Struct autodiff::forward_autodiff::F

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

A generic forward differentiation Dual number.

The derivative is generic in V to support composition and alternative numeric types and in D to support higher order differentiation.

Fields

x: V

The value of the variable.

dx: D

The derivative of the variable.

Implementations

impl<V, D> F<V, D>

pub fn new(x: V, dx: D) -> F<V, D>

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

This is equivalent to setting the fields of F directly.

impl<V, D: Zero> F<V, D>

pub fn cst(x: impl Into<V>) -> F<V, D>

Create a new constant.

Use this also to convert from a variable to a constant.

impl<V, D: One> F<V, D>

pub fn var(x: impl Into<V>) -> F<V, D>

Create a new variable.

Use this also to convert from a constant to a variable.

impl<V: Clone, D> F<V, D>

pub fn value(&self) -> V

Get the value of this variable.

impl<V, D: Clone> F<V, D>

pub fn deriv(&self) -> D

Get the current derivative of this variable.

This will be zero if this F is a constant.

impl<V, D> F<V, D>where Self: Float,

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

Raise this number to the n’th power.

This is a generic version of Float::powf.

Trait Implementations

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

type Output = F<<V as Add<V>>::Output, D>

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<F<f64, f64>> for f32

type Output = F<f64, f64>

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<F<f64, f64>> for f64

type Output = F<f64, f64>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = F<V, D>

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

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

fn add_assign(&mut self, rhs: V)

Performs the += operation.

impl<V, D> Bounded for F<V, D>where V: Bounded, D: Bounded,

fn min_value() -> Self

Returns the smallest finite number this type can represent

fn max_value() -> Self

Returns the largest finite number this type can represent

impl<V: Clone, D: Clone> Clone for F<V, D>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<V: Debug, D: Debug> Debug for F<V, D>

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

Formats the value using the given formatter.

impl<V: Default, D: Default> Default for F<V, D>

fn default() -> Self

Returns the “default value” for a type.

impl<V: Display, D: Display> Display for F<V, D>

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

Formats the value using the given formatter.

impl<V, D> Div<F<V, D>> for F<V, D>where V: Clone + Div<Output = V> + Mul<Output = V>, D: Clone + Div<V, Output = D> + Mul<V, Output = D> + Sub<Output = D>,

type Output = F<V, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<F<f64, f64>> for f32

type Output = F<f64, f64>

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<F<f64, f64>> for f64

type Output = F<f64, f64>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<V: Div + Clone, D: Div<V>> Div<V> for F<V, D>

type Output = F<<V as Div<V>>::Output, <D as Div<V>>::Output>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<V, D> DivAssign<F<V, D>> for F<V, D>where V: Clone + DivAssign + Mul<Output = V> + Div<Output = V>, D: Mul<V, Output = D> + DivAssign<V> + SubAssign,

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

Performs the /= operation.

impl<V: DivAssign + Clone, D: DivAssign<V>> DivAssign<V> for F<V, D>

fn div_assign(&mut self, rhs: V)

Performs the /= operation.

impl<V, D> Float for F<V, D>where V: Float, D: Debug + Float + Zero + Neg<Output = D> + Mul<Output = D> + Mul<V, Output = D> + Add<Output = D> + Div<V, Output = D> + Div<Output = D> + Sub<Output = D> + Clone + PartialOrd,

fn nan() -> F<V, D>

Returns the NaN value.

fn infinity() -> F<V, D>

Returns the infinite value.

fn neg_infinity() -> F<V, D>

Returns the negative infinite value.

fn neg_zero() -> F<V, D>

Returns -0.0.

fn min_value() -> F<V, D>

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> F<V, D>

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

fn max_value() -> F<V, 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<V, D>

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

fn ceil(self) -> F<V, D>

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

fn round(self) -> F<V, D>

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

fn trunc(self) -> F<V, D>

Return the integer part of a number.

fn fract(self) -> F<V, D>

Returns the fractional part of a number.

fn abs(self) -> F<V, D>

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

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

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

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

Raise a number to an integer power.

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

Raise a number to a floating point power.

fn sqrt(self) -> F<V, D>

Take the square root of a number.

fn exp(self) -> F<V, D>

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

fn exp2(self) -> F<V, D>

Returns 2^(self).

fn ln(self) -> F<V, D>

Returns the natural logarithm of the number.

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

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

fn log2(self) -> F<V, D>

Returns the base 2 logarithm of the number.

fn log10(self) -> F<V, D>

Returns the base 10 logarithm of the number.

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

Returns the maximum of the two numbers.

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

Returns the minimum of the two numbers.

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

The positive difference of two numbers.

fn cbrt(self) -> F<V, D>

Take the cubic root of a number.

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

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

fn sin(self) -> F<V, D>

Computes the sine of a number (in radians).

fn cos(self) -> F<V, D>

Computes the cosine of a number (in radians).

fn tan(self) -> F<V, D>

Computes the tangent of a number (in radians).

fn asin(self) -> F<V, 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<V, 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<V, D>

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

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

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

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

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

fn exp_m1(self) -> F<V, D>

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

fn ln_1p(self) -> F<V, D>

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

fn sinh(self) -> F<V, D>

Hyperbolic sine function.

fn cosh(self) -> F<V, D>

Hyperbolic cosine function.

fn tanh(self) -> F<V, D>

Hyperbolic tangent function.

fn asinh(self) -> F<V, D>

Inverse hyperbolic sine function.

fn acosh(self) -> F<V, D>

Inverse hyperbolic cosine function.

fn atanh(self) -> F<V, 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<V, D>

Returns epsilon, a small positive value.

fn to_degrees(self) -> F<V, D>

Converts radians to degrees.

fn to_radians(self) -> F<V, D>

Converts degrees to radians.

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

Returns a number composed of the magnitude of self and the sign of sign.

impl<V: FloatConst, D: Zero> FloatConst for F<V, D>

fn E() -> F<V, D>

Return Euler’s number.

fn FRAC_1_PI() -> F<V, D>

Return 1.0 / π.

fn FRAC_1_SQRT_2() -> F<V, D>

Return 1.0 / sqrt(2.0).

fn FRAC_2_PI() -> F<V, D>

Return 2.0 / π.

fn FRAC_2_SQRT_PI() -> F<V, D>

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> F<V, D>

Return π / 2.0.

fn FRAC_PI_3() -> F<V, D>

Return π / 3.0.

fn FRAC_PI_4() -> F<V, D>

Return π / 4.0.

fn FRAC_PI_6() -> F<V, D>

Return π / 6.0.

fn FRAC_PI_8() -> F<V, D>

Return π / 8.0.

fn LN_10() -> F<V, D>

Return ln(10.0).

fn LN_2() -> F<V, D>

Return ln(2.0).

fn LOG10_E() -> F<V, D>

Return log10(e).

fn LOG2_E() -> F<V, D>

Return log2(e).

fn PI() -> F<V, D>

Return Archimedes’ constant π.

fn SQRT_2() -> F<V, D>

Return sqrt(2.0).

impl<V: Zero> From<V> for F<V, V>

fn from(x: V) -> Self

Converts to this type from the input type.

impl<V: FromPrimitive, D: Zero> FromPrimitive for F<V, 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<V: ToPrimitive, D> Into<f32> for F<V, D>

fn into(self) -> f32

Converts the dual number into an f32.

Panics

This function panics if this conversion fails.

impl<V: ToPrimitive, D> Into<f64> for F<V, D>

fn into(self) -> f64

Converts the dual number into an f64.

Panics

This function panics if this conversion fails.

impl<V, D> Mul<F<V, D>> for F<V, D>where V: Clone + Mul, D: Clone + Mul<V>, D::Output: Add,

type Output = F<<V as Mul<V>>::Output, <<D as Mul<V>>::Output as Add<<D as Mul<V>>::Output>>::Output>

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<F<f64, f64>> for f32

type Output = F<f64, f64>

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<F<f64, f64>> for f64

type Output = F<f64, f64>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<V: Mul<Output = V> + Clone, D: Mul<V, Output = D>> Mul<V> for F<V, D>

type Output = F<V, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<V, D> MulAssign<F<V, D>> for F<V, D>where V: Clone + MulAssign, D: MulAssign<V> + Mul<V, Output = D> + AddAssign,

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

Performs the *= operation.

impl<V: MulAssign + Clone, D: MulAssign<V>> MulAssign<V> for F<V, D>

fn mul_assign(&mut self, rhs: V)

Performs the *= operation.

impl<V: Neg<Output = V>, D: Neg<Output = D>> Neg for F<V, D>

type Output = F<V, D>

The resulting type after applying the - operator.

fn neg(self) -> F<V, D>

Performs the unary - operation.

impl<V, D> Num for F<V, D>where V: Clone + Num, D: Clone + Debug + Zero + PartialEq + Sub<Output = D> + Mul<V, Output = D> + Mul<Output = D> + Div<V, Output = D> + Div<Output = D>,

type FromStrRadixErr = <V as Num>::FromStrRadixErr

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

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

impl<V: NumCast, D: Zero> NumCast for F<V, D>

fn from<T: ToPrimitive>(n: T) -> Option<F<V, 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<V, D> One for F<V, D>where V: Clone + One, D: Clone + Zero + Debug + Mul<V, Output = D>,

fn one() -> F<V, D>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

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

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

fn eq(&self, rhs: &F<V, U>) -> 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<V: PartialOrd, D, U> PartialOrd<F<V, U>> for F<V, D>

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

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

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

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

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

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

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

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

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<V, D> Rem<F<V, D>> for F<V, D>where V: Clone + Rem<Output = V> + Div<Output = V> + Sub<Output = V> + One, D: Clone + Mul<V, Output = D> + Sub<Output = D>,

type Output = F<<V as Rem<V>>::Output, D>

The resulting type after applying the % operator.

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

Performs the % operation.

impl Rem<F<f64, f64>> for f64

type Output = F<f64, f64>

The resulting type after applying the % operator.

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

Performs the % operation.

impl<V: Rem<f64>, D: Rem<f64>> Rem<f64> for F<V, D>

type Output = F<<V as Rem<f64>>::Output, <D as Rem<f64>>::Output>

The resulting type after applying the % operator.

fn rem(self, rhs: f64) -> Self::Output

Performs the % operation.

impl<V, D> RemAssign<F<V, D>> for F<V, D>where V: Clone + RemAssign + Div<Output = V> + Sub<Output = V> + Rem<Output = V> + One, D: Mul<V, Output = D> + SubAssign,

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

Performs the %= operation.

impl<V: RemAssign<f32>, D: RemAssign<f32>> RemAssign<f32> for F<V, D>

fn rem_assign(&mut self, rhs: f32)

Performs the %= operation.

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

fn rem_assign(&mut self, rhs: f64)

Performs the %= operation.

impl<V, D> Signed for F<V, D>where V: Signed + Clone + Num + PartialOrd, D: Signed + Clone + Debug + Zero + PartialEq + Sub<Output = D> + Mul<V, Output = D> + Mul<Output = D> + Div<V, Output = D> + Div<Output = D>,

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

type Output = F<V, D>

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<F<f64, f64>> for f32

type Output = F<f64, f64>

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<F<f64, f64>> for f64

type Output = F<f64, f64>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<V: Sub, D> Sub<V> for F<V, D>

type Output = F<<V as Sub<V>>::Output, D>

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

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

fn sub_assign(&mut self, rhs: V)

Performs the -= operation.

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

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<V: AddAssign + Zero, D: AddAssign + Zero> Sum<V> for F<V, D>

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

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

impl<V: ToPrimitive, D> ToPrimitive for F<V, 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.

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.

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<V: Zero, D: Zero> Zero for F<V, D>

fn zero() -> F<V, D>

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<V: Copy, D: Copy> Copy for F<V, D>