(&mut self, other: F)

Performs the /= operation.

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

fn div_assign(&mut self, other: Self)

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

type Inner = T

Type of the elements of this generalized (hyper) dual number

fn from_inner(inner: Self::Inner) -> Self

Construct a new generalized (hyper) dual number from its real part

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 atan2(&self, other: 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() -> Self

where Self: Sized + Add<Output = Self>,

Return the full circle constant τ.

fn LOG10_2() -> Self

where Self: Sized + Div<Output = Self>,

Return log10(2.0).

fn LOG2_10() -> Self

where Self: Sized + Div<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<T: DualNum<F>, F: Float> Lift<Dual2<T, F>, F> for Dual2<T, F>

type Lifted<D2: DualNum<F, Inner = Self>> = D2

fn lift<D2: DualNum<F, Inner = Self>>(&self) -> Self::Lifted<D2>

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, 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: 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> Mul 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> MulAssign<F> for Dual2<T, F>

fn mul_assign(&mut self, other: F)

Performs the *= operation.

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

fn mul_assign(&mut self, other: Self)

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

Comparisons are only made based on the real part. This allows the code to follow the same execution path as real-valued code would.

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

Tests for self and other values to be equal, and is used by ==.

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

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

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

Like PartialEq, comparisons are only made based on the real part. This allows the code to follow the same execution path as real-valued code would.

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

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

fn product<I>(iter: I) -> Self

where I: Iterator<Item = &'a Dual2<T, F>>,

Takes an iterator and generates Self from the elements by multiplying the items.

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

fn product<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T> RealField for Dual2<T, T::Element>

where T: DualNum<T::Element> + SupersetOf<T> + Sync + Send + SupersetOf<T::Element> + SupersetOf<f32> + SupersetOf<f64> + SimdPartialOrd + PartialOrd + RelativeEq + AbsDiffEq<Epsilon = T> + SimdValue<Element = T, SimdBool = bool> + UlpsEq + AbsDiffEq, T::Element: DualNum<T::Element> + Scalar + DualNumFloat,

fn max(self, other: Self) -> Self

Got to be careful using this, because it throws away the derivatives of the one not chosen

fn min(self, other: Self) -> Self

Got to be careful using this, because it throws away the derivatives of the one not chosen

fn clamp(self, min: Self, max: Self) -> Self

If the min/max values are constants and the clamping has an effect, you lose your gradients.

fn copysign(self, sign: Self) -> Self

Copies the sign of sign to self.

fn atan2(self, other: Self) -> Self

fn pi() -> Self

fn two_pi() -> Self

fn frac_pi_2() -> Self

fn frac_pi_3() -> Self

fn frac_pi_4() -> Self

fn frac_pi_6() -> Self

fn frac_pi_8() -> Self

fn frac_1_pi() -> Self

fn frac_2_pi() -> Self

fn frac_2_sqrt_pi() -> Self

fn e() -> Self

fn log2_e() -> Self

fn log10_e() -> Self

fn ln_2() -> Self

fn ln_10() -> Self

fn is_sign_positive(&self) -> bool

Is the sign of this real number positive?

fn is_sign_negative(&self) -> bool

Is the sign of this real number negative?

fn min_value() -> Option<Self>

The smallest finite positive value representable using this type.

fn max_value() -> Option<Self>

The largest finite positive value representable using this type.

impl<T: DualNum<F> + RelativeEq<Epsilon = T>, F: Float> RelativeEq for Dual2<T, F>

Like PartialEq, comparisons are only made based on the real part. This allows the code to follow the same execution path as real-valued code would.

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of RelativeEq::relative_eq.

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> 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: Float> Rem 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> RemAssign<F> for Dual2<T, F>

fn rem_assign(&mut self, _other: F)

Performs the %= operation.

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

fn rem_assign(&mut self, _other: Self)

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<T> SimdValue for Dual2<T, T::Element>

where T: DualNum<T::Element> + SimdValue + Scalar, T::Element: DualNum<T::Element> + Scalar,

The SimdValue trait is for rearranging data into a form more suitable for Simd, and rearranging it back into a usable form. It is not documented particularly well.

The primary job of this SimdValue impl is to allow people to use simba::simd::f32x4 etc, instead of f32/f64. Those types implement nalgebra::SimdRealField/ComplexField, so they behave like scalars. When we use them, we would have Dual<f32x4, f32, N> etc, with our F parameter set to <T as SimdValue>::Element. We will need to be able to split up that type into four of Dual in order to get out of simd-land. That’s what the SimdValue trait is for.

Ultimately, someone will have to to implement SimdRealField on Dual and call the simd_ functions of <T as SimdRealField>. That’s future work for someone who finds num_dual is not fast enough.

Unfortunately, doing anything with SIMD is blocked on https://github.com/dimforge/simba/issues/44.

const LANES: usize = T::LANES

The number of lanes of this SIMD value.

type Element = Dual2<<T as SimdValue>::Element, <T as SimdValue>::Element>

The type of the elements of each lane of this SIMD value.

type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.

fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to val.

fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of self.

unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of self without bound-checking.

fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val.

unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val without bound-checking.

fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges self and other depending on the lanes of cond.

fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self

where Self: Clone,

Applies a function to each lane of self.

fn zip_map_lanes( self, b: Self, f: impl Fn(Self::Element, Self::Element) -> Self::Element, ) -> Self

where Self: Clone,

Applies a function to each lane of self paired with the corresponding lane of b.

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> 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: Float> Sub 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> SubAssign<F> for Dual2<T, F>

fn sub_assign(&mut self, other: F)

Performs the -= operation.

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

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<TSuper, FSuper, T, F> SubsetOf<Dual2<TSuper, FSuper>> for Dual2<T, F>

where TSuper: DualNum<FSuper> + SupersetOf<T>, T: DualNum<F>,

fn to_superset(&self) -> Dual2<TSuper, FSuper>

The inclusion map: converts self to the equivalent element of its superset.

fn from_superset(element: &Dual2<TSuper, FSuper>) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

fn from_superset_unchecked(element: &Dual2<TSuper, FSuper>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn is_in_subset(element: &Dual2<TSuper, FSuper>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

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

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = &'a Dual2<T, F>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

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

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<TSuper, FSuper> SupersetOf<f32> for Dual2<TSuper, FSuper>

where TSuper: DualNum<FSuper> + SupersetOf<f32>,

fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).

fn to_subset_unchecked(&self) -> f32

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

fn from_subset(element: &f32) -> Self

The inclusion map: converts self to the equivalent element of its superset.

fn to_subset(&self) -> Option<T>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<TSuper, FSuper> SupersetOf<f64> for Dual2<TSuper, FSuper>

where TSuper: DualNum<FSuper> + SupersetOf<f64>,

fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).

fn to_subset_unchecked(&self) -> f64

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

fn from_subset(element: &f64) -> Self

The inclusion map: converts self to the equivalent element of its superset.

fn to_subset(&self) -> Option<T>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T: DualNum<F> + UlpsEq<Epsilon = T>, F: Float> UlpsEq for Dual2<T, F>

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.

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> Field for Dual2<T, T::Element>

where T: DualNum<T::Element> + SimdValue, T::Element: DualNum<T::Element> + Scalar + Float,