added fields/oper

Author: Manpreet

Chapter_02/breeze/src/main/scala/linalg/fields/ComplexNumber.scala

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+package linalg.fields
+
+import breeze.math.Complex
+
+/**
+  * Created by manpreet.singh on 27/01/16.
+  */
+object ComplexNumber {
+
+  def complexNumbers(): Unit = {
+    val i = Complex.i
+    // add
+    println((1 + 2 * i) + (2 + 3 * i))
+
+    // sub
+    println((1 + 2 * i) - (2 + 3 * i))
+
+    // divide
+    println((5 + 10 * i) / (3 - 4 * i))
+
+    // mul
+    println((1 + 2 * i) * (-3 + 6 * i))
+    println((1 + 5 * i) * (-3 + 2 * i))
+
+    // neg
+    println(-(1 + 2 * i))
+
+    // sum of complex numbers
+    val x = List((5 + 7 * i), (1 + 3 * i), (13 + 17 * i))
+    println(x.sum)
+
+    // product of complex numbers
+    val x1 = List((5 + 7 * i), (1 + 3 * i), (13 + 17 * i))
+    println(x1.product)
+
+    // sort list of complex numbers
+    val x2 = List((5 + 7 * i), (1 + 3 * i), (13 + 17 * i))
+    println(x2.sorted)
+
+  }
+
+  def main(args: Array[String]) {
+    complexNumbers()
+  }
+
+
+}

Chapter_02/breeze/src/main/scala/linalg/fields/GF2.scala

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+package linalg.fields
+
+/**
+  * Created by manpreet.singh on 27/01/16.
+  */
+trait GF2 {
+  def + (that: GF2): GF2
+  def * (that: GF2): GF2
+
+  def / (that: GF2) = that match {
+    case Zero => throw new IllegalArgumentException("Div by 0")
+    case _ => this
+  }
+}
+
+object Zero extends GF2 {
+  override def toString = "Zero"
+  def + (that: GF2) = that
+  def * (that: GF2) = this
+}
+
+object One extends GF2 {
+  override def toString = "One"
+  def + (that: GF2) = that match { case One => Zero ; case _ => this }
+  def * (that: GF2) = that match { case One => this ; case _ => that }
+}

Chapter_02/breeze/src/main/scala/linalg/fields/GaloisField.scala

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+package linalg.fields
+
+/**
+  * Created by manpreet.singh on 27/01/16.
+  */
+object GaloisField {
+
+  // GF2 operations
+  def GaloisField2(): Unit = {
+    println(Zero + Zero)
+    println(One + Zero)
+    println(One + One)
+  }
+
+  def main(args: Array[String]) {
+    GaloisField2()
+  }
+
+}

Chapter_02/breeze/src/main/scala/linalg/operations/common.scala

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+package linalg.operations
+
+import breeze.linalg._
+import breeze.numerics.{floor, ceil}
+
+/**
+  * Created by manpreet.singh on 28/01/16.
+  */
+object common {
+
+  // vector's
+  val v1 = DenseVector(3, 7, 8.1, 4, 5)
+  val v2 = DenseVector(1, 9, 3, 2.3, 8)
+
+  // column matrix (3 * 3)
+  val m1 = DenseMatrix((2, 3, 1), (4, 5, 1), (6, 7, 1))
+  val m2 = DenseMatrix((3, 4, 1), (2, 6, 1), (8, 2, 1))
+
+  // elementwise add operation
+  def add(): Unit = {
+    println(v1 + v2)
+    println(m1 + m2)
+  }
+
+  // elementwise mul operation
+  def mul(): Unit = {
+    println(v1 :* v2)
+    println(m1 :* m2)
+  }
+
+  // elementwise compare operation
+  def compare(): Unit = {
+    println(v1 :< v2)
+    println(m1 :< m2)
+  }
+
+  // inplace addition operation
+//  def inplace(): Unit = {
+//    println(v1 += 2)
+//    println(m1 += 3)
+//  }
+
+  // vector dot product operation
+  def dot(): Unit = {
+    println(v1 dot v2)
+  }
+
+  // elementwise sum
+  def sumof(): Unit = {
+    println(sum(v1))
+  }
+
+  // elementwise max
+  def maxElement(): Unit = {
+    println(max(v1))
+    println(max(m1))
+  }
+
+  // elementwise argmax
+  def argmaxElement(): Unit = {
+    println(argmax(v1))
+    println(argmax(m1))
+  }
+
+  // ceiling (Rounds numbers to the next highest integer)
+  def ceiling(): Unit = {
+    println(ceil(v1))
+    println(ceil(m1))
+  }
+
+  // floor (Rounds numbers to the next lowest integer.)
+  def flooring(): Unit = {
+    println(floor(v1))
+    println(floor(m1))
+  }
+
+  def main(args: Array[String]) {
+    add()
+    mul()
+    compare()
+    dot()
+    sumof()
+    maxElement()
+    argmaxElement()
+    ceiling()
+    flooring()
+  }
+}