Struct Dual 

pub struct Dual { /* private fields */ }

First-order dual number.

Implementations

impl Dual

pub fn new(real: f64, dual: f64) -> Dual

Constructor.

Arguments

• real - Real part.
• dual - Dual part.

Returns

Dual number.

Example

use numdiff::Dual;

let num = Dual::new(1.0, 2.0);

pub fn get_real(self) -> f64

Get the real part of the dual number.

Returns

Real part of the dual number.

Example

use numdiff::Dual;

let num = Dual::new(1.0, 2.0);
assert_eq!(num.get_real(), 1.0);

pub fn get_dual(self) -> f64

Get the dual part of the dual number.

Returns

Dual part of the dual number.

Example

use numdiff::Dual;

let num = Dual::new(1.0, 2.0);
assert_eq!(num.get_dual(), 2.0);

Trait Implementations

impl Add<Dual> for f64

type Output = Dual

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<f64> for Dual

type Output = Dual

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for Dual

type Output = Dual

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign<f64> for Dual

fn add_assign(&mut self, rhs: f64)

Performs the += operation.

impl AddAssign for Dual

fn add_assign(&mut self, other: Dual)

Performs the += operation.

impl Clone for Dual

fn clone(&self) -> Dual

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Dual

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

Formats the value using the given formatter.

impl Div<Dual> for f64

type Output = Dual

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<f64> for Dual

type Output = Dual

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div for Dual

type Output = Dual

The resulting type after applying the / operator.

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

Performs the / operation.

impl DivAssign<f64> for Dual

fn div_assign(&mut self, rhs: f64)

Performs the /= operation.

impl DivAssign for Dual

fn div_assign(&mut self, other: Dual)

Performs the /= operation.

impl Float for Dual

fn nan() -> Self

Returns the NaN value.

fn infinity() -> Self

Returns the infinite value.

fn neg_infinity() -> Self

Returns the negative infinite value.

fn neg_zero() -> Self

Returns -0.0.

fn min_value() -> Self

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> Self

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

fn max_value() -> Self

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) -> Self

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

fn ceil(self) -> Self

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

fn round(self) -> Self

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

fn trunc(self) -> Self

Return the integer part of a number.

fn fract(self) -> Self

Returns the fractional part of a number.

fn abs(self) -> Self

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

fn signum(self) -> Self

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 Float::nan().

fn is_sign_negative(self) -> bool

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

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

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) -> Self

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

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

Raise a number to an integer power.

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

Raise a number to a floating point power.

fn sqrt(self) -> Self

Take the square root of a number.

fn exp(self) -> Self

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

fn exp2(self) -> Self

Returns 2^(self).

fn ln(self) -> Self

Returns the natural logarithm of the number.

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

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

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

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

Returns the maximum of the two numbers.

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

Returns the minimum of the two numbers.

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

The positive difference of two numbers.

fn cbrt(self) -> Self

Take the cubic root of a number.

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

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

fn sin(self) -> Self

Computes the sine of a number (in radians).

fn cos(self) -> Self

Computes the cosine of a number (in radians).

fn tan(self) -> Self

Computes the tangent of a number (in radians).

fn asin(self) -> Self

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) -> Self

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) -> Self

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

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

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

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

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

fn exp_m1(self) -> Self

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

fn ln_1p(self) -> Self

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

fn sinh(self) -> Self

Hyperbolic sine function.

fn cosh(self) -> Self

Hyperbolic cosine function.

fn tanh(self) -> Self

Hyperbolic tangent function.

fn asinh(self) -> Self

Inverse hyperbolic sine function.

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

fn atanh(self) -> Self

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() -> Self

Returns epsilon, a small positive value.

fn is_subnormal(self) -> bool

Returns true if the number is subnormal.

fn to_degrees(self) -> Self

Converts radians to degrees.

fn to_radians(self) -> Self

Converts degrees to radians.

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

Clamps a value between a min and max.

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

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

impl Mul<Dual> for f64

type Output = Dual

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<f64> for Dual

type Output = Dual

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul for Dual

type Output = Dual

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<f64> for Dual

fn mul_assign(&mut self, rhs: f64)

Performs the *= operation.

impl MulAssign for Dual

fn mul_assign(&mut self, other: Dual)

Performs the *= operation.

impl Neg for Dual

type Output = Dual

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Num for Dual

type FromStrRadixErr = <f64 as Num>::FromStrRadixErr

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

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

impl NumCast for Dual

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

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 One for Dual

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 PartialEq for Dual

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 PartialOrd for Dual

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 Rem<Dual> for f64

type Output = Dual

The resulting type after applying the % operator.

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

Performs the % operation.

impl Rem<f64> for Dual

type Output = Dual

The resulting type after applying the % operator.

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

Performs the % operation.

impl Rem for Dual

type Output = Dual

The resulting type after applying the % operator.

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

Performs the % operation.

impl RemAssign<f64> for Dual

fn rem_assign(&mut self, rhs: f64)

Performs the %= operation.

impl RemAssign for Dual

fn rem_assign(&mut self, rhs: Self)

Performs the %= operation.

impl Sub<Dual> for f64

type Output = Dual

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<f64> for Dual

type Output = Dual

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for Dual

type Output = Dual

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign<f64> for Dual

fn sub_assign(&mut self, rhs: f64)

Performs the -= operation.

impl SubAssign for Dual

fn sub_assign(&mut self, other: Dual)

Performs the -= operation.

impl ToPrimitive for Dual

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_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_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_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_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_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.

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.

impl Trig for Dual

Available on crate feature trig only.

fn sin(&self) -> Dual

Computes the sine of this value, where this value is in radians.

fn cos(&self) -> Dual

Computes the cosine of this value, where this value is in radians.

fn tan(&self) -> Dual

Computes the tangent of this value, where this value is in radians.

fn csc(&self) -> Dual

Computes the cosecant of this value, where this value is in radians.

fn sec(&self) -> Dual

Computes the secant of this value, where this value is in radians.

fn cot(&self) -> Dual

Computes the cotangent of this value, where this value is in radians.

fn asin(&self) -> Dual

Computes the inverse sine of this value, returning the result in radians.

fn acos(&self) -> Dual

Computes the inverse cosine of this value, returning the result in radians.

fn atan(&self) -> Dual

Computes the inverse tangent of this value, returning the result in radians.

fn atan2(&self, other: &Dual) -> Dual

Computes the four-quadrant inverse tangent of self (y) and other (x), returning the result in radians.

fn acsc(&self) -> Dual

Computes the inverse cosecant of this value, returning the result in radians.

fn asec(&self) -> Dual

Computes the inverse secant of this value, returning the result in radians.

fn acot(&self) -> Dual

Computes the inverse cotangent of this value, returning the result in radians.

fn deg2rad(&self) -> Dual

Convert this value from degrees to radians.

fn rad2deg(&self) -> Dual

Convert this value from radians to degrees.

fn sind(&self) -> Dual

Computes the sine of this value, where this value is in degrees.

fn cosd(&self) -> Dual

Computes the cosine of this value, where this value is in degrees.

fn tand(&self) -> Dual

Computes the tangent of this value, where this value is in degrees.

fn cscd(&self) -> Dual

Computes the cosecant of this value, where this value is in degrees.

fn secd(&self) -> Dual

Computes the secant of this value, where this value is in degrees.

fn cotd(&self) -> Dual

Computes the cotangent of this value, where this value is in degrees.

fn asind(&self) -> Dual

Computes the inverse sine of this value, returning the result in degrees.

fn acosd(&self) -> Dual

Computes the inverse cosine of this value, returning the result in degrees.

fn atand(&self) -> Dual

Computes the inverse tangent of this value, returning the result in degrees.

fn atan2d(&self, other: &Dual) -> Dual

Computes the four-quadrant inverse tangent of self (y) and other (x), returning the result in degrees.

fn acscd(&self) -> Dual

Computes the inverse cosecant of this value, returning the result in degrees.

fn asecd(&self) -> Dual

Computes the inverse secant of this value, returning the result in degrees.

fn acotd(&self) -> Dual

Computes the inverse cotangent of this value, returning the result in degrees.

fn sinh(&self) -> Dual

Computes the hyperbolic sine of this value.

fn cosh(&self) -> Dual

Computes the hyperbolic cosine of this value.

fn tanh(&self) -> Dual

Computes the hyperbolic tangent of this value.

fn csch(&self) -> Dual

Computes the hyperbolic cosecant of this value.

fn sech(&self) -> Dual

Computes the hyperbolic secant of this value.

fn coth(&self) -> Dual

Computes the hyperbolic cotangent of this value.

fn asinh(&self) -> Dual

Computes the inverse hyperbolic sine of this value.

fn acosh(&self) -> Dual

Computes the inverse hyperbolic cosine of this value.

fn atanh(&self) -> Dual

Computes the inverse hyperbolic tangent of this value.

fn acsch(&self) -> Dual

Computes the inverse hyperbolic cosecant of this value.

fn asech(&self) -> Dual

Computes the inverse hyperbolic secant of this value.

fn acoth(&self) -> Dual

Computes the inverse hyperbolic cotangent of this value.

impl Zero for Dual

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 Copy for Dual