function Matrix() {
}


/**Add two matrixes.
*It can be used to combine multiple transformations into one.
*@param {Array} m1 - first matrix
*@param {Array} m2 - second matrix
*@return {Array} the sum of those 2 matrix
*@see <a href="http://en.wikipedia.org/wiki/Transformation_matrix#Composing_and_inverting_transformations">http://en.wikipedia.org/wiki/Transformation_matrix#Composing_and_inverting_transformations></a>
**/
Matrix.add = function (m1, m2) {
    var mReturn = [];
    if (m1.length == m2.length) {
        for (var row = 0; row < m1.length; row++) {
            mReturn[row] = [];
            for (var column = 0; column < m1[row].length; column++) {
                mReturn[row][column] = m1[row][column] + m2[row][column];
            }
        }
    }
    return mReturn;
};


/**Clones a matrix. Recursivelly
*@param {Array} m - the matrix to clone
*@return {Array} - the clone of orriginal matrix
*@author Alex Gheorghiu <alex@scriptoid.com>
**/
Matrix.clone = function (m) {
    if (typeof (m) == 'undefined' || m == null) {
        return null;
    }

    var mReturn = [];
    for (var i = 0; i < m.length; i++) {
        /*If the element is also an array. As we can not tell if this is an array or object as both array and object return objects
        *we will at least try to see if it's object and if it has some length */
        if (typeof (m) == 'object' && m[i].length) {
            mReturn.push(Matrix.clone(m[i]));
        }
        else {
            mReturn.push(m[i]);
        }
    }
    return mReturn;
};




/**Substract matrix m2 from m1
*@param {Array} m1 - first matrix
*@param {Array} m2 - second matrix
*@return {Array} the m1 - m2 matrix
**/
Matrix.subtract = function (m1, m2) {
    var mReturn = [];
    if (m1.length == m2.length) {
        for (var row = 0; row < m1.length; row++) {
            mReturn[row] = [];
            for (var column = 0; column < m1[row].length; column++) {
                mReturn[row][column] = m1[row][column] - m2[row][column];
            }
        }
    }
    return mReturn;
};


/**Check againsts NaN values
*@param {Array} m - the matrix
*@return {boolean} true - if it contains NaN values, false otherwise
**/
Matrix.isNaN = function (m) {
    for (var row = 0; row < m.length; row++) {
        if (m[row] instanceof Array) {
            for (var column = 0; column < m[row].length; column++) {
                if (isNaN(m[row][column])) {
                    return true;
                }
            }
        }
        else {
            if (isNaN(m[row])) {
                return true;
            }
        }
    }
    return false;
};


/**Multiply matrix m2 with m1
*@param {Array} m1 - first matrix
*@param {Array} m2 - second matrix
*@return {Array} the multiplication of those 2 matrix
*@see <a href="http://en.wikipedia.org/wiki/Matrix_multiplication">http://en.wikipedia.org/wiki/Matrix_multiplication</a>
**/
Matrix.multiply = function (m1, m2) {
    var mReturn = [];
    if (m1[0].length == m2.length) {//check that width=height
        for (var m1Row = 0; m1Row < m1.length; m1Row++) {
            mReturn[m1Row] = [];
            for (var m2Column = 0; m2Column < m2[0].length; m2Column++) {
                mReturn[m1Row][m2Column] = 0
                for (var m2Row = 0; m2Row < m2.length; m2Row++) {
                    mReturn[m1Row][m2Column] += m1[m1Row][m2Row] * m2[m2Row][m2Column];
                }
            }
        }
    }
    return mReturn;
};


/**Multiply matrix m2 with m1
*If you apply a transformation T to a point P the new point is:
*  P' = T x P
*So if you apply more then one transformation (T1, T2, T3) then the new point is:
*  P'= T3 x (T2 x (T1 x P)))
*@return {Array} the equivalent matrix ( of all transformations)
*@see <a href="http://en.wikipedia.org/wiki/Transformation_matrix#Composing_and_inverting_transformations">http://en.wikipedia.org/wiki/Transformation_matrix#Composing_and_inverting_transformations</a>
*@see <a href="http://en.wikipedia.org/wiki/Matrix_multiplication">http://en.wikipedia.org/wiki/Matrix_multiplication</a>
**/
Matrix.mergeTransformations = function () {
    var mReturn = [];

    if (arguments.length > 0) {
        mReturn = Matrix.clone(arguments[arguments.length - 1]);

        for (var m = arguments.length - 2; m >= 0; m--) {
            mReturn = Matrix.multiply(mReturn, arguments[m]);
        }
    }

    return mReturn;
};

/**
* Inverts a matrix
*http://en.wikipedia.org/wiki/Invertible_matrix
**/
Matrix.invertMatrix = function (m) {

};

/**Compares two matrixes
*@param {Array} m1 - first matrix
*@param {Array} m2 - second matrix
*@return {Boolean} true if matrixes are equal , false otherwise
**/
Matrix.equals = function (m1, m2) {
    if (m1.length != m2.length) { //nr or rows not equal
        return false;
    }
    else {
        for (var i in m1) {
            if (m1[i].length != m2[i].length) { //nr or cols not equal
                return false;
                break;
            }
            else {
                for (var j in m1[i]) {
                    if (m1[i][j] != m2[i][j]) {
                        return false;
                        break;
                    }
                }
            }
        }
    }
    return true;
}


/**Creates a clockwise rotation matrix around the origin.
*
*Note: don't use this to rotate a Figure. You must first move it to origin.
*(by using a translation)
*@param {Number} angle - the angle expressed in radians
*@return {Array} - the ready to use rotation matrix
*@see <a href="http://en.wikipedia.org/wiki/Rotation_matrix#In_an_oriented_plane">http://en.wikipedia.org/wiki/Rotation_matrix#In_an_oriented_plane</a>
*@see <a href="http://en.wikipedia.org/wiki/Rotation_matrix">http://en.wikipedia.org/wiki/Rotation_matrix</a>
*@see <a href="http://en.wikipedia.org/wiki/Transformation_matrix#Rotation">http://en.wikipedia.org/wiki/Transformation_matrix#Rotation</a>
**/
Matrix.rotationMatrix = function (angle) {
    var mReturn = [
    [Math.cos(angle), -Math.sin(angle), 0],
    [Math.sin(angle), Math.cos(angle), 0],
    [0, 0, 1]];
    return mReturn;
};


/**Creates a translation matrix
*@param {Number} dx - variation of movement on [Ox axis
*@param {Number} dy - variation of movement on [Oy axis
*@return {Array} - the ready to use translation matrix
**/
Matrix.translationMatrix = function (dx, dy) {
    return [
    [1, 0, dx],
    [0, 1, dy],
    [0, 0, 1]
    ];
};

/**Creates a scale matrix
*@param {Number} sx - scale factor by which the x will be multiply
*@param {Number} sy - scale factor by which the y will be multiply
*@return {Array} - the ready to use scale matrix
*@see <a href="http://en.wikipedia.org/wiki/Transformation_matrix#Scaling">http://en.wikipedia.org/wiki/Transformation_matrix#Scaling</a>
**/
Matrix.scaleMatrix = function (sx, sy) {
    if (sy == null) {
        sy = sx;
    }


    return [
    [sx, 0, 0],
    [0, sy, 0],
    [0, 0, 1]
    ];
    //we should allow a single parameter too, in which case we will have sx = sy
};


/**A ready to use matrix to make a 90 degree rotation.
*It acts like a singleton.
*It's more used for example and testings
**/
Matrix.R90 = [[0, -1, 0], [0, 1, 0], [0, 0, 1]];

/**The identity matrix*/
Matrix.IDENTITY = [[1, 0, 0], [0, 1, 0], [0, 0, 1]];

/**The move up by 1 unit matrix*/
Matrix.UP = [
    [1, 0, 0],
    [0, 1, -1],
    [0, 0, 1]
    ];

/**The move down by 1 unit matrix*/
Matrix.DOWN = [
    [1, 0, 0],
    [0, 1, 1],
    [0, 0, 1]
    ];

/**The move left by 1 unit matrix*/
Matrix.LEFT = [
    [1, 0, -1],
    [0, 1, 0],
    [0, 0, 1]
    ];

/**The move right by 1 unit matrix*/
Matrix.RIGHT = [
    [1, 0, 1],
    [0, 1, 0],
    [0, 0, 1]
    ];