Struct autodiff::forward_autodiff::F

pub struct F {
    pub x: f64,
    pub dx: f64,
}

Fields

x: f64

dx: f64

Methods

impl F

pub fn cst<T: ToPrimitive>(x: T) -> F

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.

pub fn var<T: ToPrimitive>(x: T) -> F

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.

pub fn full_eq(&self, rhs: &F) -> bool

Compare two Fs in full, including the derivative part.

pub fn value(&self) -> f64

Get the value of this variable.

pub fn deriv(&self) -> f64

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

Trait Implementations

impl Into<f64> for F

Panic-less conversion into f64 type.

fn into(self) -> f64

Performs the conversion.

impl Into<f32> for F

Panic-less conversion into f32 type.

fn into(self) -> f32

Performs the conversion.

impl Clone for F

fn clone(&self) -> F

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Copy for F

impl Default for F

fn default() -> Self

Returns the "default value" for a type.

impl PartialEq<F> for F

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

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

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

This method tests for !=.

impl PartialOrd<F> for F

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

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

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

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

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

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

#[must_use] 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 Debug for F

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

Formats the value using the given formatter.

impl Div<F> for F

type Output = F

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<f64> for F

type Output = F

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<F> for f64

type Output = F

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<f32> for F

type Output = F

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<F> for f32

type Output = F

The resulting type after applying the / operator.

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

Performs the / operation.

impl Rem<F> for F

type Output = F

The resulting type after applying the % operator.

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

Performs the % operation.

impl Rem<f64> for F

type Output = F

The resulting type after applying the % operator.

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

Performs the % operation.

impl Rem<F> for f64

type Output = F

The resulting type after applying the % operator.

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

Performs the % operation.

impl Sub<F> for F

type Output = F

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<f64> for F

type Output = F

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<F> for f64

type Output = F

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<f32> for F

type Output = F

The resulting type after applying the - operator.

fn sub(self, rhs: f32) -> F

Performs the - operation.

impl Sub<F> for f32

type Output = F

The resulting type after applying the - operator.

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

Performs the - operation.

impl Add<F> for F

type Output = F

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<f64> for F

type Output = F

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<F> for f64

type Output = F

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<f32> for F

type Output = F

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<F> for f32

type Output = F

The resulting type after applying the + operator.

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

Performs the + operation.

impl Mul<F> for F

type Output = F

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<F> for f64

type Output = F

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<f64> for F

type Output = F

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<F> for f32

type Output = F

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<f32> for F

type Output = F

The resulting type after applying the * operator.

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

Performs the * operation.

impl Neg for F

type Output = F

The resulting type after applying the - operator.

fn neg(self) -> F

Performs the unary - operation.

impl AddAssign<F> for F

fn add_assign(&mut self, rhs: F)

Performs the += operation.

impl AddAssign<f64> for F

fn add_assign(&mut self, rhs: f64)

Performs the += operation.

impl AddAssign<f32> for F

fn add_assign(&mut self, rhs: f32)

Performs the += operation.

impl SubAssign<F> for F

fn sub_assign(&mut self, rhs: F)

Performs the -= operation.

impl SubAssign<f64> for F

fn sub_assign(&mut self, rhs: f64)

Performs the -= operation.

impl SubAssign<f32> for F

fn sub_assign(&mut self, rhs: f32)

Performs the -= operation.

impl MulAssign<F> for F

fn mul_assign(&mut self, rhs: F)

Performs the *= operation.

impl MulAssign<f64> for F

fn mul_assign(&mut self, rhs: f64)

Performs the *= operation.

impl MulAssign<f32> for F

fn mul_assign(&mut self, rhs: f32)

Performs the *= operation.

impl DivAssign<F> for F

fn div_assign(&mut self, rhs: F)

Performs the /= operation.

impl DivAssign<f64> for F

fn div_assign(&mut self, rhs: f64)

Performs the /= operation.

impl DivAssign<f32> for F

fn div_assign(&mut self, rhs: f32)

Performs the /= operation.

impl RemAssign<F> for F

fn rem_assign(&mut self, rhs: F)

Performs the %= operation.

impl RemAssign<f64> for F

fn rem_assign(&mut self, rhs: f64)

Performs the %= operation.

impl RemAssign<f32> for F

fn rem_assign(&mut self, rhs: f32)

Performs the %= operation.

impl Sum<F> for F

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 Sum<f64> for F

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 ToPrimitive for F

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

Converts the value of self to an i64.

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

Converts the value of self to an u64.

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

Converts the value of self to an isize.

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

Converts the value of self to an i8.

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

Converts the value of self to an i16.

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

Converts the value of self to an i32.

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

Converts the value of self to a usize.

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

Converts the value of self to an u8.

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

Converts the value of self to an u16.

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

Converts the value of self to an u32.

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

Converts the value of self to an f32.

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

Converts the value of self to an f64.

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

Converts the value of self to an i128.

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

Converts the value of self to an u128.

impl FromPrimitive for F

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

impl NumCast for F

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

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait.

impl Float for F

fn nan() -> F

Returns the NaN value.

fn infinity() -> F

Returns the infinite value.

fn neg_infinity() -> F

Returns the negative infinite value.

fn neg_zero() -> F

Returns -0.0.

fn min_value() -> F

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> F

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

fn max_value() -> F

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][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

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

fn ceil(self) -> F

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

fn round(self) -> F

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

fn trunc(self) -> F

Return the integer part of a number.

fn fract(self) -> F

Returns the fractional part of a number.

fn abs(self) -> F

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

fn signum(self) -> F

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, b: F) -> F

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

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

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

Raise a number to an integer power.

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

Raise a number to a floating point power.

fn sqrt(self) -> F

Take the square root of a number.

fn exp(self) -> F

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

fn exp2(self) -> F

Returns 2^(self).

fn ln(self) -> F

Returns the natural logarithm of the number.

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

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

fn log2(self) -> F

Returns the base 2 logarithm of the number.

fn log10(self) -> F

Returns the base 10 logarithm of the number.

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

Returns the maximum of the two numbers.

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

Returns the minimum of the two numbers.

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

The positive difference of two numbers.

fn cbrt(self) -> F

Take the cubic root of a number.

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

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

fn sin(self) -> F

Computes the sine of a number (in radians).

fn cos(self) -> F

Computes the cosine of a number (in radians).

fn tan(self) -> F

Computes the tangent of a number (in radians).

fn asin(self) -> F

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

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

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

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

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

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

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

fn exp_m1(self) -> F

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

fn ln_1p(self) -> F

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

fn sinh(self) -> F

Hyperbolic sine function.

fn cosh(self) -> F

Hyperbolic cosine function.

fn tanh(self) -> F

Hyperbolic tangent function.

fn asinh(self) -> F

Inverse hyperbolic sine function.

fn acosh(self) -> F

Inverse hyperbolic cosine function.

fn atanh(self) -> F

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

Returns epsilon, a small positive value.

fn to_degrees(self) -> F

Converts radians to degrees.

fn to_radians(self) -> F

Converts degrees to radians.

impl FloatConst for F

fn E() -> F

Return Euler’s number.

fn FRAC_1_PI() -> F

Return 1.0 / π.

fn FRAC_1_SQRT_2() -> F

Return 1.0 / sqrt(2.0).

fn FRAC_2_PI() -> F

Return 2.0 / π.

fn FRAC_2_SQRT_PI() -> F

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> F

Return π / 2.0.

fn FRAC_PI_3() -> F

Return π / 3.0.

fn FRAC_PI_4() -> F

Return π / 4.0.

fn FRAC_PI_6() -> F

Return π / 6.0.

fn FRAC_PI_8() -> F

Return π / 8.0.

fn LN_10() -> F

Return ln(10.0).

fn LN_2() -> F

Return ln(2.0).

fn LOG10_E() -> F

Return log10(e).

fn LOG2_E() -> F

Return log2(e).

fn PI() -> F

Return Archimedes’ constant.

fn SQRT_2() -> F

Return sqrt(2.0).

impl Num for F

type FromStrRadixErr = ParseFloatError

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

Convert from a string and radix <= 36.

impl Zero for F

fn zero() -> F

Returns the additive identity element of Self, 0. # Purity

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 One for F

fn one() -> F

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<Self>, 

Returns true if self is equal to the multiplicative identity.