//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** @author  John Miller
 *  @version 1.1
 *  @date    Sun Jan 11 19:05:20 EST 2015
 *  @see     LICENSE (MIT style license file).
 */

// U N D E R   D E V E L O P M E N T
// FIX: needs improved optimization

package scalation.analytics

import scalation.linalgebra.{Matrix, MatrixD, VectorD}
import scalation.math.IntWithExp._
import scalation.math.DoubleWithExp._
import scalation.plot.Plot
import scalation.util.Error

import RegTechnique._

//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `ExpRegression` class supports exponential regression.  In this case,
 *  'x' is multi-dimensional [1, x_1, ... x_k].  Fit the parameter vector 'b' in the
 *  exponential regression equation
 *  <p>
 *      log (mu (x))  =  b dot x  =  b_0 + b_1 * x_1 + ... b_k * x_k
 *  <p>
 *  @see www.stat.uni-muenchen.de/~leiten/Lehre/Material/GLM_0708/chapterGLM.pdf 
 *  @param x       the data/design matrix
 *  @param nonneg  whether to check that responses are nonnegative
 *  @param y       the response vector
 */
class ExpRegression (x: MatrixD, nonneg: Boolean, y: VectorD)
      extends Predictor with Error
{
    if (x.dim1 != y.dim) flaw ("constructor", "dimensions of x and y are incompatible")
    if (nonneg && ! y.isNonnegative) flaw ("constructor", "response vector y must be nonnegative")

    def ll (b: VectorD): Double = 0.0

    def ll_null (b: VectorD): Double = 0.0

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Train the predictor by fitting the parameter vector (b-vector) in the
     *  regression equation
     *      y  =  b dot x + e  =  [b_0, ... b_k] dot [1, t, t^2 ... t^k] + e
     *  using the least squares method.
     */
    def train () { }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Retrain the predictor by fitting the parameter vector (b-vector) in the
     *  multiple regression equation
     *      yy  =  b dot x + e  =  [b_0, ... b_k] dot [1, t, t^2 ... t^k] + e
     *  using the least squares method.
     *  @param yy  the new response vector
     */
    def train (yy: VectorD) { }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the fit (parameter vector b, quality of fit including rSquared).
     */
    def fit: Tuple4 [VectorD, Double, Double, Double] = null

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Predict the value of y = f(z) by evaluating the formula y = b dot z,
     *  e.g., (b_0, b_1, b_2) dot (1, z_1, z_2).
     *  @param z  the new vector to predict
     */
    def predict (z: VectorD): Double = 0.0

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Predict the value of y = f(z) by evaluating the formula y = b dot zi for
     *  each row zi of matrix z.
     *  @param z  the new matrix to predict
     */
    def predict (z: Matrix): VectorD = null

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Perform backward elimination to remove the least predictive variable
     *  from the model, returning the variable to eliminate, the new parameter
     *  vector, the new R-squared value and the new F statistic.
     */
    def backElim (): Tuple4 [Int, VectorD, Double, Double] = null

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Compute the Variance Inflation Factor (VIF) for each variable to test
     *  for multi-colinearity by regressing xj against the rest of the variables.
     *  A VIF over 10 indicates that over 90% of the varaince of xj can be predicted
     *  from the other variables, so xj is a candidate for removal from the model.
     */
    def vif: VectorD = null

} // ExpRegression class


//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `ExpRegressionTest` object tests `ExpRegression` class using the following
 *  regression equation.
 *  <p>
 *      y  =  b dot x  =  b_0 + b_1*t + b_2*t^2.
 *  <p>
 */
object ExpRegressionTest extends App
{
    val x = new MatrixD ((5, 3), 1.0, 36.0,  66.0,               // 5-by-3 matrix
                                 1.0, 37.0,  68.0,
                                 1.0, 47.0,  64.0,
                                 1.0, 32.0,  53.0,
                                 1.0,  1.0, 101.0)
    val y = VectorD (745.0, 895.0, 442.0, 440.0, 1598.0)
    val z = VectorD (1.0, 20.0, 80.0)

    println ("x = " + x)
    println ("y = " + y)

    val erg = new ExpRegression (x, true, y)
    erg.train ()
    println ("fit = " + erg.fit)

    val yp = erg.predict (z)
    println ("predict (" + z + ") = " + yp)

} // ExpRegressionTest object