matrix.php

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        if (PEAR::isError($det)) {
            return $det;
        }
        $norm = $this->norm();
        if (PEAR::isError($norm)) {
            return $norm;
        }
        if ($norm == 0) {
            return PEAR::raiseError('Undefined normalized determinant, euclidean norm is zero');
        }
        return abs($det / $norm);
    }/*}}}*/

    /**
     * Returns the index of the row with the maximum value under column of the element e[i][i]
     *
     * @access protected
     * @return an integer
     */
    function _maxElementIndex($r) {/*{{{*/
        $max = 0;
        $idx = -1;
        list($nr, $nc) = $this->getSize();
        $arr = array();
        for ($i=$r; $i<$nr; $i++) {
            $val = abs($this->_data[$i][$r]);
            if ($val > $max) {
                $max = $val;
                $idx = $i;
            }
        }
        if ($idx == -1) {
            $idx = $r;
        }
        return $idx;
    }/*}}}*/

    /**
     * Inverts a matrix using Gauss-Jordan elimination with partial pivoting
     *
     * @access public
     * @return mixed the value of the matrix determinant on success, PEAR_Error otherwise
     * @see scaleRow()
     */
    function invert() {
		if ($this->isEmpty()) {
			return PEAR::raiseError('Matrix has not been populated');
        }
        if (!$this->isSquare()) {
			return PEAR::raiseError('Determinant undefined for non-square matrices');
        }
        $norm = $this->norm();
        $sign = 1;
        $det = 1.0;
        // work on a copy to be safe
        $m = $this->clone();
        list($nr, $nc) = $m->getSize();
        // Unit matrix to use as target
        $q = Math_Matrix::makeUnit($nr);
        for ($i=0; $i<$nr; $i++) {
            $ridx = $this->_maxElementIndex($i);
            if ($i != $ridx) { 
                $sign = -$sign;
                $e = $m->swapRows($i, $ridx);
                if (PEAR::isError($e)) {
                    return $e;
                }
                $e = $q->swapRows($i, $ridx);
                if (PEAR::isError($e)) {
                    return $e;
                }
            }
            $pelement = $m->getElement($i, $i);
            if (PEAR::isError($pelement)) {
                return $pelement;
            }
            if ($pelement == 0) {
                return PEAR::raiseError('Cannot continue inversion, pivoting element is zero');
            }
            $det *= $pelement;
            if ((abs($det)/$norm) < $this->_epsilon) {
                return PEAR::raiseError('Probable singular or ill-conditioned matrix, normalized determinant = '
                        .(abs($det)/$norm));
            }
            $e = $m->scaleRow($i, 1/$pelement);
            if (PEAR::isError($e)) {
                return $e;
            }
            $e = $q->scaleRow($i, 1/$pelement);
            if (PEAR::isError($e)) {
                return $e;
            }
            // zero all column elements execpt for the current one
            $tpelement = $m->getElement($i, $i);
            for ($j=0; $j<$nr; $j++) {
                if ($j == $i) {
                    continue;
                }
                $factor = $m->getElement($j, $i) / $tpelement;
                for ($k=0; $k<$nc; $k++) {
                    $vm = $m->getElement($j, $k) - $factor * $m->getElement($i, $k);
                    $vq = $q->getElement($j, $k) - $factor * $q->getElement($i, $k);
                    $m->setElement($j, $k, $vm);
                    $q->setElement($j, $k, $vq);
                }
            }
            // for debugging
            /*
            echo "COLUMN: $i\n";
            echo $m->toString()."\n";
            echo $q->toString()."\n";
            */
        }
        $data = $q->getData();
        /*
        // for debugging
        echo $m->toString()."\n";
        echo $q->toString()."\n";
        */
        unset($m);
        unset($q);
        $e = $this->setData($data);
        if (PEAR::isError($e)) {
            return $e;
        }
        if ($sign < 0) {
            $det = -$det;
        }
        $this->_det = $det;
        return $det;
    }

    /**
     * Returns a submatrix from the position (row, col), with nrows and ncols
     *
     * @access public
     * @return object Math_Matrix on success, PEAR_Error otherwise
     */
    function &getSubMatrix ($row, $col, $nrows, $ncols) {/*{{{*/
        if (!is_numeric($row) || !is_numeric($col)
            || !is_numeric($nrows) || !is_numeric($ncols)) {
            return PEAR::raiseError('Parameters must be a initial row and column, and number of rows and columns in submatrix');
        }
        list($nr, $nc) = $this->getSize();
        if ($rows + $nrows > $nr) {
            return PEAR::raiseError('Rows in submatrix more than in original matrix');
        }
        if ($cols + $ncols > $nr) {
            return PEAR::raiseError('Columns in submatrix more than in original matrix');
        }
        $data = array();
        for ($i=0; $i < $nrows; $i++) {
            for ($j=0; $j < $ncols; $j++) {
                $data[$i][$j] = $this->getElement($i + $row, $j + $col);
            }
        }
        return new Math_Matrix($data);
    }/*}}}*/
    
    /**
     * Returns a simple string representation of the matrix
     *
     * @param optional string $format a sprintf() format used to print the matrix elements (default = '%6.2f')
     * @return mixed a string on success, PEAR_Error otherwise
     */
    function toString ($format='%6.2f') {/*{{{*/
		if ($this->isEmpty()) {
			return PEAR::raiseError('Matrix has not been populated');
        }
        $out = "";
        for ($i=0; $i < $this->_num_rows; $i++) {
            for ($j=0; $j < $this->_num_cols; $j++) {
                $out .= sprintf($format, $this->_data[$i][$j]);
            }
            $out .= "\n";
        }
        return $out;
    }/*}}}*/
    
    /**
     * Returns an HTML table representation of the matrix elements
     *
     * @access public
     * @return a string on success, PEAR_Error otherwise
     */
    function toHTML() {/*{{{*/
		if ($this->isEmpty()) {
			return PEAR::raiseError('Matrix has not been populated');
        }
        $out = "<table border>\n\t<caption align=\"top\"><b>Matrix</b>";
        $out .= "</caption>\n\t<tr align=\"center\">\n\t\t<th>";
        $out .= $this->_num_rows."x".$this->_num_cols."</th>";
        for ($i=0; $i < $this->_num_cols; $i++) {
            $out .= "<th>".$i."</th>";
        }
        $out .= "\n\t</tr>\n";
        for ($i=0; $i < $this->_num_rows; $i++) {
            $out .= "\t<tr align=\"center\">\n\t\t<th>".$i."</th>";
            for ($j=0; $j < $this->_num_cols; $j++) {
                $out .= "<td bgcolor=\"#ffffdd\">".$this->_data[$i][$j]."</td>";
            }
            $out .= "\n\t</tr>";
        }
        return $out."\n</table>\n";
    }/*}}}*/


    // Binary operations
    
    /**
     * Adds a matrix to this one
     *
     * @param object Math_Matrix $m1
     * @return mixed TRUE on success, PEAR_Error otherwise
     * @see getSize()
     * @see getElement()
     * @see setData()
     */
    function add ($m1) {/*{{{*/
        if (!Math_Matrix::isMatrix($m1)) {
            return PEAR::raiseError("Parameter must be a Math_Matrix object");
        }
        if ($this->getSize() != $m1->getSize()) {
            return PEAR::raiseError("Matrices must have the same dimensions");
        }
        list($nr, $nc) = $m1->getSize();
        $data = array();
        for ($i=0; $i < $nr; $i++) {
            for ($j=0; $j < $nc; $j++) {
                $el1 = $m1->getElement($i,$j);
                if (PEAR::isError($el1)) {
                    return $el1;
                }
                $el = $this->getElement($i,$j);
                if (PEAR::isError($el)) {
                    return $el;
                }
                $data[$i][$j] = $el + $el1;
            }
        }
        if (!empty($data)) {
            return $this->setData($data);
        } else {
            return PEAR::raiseError('Undefined error');
        }
    }/*}}}*/

    /**
     * Substracts a matrix from this one
     *
     * @param object Math_Matrix $m1
     * @return mixed TRUE on success, PEAR_Error otherwise
     * @see getSize()
     * @see getElement()
     * @see setData()
     */
    function sub (&$m1) {/*{{{*/
        if (!Math_Matrix::isMatrix($m1)) {
            return PEAR::raiseError("Parameter must be a Math_Matrix object");
        }
        if ($this->getSize() != $m1->getSize()) {
            return PEAR::raiseError("Matrices must have the same dimensions");
        }
        list($nr, $nc) = $m1->getSize();
        $data = array();
        for ($i=0; $i < $nr; $i++) {
            for ($j=0; $j < $nc; $j++) {
                $el1 = $m1->getElement($i,$j);
                if (PEAR::isError($el1)) {
                    return $el1;
                }
                $el = $this->getElement($i,$j);
                if (PEAR::isError($el)) {
                    return $el;
                }
                $data[$i][$j] = $el - $el1;
            }
        }
        if (!empty($data)) {
            return $this->setData($data);
        } else {
            return PEAR::raiseError('Undefined error');
        }
    }/*}}}*/

    /**
     * Scales the matrix by a given factor
     *
     * @param numeric $scale the scaling factor
     * @return mixed TRUE on success, PEAR_Error otherwise
     * @see getSize()
     * @see getElement()
     * @see setData()
     */
    function scale ($scale) {/*{{{*/
        if (!is_numeric($scale)) {
            return PEAR::raiseError("Parameter must be a number");
        }
        list($nr, $nc) = $this->getSize();
        $data = array();
        for ($i=0; $i < $nr; $i++) {
            for ($j=0; $j < $nc; $j++) {
                $data[$i][$j] = $scale * $this->getElement($i,$j);
            }
        }
        if (!empty($data)) {
            return $this->setData($data);
        } else {
            return PEAR::raiseError('Undefined error');
        }
    }/*}}}*/

    /**
     * Multiplies (scales) a row by the given factor
     *
     * @access public
     * @param integer $row the row index
     * @param numeric $factor the scaling factor
     * @return mixed TRUE on success, a PEAR_Error otherwise
     * @see invert()
     */
    function scaleRow($row, $factor) {/*{{{*/
        if ($this->isEmpty()) {
            return PEAR::raiseError('Uninitialized Math_Matrix object');
        }
        if (!is_integer($row) || !is_numeric($factor)) {
            return PEAR::raiseError('Row index must be an integer, and factor a valid number');
        }
        if ($row >= $this->_num_rows) {
            return PEAR::raiseError('Row index out of bounds');
        }
        $r = $this->getRow($row);
        if (PEAR::isError($r)) {
            return $r;
        }
        $nr = count($r);
        for ($i=0; $i<$nr; $i++) {
            $r[$i] *= $factor;
        }
        return $this->setRow($row, $r);
    }/*}}}*/

    /**
     * Multiplies a matrix by this one
     *
     * @param object Math_Matrix $m1
     * @return mixed TRUE on success, PEAR_Error otherwise
     * @see getSize()
     * @see getRow()
     * @see getCol()
     * @see setData()
     */
    function multiply(&$m1) {/*{{{*/
        $epsilon = 1E-10;
        if (!Math_Matrix::isMatrix($m1)) {
            return PEAR::raiseError ('Wrong parameter, expected a Math_Matrix object');
        }
        list($nr, $nc) = $this->getSize();
        list($nr1, $nc1) = $m1->getSize();
        if ($nc1 != $nr) {
            return PEAR::raiseError('Incompatible sizes columns in matrix must be the same as rows in parameter matrix');
        }
        $data = array();
        for ($i=0; $i < $nr; $i++) {
            for ($j=0; $j < $nc1; $j++) {
                $data[$i][$j] = 0;
                for ($k=0; $k < $nc; $k++) {
                    $data[$i][$j] += $this->getElement($i,$k) * $m1->getElement($k, $j);
                }
                // take care of some round-off errors
                if ($data[$i][$j] <= $epsilon) {
                    $data[$i][$j] = 0.0;
                }