//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** @author  John Miller
 *  @version 1.4
 *  @date    Sun Dec 28 21:52:38 EST 2014
 *  @see     LICENSE (MIT style license file).
 */

package scalation.analytics
package classifier

import scala.math.{exp, log}

import scalation.linalgebra.{MatriD, MatrixD, VectoD, VectorD, VectoI, VectorI}
import scalation.minima.QuasiNewton
import scalation.plot.Plot
import scalation.util.banner

import ActivationFun.sigmoid

//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `SimpleLogisticRegression` class supports (binomial) logistic regression.
 *  In this case, 'x' is two-dimensional '[1, x_1]'.  Fit the parameter vector
 *  'b' in the logistic regression equation
 *  <p>
 *      logit (p_y)  =  b dot x + e  =  b_0 + b_1 * x_1 + e
 *  <p>
 *  where 'e' represents the residuals (the part not explained by the model)
 *  and 'y' is now binary.
 *  @see see.stanford.edu/materials/lsoeldsee263/05-ls.pdf
 *  @param x   the input/design matrix augmented with a first column of ones
 *  @param y   the binary response vector, y_i in {0, 1}
 *  @param fn  the names for all features/variables
 *  @param cn  the names for both classes
 */
class SimpleLogisticRegression (x: MatriD, y: VectoI, fn: Array [String] = Array ("one", "x1"),
                                cn: Array [String] = Array ("no", "yes"))
      extends ClassifierReal (x, y, fn, 2, cn)
{
    if (y != null && x.dim1 != y.dim) flaw ("constructor", "dimensions of x and y are incompatible")

    private val DEBUG      = false                    // debug flag
    private val k          = x.dim2 - 1               // number of variables 
    private val r_df       = (n-1.0) / (n-k-1.0)      // ratio of degrees of freedom
    private var b: VectoD  = null                     // parameter vector (b_0, b_1, ... b_k)
    private var n_dev      = -1.0                     // null dev: -2l, for null model (intercept only)
    private var r_dev      = -1.0                     // residual dev: -2l, for full model
    private var aic        = -1.0                     // Akaike’s Information Criterion
    private var pseudo_rSq = -1.0                     // McFaffen's pseudo R-squared

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** For a given parameter vector 'b', compute '-2 * Log-Likelihood (-2l)'.
     *  '-2l' is the standard measure that follows a Chi-Square distribution. 
     *  @see www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf
     *  @see www.statisticalhorizons.com/wp-content/uploads/Allison.StatComp.pdf
     *  @param b  the parameters to fit
     */
    def ll (b: VectoD): Double =
    {
        var sum = 0.0
        var bx  = 0.0                                       // beta
        for (i <- y.range) {
            bx = b(0) + b(1) * x(i, 1)
            println (s"i: ${1.0 + exp (bx)}")
            println (s"i: ${y(i) * bx} \t ${log (1.0 + exp (bx))}")
//          sum += y(i) * bx - log (1.0 + exp (bx))
            sum += y(i) * bx - bx - log (exp (-bx) + 1.0)   // less prone to overflow (infinity)
        } // for
        -2.0 * sum                                          // set up for minimization
    } // ll
   
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** For a given parameter vector 'b = [b(0)]', compute '-2 * Log-Likelihood (-2l)'.
     *  '-2l' is the standard measure that follows a Chi-Square distribution. 
     *  @see www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf
     *  @see www.statisticalhorizons.com/wp-content/uploads/Allison.StatComp.pdf
     *  @param b  the parameters to fit
     */
    def ll_null (b: VectoD): Double =
    {
        var sum = 0.0
        val bx = b(0)                                       // only use the intercept
        for (i <- y.range) {
//          sum += y(i) * bx - log (1.0 + exp (bx))
            sum += y(i) * bx - bx - log (exp (-bx) + 1.0)   // less prone to overflow (infinity)
        } // for
        -2.0 * sum                                          // set up for minimization
    } // ll_null

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** For the full model, train the classifier by fitting the parameter vector
     *  (b-vector) in the logistic regression equation using maximum likelihood.
     *  Do this by minimizing '-2l'.
     *  FIX: Use improved BFGS implementation or IRWLS
     *  @see stats.stackexchange.com/questions/81000/calculate-coefficients-in-a-logistic-regression-with-r
     *  @see en.wikipedia.org/wiki/Iteratively_reweighted_least_squares
     *  @param itest  the indices of test data
     */
    def train (itest: IndexedSeq [Int]): SimpleLogisticRegression =     // FIX - use these parameters
    {
        train_null ()
        val b0   = new VectorD (x.dim2)        // use b_0 = 0 for starting guess for parameters
        val bfgs = new QuasiNewton (ll)        // minimizer for -2l
        b     = bfgs.solve (b0)                // find optimal solution for parameters

        r_dev = ll (b)                         // measure of fitness for full model
        aic   = r_dev + 2.0 * x.dim2
        this
    } // train

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** For the null model, train the classifier by fitting the parameter vector
     *  (b-vector) in the logistic regression equation using maximum likelihood.
     *  Do this by minimizing -2l.
     */
    def train_null ()
    {
        val b0   = new VectorD (x.dim2)        // use b0 = 0 for starting guess for parameters
        val bfgs = new QuasiNewton (ll_null)   // minimizer for -2l
        val b_n = bfgs.solve (b0)              // find optimal solution for parameters

        n_dev   = ll_null (b_n)                // measure of fitness for null model
    } // train_null

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the vector of coefficient/parameter values.
     */
    def coefficient: VectoD = b

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the quality of fit.  Assumes both 'train_null' and 'train' have
     *  already been called.
     *  @param y   the actual class labels
     *  @param yp  the predicted class labels
     *  @param k   the number of class labels
     */
    override def fit (y: VectoI, yp: VectoI, k: Int = 2): VectoD = 
    {
        pseudo_rSq = 1.0 - r_dev / n_dev
        super.fit (y, yp) ++ VectorD (n_dev, r_dev, aic, pseudo_rSq)
    } // fit

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the labels for the fit.  Override when necessary.
     */
    override def fitLabel: Seq [String] = super.fitLabel ++ Seq ("n_dev", "r_dev", "aic", "pseudo_rSq")

    val index_prSq = 7                                        // index of pseudo_rSq

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Classify the value of 'y = f(z)' by evaluating the formula 'y = sigmoid (b dot z)'.
     *  Return the best class, its name and quality metric
     *  @param z  the new vector to classify
     */
    override def classify (z: VectoD): (Int, String, Double) =
    {
        val c = if (sigmoid (b dot z) > 0.5) 1 else 0
        (c, cn(c), -1.0)                                    // Fix - need metric
    } // classify

    //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Reset or re-initialize the frequency tables and the probability tables.
     */
    def reset () { /* Not Applicable */ }

} // SimpleLogisticRegression class


//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `SimpleLogisticRegression` companion object provide factory methods.
 */
object SimpleLogisticRegression
{
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a `SimpleLogisticRegression` object. 
     *  @param x1  the vector of values for the predictor
     *  @param y   the binary response vector, y_i in {0, 1}
     *  @param fn  the names for all factors
     *  @param cn  the names for both classes
     */
    def apply (x1: VectorD, y: VectorI, fn: Array [String] = Array ("one", "x1"),
               cn: Array [String] = Array ("no", "yes")): SimpleLogisticRegression =
    {
        new SimpleLogisticRegression (MatrixD.++^ (VectorD.one (x1.dim), x1), y, fn, cn)
    } // apply

} // SimpleLogisticRegression object


//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `SimpleLogisticRegressionTest` object tests the `SimpleLogisticRegression` class
 *  on the mtcars dataseet.
 *  @see www.cookbook-r.com/Statistical_analysis/Logistic_regression/
 *  Answer: b = (-8.8331, 0.4304),
 *          n_dev = 43.860, r_dev = 25.533, aic = 29.533, pseudo_rSq = 0.4178
 *  > runMain scalation.analytics.classifier.SimpleLogisticRegressionTest
 */
object SimpleLogisticRegressionTest extends App
{
    // 32 data points:            One    Mpg
    val x = new MatrixD ((32, 2), 1.0,  21.0,        //  1 - Mazda RX4 
                                  1.0,  21.0,        //  2 - Mazda RX4 Wa
                                  1.0,  22.8,        //  3 - Datsun 710
                                  1.0,  21.4,        //  4 - Hornet 4 Drive
                                  1.0,  18.7,        //  5 - Hornet Sportabout
                                  1.0,  18.1,        //  6 - Valiant
                                  1.0,  14.3,        //  7 - Duster 360
                                  1.0,  24.4,        //  8 - Merc 240D 
                                  1.0,  22.8,        //  9 - Merc 230
                                  1.0,  19.2,        // 10 - Merc 280
                                  1.0,  17.8,        // 11 - Merc 280C
                                  1.0,  16.4,        // 12 - Merc 450S
                                  1.0,  17.3,        // 13 - Merc 450SL
                                  1.0,  15.2,        // 14 - Merc 450SLC
                                  1.0,  10.4,        // 15 - Cadillac Fleetwood
                                  1.0,  10.4,        // 16 - Lincoln Continental
                                  1.0,  14.7,        // 17 - Chrysler Imperial
                                  1.0,  32.4,        // 18 - Fiat 128
                                  1.0,  30.4,        // 19 - Honda Civic
                                  1.0,  33.9,        // 20 - Toyota Corolla
                                  1.0,  21.5,        // 21 - Toyota Corona
                                  1.0,  15.5,        // 22 - Dodge Challenger
                                  1.0,  15.2,        // 23 - AMC Javelin
                                  1.0,  13.3,        // 24 - Camaro Z28
                                  1.0,  19.2,        // 25 - Pontiac Firebird
                                  1.0,  27.3,        // 26 - Fiat X1-9
                                  1.0,  26.0,        // 27 - Porsche 914-2
                                  1.0,  30.4,        // 28 - Lotus Europa
                                  1.0,  15.8,        // 29 - Ford Pantera L
                                  1.0,  19.7,        // 30 - Ferrari Dino
                                  1.0,  15.0,        // 31 - Maserati Bora
                                  1.0,  21.4)        // 32 - Volvo 142E

    // V/S (e.g., V-6 vs. I-4)
    val y = VectorI (0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0,
                     0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1)

    var z: VectoD = null

    println ("x = " + x)

    val fn = Array ("One", "Mpg")

    val lrg = new SimpleLogisticRegression (x, y, fn)
//  lrg.train_null ()                                    // train based on null model
    lrg.train ()                                         // train based on full model

    banner ("Simple Logistic Regression Results")
    println ("b = " + lrg.coefficient)

    val yp = lrg.classify (x)
    println ("y  = " + y)
    println ("yp = " + yp)
    println (lrg.fitLabel)
    println (lrg.fit (y, yp))

    z = VectorD (1.0, 15.0)                              // classify point z
    println ("classify (" + z + ") = " + lrg.classify (z))

    z = VectorD (1.0, 30.0)                              // classify point z
    println ("classify (" + z + ") = " + lrg.classify (z))

    println ("acc = " + lrg.crossValidate (10, true))

    for (b_0 <- -9.0 to -8.0 by 0.1; b_1 <- 0.0 to 1.0 by 0.1) {
        val b = VectorD (b_0, b_1)
        println (s"ll ($b) = ${lrg.ll (b)}")
    } // for

    new Plot (x.col(1), y.toDouble, yp.toDouble)

} // SimpleLogisticRegressionTest object


//:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `SimpleLogisticRegressionTest2` object tests the `SimpleLogisticRegression` class.
 *  @see www.cookbook-r.com/Statistical_analysis/Logistic_regression/
 *  Answer: b = (-8.8331, 0.4304),
 *          n_dev = 43.860, r_dev = 25.533, aic = 29.533, pseudo_rSq = 0.4178
 *  > runMain scalation.analytics.classifier.SimpleLogisticRegressionTest2
 */
object SimpleLogisticRegressionTest2 extends App
{
    // Mpg
    val x1 = VectorD (21.0, 21.0, 22.8, 21.4, 18.7, 18.1, 14.3, 24.4, 22.8, 19.2, 17.8, 16.4, 17.3, 15.2, 10.4, 10.4,
                      14.7, 32.4, 30.4, 33.9, 21.5, 15.5, 15.2, 13.3, 19.2, 27.3, 26.0, 30.4, 15.8, 19.7, 15.0, 21.4)

    // V/S (e.g., V-6 vs. I-4)
    val y = VectorI (0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0,
                     0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1)

    val lrg = SimpleLogisticRegression (x1, y)
//  lrg.train_null ()                                    // train based on null model
    lrg.train ()                                         // train based on full model

    banner ("Simple Logistic Regression Results")
    println ("b = " + lrg.coefficient)

    val xx = new MatrixD (x1.dim, 1)
    for (i <- x1.range) xx(i) = VectorD (x1(i))
    val yp = lrg.classify (xx)
    println ("y  = " + y)
    println ("yp = " + yp)
    println (lrg.fitLabel)
    println (lrg.fit (y, yp))

    val srg = SimpleRegression (x1, y.toDouble)
    srg.train ().eval ()
    println (srg.fitLabel)
    println (srg.fit)

} // SimpleLogisticRegressionTest2


//::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `SimpleLogisticRegressionTest3` is used to test the `SimpleLogisticRegression` class.
 *  @see people.revoledu.com/kardi/tutorial/LDA/Numerical%20Example.html
 *  > runMain scalation.analytics.classifier.SimpleLogisticRegressionTest3
 */
object SimpleLogisticRegressionTest3 extends App
{
    // features/variable:
    // x1: curvature
    //                 x1
    val x = VectorD (2.95, 2.53, 3.57, 3.16, 2.58, 2.16, 3.27)
    val y = VectorI (   0,    0,    0,    0,    1,    1,    1)
    val xm = new MatrixD (x.dim, 2)
    xm.setCol(0, VectorD.one (x.dim))
    xm.setCol(1, x)

    val k  = 2                                                 // number of classes
    val fn = Array ("curvature")                               // feature name
    val cn = Array ("pass", "fail")                            // class names
    val lrg = new SimpleLogisticRegression (xm, y, fn, cn)     // create SimpleLogisticRegression classifier
    lrg.train ()
    println ("b = " + lrg.coefficient)

    banner ("classify")
    val z  = VectorD (1.0, 2.81)
    println (s"classify ($z) = ${lrg.classify (z)}")

    banner ("test")
    val xx = new MatrixD (x.dim, 1)
    for (i <- x.range) xx(i) = VectorD (x(i))
    val yp = lrg.classify (xm)
    println (lrg.fitLabel)
    println (lrg.fit (y, yp))

    val t = VectorD.range (0, x.dim)
    new Plot (t, y.toDouble, yp.toDouble, "y(black)/yp(red) vs. t")
    new Plot (x, y.toDouble, yp.toDouble, "y(black)/yp(red) vs. x")

    banner ("log-likelihood")
    val b1 = VectorD (1, -1)
    val b2 = VectorD (5, -2)
    println (s"ll ($b1) =${lrg.ll (b1)}") 
    println (s"ll ($b2) =${lrg.ll (b2)}") 

} // SimpleLogisticRegressionTest3