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<?php |
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/** |
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* Trait MathAndTrigonometry-M |
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* |
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* @link https://www.icy2003.com/ |
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* @author icy2003 <[email protected]> |
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* @copyright Copyright (c) 2017, icy2003 |
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*/ |
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namespace icy2003\php\icomponents\excel\mathAndTrigonometry; |
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use icy2003\php\ihelpers\Arrays; |
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/** |
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* MathAndTrigonometry-M |
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*/ |
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trait MMAT |
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{ |
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/** |
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* 返回一个数组的矩阵行列式的值 |
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* |
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* - det(A) = ai1Ai1 + ... + ainAin |
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* |
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* @param array $array 必需。 行数和列数相等的数值数组 |
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* |
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* @return double |
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*/ |
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public static function mdeterm($array) |
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{ |
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$n = count($array); |
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$sum = 0; |
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$prod = 1; |
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for ($i = 0; $i < $n - 1; $i++) { |
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for ($j = 0; $j < $n; $j++) { |
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$x = ($j + $i) % $n; |
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$y = $j % $n; |
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$prod *= $array[$x][$y]; |
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} |
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$sum += $prod; |
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$prod = 1; |
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for ($j = $n - 1; $j >= 0; $j--) { |
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$x = ($j + $i) % $n; |
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$y = ($n - $j - 1) % $n; |
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$prod *= $array[$x][$y]; |
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} |
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$sum -= $prod; |
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$prod = 1; |
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} |
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return $sum; |
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} |
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/** |
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* 返回数组中存储的矩阵的逆矩阵 |
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* |
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* @todo |
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* |
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* @return array |
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*/ |
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public static function minverse() |
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{ |
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return []; |
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} |
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/** |
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* 返回两个数组的矩阵乘积。 结果矩阵的行数与 array1 的行数相同，矩阵的列数与 array2 的列数相同 |
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* |
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* - Aij = ∑(k = 1, n)Bik * Ckj，其中 i 为行数，j 为列数 |
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* - 矩阵乘积物理含义： |
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* |
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* | 买家\产品 | A | B | C | |
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* | - | - | - | - | |
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* | 甲 | 3 个 | 4 个 | 1 个 | |
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* | 乙 | 4 个 | 1 个 | 2 个 | |
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* |
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* | 产品 | 价格 | 重量 | |
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* | - | - | - | |
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* | A | 5 元 | 10 斤 | |
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* | B | 10 元 | 5 斤 | |
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* | C | 9 元 | 6 斤 | |
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* |
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* | 买家 | 总花费 | 总重量 | |
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* | - | - | - | |
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* | 甲 | 64 | 56 | |
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* | 乙 | 48 | 57 | |
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* |
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* @param array $array1 |
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* @param array $array2 |
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* |
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* @return array|false |
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*/ |
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public static function mmult($array1, $array2) |
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{ |
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list($col1, $row1) = Arrays::colRowCount($array1); |
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list($col2, $row2) = Arrays::colRowCount($array2); |
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if ($col1 === $row2 && $row1 === $col2) { |
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$arr = []; |
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for ($r = 0; $r < $row1; $r++) { |
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for ($c = 0; $c < $col2; $c++) { |
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$arr[$r][$c] = array_sum(array_map(function ($a1, $a2) { |
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return $a1 * $a2; |
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}, $array1[$r], Arrays::column($array2, $c))); |
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} |
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} |
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return $arr; |
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} else { |
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return false; |
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} |
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} |
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/** |
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* 返回两数相除的余数 |
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* |
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* - 结果的符号与除数相同 |
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* |
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* @param integer $number 必需。 要计算余数的被除数 |
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* @param integer $divisor 必需。 除数 |
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* |
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* @return integer |
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*/ |
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public static function mod($number, $divisor) |
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{ |
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return self::sign($divisor) * self::abs($number % $divisor); |
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} |
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/** |
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* 返回舍入到所需倍数的数字 |
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* |
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* @param double $number 必需。 要舍入的值 |
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* @param double $multiple 必需。 要舍入到的倍数 |
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* |
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* @return double|false |
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*/ |
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public static function mround($number, $multiple) |
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{ |
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if ($number * $multiple < 0) { |
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return false; |
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} |
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return round($number / $multiple) * $multiple; |
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} |
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/** |
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* 返回参数和的阶乘与各参数阶乘乘积的比值 |
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* |
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* @param double $number1 Number1 是必需的，后续数字是可选的 |
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* |
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* @return double |
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*/ |
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public static function multinomial($number1) |
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{ |
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$numbers = is_array($number1) ? $number1 : func_get_args(); |
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return self::fact(array_sum($numbers)) / array_product(array_map(function ($num) { |
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return self::fact($num); |
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}, $numbers)); |
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} |
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/** |
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* 返回指定维度的单位矩阵 |
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* |
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* - 1NxN = |
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* ``` |
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* 1 0 ... 0 |
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* 0 1 ... 0 |
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* ... ... |
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* 0 0 ... 1 |
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* ``` |
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* - 注：null 值在 php 里做运算时被看成 0，因此无需对 0 的元素进行赋值 |
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* |
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* @param integer $dimension 必需。 Dimension 是一个整数, 指定要返回的单位矩阵的维度。 它返回一个数组。 维度必须大于零 |
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* |
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* @return array |
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*/ |
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public static function munit($dimension) |
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{ |
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$array = []; |
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for ($i = 0; $i < $dimension; $i++) { |
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$array[$i][$i] = 1; |
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} |
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return $array; |
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} |
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} |
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icy2003 /
php
