mathol 0.1.1

Math library in Rust
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214

use num::{PrimInt, Integer, Float, Zero, One, range};
use std::iter::{Product};
use std::ops::{Sub};
use std::iter::Iterator;
use std::f64::consts::PI;
use basics::pow;
use basics::convert_trait::Convert;
use stochastics::probability::{factorial, combination};
use error::*;


/// Calculates the binomial distribution in dependency of n and p.
/// # Remarks
/// n is the number of Bernoulli experiments
///
/// p is the probability for an event.
///
/// Returns the binomial distribution as a vector or an error message if p is not between 0 and 1.
/// # Examples
/// ```
/// let mut vec = vec![];
/// vec.push(0.5314410000000002);
/// vec.push(0.35429400000000016);
/// vec.push(0.09841500000000003);
/// vec.push(0.014580000000000004);
/// vec.push(0.0012150000000000004);
/// vec.push(0.00005400000000000002);
/// vec.push(0.0000010000000000000004);
/// assert_eq!(vec, binomial_distribution(6_i32, 0.1).unwrap());
/// ```
pub fn binomial_distribution<T, U>(n: T, p: U) -> Result<Vec<f64>, MatholError>
    where T: Zero + PrimInt + Integer + Product + Convert,
          U: One + Sub + Float + Convert
{
    if n < T::one() {
        return Err(MatholError::NegativeValueCause(NegativeValueError {
            message: "Parameter n must be a positive integer!".to_string(),
        }));
    }
    if p < U::zero() || p > U::one() {
        return Err(MatholError::RangeCause(RangeError {
            message: "p must be in a range between 0 and 1!".to_string(),
        }));
    }

    let q = U::one() - p;

    let binomial = range(T::zero(), n + T::one()).fold(Vec::new(), |mut vec, x| {
        let a = factorial(n).unwrap() / (factorial(x).unwrap() * factorial(n - x).unwrap());
        let b = pow(p, x);
        let c = pow(q, n - x);
        let result = a.to_f64() * b.to_f64() * c.to_f64();
        vec.push(result);
        vec
    });

    Ok(binomial)
}

/// Calculates the hypergeometric distribution in dependency of N, M and n.
/// # Remarks
/// In a set with two types of elements,
///
/// N is the total number of elements in the set.
///
/// M is the number of elements in one of the two subsets.
///
/// n is the number of elements that are picked from the set
///
/// Returns the hypergeometric distribution as a vector or an error message if M or n are bigger than N.
/// # Examples
/// ```
/// let mut vec = vec![];
/// vec.push(0.010101010101010102);
/// vec.push(0.1414141414141414);
/// vec.push(0.42424242424242425);
/// vec.push(0.35353535353535354);
/// vec.push(0.0707070707070707);
/// assert_eq!(vec, hypergeometric_distribution(12, 7, 4).unwrap());
/// ```
#[allow(non_snake_case)]
pub fn hypergeometric_distribution<T>(N: T, M: T, n: T) -> Result<Vec<f64>, MatholError>
    where T: PrimInt + Integer + Product + Sub + Convert
{
    if N < T::one() {
        return Err(MatholError::NegativeValueCause(NegativeValueError {
            message: "Parameter N must be a positive integer!".to_string(),
        }));
    }
    if M < T::one() {
        return Err(MatholError::NegativeValueCause(NegativeValueError {
            message: "Parameter M must be a positive integer!".to_string(),
        }));
    }
    if n < T::one() {
        return Err(MatholError::NegativeValueCause(NegativeValueError {
            message: "Parameter n must be a positive integer!".to_string(),
        }));
    }
    if M > N {
        return Err(MatholError::ComparisonCause(ComparisonError {
            message: "Parameter M must be smaller than N!".to_string(),
        }));
    }
    if n > N {
        return Err(MatholError::ComparisonCause(ComparisonError {
            message: "Parameter n must be smaller than N!".to_string(),
        }));
    }

    let hypergeometric = range(T::zero(), n + T::one()).fold(Vec::new(), |mut vec, x| {
        let a = combination(M, x).unwrap();
        let b = combination(N - M, n - x).unwrap();
        let c = combination(N, n).unwrap();
        let result = a.to_f64() * b.to_f64() / c.to_f64();
        vec.push(result);
        vec
    });

    Ok(hypergeometric)
}

/// Calculates the poisson distribution in dependency of my and x
/// # Remarks
/// Returns the poisson distribution for x or an error message if either my or x are zero.
/// # Examples
/// ```
/// assert_eq!(0.015328310048810096, poisson_distribution(1, 4).unwrap());
/// ```
pub fn poisson_distribution<T>(my: T, x: T) -> Result<f64, MatholError>
    where T: PrimInt + Integer + Product + Convert
{
    if my <= T::zero() {
        return Err(MatholError::NegativeValueCause(NegativeValueError {
            message: "Parameter ยต must be a positive integer!".to_string(),
        }));
    }
    if x < T::zero() {
        return Err(MatholError::NegativeValueCause(NegativeValueError {
            message: "Parameter x must be a positive Integer!".to_string(),
        }));
    }

    let a = pow(my, x).to_f64();
    let b = factorial(x)?.to_f64();
    let c = (my.to_f64() * (-1.0)).exp();

    Ok(a / b * c)
}

/// Calculates the gaussian distribution in dependency of my, sigma and x
/// # Remarks
/// Returns the gaussian distribution for x or an error message if sigma is smaller than 1.
/// # Examples
/// ```
/// assert_eq!(0.10648266850745075, gaussian_distribution(2, 3, 4).unwrap());
/// ```
pub fn gaussian_distribution<T>(my: T, sigma: T, x: T) -> Result<f64, MatholError>
    where T: Convert + Copy + Zero + PartialOrd
{
    if sigma <= T::zero() {
        return Err(MatholError::ComparisonCause(ComparisonError {
            message: "Parameter \u{03c3} must be bigger than 0!".to_string(),
        }));
    }

    let a = (2.0 * PI).sqrt() * sigma.to_f64();
    let b = (x.to_f64() - my.to_f64()) / sigma.to_f64();
    let c = -0.5 * pow(b, 2);
    let d = c.exp();

    Ok((1.0 / a) * d)
}

/// Calculates the standard distribution in dependency of x
/// # Remarks
/// Returns the standard distribution for x
/// # Examples
/// ```
/// assert_eq!(0.05399096651318806, standard_distribution(2.0));
/// ```
pub fn standard_distribution<T>(x: T) -> f64
    where T: Convert
{
    let a = (2.0 * PI).sqrt();
    let b = -0.5 * pow(x.to_f64(), 2);
    let c = b.exp();

    (1.0 / a) * c
}

/// Calculates the exponential distribution in dependency of lambda x
/// # Remarks
/// Returns the exponential distribution for x or an error message if lambda is smaller than 1.
/// # Examples
/// ```
/// assert_eq!(0.03663127777746836, exponential_distribution(2.0, 2.0).unwrap());
/// ```
pub fn exponential_distribution<T>(lambda: T, x: T) -> Result<f64, MatholError>
    where T: Zero + Convert + PartialOrd + Copy
{
    if lambda <= T::zero() {
        return Err(MatholError::ComparisonCause(ComparisonError {
            message: "Parameter \u{03bb} must be bigger than 0!".to_string(),
        }));
    }

    if x < T::zero() {
        Ok(0.0)
    } else {
        let a = lambda.to_f64() * (-1.0) * x.to_f64();
        Ok(lambda.to_f64() * a.exp())
    }
}