PHP利用数组实现矩阵数学运算的方法
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2022-03-28 16:03:28
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这篇文章主要介绍了PHP使用数组实现矩阵数学运算的方法,结合具体实例形式分析了php基于数组实现矩阵表示与运算的相关操作技巧,需要的朋友可以参考下
具体如下：
矩阵运算就是对两个数据表进行某种数学运算，并得到另一个数据表.
下面的例子中我们创建了一个基本完整的矩阵运算函数库，以便用于矩阵操作的程序中.
来自 PHP5 in Practice (U.S.)Elliott III & Jonathan D.Eisenhamer
<?php
// A Library of Matrix Math functions.
// All assume a Matrix defined by a 2 dimensional array, where the first
// index (array[x]) are the rows and the second index (array[x][y])
// are the columns
// First create a few helper functions
// A function to determine if a matrix is well formed. That is to say that
// it is perfectly rectangular with no missing values:
function _matrix_well_formed($matrix) {
// If this is not an array, it is badly formed, return false.
if (!(is_array($matrix))) {
return false;
} else {
// Count the number of rows.
$rows = count($matrix);
// Now loop through each row:
for ($r = 0; $r < $rows; $r++) {
// Make sure that this row is set, and an array. Checking to
// see if it is set is ensuring that this is a 0 based
// numerically indexed array.
if (!(isset($matrix[$r]) && is_array($matrix[$r]))) {
return false;
} else {
// If this is row 0, calculate the columns in it:
if ($r == 0) {
$cols = count($matrix[$r]);
// Ensure that the number of columns is identical else exit
} elseif (count($matrix[$r]) != $cols) {
return false;
}
// Now, loop through all the columns for this row
for ($c = 0; $c < $cols; $c++) {
// Ensure this entry is set, and a number
if (!(isset($matrix[$r][$c]) &&
is_numeric($matrix[$r][$c]))) {
return false;
}
}
}
}
}
// Ok, if we actually made it this far, then we have not found
// anything wrong with the matrix.
return true;
}
// A function to return the rows in a matrix -
// Does not check for validity, it assumes the matrix is well formed.
function _matrix_rows($matrix) {
return count($matrix);
}
// A function to return the columns in a matrix -
// Does not check for validity, it assumes the matrix is well formed.
function _matrix_columns($matrix) {
return count($matrix[0]);
}
// This function performs operations on matrix elements, such as addition
// or subtraction. To use it, pass it 2 matrices, and the operation you
// wish to perform, as a string: '+', '-'
function matrix_element_operation($a, $b, $operation) {
// Verify both matrices are well formed
$valid = false;
if (_matrix_well_formed($a) && _matrix_well_formed($b)) {
// Make sure they have the same number of columns & rows
$rows = _matrix_rows($a);
$columns = _matrix_columns($a);
if (($rows == _matrix_rows($b)) &&
($columns == _matrix_columns($b))) {
// We have a valid setup for continuing with element math
$valid = true;
}
}
// If invalid, return false
if (!($valid)) { return false; }
// For each element in the matrices perform the operatoin on the
// corresponding element in the other array to it:
for ($r = 0; $r < $rows; $r++) {
for ($c = 0; $c < $columns; $c++) {
eval('$a[$r][$c] '.$operation.'= $b[$r][$c];');
}
}
// Return the finished matrix:
return $a;
}
// This function performs full matrix operations, such as matrix addition
// or matrix multiplication. As above, pass it to matrices and the
// operation: '*', '-', '+'
function matrix_operation($a, $b, $operation) {
// Verify both matrices are well formed
$valid = false;
if (_matrix_well_formed($a) && _matrix_well_formed($b)) {
// Make sure they have complementary numbers of rows and columns.
// The number of rows in A should be the number of columns in B
$rows = _matrix_rows($a);
$columns = _matrix_columns($a);
if (($columns == _matrix_rows($b)) &&
($rows == _matrix_columns($b))) {
// We have a valid setup for continuing
$valid = true;
}
}
// If invalid, return false
if (!($valid)) { return false; }
// Create a blank matrix the appropriate size, initialized to 0
$new = array_fill(0, $rows, array_fill(0, $rows, 0));
// For each row in a ...
for ($r = 0; $r < $rows; $r++) {
// For each column in b ...
for ($c = 0; $c < $rows; $c++) {
// Take each member of column b, with each member of row a
// and add the results, storing this in the new table:
// Loop over each column in A ...
for ($ac = 0; $ac < $columns; $ac++) {
// Evaluate the operation
eval('$new[$r][$c] += $a[$r][$ac] '.
$operation.' $b[$ac][$c];');
}
}
}
// Return the finished matrix:
return $new;
}
// A function to perform scalar operations. This means that you take the scalar value,
// and the operation provided, and apply it to every element.
function matrix_scalar_operation($matrix, $scalar, $operation) {
// Verify it is well formed
if (_matrix_well_formed($matrix)) {
$rows = _matrix_rows($matrix);
$columns = _matrix_columns($matrix);
// For each element in the matrix, multiply by the scalar
for ($r = 0; $r < $rows; $r++) {
for ($c = 0; $c < $columns; $c++) {
eval('$matrix[$r][$c] '.$operation.'= $scalar;');
}
}
// Return the finished matrix:
return $matrix;
} else {
// It wasn't well formed:
return false;
}
}
// A handy function for printing matrices (As an HTML table)
function matrix_print($matrix) {
// Verify it is well formed
if (_matrix_well_formed($matrix)) {
$rows = _matrix_rows($matrix);
$columns = _matrix_columns($matrix);
// Start the table
echo '<table>';
// For each row in the matrix:
for ($r = 0; $r < $rows; $r++) {
// Begin the row:
echo '<tr>';
// For each column in this row
for ($c = 0; $c < $columns; $c++) {
// Echo the element:
echo "<td>{$matrix[$r][$c]}</td>";
}
// End the row.
echo '</tr>';
}
// End the table.
echo "</table>/n";
} else {
// It wasn't well formed:
return false;
}
}
// Let's do some testing. First prepare some formatting:
echo "<mce:style><!--
table { border: 1px solid black; margin: 20px; }
td { text-align: center; }
--></mce:style><style mce_bogus="1">table { border: 1px solid black; margin: 20px; }
td { text-align: center; }</style>/n";
// Now let's test element operations. We need identical sized matrices:
$m1 = array(
array(5, 3, 2),
array(3, 0, 4),
array(1, 5, 2),
);
$m2 = array(
array(4, 9, 5),
array(7, 5, 0),
array(2, 2, 8),
);
// Element addition should give us: 9 12 7
// 10 5 4
// 3 7 10
matrix_print(matrix_element_operation($m1, $m2, '+'));
// Element subtraction should give us: 1 -6 -3
// -4 -5 4
// -1 3 -6
matrix_print(matrix_element_operation($m1, $m2, '-'));
// Do a scalar multiplication on the 2nd matrix: 8 18 10
// 14 10 0
// 4 4 16
matrix_print(matrix_scalar_operation($m2, 2, '*'));
// Define some matrices for full matrix operations.
// Need to be complements of each other:
$m3 = array(
array(1, 3, 5),
array(-2, 5, 1),
);
$m4 = array(
array(1, 2),
array(-2, 8),
array(1, 1),
);
// Matrix multiplication gives: 0 31
// -11 37
matrix_print(matrix_operation($m3, $m4, '*'));
// Matrix addition gives: 9 20
// 4 15
matrix_print(matrix_operation($m3, $m4, '+'));
?>
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