JAMA

# Source for file Matrix.php Documentation is available at Matrix.php <?php /** * @package JAMA */ define('RAND_MAX', mt_getrandmax()); define('RAND_MIN', 0); /** PHPExcel root directory */ if (!defined('PHPEXCEL_ROOT')) { /** * @ignore */ define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../../'); require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php'); PHPExcel_Autoloader::Register(); PHPExcel_Shared_ZipStreamWrapper::register(); // check mbstring.func_overload if (ini_get('mbstring.func_overload') & 2) { throw new Exception('Multibyte function overloading in PHP must be disabled for string functions (2).'); } } require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/utils/Error.php'; require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/utils/Maths.php'; require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/CholeskyDecomposition.php'; require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/LUDecomposition.php'; require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/QRDecomposition.php'; require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/EigenvalueDecomposition.php'; require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/SingularValueDecomposition.php'; require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/String.php'; require_once PHPEXCEL_ROOT . 'PHPExcel/Calculation/Functions.php'; /* * Matrix class * * @author Paul Meagher * @author Michael Bommarito * @author Lukasz Karapuda * @author Bartek Matosiuk * @version 1.8 * @license PHP v3.0 * @see http://math.nist.gov/javanumerics/jama/ */ class Matrix { /** * Matrix storage * * @var array * @access public */ public $A = array(); /** * Matrix row dimension * * @var int * @access private */ private $m; /** * Matrix column dimension * * @var int * @access private */ private $n; /** * Polymorphic constructor * * As PHP has no support for polymorphic constructors, we hack our own sort of polymorphism using func_num_args, func_get_arg, and gettype. In essence, we're just implementing a simple RTTI filter and calling the appropriate constructor. */ public function __construct() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { //Square matrix - n x n case 'integer': $this->m = $args[0]; $this->n = $args[0]; $this->A = array_fill(0, $this->m, array_fill(0, $this->n, 0)); break; //Rectangular matrix - m x n case 'integer,integer': $this->m = $args[0]; $this->n = $args[1]; $this->A = array_fill(0, $this->m, array_fill(0, $this->n, 0)); break; //Rectangular matrix constant-filled - m x n filled with c case 'integer,integer,integer': $this->m = $args[0]; $this->n = $args[1]; $this->A = array_fill(0, $this->m, array_fill(0, $this->n, $args[2])); break; //Rectangular matrix constant-filled - m x n filled with c case 'integer,integer,double': $this->m = $args[0]; $this->n = $args[1]; $this->A = array_fill(0, $this->m, array_fill(0, $this->n, $args[2])); break; //Rectangular matrix - m x n initialized from 2D array case 'array': $this->m = count($args[0]); $this->n = count($args[0][0]); $this->A = $args[0]; break; //Rectangular matrix - m x n initialized from 2D array case 'array,integer,integer': $this->m = $args[1]; $this->n = $args[2]; $this->A = $args[0]; break; //Rectangular matrix - m x n initialized from packed array case 'array,integer': $this->m = $args[1]; if ($this->m != 0) { $this->n = count($args[0]) / $this->m; } else { $this->n = 0; } if (($this->m * $this->n) == count($args[0])) { for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $this->A[$i][$j] = $args[0][$i + $j * $this->m]; } } } else { throw new Exception(JAMAError(ArrayLengthException)); } break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function __construct() /** * getArray * * @return array Matrix array */ public function getArray() { return $this->A; } // function getArray() /** * getArrayCopy * * @return array Matrix array copy */ public function getArrayCopy() { return $this->A; } // function getArrayCopy() /** * constructWithCopy * Construct a matrix from a copy of a 2-D array. * * @param double A[][] Two-dimensional array of doubles. * @exception IllegalArgumentException All rows must have the same length */ public function constructWithCopy($A) { $this->m = count($A); $this->n = count($A[0]); $newCopyMatrix = new Matrix($this->m, $this->n); for ($i = 0; $i < $this->m; ++$i) { if (count($A[$i]) != $this->n) { throw new Exception(JAMAError(RowLengthException)); } for ($j = 0; $j < $this->n; ++$j) { $newCopyMatrix->A[$i][$j] = $A[$i][$j]; } } return $newCopyMatrix; } // function constructWithCopy() /** * getColumnPackedCopy * * Get a column-packed array * @return array Column-packed matrix array */ public function getColumnPackedCopy() { $P = array(); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { array_push($P, $this->A[$j][$i]); } } return $P; } // function getColumnPackedCopy() /** * getRowPackedCopy * * Get a row-packed array * @return array Row-packed matrix array */ public function getRowPackedCopy() { $P = array(); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { array_push($P, $this->A[$i][$j]); } } return $P; } // function getRowPackedCopy() /** * getRowDimension * * @return int Row dimension */ public function getRowDimension() { return $this->m; } // function getRowDimension() /** * getColumnDimension * * @return int Column dimension */ public function getColumnDimension() { return $this->n; } // function getColumnDimension() /** * get * * Get the i,j-th element of the matrix. * @param int $i Row position * @param int $j Column position * @return mixed Element (int/float/double) */ public function get($i = null, $j = null) { return $this->A[$i][$j]; } // function get() /** * getMatrix * * Get a submatrix * @param int $i0 Initial row index * @param int $iF Final row index * @param int $j0 Initial column index * @param int $jF Final column index * @return Matrix Submatrix */ public function getMatrix() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { //A($i0...; $j0...) case 'integer,integer': list($i0, $j0) = $args; if ($i0 >= 0) { $m = $this->m - $i0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } if ($j0 >= 0) { $n = $this->n - $j0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } $R = new Matrix($m, $n); for($i = $i0; $i < $this->m; ++$i) { for($j = $j0; $j < $this->n; ++$j) { $R->set($i, $j, $this->A[$i][$j]); } } return $R; break; //A($i0...$iF; $j0...$jF) case 'integer,integer,integer,integer': list($i0, $iF, $j0, $jF) = $args; if (($iF > $i0) && ($this->m >= $iF) && ($i0 >= 0)) { $m = $iF - $i0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } if (($jF > $j0) && ($this->n >= $jF) && ($j0 >= 0)) { $n = $jF - $j0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } $R = new Matrix($m+1, $n+1); for($i = $i0; $i <= $iF; ++$i) { for($j = $j0; $j <= $jF; ++$j) { $R->set($i - $i0, $j - $j0, $this->A[$i][$j]); } } return $R; break; //$R = array of row indices; $C = array of column indices case 'array,array': list($RL, $CL) = $args; if (count($RL) > 0) { $m = count($RL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); } if (count($CL) > 0) { $n = count($CL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); } $R = new Matrix($m, $n); for($i = 0; $i < $m; ++$i) { for($j = 0; $j < $n; ++$j) { $R->set($i - $i0, $j - $j0, $this->A[$RL[$i]][$CL[$j]]); } } return $R; break; //$RL = array of row indices; $CL = array of column indices case 'array,array': list($RL, $CL) = $args; if (count($RL) > 0) { $m = count($RL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); } if (count($CL) > 0) { $n = count($CL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); } $R = new Matrix($m, $n); for($i = 0; $i < $m; ++$i) { for($j = 0; $j < $n; ++$j) { $R->set($i, $j, $this->A[$RL[$i]][$CL[$j]]); } } return $R; break; //A($i0...$iF); $CL = array of column indices case 'integer,integer,array': list($i0, $iF, $CL) = $args; if (($iF > $i0) && ($this->m >= $iF) && ($i0 >= 0)) { $m = $iF - $i0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } if (count($CL) > 0) { $n = count($CL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); } $R = new Matrix($m, $n); for($i = $i0; $i < $iF; ++$i) { for($j = 0; $j < $n; ++$j) { $R->set($i - $i0, $j, $this->A[$RL[$i]][$j]); } } return $R; break; //$RL = array of row indices case 'array,integer,integer': list($RL, $j0, $jF) = $args; if (count($RL) > 0) { $m = count($RL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); } if (($jF >= $j0) && ($this->n >= $jF) && ($j0 >= 0)) { $n = $jF - $j0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } $R = new Matrix($m, $n+1); for($i = 0; $i < $m; ++$i) { for($j = $j0; $j <= $jF; ++$j) { $R->set($i, $j - $j0, $this->A[$RL[$i]][$j]); } } return $R; break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function getMatrix() /** * setMatrix * * Set a submatrix * @param int $i0 Initial row index * @param int $j0 Initial column index * @param mixed $S Matrix/Array submatrix * ($i0, $j0, $S) $S = Matrix * ($i0, $j0, $S) $S = Array */ public function setMatrix() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'integer,integer,object': if ($args[2] instanceof Matrix) { $M = $args[2]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } if (($args[0] + $M->m) <= $this->m) { $i0 = $args[0]; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } if (($args[1] + $M->n) <= $this->n) { $j0 = $args[1]; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } for($i = $i0; $i < $i0 + $M->m; ++$i) { for($j = $j0; $j < $j0 + $M->n; ++$j) { $this->A[$i][$j] = $M->get($i - $i0, $j - $j0); } } break; case 'integer,integer,array': $M = new Matrix($args[2]); if (($args[0] + $M->m) <= $this->m) { $i0 = $args[0]; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } if (($args[1] + $M->n) <= $this->n) { $j0 = $args[1]; } else { throw new Exception(JAMAError(ArgumentBoundsException)); } for($i = $i0; $i < $i0 + $M->m; ++$i) { for($j = $j0; $j < $j0 + $M->n; ++$j) { $this->A[$i][$j] = $M->get($i - $i0, $j - $j0); } } break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function setMatrix() /** * checkMatrixDimensions * * Is matrix B the same size? * @param Matrix $B Matrix B * @return boolean */ public function checkMatrixDimensions($B = null) { if ($B instanceof Matrix) { if (($this->m == $B->getRowDimension()) && ($this->n == $B->getColumnDimension())) { return true; } else { throw new Exception(JAMAError(MatrixDimensionException)); } } else { throw new Exception(JAMAError(ArgumentTypeException)); } } // function checkMatrixDimensions() /** * set * * Set the i,j-th element of the matrix. * @param int $i Row position * @param int $j Column position * @param mixed $c Int/float/double value * @return mixed Element (int/float/double) */ public function set($i = null, $j = null, $c = null) { // Optimized set version just has this $this->A[$i][$j] = $c; /* if (is_int($i) && is_int($j) && is_numeric($c)) { if (($i < $this->m) && ($j < $this->n)) { $this->A[$i][$j] = $c; } else { echo "A[$i][$j] = $c<br />"; throw new Exception(JAMAError(ArgumentBoundsException)); } } else { throw new Exception(JAMAError(ArgumentTypeException)); } */ } // function set() /** * identity * * Generate an identity matrix. * @param int $m Row dimension * @param int $n Column dimension * @return Matrix Identity matrix */ public function identity($m = null, $n = null) { return $this->diagonal($m, $n, 1); } // function identity() /** * diagonal * * Generate a diagonal matrix * @param int $m Row dimension * @param int $n Column dimension * @param mixed $c Diagonal value * @return Matrix Diagonal matrix */ public function diagonal($m = null, $n = null, $c = 1) { $R = new Matrix($m, $n); for($i = 0; $i < $m; ++$i) { $R->set($i, $i, $c); } return $R; } // function diagonal() /** * filled * * Generate a filled matrix * @param int $m Row dimension * @param int $n Column dimension * @param int $c Fill constant * @return Matrix Filled matrix */ public function filled($m = null, $n = null, $c = 0) { if (is_int($m) && is_int($n) && is_numeric($c)) { $R = new Matrix($m, $n, $c); return $R; } else { throw new Exception(JAMAError(ArgumentTypeException)); } } // function filled() /** * random * * Generate a random matrix * @param int $m Row dimension * @param int $n Column dimension * @return Matrix Random matrix */ public function random($m = null, $n = null, $a = RAND_MIN, $b = RAND_MAX) { if (is_int($m) && is_int($n) && is_numeric($a) && is_numeric($b)) { $R = new Matrix($m, $n); for($i = 0; $i < $m; ++$i) { for($j = 0; $j < $n; ++$j) { $R->set($i, $j, mt_rand($a, $b)); } } return $R; } else { throw new Exception(JAMAError(ArgumentTypeException)); } } // function random() /** * packed * * Alias for getRowPacked * @return array Packed array */ public function packed() { return $this->getRowPacked(); } // function packed() /** * getMatrixByRow * * Get a submatrix by row index/range * @param int $i0 Initial row index * @param int $iF Final row index * @return Matrix Submatrix */ public function getMatrixByRow($i0 = null, $iF = null) { if (is_int($i0)) { if (is_int($iF)) { return $this->getMatrix($i0, 0, $iF + 1, $this->n); } else { return $this->getMatrix($i0, 0, $i0 + 1, $this->n); } } else { throw new Exception(JAMAError(ArgumentTypeException)); } } // function getMatrixByRow() /** * getMatrixByCol * * Get a submatrix by column index/range * @param int $i0 Initial column index * @param int $iF Final column index * @return Matrix Submatrix */ public function getMatrixByCol($j0 = null, $jF = null) { if (is_int($j0)) { if (is_int($jF)) { return $this->getMatrix(0, $j0, $this->m, $jF + 1); } else { return $this->getMatrix(0, $j0, $this->m, $j0 + 1); } } else { throw new Exception(JAMAError(ArgumentTypeException)); } } // function getMatrixByCol() /** * transpose * * Tranpose matrix * @return Matrix Transposed matrix */ public function transpose() { $R = new Matrix($this->n, $this->m); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $R->set($j, $i, $this->A[$i][$j]); } } return $R; } // function transpose() /** * norm1 * * One norm * @return float Maximum column sum */ public function norm1() { $r = 0; for($j = 0; $j < $this->n; ++$j) { $s = 0; for($i = 0; $i < $this->m; ++$i) { $s += abs($this->A[$i][$j]); } $r = ($r > $s) ? $r : $s; } return $r; } // function norm1() /** * norm2 * * Maximum singular value * @return float Maximum singular value */ public function norm2() { } // function norm2() /** * normInf * * Infinite norm * @return float Maximum row sum */ public function normInf() { $r = 0; for($i = 0; $i < $this->m; ++$i) { $s = 0; for($j = 0; $j < $this->n; ++$j) { $s += abs($this->A[$i][$j]); } $r = ($r > $s) ? $r : $s; } return $r; } // function normInf() /** * normF * * Frobenius norm * @return float Square root of the sum of all elements squared */ public function normF() { $f = 0; for ($i = 0; $i < $this->m; ++$i) { for ($j = 0; $j < $this->n; ++$j) { $f = hypo($f,$this->A[$i][$j]); } } return $f; } // function normF() /** * Matrix rank * * @return effective numerical rank, obtained from SVD. */ public function rank () { $svd = new SingularValueDecomposition($this); return $svd->rank(); } // function rank () /** * Matrix condition (2 norm) * * @return ratio of largest to smallest singular value. */ public function cond () { $svd = new SingularValueDecomposition($this); return $svd->cond(); } // function cond () /** * trace * * Sum of diagonal elements * @return float Sum of diagonal elements */ public function trace() { $s = 0; $n = min($this->m, $this->n); for($i = 0; $i < $n; ++$i) { $s += $this->A[$i][$i]; } return $s; } // function trace() /** * uminus * * Unary minus matrix -A * @return Matrix Unary minus matrix */ public function uminus() { } // function uminus() /** * plus * * A + B * @param mixed $B Matrix/Array * @return Matrix Sum */ public function plus() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $M->set($i, $j, $M->get($i, $j) + $this->A[$i][$j]); } } return $M; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function plus() /** * plusEquals * * A = A + B * @param mixed $B Matrix/Array * @return Matrix Sum */ public function plusEquals() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $validValues = True; $value = $M->get($i, $j); if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) { $this->A[$i][$j] = trim($this->A[$i][$j],'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]); } if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) { $value = trim($value,'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value); } if ($validValues) { $this->A[$i][$j] += $value; } else { $this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN(); } } } return $this; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function plusEquals() /** * minus * * A - B * @param mixed $B Matrix/Array * @return Matrix Sum */ public function minus() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $M->set($i, $j, $M->get($i, $j) - $this->A[$i][$j]); } } return $M; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function minus() /** * minusEquals * * A = A - B * @param mixed $B Matrix/Array * @return Matrix Sum */ public function minusEquals() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $validValues = True; $value = $M->get($i, $j); if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) { $this->A[$i][$j] = trim($this->A[$i][$j],'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]); } if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) { $value = trim($value,'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value); } if ($validValues) { $this->A[$i][$j] -= $value; } else { $this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN(); } } } return $this; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function minusEquals() /** * arrayTimes * * Element-by-element multiplication * Cij = Aij * Bij * @param mixed $B Matrix/Array * @return Matrix Matrix Cij */ public function arrayTimes() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $M->set($i, $j, $M->get($i, $j) * $this->A[$i][$j]); } } return $M; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function arrayTimes() /** * arrayTimesEquals * * Element-by-element multiplication * Aij = Aij * Bij * @param mixed $B Matrix/Array * @return Matrix Matrix Aij */ public function arrayTimesEquals() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $validValues = True; $value = $M->get($i, $j); if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) { $this->A[$i][$j] = trim($this->A[$i][$j],'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]); } if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) { $value = trim($value,'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value); } if ($validValues) { $this->A[$i][$j] *= $value; } else { $this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN(); } } } return $this; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function arrayTimesEquals() /** * arrayRightDivide * * Element-by-element right division * A / B * @param Matrix $B Matrix B * @return Matrix Division result */ public function arrayRightDivide() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $validValues = True; $value = $M->get($i, $j); if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) { $this->A[$i][$j] = trim($this->A[$i][$j],'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]); } if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) { $value = trim($value,'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value); } if ($validValues) { if ($value == 0) { // Trap for Divide by Zero error $M->set($i, $j, '#DIV/0!'); } else { $M->set($i, $j, $this->A[$i][$j] / $value); } } else { $this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN(); } } } return $M; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function arrayRightDivide() /** * arrayRightDivideEquals * * Element-by-element right division * Aij = Aij / Bij * @param mixed $B Matrix/Array * @return Matrix Matrix Aij */ public function arrayRightDivideEquals() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $this->A[$i][$j] = $this->A[$i][$j] / $M->get($i, $j); } } return $M; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function arrayRightDivideEquals() /** * arrayLeftDivide * * Element-by-element Left division * A / B * @param Matrix $B Matrix B * @return Matrix Division result */ public function arrayLeftDivide() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $M->set($i, $j, $M->get($i, $j) / $this->A[$i][$j]); } } return $M; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function arrayLeftDivide() /** * arrayLeftDivideEquals * * Element-by-element Left division * Aij = Aij / Bij * @param mixed $B Matrix/Array * @return Matrix Matrix Aij */ public function arrayLeftDivideEquals() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $this->A[$i][$j] = $M->get($i, $j) / $this->A[$i][$j]; } } return $M; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function arrayLeftDivideEquals() /** * times * * Matrix multiplication * @param mixed $n Matrix/Array/Scalar * @return Matrix Product */ public function times() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $B = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } if ($this->n == $B->m) { $C = new Matrix($this->m, $B->n); for($j = 0; $j < $B->n; ++$j) { for ($k = 0; $k < $this->n; ++$k) { $Bcolj[$k] = $B->A[$k][$j]; } for($i = 0; $i < $this->m; ++$i) { $Arowi = $this->A[$i]; $s = 0; for($k = 0; $k < $this->n; ++$k) { $s += $Arowi[$k] * $Bcolj[$k]; } $C->A[$i][$j] = $s; } } return $C; } else { throw new Exception(JAMAError(MatrixDimensionMismatch)); } break; case 'array': $B = new Matrix($args[0]); if ($this->n == $B->m) { $C = new Matrix($this->m, $B->n); for($i = 0; $i < $C->m; ++$i) { for($j = 0; $j < $C->n; ++$j) { $s = "0"; for($k = 0; $k < $C->n; ++$k) { $s += $this->A[$i][$k] * $B->A[$k][$j]; } $C->A[$i][$j] = $s; } } return $C; } else { throw new Exception(JAMAError(MatrixDimensionMismatch)); } return $M; break; case 'integer': $C = new Matrix($this->A); for($i = 0; $i < $C->m; ++$i) { for($j = 0; $j < $C->n; ++$j) { $C->A[$i][$j] *= $args[0]; } } return $C; break; case 'double': $C = new Matrix($this->m, $this->n); for($i = 0; $i < $C->m; ++$i) { for($j = 0; $j < $C->n; ++$j) { $C->A[$i][$j] = $args[0] * $this->A[$i][$j]; } } return $C; break; case 'float': $C = new Matrix($this->A); for($i = 0; $i < $C->m; ++$i) { for($j = 0; $j < $C->n; ++$j) { $C->A[$i][$j] *= $args[0]; } } return $C; break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } } else { throw new Exception(PolymorphicArgumentException); } } // function times() /** * power * * A = A ^ B * @param mixed $B Matrix/Array * @return Matrix Sum */ public function power() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } break; case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { $validValues = True; $value = $M->get($i, $j); if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) { $this->A[$i][$j] = trim($this->A[$i][$j],'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]); } if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) { $value = trim($value,'"'); $validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value); } if ($validValues) { $this->A[$i][$j] = pow($this->A[$i][$j],$value); } else { $this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN(); } } } return $this; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function power() /** * concat * * A = A & B * @param mixed $B Matrix/Array * @return Matrix Sum */ public function concat() { if (func_num_args() > 0) { $args = func_get_args(); $match = implode(",", array_map('gettype', $args)); switch($match) { case 'object': if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); } case 'array': $M = new Matrix($args[0]); break; default: throw new Exception(JAMAError(PolymorphicArgumentException)); break; } $this->checkMatrixDimensions($M); for($i = 0; $i < $this->m; ++$i) { for($j = 0; $j < $this->n; ++$j) { // $this->A[$i][$j] = '"'.trim($this->A[$i][$j],'"').trim($M->get($i, $j),'"').'"'; $this->A[$i][$j] = trim($this->A[$i][$j],'"').trim($M->get($i, $j),'"'); } } return $this; } else { throw new Exception(JAMAError(PolymorphicArgumentException)); } } // function concat() /** * chol * * Cholesky decomposition * @return Matrix Cholesky decomposition */ public function chol() { return new CholeskyDecomposition($this); } // function chol() /** * lu * * LU decomposition * @return Matrix LU decomposition */ public function lu() { return new LUDecomposition($this); } // function lu() /** * qr * * QR decomposition * @return Matrix QR decomposition */ public function qr() { return new QRDecomposition($this); } // function qr() /** * eig * * Eigenvalue decomposition * @return Matrix Eigenvalue decomposition */ public function eig() { return new EigenvalueDecomposition($this); } // function eig() /** * svd * * Singular value decomposition * @return Singular value decomposition */ public function svd() { return new SingularValueDecomposition($this); } // function svd() /** * Solve A*X = B. * * @param Matrix $B Right hand side * @return Matrix ... Solution if A is square, least squares solution otherwise */ public function solve($B) { if ($this->m == $this->n) { $LU = new LUDecomposition($this); return $LU->solve($B); } else { $QR = new QRDecomposition($this); return $QR->solve($B); } } // function solve() /** * Matrix inverse or pseudoinverse. * * @return Matrix ... Inverse(A) if A is square, pseudoinverse otherwise. */ public function inverse() { return $this->solve($this->identity($this->m, $this->m)); } // function inverse() /** * det * * Calculate determinant * @return float Determinant */ public function det() { $L = new LUDecomposition($this); return $L->det(); } // function det() /** * Older debugging utility for backwards compatability. * * @return html version of matrix */ public function mprint($A, $format="%01.2f", $width=2) { $m = count($A); $n = count($A[0]); $spacing = str_repeat('&nbsp;',$width); for ($i = 0; $i < $m; ++$i) { for ($j = 0; $j < $n; ++$j) { $formatted = sprintf($format, $A[$i][$j]); echo $formatted.$spacing; } echo "<br />"; } } // function mprint() /** * Debugging utility. * * @return Output HTML representation of matrix */ public function toHTML($width=2) { print('<table style="background-color:#eee;">'); for($i = 0; $i < $this->m; ++$i) { print('<tr>'); for($j = 0; $j < $this->n; ++$j) { print('<td style="background-color:#fff;border:1px solid #000;padding:2px;text-align:center;vertical-align:middle;">' . $this->A[$i][$j] . '</td>'); } print('</tr>'); } print('</table>'); } // function toHTML() } // class Matrix Documentation generated on Tue, 01 Jun 2010 17:05:12 +0200 by phpDocumentor 1.4.3