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),
  );
$m2 = array(
  array(4, 9, 5),
  array(7, 5, 0),
  array(2, 2, 8),
  );
// element addition should give us: 9  12   7
//                 10   5   4
//                  3   7  10
matrix_print(matrix_element_operation($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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更多关于php相关内容感兴趣的读者可查看本站专题：《php数学运算技巧总结》、《php运算与运算符用法总结》、《php字符串(string)用法总结》、《php数组(array)操作技巧大全》、《php常用遍历算法与技巧总结》、《php数据结构与算法教程》、《php程序设计算法总结》、《php正则表达式用法总结》及《php常见数据库操作技巧汇总》

希望本文所述对大家php程序设计有所帮助。