PHP使用数组实现矩阵数学运算的方法示例

本文实例讲述了PHP使用数组实现矩阵数学运算的方法。分享给大家供大家参考，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  10matrix_print(matrix_element_operation($m1, $m2, '+'));// Element subtraction should give us:   1  -6  -3//                    -4  -5   4//                    -1   3  -6matrix_print(matrix_element_operation($m1, $m2, '-'));// Do a scalar multiplication on the 2nd matrix:  8 18 10//                        14 10  0//                         4  4 16matrix_print(matrix_scalar_operation($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  37matrix_print(matrix_operation($m3, $m4, '*'));// Matrix addition gives:   9 20//              4 15matrix_print(matrix_operation($m3, $m4, '+'));?>