This article mainly introduces the method of PHP using arrays to implement matrix mathematical operations, and analyzes the related operating skills of PHP based on arrays to implement matrix representation and operations based on specific examples. Friends in need can refer to the following
The details are as follows:
Matrix operation is to perform some kind of mathematical operation on two data tables and obtain another data table.
In the following example, we have created a basically complete matrix operation function library so that Programs for matrix operations.
From 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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