Struct autodiff::forward_autodiff::F

#[repr(C)]pub struct F<D> {
    pub x: f64,
    pub dx: D,
}

A generic forward differentiation Dual number.

The derivative is generic to support higher order differentiation.

Fields

x: f64

The value of the variable

dx: D

The derivative of the variable

Implementations

impl<D> F<D>

pub fn new<T: ToPrimitive>(x: T, d: D) -> F<D>

Create a new dual number with value x and initial derivative d.

Panics

This constructor panics if x cannot be converted to f64.

impl<D: Zero> F<D>

pub fn cst<T: ToPrimitive>(x: T) -> F<D>

Create a new constant.

Use this also to convert from a variable to a constant. This constructor panics if x cannot be converted to f64.

impl<D: One> F<D>

pub fn var<T: ToPrimitive>(x: T) -> F<D>

Create a new variable.

Use this also to convert from a constant to a variable. This constructor panics if x cannot be converted to f64.

impl<D> F<D>

pub fn value(&self) -> f64

Get the value of this variable.

impl<D: Copy> F<D>

pub fn deriv(&self) -> D

Get the current derivative of this variable. This will be zero if this F is a constant.

impl<D> F<D> where
    Self: Float, 

pub fn pow(self, n: impl Into<F<D>>) -> F<D>

Raise this number to the n’th power.

This is a generic version of Float::powf.

Trait Implementations

impl<D: Add<D, Output = D>> Add<F<D>> for F<D>

type Output = F<D>

The resulting type after applying the + operator.

fn add(self, rhs: F<D>) -> F<D>

Performs the + operation.

impl<D> Add<f32> for F<D>

type Output = F<D>

The resulting type after applying the + operator.

fn add(self, rhs: f32) -> F<D>

Performs the + operation.

impl<D> Add<f64> for F<D>

type Output = F<D>

The resulting type after applying the + operator.

fn add(self, rhs: f64) -> F<D>

Performs the + operation.

impl<D: AddAssign> AddAssign<F<D>> for F<D>

fn add_assign(&mut self, rhs: F<D>)

Performs the += operation.

impl<D> AddAssign<f32> for F<D>

fn add_assign(&mut self, rhs: f32)

Performs the += operation.

impl<D> AddAssign<f64> for F<D>

fn add_assign(&mut self, rhs: f64)

Performs the += operation.

impl<D: Clone> Clone for F<D>

fn clone(&self) -> F<D>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<D: Copy> Copy for F<D>

impl<D: Debug> Debug for F<D>

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

Formats the value using the given formatter.

impl<D: Default> Default for F<D>

fn default() -> Self

Returns the “default value” for a type.

impl<D, R> Div<F<D>> for F<D> where
    D: Copy + Div<R, Output = D> + Mul<R, Output = D> + Sub<Output = D>,
    F<D>: ReduceOrder<Reduced = R>,
    R: Copy + Mul<Output = R>, 

type Output = F<D>

The resulting type after applying the / operator.

fn div(self, rhs: F<D>) -> F<D>

Performs the / operation.

impl<D> Div<f32> for F<D> where
    D: Div<f64, Output = D> + Mul<f64, Output = D> + Sub<Output = D>, 

type Output = F<D>

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> F<D>

Performs the / operation.

impl<D: Div<f64, Output = D>> Div<f64> for F<D>

type Output = F<D>

The resulting type after applying the / operator.

fn div(self, rhs: f64) -> F<D>

Performs the / operation.

impl<D, R> DivAssign<F<D>> for F<D> where
    D: Mul<R, Output = D> + DivAssign<R> + SubAssign,
    F<D>: ReduceOrder<Reduced = R>,
    R: Copy + Mul<Output = R> + Div<R, Output = R>, 

fn div_assign(&mut self, rhs: F<D>)

Performs the /= operation.

impl<D: DivAssign<f64>> DivAssign<f32> for F<D>

fn div_assign(&mut self, rhs: f32)

Performs the /= operation.

impl<D: DivAssign<f64>> DivAssign<f64> for F<D>

fn div_assign(&mut self, rhs: f64)

Performs the /= operation.

impl<D, R> Float for F<D> where
    D: Debug + Float + Zero + Neg<Output = D> + Mul<R, Output = D> + Mul<f64, Output = D> + Add<Output = D> + Div<f64, Output = D> + Div<R, Output = D> + Sub<Output = D> + Copy + PartialOrd,
    F<D>: ReduceOrder<Reduced = R>,
    R: Float + Mul<f64, Output = R>, 

fn nan() -> F<D>

Returns the NaN value.

fn infinity() -> F<D>

Returns the infinite value.

fn neg_infinity() -> F<D>

Returns the negative infinite value.

fn neg_zero() -> F<D>

Returns -0.0.

fn min_value() -> F<D>

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> F<D>

Returns the smallest positive, normalized value that this type can represent.

fn max_value() -> F<D>

Returns the largest finite value that this type can represent.

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise.

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal, or NaN.

fn classify(self) -> FpCategory

Returns the floating point category of the number. If only one property is going to be tested, it is generally faster to use the specific predicate instead.

fn floor(self) -> F<D>

Returns the largest integer less than or equal to a number.

fn ceil(self) -> F<D>

Returns the smallest integer greater than or equal to a number.

fn round(self) -> F<D>

Returns the nearest integer to a number. Round half-way cases away from 0.0.

fn trunc(self) -> F<D>

Return the integer part of a number.

fn fract(self) -> F<D>

Returns the fractional part of a number.

fn abs(self) -> F<D>

Computes the absolute value of self. Returns Float::nan() if the number is Float::nan().

fn signum(self) -> F<D>

Returns a number that represents the sign of self.

fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0, Float::infinity(), and since Rust 1.20 also Float::nan().

fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0, Float::neg_infinity(), and since Rust 1.20 also -Float::nan().

fn mul_add(self, a: F<D>, b: F<D>) -> F<D>

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an unfused multiply-add.

fn recip(self) -> F<D>

Take the reciprocal (inverse) of a number, 1/x.

fn powi(self, n: i32) -> F<D>

Raise a number to an integer power.

fn powf(self, n: F<D>) -> F<D>

Raise a number to a floating point power.

fn sqrt(self) -> F<D>

Take the square root of a number.

fn exp(self) -> F<D>

Returns e^(self), (the exponential function).

fn exp2(self) -> F<D>

Returns 2^(self).

fn ln(self) -> F<D>

Returns the natural logarithm of the number.

fn log(self, b: F<D>) -> F<D>

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

fn log2(self) -> F<D>

Returns the base 2 logarithm of the number.

fn log10(self) -> F<D>

Returns the base 10 logarithm of the number.

fn max(self, other: F<D>) -> F<D>

Returns the maximum of the two numbers.

fn min(self, other: F<D>) -> F<D>

Returns the minimum of the two numbers.

fn abs_sub(self, other: F<D>) -> F<D>

The positive difference of two numbers.

fn cbrt(self) -> F<D>

Take the cubic root of a number.

fn hypot(self, other: F<D>) -> F<D>

Calculate the length of the hypotenuse of a right-angle triangle given legs of length x and y.

fn sin(self) -> F<D>

Computes the sine of a number (in radians).

fn cos(self) -> F<D>

Computes the cosine of a number (in radians).

fn tan(self) -> F<D>

Computes the tangent of a number (in radians).

fn asin(self) -> F<D>

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1].

fn acos(self) -> F<D>

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1].

fn atan(self) -> F<D>

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

fn atan2(self, other: F<D>) -> F<D>

Computes the four quadrant arctangent of self (y) and other (x).

fn sin_cos(self) -> (F<D>, F<D>)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

fn exp_m1(self) -> F<D>

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

fn ln_1p(self) -> F<D>

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

fn sinh(self) -> F<D>

Hyperbolic sine function.

fn cosh(self) -> F<D>

Hyperbolic cosine function.

fn tanh(self) -> F<D>

Hyperbolic tangent function.

fn asinh(self) -> F<D>

Inverse hyperbolic sine function.

fn acosh(self) -> F<D>

Inverse hyperbolic cosine function.

fn atanh(self) -> F<D>

Inverse hyperbolic tangent function.

fn integer_decode(self) -> (u64, i16, i8)

Returns the mantissa, base 2 exponent, and sign as integers, respectively. The original number can be recovered by sign * mantissa * 2 ^ exponent.

fn epsilon() -> F<D>

Returns epsilon, a small positive value.

fn to_degrees(self) -> F<D>

Converts radians to degrees.

fn to_radians(self) -> F<D>

Converts degrees to radians.

impl<D: Zero> FloatConst for F<D>

fn E() -> F<D>

Return Euler’s number.

fn FRAC_1_PI() -> F<D>

Return 1.0 / π.

fn FRAC_1_SQRT_2() -> F<D>

Return 1.0 / sqrt(2.0).

fn FRAC_2_PI() -> F<D>

Return 2.0 / π.

fn FRAC_2_SQRT_PI() -> F<D>

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> F<D>

Return π / 2.0.

fn FRAC_PI_3() -> F<D>

Return π / 3.0.

fn FRAC_PI_4() -> F<D>

Return π / 4.0.

fn FRAC_PI_6() -> F<D>

Return π / 6.0.

fn FRAC_PI_8() -> F<D>

Return π / 8.0.

fn LN_10() -> F<D>

Return ln(10.0).

fn LN_2() -> F<D>

Return ln(2.0).

fn LOG10_E() -> F<D>

Return log10(e).

fn LOG2_E() -> F<D>

Return log2(e).

fn PI() -> F<D>

Return Archimedes’ constant π.

fn SQRT_2() -> F<D>

Return sqrt(2.0).

pub fn TAU() -> Self where
    Self: Add<Self, Output = Self>, 

Return the full circle constant τ.

pub fn LOG10_2() -> Self where
    Self: Div<Self, Output = Self>, 

Return log10(2.0).

pub fn LOG2_10() -> Self where
    Self: Div<Self, Output = Self>, 

Return log2(10.0).

impl<D: Zero> From<f32> for F<D>

fn from(x: f32) -> F<D>

Construct a constant from an f32.

impl<D: Zero> From<f64> for F<D>

fn from(x: f64) -> F<D>

Construct a constant from an f64.

impl<D: Zero> FromPrimitive for F<D>

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<D> Into<f32> for F<D>

fn into(self) -> f32

Convert the value into an f32 type.

impl<D> Into<f64> for F<D>

fn into(self) -> f64

Convert the value into an f64 type.

impl<D, R> Mul<F<D>> for F<D> where
    D: Copy + Mul<R, Output = D> + Add<Output = D>,
    F<D>: ReduceOrder<Reduced = R>, 

type Output = F<D>

The resulting type after applying the * operator.

fn mul(self, rhs: F<D>) -> F<D>

Performs the * operation.

impl<D: Mul<f64, Output = D>> Mul<f32> for F<D>

type Output = F<D>

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> F<D>

Performs the * operation.

impl<D: Mul<f64, Output = D>> Mul<f64> for F<D>

type Output = F<D>

The resulting type after applying the * operator.

fn mul(self, rhs: f64) -> F<D>

Performs the * operation.

impl<D, R> MulAssign<F<D>> for F<D> where
    D: MulAssign<R> + Mul<R, Output = D> + AddAssign,
    F<D>: ReduceOrder<Reduced = R>, 

fn mul_assign(&mut self, rhs: F<D>)

Performs the *= operation.

impl<D: MulAssign<f64>> MulAssign<f32> for F<D>

fn mul_assign(&mut self, rhs: f32)

Performs the *= operation.

impl<D: MulAssign<f64>> MulAssign<f64> for F<D>

fn mul_assign(&mut self, rhs: f64)

Performs the *= operation.

impl<D: Neg<Output = D>> Neg for F<D>

type Output = F<D>

The resulting type after applying the - operator.

fn neg(self) -> F<D>

Performs the unary - operation.

impl<D, R> Num for F<D> where
    D: Copy + Debug + Zero + PartialEq + Sub<Output = D> + Mul<f64, Output = D> + Mul<R, Output = D> + Div<f64, Output = D> + Div<R, Output = D>,
    F<D>: ReduceOrder<Reduced = R>,
    R: Float, 

type FromStrRadixErr = ParseFloatError

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

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

impl<D: Zero> NumCast for F<D>

fn from<T: ToPrimitive>(n: T) -> Option<F<D>>

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned.

impl<D: Copy + Debug + Zero + Mul<<F<D> as ReduceOrder>::Reduced, Output = D>> One for F<D> where
    F<D>: ReduceOrder, 

fn one() -> F<D>

Returns the multiplicative identity element of Self, 1.

pub fn set_one(&mut self)

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

pub fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<D, U> PartialEq<F<U>> for F<D>

fn eq(&self, rhs: &F<U>) -> bool

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

#[must_use]pub fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<D, U> PartialOrd<F<U>> for F<D>

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

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

#[must_use]pub fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

#[must_use]pub fn le(&self, other: &Rhs) -> bool

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

#[must_use]pub fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

#[must_use]pub fn ge(&self, other: &Rhs) -> bool

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

impl<D: ReduceOrder> ReduceOrder for F<D>

type Reduced = F<D::Reduced>

fn reduce_order(&self) -> Self::Reduced

Produce an equivalent dual number with a lower differentiation order.

fn reduced_value(r: &Self::Reduced) -> f64

Get the value of the reduced dual.

impl<D, R> Rem<F<D>> for F<D> where
    D: Copy + Mul<R, Output = D> + Sub<Output = D>,
    F<D>: ReduceOrder<Reduced = R>,
    R: Float, 

type Output = F<D>

The resulting type after applying the % operator.

fn rem(self, rhs: F<D>) -> F<D>

Performs the % operation.

impl<D: Rem<f64, Output = D>> Rem<f64> for F<D>

type Output = F<D>

The resulting type after applying the % operator.

fn rem(self, rhs: f64) -> F<D>

Performs the % operation.

impl<D, R> RemAssign<F<D>> for F<D> where
    D: Copy + Mul<R, Output = D> + SubAssign,
    F<D>: ReduceOrder<Reduced = R>,
    R: Float, 

fn rem_assign(&mut self, rhs: F<D>)

Performs the %= operation.

impl<D: RemAssign<f64>> RemAssign<f32> for F<D>

fn rem_assign(&mut self, rhs: f32)

Performs the %= operation.

impl<D: RemAssign<f64>> RemAssign<f64> for F<D>

fn rem_assign(&mut self, rhs: f64)

Performs the %= operation.

impl<D: Sub<D, Output = D>> Sub<F<D>> for F<D>

type Output = F<D>

The resulting type after applying the - operator.

fn sub(self, rhs: F<D>) -> F<D>

Performs the - operation.

impl<D> Sub<f64> for F<D>

type Output = F<D>

The resulting type after applying the - operator.

fn sub(self, rhs: f64) -> F<D>

Performs the - operation.

impl<D: SubAssign> SubAssign<F<D>> for F<D>

fn sub_assign(&mut self, rhs: F<D>)

Performs the -= operation.

impl<D> SubAssign<f32> for F<D>

fn sub_assign(&mut self, rhs: f32)

Performs the -= operation.

impl<D> SubAssign<f64> for F<D>

fn sub_assign(&mut self, rhs: f64)

Performs the -= operation.

impl<D: AddAssign + Zero> Sum<F<D>> for F<D>

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

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

impl<D: AddAssign + Zero> Sum<f64> for F<D>

fn sum<I>(iter: I) -> Self where
    I: Iterator<Item = f64>, 

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

impl<D> ToPrimitive for F<D>

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

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.

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

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.

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

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.

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

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.

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

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.

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

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.

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

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.

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

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.

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

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.

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

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.

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

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.

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

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64.

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

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned.

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

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned.

impl<D: Zero> Zero for F<D>

fn zero() -> F<D>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

pub fn set_zero(&mut self)

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