Struct bio::stats::probs::LogProb

pub struct LogProb(pub f64);

A newtype for log-scale probabilities.

Example

#[macro_use]
extern crate approx;
use bio::stats::{LogProb, Prob};

// convert from probability
let p = LogProb::from(Prob(0.5));
// convert manually
let q = LogProb(0.2f64.ln());
// obtain zero probability in log-space
let o = LogProb::ln_one();

assert_relative_eq!(*Prob::from(p.ln_add_exp(q) + o), *Prob(0.7));

Methods

impl LogProb

fn ln_zero() -> LogProb

Log-space representation of Pr=0

fn ln_one() -> LogProb

Log-space representation of Pr=1

fn ln_one_minus_exp(&self) -> LogProb

Numerically stable calculation of 1 - p in log-space.

fn ln_sum_exp(probs: &[LogProb]) -> LogProb

Numerically stable sum of probabilities in log-space.

fn ln_add_exp(self, other: LogProb) -> LogProb

Numerically stable addition probabilities in log-space.

fn ln_sub_exp(self, other: LogProb) -> LogProb

Numerically stable subtraction of probabilities in log-space.

fn ln_cumsum_exp<I: IntoIterator<Item=LogProb>>(probs: I) -> ScanIter<I>

Calculate the cumulative sum of the given probabilities in a numerically stable way (Durbin 1998).

fn ln_trapezoidal_integrate_exp<T, D>(density: &D, a: T, b: T, n: usize) -> LogProb where T: Copy + Add<Output=T> + Sub<Output=T> + Div<Output=T> + Mul<Output=T>, D: Fn(T) -> LogProb, usize: ToFloat<T>, f64: From<T>

Integrate numerically stable over given log-space density in the interval [a, b]. Uses the trapezoidal rule with n grid points.

fn ln_simpsons_integrate_exp<T, D>(density: &D, a: T, b: T, n: usize) -> LogProb where T: Copy + Add<Output=T> + Sub<Output=T> + Div<Output=T> + Mul<Output=T>, D: Fn(T) -> LogProb, usize: ToFloat<T>, f64: From<T>

Integrate numerically stable over given log-space density in the interval [a, b]. Uses Simpson's rule with n (odd) grid points.

Methods from Deref<Target=f64>

fn is_nan(self) -> bool

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());

fn is_infinite(self) -> bool

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());

fn is_finite(self) -> bool

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());

fn is_normal(self) -> bool

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());

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.

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);

fn integer_decode(self) -> (u64, i16, i8)

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);

fn floor(self) -> f64

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);

fn ceil(self) -> f64

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);

fn round(self) -> f64

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);

fn trunc(self) -> f64

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);

fn fract(self) -> f64

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);

fn abs(self) -> f64

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());

fn signum(self) -> f64

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());

fn is_sign_positive(self) -> bool

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());

fn is_positive(self) -> bool

Deprecated since 1.0.0

: renamed to is_sign_positive

fn is_sign_negative(self) -> bool

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());

fn is_negative(self) -> bool

Deprecated since 1.0.0

: renamed to is_sign_negative

fn mul_add(self, a: f64, b: f64) -> f64

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);

fn recip(self) -> f64

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);

fn powi(self, n: i32) -> f64

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);

fn powf(self, n: f64) -> f64

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);

fn sqrt(self) -> f64

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());

fn exp(self) -> f64

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);

fn exp2(self) -> f64

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);

fn ln(self) -> f64

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);

fn log(self, base: f64) -> f64

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);

fn log2(self) -> f64

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);

fn log10(self) -> f64

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);

fn to_degrees(self) -> f64

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);

fn to_radians(self) -> f64

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);

fn frexp(self) -> (f64, isize)

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);

fn next_after(self, other: f64) -> f64

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);

fn max(self, other: f64) -> f64

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.

fn min(self, other: f64) -> f64

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.

fn abs_sub(self, other: f64) -> f64

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);

fn cbrt(self) -> f64

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);

fn hypot(self, other: f64) -> f64

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);

fn sin(self) -> f64

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);

fn cos(self) -> f64

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);

fn tan(self) -> f64

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);

fn asin(self) -> f64

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);

fn acos(self) -> f64

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);

fn atan(self) -> f64

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);

fn atan2(self, other: f64) -> f64

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);

fn sin_cos(self) -> (f64, f64)

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);

fn exp_m1(self) -> f64

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);

fn ln_1p(self) -> f64

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);

fn sinh(self) -> f64

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);

fn cosh(self) -> f64

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);

fn tanh(self) -> f64

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);

fn asinh(self) -> f64

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);

fn acosh(self) -> f64

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);

fn atanh(self) -> f64

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 Encodable for LogProb

fn encode<__S: Encoder>(&self, __arg_0: &mut __S) -> Result<(), __S::Error>

impl Decodable for LogProb

fn decode<__D: Decoder>(__arg_0: &mut __D) -> Result<LogProb, __D::Error>

impl Debug for LogProb

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

impl Clone for LogProb

fn clone(&self) -> LogProb

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Copy for LogProb

impl PartialOrd for LogProb

fn partial_cmp(&self, __arg_0: &LogProb) -> Option<Ordering>

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

fn lt(&self, __arg_0: &LogProb) -> bool

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

fn le(&self, __arg_0: &LogProb) -> bool

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

fn gt(&self, __arg_0: &LogProb) -> bool

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

fn ge(&self, __arg_0: &LogProb) -> bool

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

impl PartialEq for LogProb

fn eq(&self, __arg_0: &LogProb) -> bool

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

fn ne(&self, __arg_0: &LogProb) -> bool

This method tests for !=.

impl From<f64> for LogProb

fn from(v: f64) -> Self

Performs the conversion.

impl Deref for LogProb

type Target = f64

The resulting type after dereferencing

fn deref(&self) -> &Self::Target

The method called to dereference a value

impl Add<LogProb> for LogProb

type Output = LogProb

The resulting type after applying the + operator

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

The method for the + operator

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

type Output = LogProb

The resulting type after applying the + operator

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

The method for the + operator

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

type Output = LogProb

The resulting type after applying the + operator

fn add(self, rhs: &'a LogProb) -> LogProb

The method for the + operator

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

type Output = LogProb

The resulting type after applying the + operator

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

The method for the + operator

impl Sub<LogProb> for LogProb

type Output = LogProb

The resulting type after applying the - operator

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

The method for the - operator

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

type Output = LogProb

The resulting type after applying the - operator

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

The method for the - operator

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

type Output = LogProb

The resulting type after applying the - operator

fn sub(self, rhs: &'a LogProb) -> LogProb

The method for the - operator

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

type Output = LogProb

The resulting type after applying the - operator

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

The method for the - operator

impl From<Prob> for LogProb

fn from(p: Prob) -> LogProb

Performs the conversion.

impl From<PHREDProb> for LogProb

fn from(p: PHREDProb) -> LogProb

Performs the conversion.

impl Default for LogProb

fn default() -> LogProb

Returns the "default value" for a type.