Struct Dual 

pub struct Dual<T: Scalar>(/* private fields */);

Dual Number structure

Although Dual does implement PartialEq and PartialOrd, it only compares the real part.

Additionally, min and max only compare the real parts, and keep the dual parts.

Lastly, the Rem remainder operator is not correctly or fully defined for Dual, and will panic.

Implementations

impl<T: Scalar> Dual<T>

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

Create a new dual number from its real and dual parts.

pub fn from_real(real: T) -> Dual<T>

where T: Zero,

Create a new dual number from a real number.

The dual part is set to zero.

pub fn real(&self) -> T

Returns the real part

pub fn dual(&self) -> T

Returns the dual part

pub fn into_tuple(self) -> (T, T)

Returns both real and dual parts as a tuple

pub fn real_ref(&self) -> &T

Returns a reference to the real part

pub fn dual_ref(&self) -> &T

Returns a reference to the dual part

pub fn real_mut(&mut self) -> &mut T

Returns a mutable reference to the real part

pub fn dual_mut(&mut self) -> &mut T

Returns a mutable reference to the dual part

impl<T: Scalar + Neg<Output = T>> Dual<T>

pub fn conjugate(self) -> Self

Returns the conjugate of the dual number.

Trait Implementations

impl<T: Scalar + Num> Add<T> for Dual<T>

type Output = Dual<T>

The resulting type after applying the + operator.

fn add(self, rhs: T) -> Self

Performs the + operation.

impl<T: Scalar + Num> Add for Dual<T>

type Output = Dual<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: Scalar + Num> AddAssign<T> for Dual<T>

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl<T: Scalar + Num> AddAssign for Dual<T>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<T: Scalar> AsMut<Matrix<T, U2, U1, <DefaultAllocator as Allocator<T, U2>>::Buffer>> for Dual<T>

fn as_mut(&mut self) -> &mut Vector2<T>

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar> AsRef<Matrix<T, U2, U1, <DefaultAllocator as Allocator<T, U2>>::Buffer>> for Dual<T>

fn as_ref(&self) -> &Vector2<T>

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Clone + Scalar> Clone for Dual<T>

fn clone(&self) -> Dual<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Scalar> Debug for Dual<T>

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

Formats the value using the given formatter.

impl<T: Scalar + Zero> Default for Dual<T>

fn default() -> Dual<T>

Returns the “default value” for a type.

impl<T: Scalar> Deref for Dual<T>

type Target = Matrix<T, U2, U1, <DefaultAllocator as Allocator<T, U2>>::Buffer>

The resulting type after dereferencing.

fn deref(&self) -> &Vector2<T>

Dereferences the value.

impl<T: Scalar> DerefMut for Dual<T>

fn deref_mut(&mut self) -> &mut Vector2<T>

Mutably dereferences the value.

impl<T: Scalar + Display> Display for Dual<T>

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

Formats the value using the given formatter.

impl<T: Scalar + Num> Div<T> for Dual<T>

type Output = Dual<T>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Self

Performs the / operation.

impl<T: Scalar + Num> Div for Dual<T>

type Output = Dual<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: Scalar + Num> DivAssign<T> for Dual<T>

fn div_assign(&mut self, rhs: T)

Performs the /= operation.

impl<T: Scalar + Num> DivAssign for Dual<T>

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl<T> Float for Dual<T>

where T: Float + Signed + FloatConst + Scalar,

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_positive_value() -> Self

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

fn epsilon() -> Self

Returns epsilon, a small positive value.

fn min_value() -> Self

Returns the smallest finite 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 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 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 signum(self) -> Self

Returns a number that represents the sign of self.

fn abs(self) -> Self

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

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, rhs: Self) -> Self

The positive difference of two numbers.

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 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 sqrt(self) -> Self

Take the square root of a number.

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 to_degrees(self) -> Self

Converts radians to degrees.

fn to_radians(self) -> Self

Converts degrees to radians.

fn is_subnormal(self) -> bool

Returns true if the number is subnormal.

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<T: Scalar + FloatConst + Zero> FloatConst for Dual<T>

fn E() -> Dual<T>

Return Euler’s number.

fn FRAC_1_PI() -> Dual<T>

Return 1.0 / π.

fn FRAC_1_SQRT_2() -> Dual<T>

Return 1.0 / sqrt(2.0).

fn FRAC_2_PI() -> Dual<T>

Return 2.0 / π.

fn FRAC_2_SQRT_PI() -> Dual<T>

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> Dual<T>

Return π / 2.0.

fn FRAC_PI_3() -> Dual<T>

Return π / 3.0.

fn FRAC_PI_4() -> Dual<T>

Return π / 4.0.

fn FRAC_PI_6() -> Dual<T>

Return π / 6.0.

fn FRAC_PI_8() -> Dual<T>

Return π / 8.0.

fn LN_10() -> Dual<T>

Return ln(10.0).

fn LN_2() -> Dual<T>

Return ln(2.0).

fn LOG10_E() -> Dual<T>

Return log10(e).

fn LOG2_E() -> Dual<T>

Return log2(e).

fn PI() -> Dual<T>

Return Archimedes’ constant π.

fn SQRT_2() -> Dual<T>

Return sqrt(2.0).

fn TAU() -> Self

where Self: Sized + Add<Output = Self>,

Return the full circle constant τ.

fn LOG10_2() -> Self

where Self: Sized + Div<Output = Self>,

Return log10(2.0).

fn LOG2_10() -> Self

where Self: Sized + Div<Output = Self>,

Return log2(10.0).

impl<T: Scalar + Zero> From<T> for Dual<T>

fn from(real: T) -> Dual<T>

Converts to this type from the input type.

impl<T> FromPrimitive for Dual<T>

where T: Zero + Scalar + FromPrimitive,

fn from_isize(n: isize) -> Option<Dual<T>>

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<Dual<T>>

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<Dual<T>>

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<Dual<T>>

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<Dual<T>>

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_usize(n: usize) -> Option<Dual<T>>

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<Dual<T>>

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<Dual<T>>

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<Dual<T>>

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<Dual<T>>

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_f32(n: f32) -> Option<Dual<T>>

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<Dual<T>>

Converts a f64 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_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.

impl<T: Scalar> Inv for Dual<T>

where Self: One + Div<Output = Self>,

type Output = Dual<T>

The result after applying the operator.

fn inv(self) -> Self

Returns the multiplicative inverse of self.

impl<T: Scalar + Num> Mul<T> for Dual<T>

type Output = Dual<T>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Self

Performs the * operation.

impl<T: Scalar + Num> Mul for Dual<T>

type Output = Dual<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: Scalar + Num + Mul + Add> MulAdd<Dual<T>, T> for Dual<T>

type Output = Dual<T>

The resulting type after applying the fused multiply-add.

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

Performs the fused multiply-add operation (self * a) + b

impl<T: Scalar + Num + Mul + Add> MulAdd<T> for Dual<T>

type Output = Dual<T>

The resulting type after applying the fused multiply-add.

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

Performs the fused multiply-add operation (self * a) + b

impl<T: Scalar + Num + Mul + Add> MulAdd<T, T> for Dual<T>

type Output = Dual<T>

The resulting type after applying the fused multiply-add.

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

Performs the fused multiply-add operation (self * a) + b

impl<T: Scalar + Num + Mul + Add> MulAdd for Dual<T>

type Output = Dual<T>

The resulting type after applying the fused multiply-add.

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

Performs the fused multiply-add operation (self * a) + b

impl<T: Scalar + Num + Mul + Add> MulAddAssign<Dual<T>, T> for Dual<T>

fn mul_add_assign(&mut self, a: Self, b: T)

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<T: Scalar + Num + Mul + Add> MulAddAssign<T> for Dual<T>

fn mul_add_assign(&mut self, a: T, b: Self)

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<T: Scalar + Num + Mul + Add> MulAddAssign<T, T> for Dual<T>

fn mul_add_assign(&mut self, a: T, b: T)

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<T: Scalar + Num + Mul + Add> MulAddAssign for Dual<T>

fn mul_add_assign(&mut self, a: Self, b: Self)

Performs the fused multiply-add assignment operation *self = (*self * a) + b

impl<T: Scalar + Num> MulAssign<T> for Dual<T>

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T: Scalar + Num> MulAssign for Dual<T>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<T: Scalar + Signed> Neg for Dual<T>

type Output = Dual<T>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<T: Scalar + Num> Num for Dual<T>

type FromStrRadixErr = <T as Num>::FromStrRadixErr

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

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

impl<T: Scalar + Float> NumCast for Dual<T>

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

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<T: Scalar + Num + One> One for Dual<T>

fn one() -> Dual<T>

Returns 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.

fn set_one(&mut self)

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

impl<T: Scalar + PartialEq> PartialEq<T> for Dual<T>

fn eq(&self, rhs: &T) -> 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<T: Scalar + PartialEq> PartialEq for Dual<T>

fn eq(&self, rhs: &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<T: Scalar + PartialOrd> PartialOrd<T> for Dual<T>

fn partial_cmp(&self, rhs: &T) -> Option<Ordering>

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

fn lt(&self, rhs: &T) -> bool

Tests less than (for self and other) and is used by the < operator.

fn gt(&self, rhs: &T) -> bool

Tests greater 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 ge(&self, other: &Rhs) -> bool

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

impl<T: Scalar + PartialOrd> PartialOrd for Dual<T>

fn partial_cmp(&self, rhs: &Self) -> Option<Ordering>

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

fn lt(&self, rhs: &Self) -> bool

Tests less than (for self and other) and is used by the < operator.

fn gt(&self, rhs: &Self) -> bool

Tests greater 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 ge(&self, other: &Rhs) -> bool

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

impl<T: Scalar, P: Into<Dual<T>>> Pow<P> for Dual<T>

where Dual<T>: Float,

type Output = Dual<T>

The result after applying the operator.

fn pow(self, rhs: P) -> Self

Returns self to the power rhs.

impl<'a, T: Scalar + Num + One> Product<&'a Dual<T>> for Dual<T>

fn product<I: Iterator<Item = &'a Dual<T>>>(iter: I) -> Dual<T>

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T: Scalar + Num + One> Product for Dual<T>

fn product<I: Iterator<Item = Dual<T>>>(iter: I) -> Dual<T>

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T: Scalar + Num> Rem for Dual<T>

fn rem(self, _: Self) -> Self

UNIMPLEMENTED!!!

As far as I know, remainder is not a valid operation on dual numbers, but is required for the Float trait to be implemented.

type Output = Dual<T>

The resulting type after applying the % operator.

impl<T> Signed for Dual<T>

where T: Signed + PartialOrd + Scalar,

fn abs(&self) -> Self

Computes the absolute value.

fn abs_sub(&self, rhs: &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<T: Scalar + Num> Sub<T> for Dual<T>

type Output = Dual<T>

The resulting type after applying the - operator.

fn sub(self, rhs: T) -> Self

Performs the - operation.

impl<T: Scalar + Num> Sub for Dual<T>

type Output = Dual<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: Scalar + Num> SubAssign<T> for Dual<T>

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl<T: Scalar + Num> SubAssign for Dual<T>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a, T: Scalar + Num + Zero> Sum<&'a Dual<T>> for Dual<T>

fn sum<I: Iterator<Item = &'a Dual<T>>>(iter: I) -> Dual<T>

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T: Scalar + Num + Zero> Sum for Dual<T>

fn sum<I: Iterator<Item = Dual<T>>>(iter: I) -> Dual<T>

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T: Scalar + ToPrimitive> ToPrimitive for Dual<T>

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_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_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_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_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<T: Scalar + Num + Zero> Zero for Dual<T>

fn zero() -> Dual<T>

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<T: Copy + Scalar> Copy for Dual<T>

impl<T: Scalar + Unsigned> Unsigned for Dual<T>

where Self: Num,