Struct Ad 

pub struct Ad<const N: usize> { /* private fields */ }

Automatic differentiation value tracking first and second derivatives

Value getters:

• value() -> f64: Returns the current numerical value
• grad() -> SVector<f64, N>: Returns the gradient vector
• hess() -> SMatrix<f64, N, N>: Returns the Hessian matrix

Type Parameters

• N - The dimension of the input space (number of variables)

Fields (private)

• value - The current value of the function
• grad - The gradient (first derivatives) as a vector
• hess - The Hessian matrix (second derivatives)

Implementations

impl<const N: usize> Ad<N>

pub fn neg(&self) -> Self

pub fn sqrt(&self) -> Self

pub fn square(&self) -> Self

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

Examples found in repository

src/examples/mass_spring.rs (line 20)

    fn eval(&self, variables: &raddy::types::advec<4, 4>, _: &()) -> raddy::Ad<4> {
        let p1 = advec::<4, 2>::new(variables[0].clone(), variables[1].clone());
        let p2 = advec::<4, 2>::new(variables[2].clone(), variables[3].clone());

        let len = (p2 - p1).norm();
        // Hooke's law
        let potential = val::scalar(0.5 * self.k) * (len - val::scalar(self.restlen)).powi(2);

        potential
    }

pub fn powf(&self, exponent: f64) -> Self

pub fn abs(&self) -> Self

pub fn exp(&self) -> Self

pub fn ln(&self) -> Self

Examples found in repository

src/examples/basic.rs (line 17)

fn main() {
    // 1.
    // ################ scalar ################
    let mut rng = thread_rng();
    let val = rng.gen_range(0.0..10.0);

    let var = var::scalar(val);
    let var = &var;
    let y = var.sin() * var + var.ln();
    let g = val * val.cos() + val.sin() + val.recip();
    let h = -val * val.sin() + 2.0 * val.cos() - val.powi(-2);

    assert_abs_diff_eq!(y.grad()[(0, 0)], g, epsilon = EPS);
    assert_abs_diff_eq!(y.hess()[(0, 0)], h, epsilon = EPS);

    // 2.
    // ############################# Matrix #############################

    const N_TEST_MAT_4: usize = 4;
    type NaConst = Const<N_TEST_MAT_4>;
    const N_VEC_4: usize = N_TEST_MAT_4 * N_TEST_MAT_4;

    let vals: &[f64] = &(0..N_VEC_4)
        .map(|_| rng.gen_range(-4.0..4.0))
        .collect::<Vec<_>>();

    let s: SVector<Ad<N_VEC_4>, N_VEC_4> = var::vector_from_slice(vals);
    let z = s
        .clone()
        // This reshape is COL MAJOR!!!!!!!!!!!!!
        .reshape_generic(NaConst {}, NaConst {})
        .transpose();

    let det = z.determinant();
    let _grad = det.grad();
    let _hess = det.hess();
    // core logic ends ####################################################

    // correctness
    // let expected_grad = grad_det4(
    //     vals[0], vals[1], vals[2], vals[3], vals[4], vals[5], vals[6], vals[7], vals[8], vals[9],
    //     vals[10], vals[11], vals[12], vals[13], vals[14], vals[15],
    // );
    // let g_diff = (expected_grad - det.grad()).norm_squared();
    // assert_abs_diff_eq!(g_diff, 0.0, epsilon = EPS);

    // let expected_hess = hess_det4(
    //     vals[0], vals[1], vals[2], vals[3], vals[4], vals[5], vals[6], vals[7], vals[8], vals[9],
    //     vals[10], vals[11], vals[12], vals[13], vals[14], vals[15],
    // );
    // let h_diff = (det.hess() - expected_hess).norm_squared();
    // assert_abs_diff_eq!(h_diff, 0.0, epsilon = EPS);
}

pub fn log(&self, base: f64) -> Self

pub fn log2(&self) -> Self

pub fn log10(&self) -> Self

pub fn sin(&self) -> Self

Examples found in repository

src/examples/basic.rs (line 17)

fn main() {
    // 1.
    // ################ scalar ################
    let mut rng = thread_rng();
    let val = rng.gen_range(0.0..10.0);

    let var = var::scalar(val);
    let var = &var;
    let y = var.sin() * var + var.ln();
    let g = val * val.cos() + val.sin() + val.recip();
    let h = -val * val.sin() + 2.0 * val.cos() - val.powi(-2);

    assert_abs_diff_eq!(y.grad()[(0, 0)], g, epsilon = EPS);
    assert_abs_diff_eq!(y.hess()[(0, 0)], h, epsilon = EPS);

    // 2.
    // ############################# Matrix #############################

    const N_TEST_MAT_4: usize = 4;
    type NaConst = Const<N_TEST_MAT_4>;
    const N_VEC_4: usize = N_TEST_MAT_4 * N_TEST_MAT_4;

    let vals: &[f64] = &(0..N_VEC_4)
        .map(|_| rng.gen_range(-4.0..4.0))
        .collect::<Vec<_>>();

    let s: SVector<Ad<N_VEC_4>, N_VEC_4> = var::vector_from_slice(vals);
    let z = s
        .clone()
        // This reshape is COL MAJOR!!!!!!!!!!!!!
        .reshape_generic(NaConst {}, NaConst {})
        .transpose();

    let det = z.determinant();
    let _grad = det.grad();
    let _hess = det.hess();
    // core logic ends ####################################################

    // correctness
    // let expected_grad = grad_det4(
    //     vals[0], vals[1], vals[2], vals[3], vals[4], vals[5], vals[6], vals[7], vals[8], vals[9],
    //     vals[10], vals[11], vals[12], vals[13], vals[14], vals[15],
    // );
    // let g_diff = (expected_grad - det.grad()).norm_squared();
    // assert_abs_diff_eq!(g_diff, 0.0, epsilon = EPS);

    // let expected_hess = hess_det4(
    //     vals[0], vals[1], vals[2], vals[3], vals[4], vals[5], vals[6], vals[7], vals[8], vals[9],
    //     vals[10], vals[11], vals[12], vals[13], vals[14], vals[15],
    // );
    // let h_diff = (det.hess() - expected_hess).norm_squared();
    // assert_abs_diff_eq!(h_diff, 0.0, epsilon = EPS);
}

pub fn cos(&self) -> Self

pub fn tan(&self) -> Self

pub fn asin(&self) -> Self

pub fn acos(&self) -> Self

pub fn atan(&self) -> Self

👎Deprecated: Please use atan2 instead.

pub fn sinh(&self) -> Self

pub fn cosh(&self) -> Self

pub fn tanh(&self) -> Self

pub fn asinh(&self) -> Self

pub fn acosh(&self) -> Self

pub fn atanh(&self) -> Self

impl<const N: usize> Ad<N>

pub fn add_value(&self, other: f64) -> Self

pub fn sub_value(&self, other: f64) -> Self

pub fn mul_value(&self, other: f64) -> Self

pub fn recip(&self) -> Self

pub fn div_value(&self, other: f64) -> Self

pub fn atan2(&self, x: &Self) -> Self

self is y

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

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

pub fn clamp(&self, low: &Self, high: &Self) -> Self

pub fn hypot(&self, other: &Self) -> Self

impl<const N: usize> Ad<N>

pub fn value(&self) -> f64

Returns the current value of the AD variable

pub fn grad(&self) -> SVector<f64, L>

Returns the gradient (first derivatives) of the AD variable

Returns

The gradient (A vector containing the partial derivatives with respect to each input variable).

Examples found in repository

src/examples/basic.rs (line 21)

fn main() {
    // 1.
    // ################ scalar ################
    let mut rng = thread_rng();
    let val = rng.gen_range(0.0..10.0);

    let var = var::scalar(val);
    let var = &var;
    let y = var.sin() * var + var.ln();
    let g = val * val.cos() + val.sin() + val.recip();
    let h = -val * val.sin() + 2.0 * val.cos() - val.powi(-2);

    assert_abs_diff_eq!(y.grad()[(0, 0)], g, epsilon = EPS);
    assert_abs_diff_eq!(y.hess()[(0, 0)], h, epsilon = EPS);

    // 2.
    // ############################# Matrix #############################

    const N_TEST_MAT_4: usize = 4;
    type NaConst = Const<N_TEST_MAT_4>;
    const N_VEC_4: usize = N_TEST_MAT_4 * N_TEST_MAT_4;

    let vals: &[f64] = &(0..N_VEC_4)
        .map(|_| rng.gen_range(-4.0..4.0))
        .collect::<Vec<_>>();

    let s: SVector<Ad<N_VEC_4>, N_VEC_4> = var::vector_from_slice(vals);
    let z = s
        .clone()
        // This reshape is COL MAJOR!!!!!!!!!!!!!
        .reshape_generic(NaConst {}, NaConst {})
        .transpose();

    let det = z.determinant();
    let _grad = det.grad();
    let _hess = det.hess();
    // core logic ends ####################################################

    // correctness
    // let expected_grad = grad_det4(
    //     vals[0], vals[1], vals[2], vals[3], vals[4], vals[5], vals[6], vals[7], vals[8], vals[9],
    //     vals[10], vals[11], vals[12], vals[13], vals[14], vals[15],
    // );
    // let g_diff = (expected_grad - det.grad()).norm_squared();
    // assert_abs_diff_eq!(g_diff, 0.0, epsilon = EPS);

    // let expected_hess = hess_det4(
    //     vals[0], vals[1], vals[2], vals[3], vals[4], vals[5], vals[6], vals[7], vals[8], vals[9],
    //     vals[10], vals[11], vals[12], vals[13], vals[14], vals[15],
    // );
    // let h_diff = (det.hess() - expected_hess).norm_squared();
    // assert_abs_diff_eq!(h_diff, 0.0, epsilon = EPS);
}

pub fn hess(&self) -> SMatrix<f64, RC, RC>

Returns the Hessian matrix (second derivatives) of the AD variable

Returns

The hessian.

Examples found in repository

src/examples/basic.rs (line 22)

fn main() {
    // 1.
    // ################ scalar ################
    let mut rng = thread_rng();
    let val = rng.gen_range(0.0..10.0);

    let var = var::scalar(val);
    let var = &var;
    let y = var.sin() * var + var.ln();
    let g = val * val.cos() + val.sin() + val.recip();
    let h = -val * val.sin() + 2.0 * val.cos() - val.powi(-2);

    assert_abs_diff_eq!(y.grad()[(0, 0)], g, epsilon = EPS);
    assert_abs_diff_eq!(y.hess()[(0, 0)], h, epsilon = EPS);

    // 2.
    // ############################# Matrix #############################

    const N_TEST_MAT_4: usize = 4;
    type NaConst = Const<N_TEST_MAT_4>;
    const N_VEC_4: usize = N_TEST_MAT_4 * N_TEST_MAT_4;

    let vals: &[f64] = &(0..N_VEC_4)
        .map(|_| rng.gen_range(-4.0..4.0))
        .collect::<Vec<_>>();

    let s: SVector<Ad<N_VEC_4>, N_VEC_4> = var::vector_from_slice(vals);
    let z = s
        .clone()
        // This reshape is COL MAJOR!!!!!!!!!!!!!
        .reshape_generic(NaConst {}, NaConst {})
        .transpose();

    let det = z.determinant();
    let _grad = det.grad();
    let _hess = det.hess();
    // core logic ends ####################################################

    // correctness
    // let expected_grad = grad_det4(
    //     vals[0], vals[1], vals[2], vals[3], vals[4], vals[5], vals[6], vals[7], vals[8], vals[9],
    //     vals[10], vals[11], vals[12], vals[13], vals[14], vals[15],
    // );
    // let g_diff = (expected_grad - det.grad()).norm_squared();
    // assert_abs_diff_eq!(g_diff, 0.0, epsilon = EPS);

    // let expected_hess = hess_det4(
    //     vals[0], vals[1], vals[2], vals[3], vals[4], vals[5], vals[6], vals[7], vals[8], vals[9],
    //     vals[10], vals[11], vals[12], vals[13], vals[14], vals[15],
    // );
    // let h_diff = (det.hess() - expected_hess).norm_squared();
    // assert_abs_diff_eq!(h_diff, 0.0, epsilon = EPS);
}

impl Ad<1>

pub fn given_scalar(value: f64, grad: f64, hess: f64) -> Self

Creates an AD scalar with explicitly specified value, gradient and Hessian

Arguments

• value - The scalar value
• grad - The gradient (first derivative)
• hess - The Hessian (second derivative)

Returns

A new Ad<1> instance with the specified properties

pub fn active_scalar(value: f64) -> Self

Creates an active scalar AD value with unit gradient

Arguments

• value - The scalar value

Returns

A new Ad<1> instance that is active (gradient = 1.0)

impl<const N: usize> Ad<N>

pub fn inactive_scalar(value: f64) -> Self

Creates an inactive scalar AD value with zero gradient and Hessian

Arguments

• value - The scalar value

Returns

A new Ad<N> instance that is inactive (gradient = 0)

pub fn inactive_vector<const L: usize>( values: &SVector<f64, N>, ) -> SVector<Self, L>

Creates a vector of inactive AD values from a vector of f64 values

Arguments

• values - Input vector of numerical values

Type Parameters

• L - Length of the output vector

Returns

A vector of inactive AD values

pub fn inactive_from_slice<const L: usize>(values: &[f64]) -> SVector<Self, L>

Creates a vector of inactive AD values from a slice of f64 values

Arguments

• values - Slice of numerical values

Type Parameters

• L - Length of the output vector

Returns

A vector of inactive AD values

Panics

If the slice length doesn’t match the input dimension N

pub fn given_vector( value: f64, grad: &SVector<f64, L>, hess: &SMatrix<f64, RC, RC>, ) -> Self

Creates an AD value with explicitly specified value, gradient and Hessian

Arguments

• value - The scalar value
• grad - The gradient vector
• hess - The Hessian matrix

Returns

A new Ad<N> instance with the specified properties

pub fn active_vector(vector: &SVector<f64, N>) -> SVector<Self, N>

Creates a vector of active AD values from a vector of f64 values

Arguments

• values - Input vector of numerical values

Returns

A vector of active AD values where each element has unit gradient in its corresponding dimension

pub fn active_from_slice(values: &[f64]) -> SVector<Self, N>

Creates a vector of active AD values from a slice of f64 values

Arguments

• values - Slice of numerical values

Returns

A vector of active AD values

Panics

If the slice length doesn’t match the input dimension N

Trait Implementations

impl<const N: usize> AbsDiffEq for Ad<N>

type Epsilon = Ad<N>

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

The inverse of AbsDiffEq::abs_diff_eq.

impl<const N: usize> Add<&Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<const N: usize> Add<&Ad<N>> for Ad<N>

type Output = Ad<N>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<const N: usize> Add<Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the + operator.

fn add(self, rhs: Ad<N>) -> Self::Output

Performs the + operation.

impl<const N: usize> Add for Ad<N>

type Output = Ad<N>

The resulting type after applying the + operator.

fn add(self, rhs: Ad<N>) -> Self::Output

Performs the + operation.

impl<const N: usize> AddAssign<&Ad<N>> for Ad<N>

fn add_assign(&mut self, rhs: &Ad<N>)

Performs the += operation.

impl<const N: usize> AddAssign for Ad<N>

fn add_assign(&mut self, rhs: Ad<N>)

Performs the += operation.

impl<const N: usize> Clone for Ad<N>

fn clone(&self) -> Ad<N>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const N: usize> ComplexField for Ad<N>

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. This should be zero with no grad w.r.t. self, but the use of this method is itself a bug.

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 abs(self) -> Self::RealField

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

This is equivalent to self.modulus().

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

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

fn conjugate(self) -> Self

Real number has itself as conjugate

type RealField = Ad<N>

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 recip(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, exponent: 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<const N: usize> Debug for Ad<N>

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

Formats the value using the given formatter.

impl<const N: usize> Display for Ad<N>

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

Formats the value using the given formatter.

impl<const N: usize> Div<&Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<const N: usize> Div<&Ad<N>> for Ad<N>

type Output = Ad<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<const N: usize> Div<Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the / operator.

fn div(self, rhs: Ad<N>) -> Self::Output

Performs the / operation.

impl<const N: usize> Div for Ad<N>

type Output = Ad<N>

The resulting type after applying the / operator.

fn div(self, rhs: Ad<N>) -> Self::Output

Performs the / operation.

impl<const N: usize> DivAssign<&Ad<N>> for Ad<N>

fn div_assign(&mut self, rhs: &Ad<N>)

Performs the /= operation.

impl<const N: usize> DivAssign for Ad<N>

fn div_assign(&mut self, rhs: Ad<N>)

Performs the /= operation.

impl<const N: usize> FromPrimitive for Ad<N>

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_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_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_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_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<const N: usize> Mul<&Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<const N: usize> Mul<&Ad<N>> for Ad<N>

type Output = Ad<N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<const N: usize, const R: usize, const C: usize> Mul<&Matrix<Ad<N>, Const<R>, Const<C>, ArrayStorage<Ad<N>, R, C>>> for &Ad<N>

type Output = Matrix<Ad<N>, Const<R>, Const<C>, ArrayStorage<Ad<N>, R, C>>

The resulting type after applying the * operator.

fn mul(self, rhs: &SMatrix<Ad<N>, R, C>) -> Self::Output

Performs the * operation.

impl<const N: usize, const R: usize, const C: usize> Mul<&Matrix<Ad<N>, Const<R>, Const<C>, ArrayStorage<Ad<N>, R, C>>> for Ad<N>

type Output = Matrix<Ad<N>, Const<R>, Const<C>, ArrayStorage<Ad<N>, R, C>>

The resulting type after applying the * operator.

fn mul(self, rhs: &SMatrix<Ad<N>, R, C>) -> Self::Output

Performs the * operation.

impl<const N: usize> Mul<Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Ad<N>) -> Self::Output

Performs the * operation.

impl<const N: usize, const R: usize, const C: usize> Mul<Matrix<Ad<N>, Const<R>, Const<C>, ArrayStorage<Ad<N>, R, C>>> for &Ad<N>

type Output = Matrix<Ad<N>, Const<R>, Const<C>, ArrayStorage<Ad<N>, R, C>>

The resulting type after applying the * operator.

fn mul(self, rhs: SMatrix<Ad<N>, R, C>) -> Self::Output

Performs the * operation.

impl<const N: usize, const R: usize, const C: usize> Mul<Matrix<Ad<N>, Const<R>, Const<C>, ArrayStorage<Ad<N>, R, C>>> for Ad<N>

type Output = Matrix<Ad<N>, Const<R>, Const<C>, ArrayStorage<Ad<N>, R, C>>

The resulting type after applying the * operator.

fn mul(self, rhs: SMatrix<Ad<N>, R, C>) -> Self::Output

Performs the * operation.

impl<const N: usize> Mul for Ad<N>

type Output = Ad<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Ad<N>) -> Self::Output

Performs the * operation.

impl<const N: usize> MulAssign<&Ad<N>> for Ad<N>

fn mul_assign(&mut self, rhs: &Ad<N>)

Performs the *= operation.

impl<const N: usize> MulAssign for Ad<N>

fn mul_assign(&mut self, rhs: Ad<N>)

Performs the *= operation.

impl<const N: usize> Neg for &Ad<N>

type Output = Ad<N>

The resulting type after applying the - operator.

fn neg(self) -> Ad<N>

Performs the unary - operation.

impl<const N: usize> Neg for Ad<N>

type Output = Ad<N>

The resulting type after applying the - operator.

fn neg(self) -> Ad<N>

Performs the unary - operation.

impl<const N: usize> Num for Ad<N>

type FromStrRadixErr = ()

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

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

impl<const N: usize> One for Ad<N>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

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

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<const N: usize> PartialEq<Ad<N>> for f64

fn eq(&self, other: &Ad<N>) -> 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<const N: usize> PartialEq<f64> for Ad<N>

fn eq(&self, other: &f64) -> 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<const N: usize> PartialEq for Ad<N>

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<const N: usize> PartialOrd<Ad<N>> for f64

fn partial_cmp(&self, other: &Ad<N>) -> 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<const N: usize> PartialOrd<f64> for Ad<N>

fn partial_cmp(&self, other: &f64) -> 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<const N: usize> PartialOrd for Ad<N>

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<const N: usize> RealField for Ad<N>

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 copysign(self, sign: Self) -> Self

Copies the sign of sign to self.

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

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

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

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

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.

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

impl<const N: usize> RelativeEq for Ad<N>

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<const N: usize> Rem<&Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the % operator.

fn rem(self, rhs: &Ad<N>) -> Self::Output

Performs the % operation.

impl<const N: usize> Rem<&Ad<N>> for Ad<N>

type Output = Ad<N>

The resulting type after applying the % operator.

fn rem(self, rhs: &Ad<N>) -> Self::Output

Performs the % operation.

impl<const N: usize> Rem<Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the % operator.

fn rem(self, rhs: Ad<N>) -> Self::Output

Performs the % operation.

impl<const N: usize> Rem for Ad<N>

type Output = Ad<N>

The resulting type after applying the % operator.

fn rem(self, rhs: Ad<N>) -> Self::Output

Performs the % operation.

impl<const N: usize> RemAssign<&Ad<N>> for Ad<N>

fn rem_assign(&mut self, rhs: &Ad<N>)

Performs the %= operation.

impl<const N: usize> RemAssign for Ad<N>

fn rem_assign(&mut self, rhs: Ad<N>)

Performs the %= operation.

impl<const N: usize> Signed for Ad<N>

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<const N: usize> SimdValue for Ad<N>

const LANES: usize = 1usize

The number of lanes of this SIMD value.

type Element = Ad<N>

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

type SimdBool = bool

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<const N: usize> Sub<&Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<const N: usize> Sub<&Ad<N>> for Ad<N>

type Output = Ad<N>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<const N: usize> Sub<Ad<N>> for &Ad<N>

type Output = Ad<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Ad<N>) -> Self::Output

Performs the - operation.

impl<const N: usize> Sub for Ad<N>

type Output = Ad<N>

The resulting type after applying the - operator.

fn sub(self, rhs: Ad<N>) -> Self::Output

Performs the - operation.

impl<const N: usize> SubAssign<&Ad<N>> for Ad<N>

fn sub_assign(&mut self, rhs: &Ad<N>)

Performs the -= operation.

impl<const N: usize> SubAssign for Ad<N>

fn sub_assign(&mut self, rhs: Ad<N>)

Performs the -= operation.

impl<const N: usize> SubsetOf<Ad<N>> for Ad<N>

fn to_superset(&self) -> Ad<N>

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

fn from_superset_unchecked(element: &Ad<N>) -> Self

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

fn is_in_subset(element: &Ad<N>) -> bool

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

fn from_superset(element: &T) -> Option<Self>

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

impl<const N: usize> SubsetOf<Ad<N>> for f32

fn to_superset(&self) -> Ad<N>

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

fn from_superset_unchecked(element: &Ad<N>) -> Self

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

fn is_in_subset(element: &Ad<N>) -> bool

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

fn from_superset(element: &T) -> Option<Self>

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

impl<const N: usize> SubsetOf<Ad<N>> for f64

fn to_superset(&self) -> Ad<N>

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

fn from_superset_unchecked(element: &Ad<N>) -> Self

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

fn is_in_subset(element: &Ad<N>) -> bool

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

fn from_superset(element: &T) -> Option<Self>

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

impl<const N: usize> UlpsEq for Ad<N>

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<const N: usize> Zero for Ad<N>

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<const N: usize> Field for Ad<N>