配列を使用して PHP で行列数学演算を実装する方法

<?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($matrix[0]);
}
// This function performs operations on matrix elements, such as addition
// or subtraction. To use it, pass it 2 matrices, and the operation you
// wish to perform, as a string: &#39;+&#39;, &#39;-&#39;
function matrix_element_operation($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; $c++) {
      eval(&#39;$a[$r][$c] &#39;.$operation.&#39;= $b[$r][$c];&#39;);
    }
  }
  // Return the finished matrix:
  return $a;
}
// This function performs full matrix operations, such as matrix addition
// or matrix multiplication. As above, pass it to matrices and the
// operation: &#39;*&#39;, &#39;-&#39;, &#39;+&#39;
function matrix_operation($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; $ac++) {
        // Evaluate the operation
        eval(&#39;$new[$r][$c] += $a[$r][$ac] &#39;.
          $operation.&#39; $b[$ac][$c];&#39;);
      }
    }
  }
  // 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; $c++) {
        eval(&#39;$matrix[$r][$c] &#39;.$operation.&#39;= $scalar;&#39;);
      }
    }
    // Return the finished matrix:
    return $matrix;
  } else {
    // It wasn&#39;t well formed:
    return false;
  }
}
// A handy function for printing matrices (As an HTML table)
function matrix_print($matrix) {
  // Verify it is well formed
  if (_matrix_well_formed($matrix)) {
    $rows = _matrix_rows($matrix);
    $columns = _matrix_columns($matrix);
    // Start the table
    echo &#39;<table>&#39;;
    // For each row in the matrix:
    for ($r = 0; $r < $rows; $r++) {
      // Begin the row:
      echo &#39;<tr>&#39;;
      // For each column in this row
      for ($c = 0; $c < $columns; $c++) {
        // Echo the element:
        echo "<td>{$matrix[$r][$c]}</td>";
      }
      // End the row.
      echo &#39;</tr>&#39;;
    }
    // End the table.
    echo "</table>/n";
  } else {
    // It wasn&#39;t well formed:
    return false;
  }
}
// Let&#39;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&#39;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, $m2, &#39;+&#39;));
// Element subtraction should give us:   1  -6  -3
//                    -4  -5   4
//                    -1   3  -6
matrix_print(matrix_element_operation($m1, $m2, &#39;-&#39;));
// Do a scalar multiplication on the 2nd matrix:  8 18 10
//                        14 10  0
//                         4  4 16
matrix_print(matrix_scalar_operation($m2, 2, &#39;*&#39;));
// 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, $m4, &#39;*&#39;));
// Matrix addition gives:   9 20
//              4 15
matrix_print(matrix_operation($m3, $m4, &#39;+&#39;));
?>