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/** @author  John Miller
 *  @version 1.6
 *  @date    Wed Dec 23 14:12:56 EST 2020
 *  @see     LICENSE (MIT style license file).
 *
 *  @title   Simulate a System of Dynamic Equations over Time
 */

package scalation.dynamics

import scala.math.exp

import scalation.linalgebra.{MatriD, MatrixD, VectoD, VectorD}
import scalation.math.double_exp
import scalation.plot.Plot

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/** The `DynamicEq` class may be used for determining trajectories 'x_t' from a
 *  system of dynamic equations.
 *  <p>
 *      x_t = f(t)
 *  <p>
 *  'f(t)' is the vector function of time.
 *  @param f  the vector-valued function of time
 *  @param d  the number of dimensions
 */
class DynamicEq (f: Double => VectoD, d: Int = 2)
      extends Error
{
    def eval (t: Double): VectoD = f(t)

    def trajectory (t0: Double, t1: Double, n: Int): MatriD =
    {
        val traj = new MatrixD (n, d)
        val dt   = (t1 - t0) / n.toDouble
        var t    = t0
        for (i <- 0 until n) {
            traj(i) = f(t)
            t += dt
        } // for
        traj
    } // trajectory

} // DynamicEq class


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/** The `DynamicEqTest` object to test the `DynamicEq` class using example at
 *  in Introduction to Computational Data Science using ScalaTion, section 13.1.
 *  > runMain scalation.dynamics.DynamicEqTest
 */
object DynamicEqTest extends App
{
    val g   = 9.807                                                                // graivational constant
    val mps = 60.0                                                                 // meters per second (mps)
    def f (t: Double): VectorD = VectorD (-0.5 * g * t~^2 + mps * t, -g * t + mps)

    val dyn = new DynamicEq (f)
    val n   = 100
    val te  = 12.0
    val t   = VectorD.range (0, n) * (te / n.toDouble)
    val trj = dyn.trajectory (0.0, te, n) 
    new Plot (t, trj.col(0), trj.col(1), "Plot (x_t0, x_t1) vs. t")

} // DynamicEqTest object