Struct bio::stats::probs::Prob [−] 

pub struct Prob(pub f64);

A newtype for probabilities.

Example

#[macro_use]
extern crate approx;
use bio::stats::Prob;

let p = Prob(0.5);
let q = Prob(0.2);

assert_relative_eq!(*(p + q), *Prob(0.7));

Methods

impl Prob
[src]

Methods from Deref<Target=f64>

Returns true if this value is NaN and false otherwise.

use std::f64;

let nan = f64::NAN;
let f = 7.0_f64;

assert!(nan.is_nan());
assert!(!f.is_nan());

Returns true if this value is positive infinity or negative infinity and false otherwise.

use std::f64;

let f = 7.0f64;
let inf = f64::INFINITY;
let neg_inf = f64::NEG_INFINITY;
let nan = f64::NAN;

assert!(!f.is_infinite());
assert!(!nan.is_infinite());

assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());

Returns true if this number is neither infinite nor NaN.

use std::f64;

let f = 7.0f64;
let inf: f64 = f64::INFINITY;
let neg_inf: f64 = f64::NEG_INFINITY;
let nan: f64 = f64::NAN;

assert!(f.is_finite());

assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());

Returns true if the number is neither zero, infinite, subnormal, or NaN.

use std::f64;

let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
let max = f64::MAX;
let lower_than_min = 1.0e-308_f64;
let zero = 0.0f64;

assert!(min.is_normal());
assert!(max.is_normal());

assert!(!zero.is_normal());
assert!(!f64::NAN.is_normal());
assert!(!f64::INFINITY.is_normal());
// Values between `0` and `min` are Subnormal.
assert!(!lower_than_min.is_normal());

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.

use std::num::FpCategory;
use std::f64;

let num = 12.4_f64;
let inf = f64::INFINITY;

assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);

Deprecated since 1.11.0

: never really came to fruition and easily implementable outside the standard library

Unstable (float_extras)

: never really came to fruition and easily implementable outside the standard library

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.

#![feature(float_extras)]

let num = 2.0f64;

// (8388608, -22, 1)
let (mantissa, exponent, sign) = num.integer_decode();
let sign_f = sign as f64;
let mantissa_f = mantissa as f64;
let exponent_f = num.powf(exponent as f64);

// 1 * 8388608 * 2^(-22) == 2
let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();

assert!(abs_difference < 1e-10);

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

let f = 3.99_f64;
let g = 3.0_f64;

assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);

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

let f = 3.01_f64;
let g = 4.0_f64;

assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);

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

let f = 3.3_f64;
let g = -3.3_f64;

assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);

Returns the integer part of a number.

let f = 3.3_f64;
let g = -3.7_f64;

assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), -3.0);

Returns the fractional part of a number.

let x = 3.5_f64;
let y = -3.5_f64;
let abs_difference_x = (x.fract() - 0.5).abs();
let abs_difference_y = (y.fract() - (-0.5)).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

Computes the absolute value of self. Returns NAN if the number is NAN.

use std::f64;

let x = 3.5_f64;
let y = -3.5_f64;

let abs_difference_x = (x.abs() - x).abs();
let abs_difference_y = (y.abs() - (-y)).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

assert!(f64::NAN.abs().is_nan());

Returns a number that represents the sign of self.

  • 1.0 if the number is positive, +0.0 or INFINITY
  • -1.0 if the number is negative, -0.0 or NEG_INFINITY
  • NAN if the number is NAN
use std::f64;

let f = 3.5_f64;

assert_eq!(f.signum(), 1.0);
assert_eq!(f64::NEG_INFINITY.signum(), -1.0);

assert!(f64::NAN.signum().is_nan());

Returns true if self's sign bit is positive, including +0.0 and INFINITY.

use std::f64;

let nan: f64 = f64::NAN;

let f = 7.0_f64;
let g = -7.0_f64;

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());
// Requires both tests to determine if is `NaN`
assert!(!nan.is_sign_positive() && !nan.is_sign_negative());

Deprecated since 1.0.0

: renamed to is_sign_positive

Returns true if self's sign is negative, including -0.0 and NEG_INFINITY.

use std::f64;

let nan = f64::NAN;

let f = 7.0_f64;
let g = -7.0_f64;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
// Requires both tests to determine if is `NaN`.
assert!(!nan.is_sign_positive() && !nan.is_sign_negative());

Deprecated since 1.0.0

: renamed to is_sign_negative

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.

let m = 10.0_f64;
let x = 4.0_f64;
let b = 60.0_f64;

// 100.0
let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();

assert!(abs_difference < 1e-10);

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

let x = 2.0_f64;
let abs_difference = (x.recip() - (1.0/x)).abs();

assert!(abs_difference < 1e-10);

Raises a number to an integer power.

Using this function is generally faster than using powf

let x = 2.0_f64;
let abs_difference = (x.powi(2) - x*x).abs();

assert!(abs_difference < 1e-10);

Raises a number to a floating point power.

let x = 2.0_f64;
let abs_difference = (x.powf(2.0) - x*x).abs();

assert!(abs_difference < 1e-10);

Takes the square root of a number.

Returns NaN if self is a negative number.

let positive = 4.0_f64;
let negative = -4.0_f64;

let abs_difference = (positive.sqrt() - 2.0).abs();

assert!(abs_difference < 1e-10);
assert!(negative.sqrt().is_nan());

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

let one = 1.0_f64;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference < 1e-10);

Returns 2^(self).

let f = 2.0_f64;

// 2^2 - 4 == 0
let abs_difference = (f.exp2() - 4.0).abs();

assert!(abs_difference < 1e-10);

Returns the natural logarithm of the number.

let one = 1.0_f64;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference < 1e-10);

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

let ten = 10.0_f64;
let two = 2.0_f64;

// log10(10) - 1 == 0
let abs_difference_10 = (ten.log(10.0) - 1.0).abs();

// log2(2) - 1 == 0
let abs_difference_2 = (two.log(2.0) - 1.0).abs();

assert!(abs_difference_10 < 1e-10);
assert!(abs_difference_2 < 1e-10);

Returns the base 2 logarithm of the number.

let two = 2.0_f64;

// log2(2) - 1 == 0
let abs_difference = (two.log2() - 1.0).abs();

assert!(abs_difference < 1e-10);

Returns the base 10 logarithm of the number.

let ten = 10.0_f64;

// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();

assert!(abs_difference < 1e-10);

Converts radians to degrees.

use std::f64::consts;

let angle = consts::PI;

let abs_difference = (angle.to_degrees() - 180.0).abs();

assert!(abs_difference < 1e-10);

Converts degrees to radians.

use std::f64::consts;

let angle = 180.0_f64;

let abs_difference = (angle.to_radians() - consts::PI).abs();

assert!(abs_difference < 1e-10);

Deprecated since 1.11.0

: never really came to fruition and easily implementable outside the standard library

Unstable (float_extras)

: never really came to fruition and easily implementable outside the standard library

Breaks the number into a normalized fraction and a base-2 exponent, satisfying:

  • self = x * 2^exp
  • 0.5 <= abs(x) < 1.0
#![feature(float_extras)]

let x = 4.0_f64;

// (1/2)*2^3 -> 1 * 8/2 -> 4.0
let f = x.frexp();
let abs_difference_0 = (f.0 - 0.5).abs();
let abs_difference_1 = (f.1 as f64 - 3.0).abs();

assert!(abs_difference_0 < 1e-10);
assert!(abs_difference_1 < 1e-10);

Deprecated since 1.11.0

: never really came to fruition and easily implementable outside the standard library

Unstable (float_extras)

: never really came to fruition and easily implementable outside the standard library

Returns the next representable floating-point value in the direction of other.

#![feature(float_extras)]

let x = 1.0f64;

let abs_diff = (x.next_after(2.0) - 1.0000000000000002220446049250313_f64).abs();

assert!(abs_diff < 1e-10);

Returns the maximum of the two numbers.

let x = 1.0_f64;
let y = 2.0_f64;

assert_eq!(x.max(y), y);

If one of the arguments is NaN, then the other argument is returned.

Returns the minimum of the two numbers.

let x = 1.0_f64;
let y = 2.0_f64;

assert_eq!(x.min(y), x);

If one of the arguments is NaN, then the other argument is returned.

Deprecated since 1.10.0

: you probably meant (self - other).abs(): this operation is (self - other).max(0.0) (also known as fdim in C). If you truly need the positive difference, consider using that expression or the C function fdim, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).

The positive difference of two numbers.

  • If self <= other: 0:0
  • Else: self - other
let x = 3.0_f64;
let y = -3.0_f64;

let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

Takes the cubic root of a number.

let x = 8.0_f64;

// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();

assert!(abs_difference < 1e-10);

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

let x = 2.0_f64;
let y = 3.0_f64;

// sqrt(x^2 + y^2)
let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();

assert!(abs_difference < 1e-10);

Computes the sine of a number (in radians).

use std::f64;

let x = f64::consts::PI/2.0;

let abs_difference = (x.sin() - 1.0).abs();

assert!(abs_difference < 1e-10);

Computes the cosine of a number (in radians).

use std::f64;

let x = 2.0*f64::consts::PI;

let abs_difference = (x.cos() - 1.0).abs();

assert!(abs_difference < 1e-10);

Computes the tangent of a number (in radians).

use std::f64;

let x = f64::consts::PI/4.0;
let abs_difference = (x.tan() - 1.0).abs();

assert!(abs_difference < 1e-14);

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].

use std::f64;

let f = f64::consts::PI / 2.0;

// asin(sin(pi/2))
let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();

assert!(abs_difference < 1e-10);

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].

use std::f64;

let f = f64::consts::PI / 4.0;

// acos(cos(pi/4))
let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();

assert!(abs_difference < 1e-10);

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

let f = 1.0_f64;

// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();

assert!(abs_difference < 1e-10);

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

  • x = 0, y = 0: 0
  • x >= 0: arctan(y/x) -> [-pi/2, pi/2]
  • y >= 0: arctan(y/x) + pi -> (pi/2, pi]
  • y < 0: arctan(y/x) - pi -> (-pi, -pi/2)
use std::f64;

let pi = f64::consts::PI;
// All angles from horizontal right (+x)
// 45 deg counter-clockwise
let x1 = 3.0_f64;
let y1 = -3.0_f64;

// 135 deg clockwise
let x2 = -3.0_f64;
let y2 = 3.0_f64;

let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();

assert!(abs_difference_1 < 1e-10);
assert!(abs_difference_2 < 1e-10);

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

use std::f64;

let x = f64::consts::PI/4.0;
let f = x.sin_cos();

let abs_difference_0 = (f.0 - x.sin()).abs();
let abs_difference_1 = (f.1 - x.cos()).abs();

assert!(abs_difference_0 < 1e-10);
assert!(abs_difference_1 < 1e-10);

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

let x = 7.0_f64;

// e^(ln(7)) - 1
let abs_difference = (x.ln().exp_m1() - 6.0).abs();

assert!(abs_difference < 1e-10);

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

use std::f64;

let x = f64::consts::E - 1.0;

// ln(1 + (e - 1)) == ln(e) == 1
let abs_difference = (x.ln_1p() - 1.0).abs();

assert!(abs_difference < 1e-10);

Hyperbolic sine function.

use std::f64;

let e = f64::consts::E;
let x = 1.0_f64;

let f = x.sinh();
// Solving sinh() at 1 gives `(e^2-1)/(2e)`
let g = (e*e - 1.0)/(2.0*e);
let abs_difference = (f - g).abs();

assert!(abs_difference < 1e-10);

Hyperbolic cosine function.

use std::f64;

let e = f64::consts::E;
let x = 1.0_f64;
let f = x.cosh();
// Solving cosh() at 1 gives this result
let g = (e*e + 1.0)/(2.0*e);
let abs_difference = (f - g).abs();

// Same result
assert!(abs_difference < 1.0e-10);

Hyperbolic tangent function.

use std::f64;

let e = f64::consts::E;
let x = 1.0_f64;

let f = x.tanh();
// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
let abs_difference = (f - g).abs();

assert!(abs_difference < 1.0e-10);

Inverse hyperbolic sine function.

let x = 1.0_f64;
let f = x.sinh().asinh();

let abs_difference = (f - x).abs();

assert!(abs_difference < 1.0e-10);

Inverse hyperbolic cosine function.

let x = 1.0_f64;
let f = x.cosh().acosh();

let abs_difference = (f - x).abs();

assert!(abs_difference < 1.0e-10);

Inverse hyperbolic tangent function.

use std::f64;

let e = f64::consts::E;
let f = e.tanh().atanh();

let abs_difference = (f - e).abs();

assert!(abs_difference < 1.0e-10);

Trait Implementations

impl PartialEq for Prob

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

This method tests for !=.

impl PartialOrd for Prob

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

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

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

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

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl Copy for Prob

impl Clone for Prob

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

impl Debug for Prob

Formats the value using the given formatter.

impl Default for Prob

Returns the "default value" for a type. Read more

impl Decodable for Prob

impl Encodable for Prob

impl From<f64> for Prob

Performs the conversion.

impl Deref for Prob

The resulting type after dereferencing

The method called to dereference a value

impl Add<Prob> for Prob

The resulting type after applying the + operator

The method for the + operator

impl<'a> Add<&'a Prob> for &'a Prob

The resulting type after applying the + operator

The method for the + operator

impl<'a> Add<&'a Prob> for Prob

The resulting type after applying the + operator

The method for the + operator

impl<'a> Add<Prob> for &'a Prob

The resulting type after applying the + operator

The method for the + operator

impl Sub<Prob> for Prob

The resulting type after applying the - operator

The method for the - operator

impl<'a> Sub<&'a Prob> for &'a Prob

The resulting type after applying the - operator

The method for the - operator

impl<'a> Sub<&'a Prob> for Prob

The resulting type after applying the - operator

The method for the - operator

impl<'a> Sub<Prob> for &'a Prob

The resulting type after applying the - operator

The method for the - operator

impl Mul<Prob> for Prob

The resulting type after applying the * operator

The method for the * operator

impl<'a> Mul<&'a Prob> for &'a Prob

The resulting type after applying the * operator

The method for the * operator

impl<'a> Mul<&'a Prob> for Prob

The resulting type after applying the * operator

The method for the * operator

impl<'a> Mul<Prob> for &'a Prob

The resulting type after applying the * operator

The method for the * operator

impl Div<Prob> for Prob

The resulting type after applying the / operator

The method for the / operator

impl<'a> Div<&'a Prob> for &'a Prob

The resulting type after applying the / operator

The method for the / operator

impl<'a> Div<&'a Prob> for Prob

The resulting type after applying the / operator

The method for the / operator

impl<'a> Div<Prob> for &'a Prob

The resulting type after applying the / operator

The method for the / operator

impl From<LogProb> for Prob
[src]

Performs the conversion.

impl From<PHREDProb> for Prob
[src]

Performs the conversion.