Struct dual::Dual
[−]
[src]
pub struct Dual<T> { pub val: T, pub der: T, }
Fields
val: T
der: T
Trait Implementations
impl<T: Add<T>> Add<Dual<T>> for Dual<T>
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type Output = Dual<<T as Add<T>>::Output>
The resulting type after applying the +
operator
fn add(self, rhs: Dual<T>) -> Dual<<T as Add<T>>::Output>
The method for the +
operator
impl<T: Sub<T>> Sub<Dual<T>> for Dual<T>
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type Output = Dual<<T as Sub<T>>::Output>
The resulting type after applying the -
operator
fn sub(self, rhs: Dual<T>) -> Dual<<T as Sub<T>>::Output>
The method for the -
operator
impl<T: Zero> Zero for Dual<T>
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fn zero() -> Dual<T>
Returns the additive identity element of Self
, 0
. Read more
fn is_zero(&self) -> bool
Returns true
if self
is equal to the additive identity.
impl<T: Num + Float> Num for Dual<T>
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type FromStrRadixErr = T::FromStrRadixErr
fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>
Convert from a string and radix <= 36. Read more
impl<T: Zero + One + Float> One for Dual<T>
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impl<T: Float> Mul<Dual<T>> for Dual<T>
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type Output = Dual<<T as Mul<T>>::Output>
The resulting type after applying the *
operator
fn mul(self, rhs: Dual<T>) -> Dual<<T as Mul<T>>::Output>
The method for the *
operator
impl<T: Float> Div<Dual<T>> for Dual<T>
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type Output = Dual<<T as Div<T>>::Output>
The resulting type after applying the /
operator
fn div(self, rhs: Dual<T>) -> Dual<<T as Div<T>>::Output>
The method for the /
operator
impl<T: Float> Rem<Dual<T>> for Dual<T>
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type Output = Dual<<T as Rem<T>>::Output>
The resulting type after applying the %
operator
fn rem(self, rhs: Dual<T>) -> Dual<<T as Rem<T>>::Output>
The method for the %
operator
impl<T: Neg> Neg for Dual<T>
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type Output = Dual<<T as Neg>::Output>
The resulting type after applying the -
operator
fn neg(self) -> Dual<<T as Neg>::Output>
The method for the unary -
operator
impl<T: PartialEq> PartialEq for Dual<T>
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fn eq(&self, other: &Dual<T>) -> bool
This method tests for self
and other
values to be equal, and is used by ==
. Read more
fn ne(&self, other: &Dual<T>) -> bool
This method tests for !=
.
impl<T: PartialOrd> PartialOrd for Dual<T>
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fn partial_cmp(&self, other: &Dual<T>) -> Option<Ordering>
This method returns an ordering between self
and other
values if one exists. Read more
fn lt(&self, other: &Rhs) -> bool
1.0.0
This method tests less than (for self
and other
) and is used by the <
operator. Read more
fn le(&self, other: &Rhs) -> bool
1.0.0
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
fn gt(&self, other: &Rhs) -> bool
1.0.0
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
fn ge(&self, other: &Rhs) -> bool
1.0.0
This method tests greater than or equal to (for self
and other
) and is used by the >=
operator. Read more
impl<T: Copy> Copy for Dual<T>
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impl<T: ToPrimitive> ToPrimitive for Dual<T>
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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_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_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_isize(&self) -> Option<isize>
Converts the value of self
to an isize
.
fn to_usize(&self) -> Option<usize>
Converts the value of self
to a usize
.
impl<T: NumCast + Zero> NumCast for Dual<T>
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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. Read more
impl<T: Clone> Clone for Dual<T>
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fn clone(&self) -> Dual<T>
Returns a copy of the value. Read more
fn clone_from(&mut self, source: &Self)
1.0.0
Performs copy-assignment from source
. Read more
impl<T: Float> Float for Dual<T>
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fn nan() -> Dual<T>
Returns the NaN
value. Read more
fn infinity() -> Dual<T>
Returns the infinite value. Read more
fn neg_infinity() -> Dual<T>
Returns the negative infinite value. Read more
fn neg_zero() -> Dual<T>
Returns -0.0
. Read more
fn min_value() -> Dual<T>
Returns the smallest finite value that this type can represent. Read more
fn min_positive_value() -> Dual<T>
Returns the smallest positive, normalized value that this type can represent. Read more
fn max_value() -> Dual<T>
Returns the largest finite value that this type can represent. Read more
fn is_nan(self) -> bool
Returns true
if this value is NaN
and false otherwise. Read more
fn is_infinite(self) -> bool
Returns true
if this value is positive infinity or negative infinity and false otherwise. Read more
fn is_finite(self) -> bool
Returns true
if this number is neither infinite nor NaN
. Read more
fn is_normal(self) -> bool
Returns true
if the number is neither zero, infinite, [subnormal][subnormal], or NaN
. Read more
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. Read more
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
. The floating point encoding is documented in the [Reference][floating-point]. Read more
fn floor(self) -> Dual<T>
Returns the largest integer less than or equal to a number. Read more
fn ceil(self) -> Dual<T>
Returns the smallest integer greater than or equal to a number. Read more
fn round(self) -> Dual<T>
Returns the nearest integer to a number. Round half-way cases away from 0.0
. Read more
fn trunc(self) -> Dual<T>
Return the integer part of a number. Read more
fn fract(self) -> Dual<T>
Returns the fractional part of a number. Read more
fn mul_add(self, a: Dual<T>, b: Dual<T>) -> Dual<T>
Fused multiply-add. Computes (self * a) + b
with only one rounding error. This produces a more accurate result with better performance than a separate multiplication operation followed by an add. Read more
fn recip(self) -> Dual<T>
Take the reciprocal (inverse) of a number, 1/x
. Read more
fn powi(self, n: i32) -> Dual<T>
Raise a number to an integer power. Read more
fn powf(self, n: Dual<T>) -> Dual<T>
Raise a number to a floating point power. Read more
fn sqrt(self) -> Dual<T>
Take the square root of a number. Read more
fn exp(self) -> Dual<T>
Returns e^(self)
, (the exponential function). Read more
fn exp2(self) -> Dual<T>
Returns 2^(self)
. Read more
fn ln(self) -> Dual<T>
Returns the natural logarithm of the number. Read more
fn log(self, base: Dual<T>) -> Dual<T>
Returns the logarithm of the number with respect to an arbitrary base. Read more
fn log2(self) -> Dual<T>
Returns the base 2 logarithm of the number. Read more
fn log10(self) -> Dual<T>
Returns the base 10 logarithm of the number. Read more
fn abs(self) -> Dual<T>
Computes the absolute value of self
. Returns Float::nan()
if the number is Float::nan()
. Read more
fn signum(self) -> Dual<T>
Returns a number that represents the sign of self
. Read more
fn is_sign_positive(self) -> bool
Returns true
if self
is positive, including +0.0
and Float::infinity()
. Read more
fn is_sign_negative(self) -> bool
Returns true
if self
is negative, including -0.0
and Float::neg_infinity()
. Read more
fn max(self, other: Dual<T>) -> Dual<T>
Returns the maximum of the two numbers. Read more
fn min(self, other: Dual<T>) -> Dual<T>
Returns the minimum of the two numbers. Read more
fn abs_sub(self, other: Dual<T>) -> Dual<T>
The positive difference of two numbers. Read more
fn cbrt(self) -> Dual<T>
Take the cubic root of a number. Read more
fn hypot(self, other: Dual<T>) -> Dual<T>
Calculate the length of the hypotenuse of a right-angle triangle given legs of length x
and y
. Read more
fn sin(self) -> Dual<T>
Computes the sine of a number (in radians). Read more
fn cos(self) -> Dual<T>
Computes the cosine of a number (in radians). Read more
fn tan(self) -> Dual<T>
Computes the tangent of a number (in radians). Read more
fn asin(self) -> Dual<T>
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]. Read more
fn acos(self) -> Dual<T>
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]. Read more
fn atan(self) -> Dual<T>
Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2]; Read more
fn atan2(self, other: Dual<T>) -> Dual<T>
Computes the four quadrant arctangent of self
(y
) and other
(x
). Read more
fn sin_cos(self) -> (Dual<T>, Dual<T>)
Simultaneously computes the sine and cosine of the number, x
. Returns (sin(x), cos(x))
. Read more
fn exp_m1(self) -> Dual<T>
Returns e^(self) - 1
in a way that is accurate even if the number is close to zero. Read more
fn ln_1p(self) -> Dual<T>
Returns ln(1+n)
(natural logarithm) more accurately than if the operations were performed separately. Read more
fn sinh(self) -> Dual<T>
Hyperbolic sine function. Read more
fn cosh(self) -> Dual<T>
Hyperbolic cosine function. Read more
fn tanh(self) -> Dual<T>
Hyperbolic tangent function. Read more
fn asinh(self) -> Dual<T>
Inverse hyperbolic sine function. Read more
fn acosh(self) -> Dual<T>
Inverse hyperbolic cosine function. Read more
fn atanh(self) -> Dual<T>
Inverse hyperbolic tangent function. Read more
fn epsilon() -> Self
Returns epsilon, a small positive value. Read more
fn to_degrees(self) -> Self
Converts radians to degrees. Read more
fn to_radians(self) -> Self
Converts degrees to radians. Read more