4061793478

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Commit Message

NonInteger::hyperharmonic(): bug fix (#463)

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/src/Sequence/NonInteger.php

<?php

namespace MathPHP\Sequence;

use MathPHP\Exception;
use MathPHP\Number\Rational;

/**
 * Non-integer sequences
 *  - Harmonic
 *  - Generalized Harmonic
 *  - Hyperharmonic
 *
 * All sequences return an array of numbers in the sequence.
 * The array index starting point depends on the sequence type.
 */
class NonInteger
{
    /**
     * Harmonic Numbers
     *
     *      n  1
     * Hᵢ = ∑  -
     *     ⁱ⁼¹ i
     *
     * https://en.wikipedia.org/wiki/Harmonic_number
     *
     * @param int $n the length of the sequence to calculate
     *
     * @return float[]
     */
    public static function harmonic(int $n): array
    {
        return self::generalizedHarmonic($n, 1);
    }

    /**
     * Generalized Harmonic Numbers
     *
     *       ₙ  1
     * Hₙₘ = ∑  --
     *      ⁱ⁼¹ iᵐ
     *
     * https://en.wikipedia.org/wiki/Harmonic_number#Generalized_harmonic_numbers
     *
     * @param int   $n the length of the sequence to calculate
     * @param float $m the exponent
     *
     * @return float[]
     */
    public static function generalizedHarmonic(int $n, float $m): array
    {
        if ($n <= 0) {
            return [];
        }

        $sequence = [];
        $∑        = 0;

        for ($i = 1; $i <= $n; $i++) {
            $∑ += 1 / $i ** $m;
            $sequence[$i] = $∑;
        }

        return $sequence;
    }

    /**
     * Hyperharmonic Numbers
     *
     *         ₙ
     * Hₙ⁽ʳ⁾ = ∑  Hₖ⁽ʳ⁻¹⁾
     *        ᵏ⁼¹
     *
     * https://en.wikipedia.org/wiki/Hyperharmonic_number
     *
     * @param int  $n the length of the sequence to calculate
     * @param int  $r the depth of recursion
     * @param bool $rational return results as a Rational object
     *
     * @return float[]|Rational[]
     *
     * @throws Exception\OutOfBoundsException
     */
    public static function hyperharmonic(int $n, int $r, $rational = false): array
    {
        if ($r < 0) {
            throw new Exception\OutOfBoundsException('Recursion depth cannot be less than 0');
        }
        if ($n <= 0) {
            return [];
        }
        $sequence = [];

        try {
            if ($r == 0) {
                for ($k = 1; $k <= $n; $k++) {
                    $sequence[$k] = new Rational(0, 1, $k);
                }
            } else {
                /** @var Rational[] $array */
                $array = self::hyperharmonic($n, $r - 1, true);
                $∑     = Rational::createZeroValue();
                for ($k = 1; $k <= $n; $k++) {
                    $∑ = $∑->add($array[$k]);
                    $sequence[$k] = $∑;
                }
            }
        } catch (\TypeError $e) {
            throw new Exception\OutOfBoundsException('Numbers too large to maintain integer precision', -1, $e);
        } catch (\Error $e) {
            throw new Exception\OutOfBoundsException("Recursion depth level error: {$e->getMessage()}", -2, $e);
        }

        if ($rational == true) {
            return $sequence;
        }

        return array_map(
            function (Rational $r) {
                return $r->toFloat();
            },
            $sequence
        );
    }
}

1	<?php
2
3	namespace MathPHP\Sequence;
4
5	use MathPHP\Exception;
6	use MathPHP\Number\Rational;
7
8	/**
9	* Non-integer sequences
10	* - Harmonic
11	* - Generalized Harmonic
12	* - Hyperharmonic
13	*
14	* All sequences return an array of numbers in the sequence.
15	* The array index starting point depends on the sequence type.
16	*/
17	class NonInteger
18	{
19	/**
20	* Harmonic Numbers
21	*
22	* n 1
23	* Hᵢ = ∑ -
24	* ⁱ⁼¹ i
25	*
26	* https://en.wikipedia.org/wiki/Harmonic_number
27	*
28	* @param int $n the length of the sequence to calculate
29	*
30	* @return float[]
31	*/
32	public static function harmonic(int $n): array
33	{
34	return self::generalizedHarmonic($n, 1);	4✔
35	}
36
37	/**
38	* Generalized Harmonic Numbers
39	*
40	* ₙ 1
41	* Hₙₘ = ∑ --
42	* ⁱ⁼¹ iᵐ
43	*
44	* https://en.wikipedia.org/wiki/Harmonic_number#Generalized_harmonic_numbers
45	*
46	* @param int $n the length of the sequence to calculate
47	* @param float $m the exponent
48	*
49	* @return float[]
50	*/
51	public static function generalizedHarmonic(int $n, float $m): array
52	{
53	if ($n <= 0) {	27✔
54	return [];	4✔
55	}
56
57	$sequence = [];	23✔
58	$∑ = 0;	23✔
59
60	for ($i = 1; $i <= $n; $i++) {	23✔
61	$∑ += 1 / $i ** $m;	23✔
62	$sequence[$i] = $∑;	23✔
63	}
64
65	return $sequence;	23✔
66	}
67
68	/**
69	* Hyperharmonic Numbers
70	*
71	* ₙ
72	* Hₙ⁽ʳ⁾ = ∑ Hₖ⁽ʳ⁻¹⁾
73	* ᵏ⁼¹
74	*
75	* https://en.wikipedia.org/wiki/Hyperharmonic_number
76	*
77	* @param int $n the length of the sequence to calculate
78	* @param int $r the depth of recursion
79	* @param bool $rational return results as a Rational object
80	*
81	* @return float[]\|Rational[]
82	*
83	* @throws Exception\OutOfBoundsException
84	*/
85	public static function hyperharmonic(int $n, int $r, $rational = false): array
86	{
87	if ($r < 0) {	7✔
88	throw new Exception\OutOfBoundsException('Recursion depth cannot be less than 0');	1✔
89	}
90	if ($n <= 0) {	6✔
91	return [];	2✔
92	}
93	$sequence = [];	4✔
94
95	try {
96	if ($r == 0) {	4✔
97	for ($k = 1; $k <= $n; $k++) {	4✔
98	$sequence[$k] = new Rational(0, 1, $k);	4✔
99	}
100	} else {
101	/** @var Rational[] $array */
102	$array = self::hyperharmonic($n, $r - 1, true);	3✔
103	$∑ = Rational::createZeroValue();	3✔
104	for ($k = 1; $k <= $n; $k++) {	4✔
105	$∑ = $∑->add($array[$k]);	3✔
106	$sequence[$k] = $∑;	3✔
107	}
108	}
109	} catch (\TypeError $e) {	1✔
110	throw new Exception\OutOfBoundsException('Numbers too large to maintain integer precision', -1, $e);	1✔
111	} catch (\Error $e) {	1✔
112	throw new Exception\OutOfBoundsException("Recursion depth level error: {$e->getMessage()}", -2, $e);	×
113	}
114
115	if ($rational == true) {	4✔
116	return $sequence;	3✔
117	}
118
119	return array_map(	3✔
120	function (Rational $r) {
121	return $r->toFloat();	3✔
122	},	3✔
123	$sequence
124	);
125	}
126	}

markrogoyski / math-php / 4061793478

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