//::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** @author  John Miller
 *  @version 1.3
 *  @date    Tue Feb  2 15:55:24 EST 2016
 *  @see     LICENSE (MIT style license file).
 */

//  U N D E R   D E V E L O P M E N T

// Issue 1 - thread-safety with minimal performance hit
// Issue 2 - make all methods parallel
// Issue 3 - move to .par package and integrate with the rest of code

package scalation.linalgebra.par

import scala.collection.{breakOut, Traversable}
import scala.collection.mutable.{IndexedSeq, WrappedArray}
import scala.util.Sorting.quickSort

import math.{abs => ABS, max => MAX, sqrt}

import scalation.linalgebra.{MatriD, VectoD, VectorI, VectorL}
import scalation.math.double_exp
import scalation.util.Error
import scalation.util.SortingD.{iqsort, qsort2}

//::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `VectorD` class stores and operates on Numeric Vectors of base type `Double`.
 *  It follows the framework of `gen.VectorN [T]` and is provided for performance.
 *  This is the parallel version.
 *  @param dim  the dimension/size of the vector
 *  @param v    the 1D array used to store vector elements
 */
class VectorD (val dim: Int,
     protected var v:   Array [Double] = null)
      extends VectoD
//    extends Traversable [Double] with PartiallyOrdered [VectorD] with Vec with Error with Serializable
{
    if (v == null) {
        v = Array.ofDim [Double] (dim)
    } else if (dim != v.length) {
        flaw ("constructor", "dimension is wrong")
    } // if

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Construct a vector from an array of values.
     *  @param u  the array of values
     */
    def this (u: Array [Double]) { this (u.length, u) }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Construct a vector and assign values from vector 'u'.
     *  @param u  the other vector
     */
    def this (u: VectorD)
    {
        this (u.dim)                               // invoke primary constructor
        for (i <- range.par) v(i) = u(i)
    } // constructor

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create an exact copy of 'this' vector.
     */
    def copy: VectorD = new VectorD (this)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a zero vector (all elements are zero) of length 'size'.
     *  @param size  the number of elements in the vector
     */
    def zero (size: Int = dim): VectorD = new VectorD (size)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a one vector (all elements are one) of length 'size'.
     *  @param size  the number of elements in the vector
     */
    def one (size: Int = dim): VectorD = new VectorD (size, Array.fill (size)(1.0))

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Expand the size (dim) of 'this' vector by 'more' elements.
     *  @param more  the number of new elements to add
     */
    def expand (more: Int = dim): VectorD =
    {
        if (more < 1) this       // no change
        else          new VectorD (dim + more, Array.concat (v, new Array [Double] (more)))
    } // expand

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a vector of the form (0, ... 1, ... 0) where the 1 is at position j.
     *  @param j     the position to place the 1
     *  @param size  the size of the vector (upper bound = size - 1)
     */
    def oneAt (j: Int, size: Int = dim): VectorD =
    {
        val c = new VectorD (size)
        c.v(j) = 1.0
        c
    } // oneAt

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a vector of the form (0, ... -1, ... 0) where the -1 is at position j.
     *  @param j     the position to place the -1
     *  @param size  the size of the vector (upper bound = size - 1)
     */
    def _oneAt (j: Int, size: Int = dim): VectorD =
    {
        val c = new VectorD (size)
        c.v(j) = -1.0
        c
    } // _oneAt

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Convert 'this' `VectorD` into a `VectorI`.
     */
    def toInt: VectorI =
    {
        val c = new VectorI (dim)
        for (i <- range.par) c(i) = v(i).toInt
        c
    } // toInt

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Convert 'this' `VectorD` into a `VectorL`.
      */
    def toLong: VectorL =
    {
        val c = new VectorL (dim)
        for (i <- range.par) c(i) = v(i).toLong
        c
    } // toLong

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Convert 'this' `VectorD` into a `VectorD`.
     */
    def toDouble: VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c(i) = v(i).toDouble
        c
    } // toDouble

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Convert 'this' `VectoD` into a dense `VectorD`.
     */
    def toDense: scalation.linalgebra.VectorD = null   // FIX

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Get 'this' vector's element at the 'i'-th index position. 
     *  @param i  the given index
     */
    def apply (i: Int): Double = v(i)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Get 'this' vector's elements within the given range (vector slicing).
     *  @param r  the given range
     */
    def apply (r: Range): VectorD = slice (r.start, r.end)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Get 'this' vector's entire array.
     */
    def apply (): WrappedArray [Double] = v

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Set 'this' vector's element at the 'i'-th index position. 
     *  @param i  the given index
     *  @param x  the value to assign
     */
    def update (i: Int, x: Double) { v(i) = x }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Set 'this' vector's elements over the given range (vector slicing).
     *  @param r  the given range
     *  @param x  the value to assign
     */
    def update (r: Range, x: Double) { for (i <- r) v(i) = x }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Set 'this' vector's elements over the given range (vector slicing).
     *  @param r  the given range
     *  @param u  the vector to assign
     */
    def update (r: Range, u: VectoD) { for (i <- r) v(i) = u(i - r.start) }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Set each value in 'this' vector to 'x'.
     *  @param x  the value to be assigned
     */
    def set (x: Double) { for (i <- range.par) v(i) = x }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Set the values in 'this' vector to the values in sequence 'u'.
     *  @param u  the sequence of values to be assigned
     */
    def set (u: Seq [Double]) { for (i <- range.par) v(i) = u(i) }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Iterate over 'this' vector element by element.
     *  @param f  the function to apply
     */
    def foreach [U] (f: Double => U)
    {
        var i = 0    
        while (i < dim) { f (v(i)); i += 1 }
    } // foreach

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Filter the elements of 'this' vector based on the predicate 'p', returning
     *  a new vector.
     *  @param p  the predicate (Boolean function) to apply
     */
    override def filter (p: Double => Boolean): VectorD = VectorD (v.filter (p))

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Filter the elements of 'this' vector based on the predicate 'p', returning
     *  the index positions.
     *  @param p  the predicate (Boolean function) to apply
     */
    def filterPos (p: Double => Boolean): IndexedSeq [Int] =
    {
        (for (i <- range if p (v(i))) yield i) (breakOut)
    } // filterPos

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Map the elements of 'this' vector by applying the mapping function 'f'.
     *  @param f  the function to apply
     */
    def map (f: Double => Double): VectorD = new VectorD (v.map (f))

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Slice 'this' vector 'from' to 'end'.
     *  @param from  the start of the slice (included)
     *  @param till  the end of the slice (excluded)
     */
    override def slice (from: Int, till: Int): VectorD = new VectorD (till - from, v.slice (from, till))

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Select a subset of elements of 'this' vector corresponding to a 'basis'.
     *  @param basis  the set of index positions (e.g., 0, 2, 5)
     */
    def select (basis: Array [Int]): VectorD =
    {
        val c = new VectorD (basis.length)
        for (i <- c.range.par) c.v(i) = v(basis(i))
        c
    } // select

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Concatenate 'this' vector and vector' b'.
     *  @param b  the vector to be concatenated
     */
    def ++ (b: VectoD): VectorD =
    {
        val c = new VectorD (dim + b.dim)
        for (i <- c.range.par) c.v(i) = if (i < dim) v(i) else b(i - dim)
        c
    } // ++

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Concatenate 'this' vector and scalar 's'.
     *  @param s  the scalar to be concatenated
     */
    def ++ (s: Double): VectorD =
    {
        val c = new VectorD (dim + 1)
        for (i <- c.range.par) c.v(i) = if (i < dim) v(i) else s
        c
    } // ++

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Add 'this' vector and vector 'b'.
     *  @param b  the vector to add
     */
    def + (b: VectoD): VectorD = 
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) + b(i)
        c
    } // +

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Add 'this' vector and scalar 's'.
     *  @param s  the scalar to add
     */
    def + (s: Double): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) + s
        c
    } // +
 
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Add 'this' vector and scalar 's._2' only at position 's._1'.
     *  @param s  the (position, scalar) to add
     */
    def + (s: Tuple2 [Int, Double]): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = if (i == s._1) v(i) + s._2 else v(i)
        c
    } // +

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Add in-place 'this' vector and vector 'b'.
     *  @param b  the vector to add
     */
    def += (b: VectoD): VectorD = { for (i <- range.par) v(i) += b(i); this }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Add in-place 'this' vector and scalar 's'.
     *  @param s  the scalar to add
     */
    def += (s: Double): VectorD = { for (i <- range.par) v(i) += s; this }
 
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the negative of 'this' vector (unary minus).
     */
    def unary_- (): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = -v(i)
        c
    } // unary_-
 
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** From 'this' vector subtract vector 'b'.
     *  @param b  the vector to subtract
     */
    def - (b: VectoD): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) - b(i)
        c
    } // -
 
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** From 'this' vector subtract scalar 's'.
     *  @param s  the scalar to subtract
     */
    def - (s: Double): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) - s
        c
    } // -

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** From 'this' vector subtract scalar 's._2' only at position 's._1'.
     *  @param s  the (position, scalar) to subtract
     */
    def - (s: Tuple2 [Int, Double]): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = if (i == s._1) v(i) - s._2 else v(i)
        c
    } // -

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** From 'this' vector subtract in-place vector 'b'.
     *  @param b  the vector to add
     */
    def -= (b: VectoD): VectorD = { for (i <- range.par) v(i) -= b(i); this }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** From 'this' vector subtract in-place scalar 's'.
     *  @param s  the scalar to add
     */
    def -= (s: Double): VectorD = { for (i <- range.par) v(i) -= s; this }
 
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Multiply 'this' vector by vector 'b'.
     *  @param b  the vector to multiply by
     */
    def * (b: VectoD): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) * b(i)
        c
    } // *

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Multiply 'this' vector by scalar 's'.
     *  @param s  the scalar to multiply by
     */
    def * (s: Double): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) * s
        c
    } // *

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Multiply 'this' (row) vector by matrix 'm'.
     *  @param m  the matrix to multiply by
     */
    def * (m: MatriD): VectorD = null  // m.t * this        // FIX

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Multiply in-place 'this' vector and vector 'b'.
     *  @param b  the vector to add
     */
    def *= (b: VectoD): VectorD = { for (i <- range.par) v(i) *= b(i); this }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Multiply in-place 'this' vector and scalar 's'.
     *  @param s  the scalar to add
     */
    def *= (s: Double): VectorD = { for (i <- range.par) v(i) *= s; this }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Divide 'this' vector by vector 'b' (element-by-element).
     *  @param b  the vector to divide by
     */
    def / (b: VectoD): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) / b(i)
        c
    } // /

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Divide 'this' vector by scalar 's'.
     *  @param s  the scalar to divide by
     */
    def / (s: Double): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) / s
        c
    } // /

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Divide in-place 'this' vector and vector 'b'.
     *  @param b  the vector to add
     */
    def /= (b: VectoD): VectorD = { for (i <- range.par) v(i) /= b(i); this }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Divide in-place 'this' vector and scalar 's'.
     *  @param s  the scalar to add
     */
    def /= (s: Double): VectorD = { for (i <- range.par) v(i) /= s; this }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the vector containing each element of 'this' vector raised to the
     *  s-th power.
     *  @param s  the scalar exponent
     */
    def ~^ (s: Double): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = v(i) ~^ s
        c
    } // ~^

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Raise each element of 'this' vector to the 's'-th power.
     *  @param s  the scalar exponent
     */
    def ~^= (s: Double): VectorD = { for (i <- range.par) v(i) = v(i) ~^ s; this }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the vector containing the reciprocal of each element of 'this' vector.
     */
    def recip: VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = 1.0 / v(i)
        c
    } // recip

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the vector that is the element-wise absolute value of 'this' vector.
     */
    def abs: VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = ABS (v(i))
        c
    } // abs

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Sum the elements of 'this' vector.
     */
    def sum: Double = v.foldLeft (0.0)((s, x) => s + x)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Sum the absolute value of the elements of 'this' vector.
     */
    def sumAbs: Double = v.foldLeft (0.0)((s, x) => s + ABS (x))

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Sum the elements of 'this' vector skipping the 'i'-th element (Not Equal 'i').
     *  @param i  the index of the element to skip
     */
    def sumNE (i: Int): Double = sum - v(i)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Sum the positive (> 0) elements of 'this' vector.
     */
    def sumPos: Double = v.foldLeft (0.0)((s, x) => s + MAX (x, 0.0))

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Establish the rank order of the elements in 'self' vector, e.g.,
     *  (8.0, 2.0, 4.0, 6.0) is (3, 0, 1, 2).
     */
    def rank: VectorI = VectorI (iqsort (v))

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Cumulate the values of 'this' vector from left to right (e.g., create a
     *  CDF from a pmf).  Example: (4, 2, 3, 1) --> (4, 6, 9, 10)
     */
    def cumulate: VectorD =
    {
        val c = new VectorD (dim)
        var sum = 0.0
        for (i <- range) { sum += v(i); c.v(i) = sum }         // FIX - make parallel
        c
    } // cumulate

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Normalize 'this' vector so that it sums to one (like a probability vector).
     */
    def normalize: VectorD = this * (1.0 / sum)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Normalize 'this' vector so its length is one (unit vector).
     */
    def normalizeU: VectorD = this * (1.0 / norm)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Normalize 'this' vector to have a maximum of one.
     */
    def normalize1: VectorD = this * (1.0 / max ())

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Compute the dot product (or inner product) of 'this' vector with vector 'b'.
     *  @param b  the other vector
     */
    def dot (b: VectoD): Double =
    {
        var sum = 0.0
        for (i <- range) sum += v(i) * b(i)
        sum
    } // dot

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Compute the dot product (or inner product) of vector 'b' and vector 'c'.
     *  It takes the dot product on a subrange from 'i' (inclusive) to 'j' exclusive.
     *  @param b  the first vector
     *  @param c  the second vector
     *  @param i  the start of the subrange (inclusive)
     *  @param j  the end of the subrange (exclusive)
     */
    def dot (b: VectorD, c: VectorD, i: Int, j: Int): Double =
    {
        var sum = 0.0
        for (k <- i until j) sum += b.v(k) * c.v(k)
        sum
    } // dot

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Compute the dot product (or inner product) of 'this' vector with vector 'b'.
     *  This is the parallel version.
     *  @param b  the other vector
     */
    def dotp (b: VectorD): Double =
    {
        import VectorD._
        val nn = dim / PAR_LEVEL
        val dt = makeThreads ()
        for (i <- dt.indices) {
            dt(i) = new VecThread (this, b, i * nn, (i+1)*nn min dim, dot)
            dt(i).start ()
        } // for

        await ()
        dt.foldLeft (0.0)((s, x) => s + x.result)
    } // dotp

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Compute the Manhattan norm (1-norm) of 'this' vector.
     */
    def norm1: Double = 
    {
        var sum = 0.0
        for (i <- range) sum += ABS (v(i))           // FIX - make parallel
        sum
    } // norm1

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Find the maximum element in 'this' vector.
     *  @param e  the ending index (exclusive) for the search
     */
    def max (e: Int = dim): Double =
    {
        var x = v(0)
        for (i <- 1 until e if v(i) > x) x = v(i)
        x
    } // max

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Take the maximum of 'this' vector with vector 'b' (element-by element).
     *  @param b  the other vector
     */
    def max (b: VectoD): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = if (b(i) > v(i)) b(i) else v(i)
        c
    } // max

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Find the minimum element in 'this' vector.
     *  @param e  the ending index (exclusive) for the search
     */
    def min (e: Int = dim): Double =
    {
        var x = v(0)
        for (i <- 1 until e if v(i) < x) x = v(i)
        x
    } // max

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Take the minimum of 'this' vector with vector 'b' (element-by element).
     *  @param b  the other vector
     */
    def min (b: VectoD): VectorD =
    {
        val c = new VectorD (dim)
        for (i <- range.par) c.v(i) = if (b(i) < v(i)) b(i) else v(i)
        c
    } // min

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Find the argument maximum of 'this' vector (index of maximum element).
     *  @param e  the ending index (exclusive) for the search
     */
    def argmax (e: Int = dim): Int =
    {
        var j = 0
        for (i <- 1 until e if v(i) > v(j)) j = i
        j
    } // argmax

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Find the argument maximum of 'this' vector (index of maximum element).
     *  @param s  the starting index (inclusive) for the search
     *  @param e  the ending index (exclusive) for the search
     */
    def argmax (s: Int, e: Int): Int =
    {
        var j = s
        for (i <- s+1 until e if v(i) > v(j)) j = i
        j
    } // argmax

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Find the argument minimum of 'this' vector (index of minimum element).
     *  @param e  the ending index (exclusive) for the search
     */
    def argmin (e: Int = dim): Int =
    {
        var j = 0
        for (i <- 1 until e if v(i) < v(j)) j = i
        j
    } // argmin

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Find the argument mainmum of 'this' vector (index of minimum element).
     *  @param s  the starting index (inclusive) for the search
     *  @param e  the ending index (exclusive) for the search
     */
    def argmin (s: Int, e: Int): Int =
    {
        var j = s
        for (i <- s+1 until e if v(i) < v(j)) j = i
        j
    } // arginm

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the argument minimum of 'this' vector (-1 if its not negative).
     *  @param e  the ending index (exclusive) for the search
     */
    def argminNeg (e: Int = dim): Int =
    {
        val j = argmin (e); if (v(j) < 0.0) j else -1
    } // argmaxNeg

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the argument maximum of 'this' vector (-1 if its not positive).
     *  @param e  the ending index (exclusive) for the search
     */
    def argmaxPos (e: Int = dim): Int =
    {
        val j = argmax (e); if (v(j) > 0.0) j else -1
    } // argmaxPos

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the index of the first negative element in 'this' vector (-1 otherwise).
     *  @param e  the ending index (exclusive) for the search
     */
    def firstNeg (e: Int = dim): Int =
    {
        for (i <- 0 until e if v(i) < 0.0) return i; -1
    } // firstNeg

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the index of the first positive element in 'this' vector (-1 otherwise).
     *  @param e  the ending index (exclusive) for the search
     */
    def firstPos (e: Int = dim): Int =
    {
        for (i <- 0 until e if v(i) > 0.0) return i; -1
    } // firstPos

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return the index of the first occurrence of element 'x' in 'this' vector,
     *  or -1 if not found.
     *  @param x  the given element
     *  @param e  the ending index (exclusive) for the search
     */
    def indexOf (x: Double, e: Int = dim): Int =
    {
        for (i <- 0 until e if v(i) == x) return i; -1
    } // indexOf

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Find and return index of first element satisfying predicate 'p', or
     *  -1 if not found.
     *  @param p  the predicate to check
     */
    def indexWhere (p: (Double) => Boolean): Int = v.indexWhere (p)

    //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Count the number of strictly negative elements in 'this' vector.
     */
    def countNeg: Int =
    {
        var count = 0
        for (i <- 0 until dim if v(i) < 0.0) count += 1
        count
    } // countNeg

    //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Count the number of strictly positive elements in 'this' vector.
     */
    def countPos: Int =
    {
        var count = 0
        for (i <- 0 until dim if v(i) > 0.0) count += 1
        count
    } // countPos

    //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Count the number of zero elements in 'this' vector.
     */
    def countZero: Int =
    {
        var count = 0
        for (i <- 0 until dim if v(i) == 0.0) count += 1
        count
    } // countZero

    //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return a new vector consisteing of the distinct elements from 'this' vector.
     */
    def distinct: VectorD = VectorD (v.distinct)

    //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Count the number of distinct elements in 'this' vector.
     */
    def countinct: Int = v.distinct.length

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Determine whether the predicate 'pred' holds for some element in 'this' vector.
     *  @param pred  the predicate to test (e.g., "_ == 5.")
     */
//  def exists (pred: (Double) => Boolean): Boolean = v.exists (pred)

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Determine whether 'x' is contained in 'this' vector.
     *  @param x  the element to be checked
     */
    def contains (x: Double): Boolean = v contains x

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Sort 'this' vector in-place in ascending (non-decreasing) order.
     */
    def sort () { quickSort (v) }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Sort 'this' vector in-place in descending (non-increasing) order.
     */
    def sort2 () { qsort2 (v) }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Swap elements 'i' and 'j' in 'this' vector.
     *  @param i  the first element in the swap
     *  @param j  the second element in the swap
     */
    def swap (i: Int, j: Int)
    {
        val t = v(j); v(j) = v(i); v(i) = t
    } // swap

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Check whether the other vector 'b' is at least as long as 'this' vector.
     *  @param b  the other vector
     */
    def sameDimensions (b: VectorD): Boolean = dim <= b.dim

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Check whether 'this' vector is nonnegative (has no negative elements).
     */
    def isNonnegative: Boolean =
    {
        for (i <- range if v(i) < 0.0) return false
        true
    } // isNonnegative

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Compare 'this' vector with vector 'b'.
     *  @param b  the other vector
     */
    def tryCompareTo [B >: VectorD] (b: B)
        (implicit view_1: (B) => PartiallyOrdered [B]): Option [Int] =
    {
        var le = true
        var ge = true

        for (i <- range.par) {
            val b_i = b.asInstanceOf [VectorD] (i)
            if      (ge && (v(i) compare b_i) < 0) ge = false
            else if (le && (v(i) compare b_i) > 0) le = false
        } // for
        if (ge && le) Some (0) else if (le) Some (-1) else if (ge) Some (1) else None
    } // tryCompareTo

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Override equals to determine whether 'this' vector equals vector 'b..
     *  @param b  the vector to compare with this
     */
    override def equals (b: Any): Boolean =
    {
        b.isInstanceOf [VectorD] && (v.deep equals b.asInstanceOf [VectorD].v.deep)
    } // equals

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Must also override hashCode for 'this' vector to be compatible with equals.
     */
    override def hashCode: Int = v.deep.hashCode

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Convert 'this' vector to a String.
     */
    override def toString: String = 
    {
        var sb = new StringBuilder ("VectorD(")
        if (dim == 0) return sb.append (")").mkString
        for (i <- range) {
            sb.append (fString.format (v(i)))
            if (i == dim-1) sb = sb.dropRight (1)
        } // for
        sb.replace (sb.length-1, sb.length, ")").mkString
    } // toString
  
} // VectorD class


//::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `VectorD` object is the companion object for the `VectorD` class.
 */
object VectorD
{
    import java.util.concurrent.CountDownLatch

    /** The number of parallel/concurrent tasks to be run.  Adjust as needed
     */
    private val PAR_LEVEL = 10

    /** Count down latch main thread to wait for `VecThread`s to finish
     */
    private var latch: CountDownLatch = null

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Make several `VecThread`s to run tasks in parallel.
     */
    def makeThreads (): Array [VecThread] =
    {
        latch = new CountDownLatch (PAR_LEVEL)
        Array.ofDim [VecThread] (PAR_LEVEL)
    } // makeThreads

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Await the completion of all `VecThread`s.
     */
    def await () { latch.await () }

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** The `VecThread` inner class allows tasks to be run in parallel.
     *  @param b     the first vector
     *  @param c     the second vector
     *  @param i     the start of the subrange (inclusive)
     *  @param j     the end of the subrange (exclusive)
     *  @param task  the task/function to be run in parallel
     */
    class VecThread (b: VectorD, c: VectorD, i: Int, j: Int, task: (VectorD, VectorD, Int, Int) => Double)
          extends Thread
    {
        var result = 0.0
        override def run ()
        {
            result = task (b, c, i, j)
            latch.countDown ()
        } // run

    } // VecThread inner class

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a `VectorD` from one or more values (repeated values Double*).
     *  @param x   the first Double number
     *  @param xs  the rest of the Double numbers
     */
    def apply (x: Double, xs: Double*): VectorD =
    {
        val c = new VectorD (1 + xs.length)
        c(0)  = x
        for (i <- 0 until c.dim-1) c.v(i+1) = xs(i)
        c
    } // apply

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a `VectorD` from a sequence of Doubles.
     *  @param xs  the sequence of the Double numbers
     */
    def apply (xs: Seq [Double]): VectorD =
    {
        val c = new VectorD (xs.length)
        for (i <- 0 until c.dim) c.v(i) = xs(i)
        c
    } // apply

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a `VectorD` from one or more values (repeated values String*).
     *  @param x   the first String
     *  @param xs  the rest of the Strings
     */
    def apply (x: String, xs: String*): VectorD =
    {
        val c = new VectorD (1 + xs.length)
        c(0)  = x.toDouble
        for (i <- 0 until c.dim-1) c.v(i+1) = xs(i).toDouble
        c
    } // apply

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a `VectorD` from an array of Strings.
     *  @param xs  the array of the Strings
     */
    def apply (xs: Array [String]): VectorD =
    {
        val c = new VectorD (xs.length)
        for (i <- c.range.par) c.v(i) = xs(i).toDouble
        c
    } // apply

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a `VectorD` from an array of Strings, skipping the first 'skip'
     *  elements.  If an element is non-numeric, use its hashcode.
     *  FIX:  Might be better to map non-numeric Strings to ordinal values.
     *  @param xs    the array of the Strings
     *  @param skip  the number of elements at the beginning to skip (e.g., id column)
     */
    def apply (xs: Array [String], skip: Int): VectorD =
    {
        val c = new VectorD (xs.length - skip)
        for (i <- skip until xs.length) {
            c.v(i - skip) = if (xs(i) matches "[\\-\\+]?\\d*(\\.\\d+)?") xs(i).toDouble else xs(i).hashCode ()
        } // for
        c
    } // apply

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Create a one vector (all elements are one) of length 'size'.
     *  @param size  the size of the vector
     */
    def one (size: Int): VectorD =
    {
        val c = new VectorD (size)
        c.set (1.0)
        c
    } // one

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Concatenate scalar 'b' and vector 'u'.
     *  @param b  the scalar to be concatenated - first part
     *  @param u  the vector to be concatenated - second part
     */
    def ++ (b: Double, u: VectorD): VectorD =
    {
        val c = new VectorD (u.dim + 1)
        for (i <- c.range.par) c(i) = if (i == 0) b else u.v(i - 1)
        c
    } // ++

    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    /** Return a `VectorD` containing a sequence of increasing integers in a range.
     *  @param start  the start value of the vector, inclusive
     *  @param end    the end value of the vector, exclusive (i.e., the first value not returned)
     */
    def range (start: Int, end: Int): VectorD =
    {
        val c = new VectorD (end - start)
        for (i <- c.range.par) c.v(i) = (start + i).toDouble
        c
    } // range

} // VectorD object


//::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
/** The `VectorDTest` object tests the operations provided by `VectorD`.
 *  > run-main scalation.linalgebra.par.VectorDTest
 */
object VectorDTest extends App
{
    import scalation.util.time

    val rng = new java.util.Random ()
    val n = 40000000
    val x = new VectorD (n)
    val y = new VectorD (n)

    for (i <- 0 until n) {
        x(i) = rng.nextDouble ()
        y(i) = rng.nextDouble ()
    } // for

    var z = 0.0
    for (k <- 0 until 6) {
        time { z = x dot y }
        println ("x dot y = " + z)
    } // for

    for (k <- 0 until 6) {
        time { z = x dotp y }
        println ("x dotp y = " + z)
    } // for

} // VectorDTest