001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
093
094
095
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
package algs12;
import stdlib.*;
/* ***********************************************************************
 *  Compilation:  javac Vector.java
 *  Execution:    java Vector
 *
 *  Implementation of a vector of real numbers.
 *
 *  This class is implemented to be immutable: once the client program
 *  initialize a Vector, it cannot change any of its fields
 *  (N or data[i]) either directly or indirectly. Immutability is a
 *  very desirable feature of a data type.
 *
 *  % java Vector
 *     x     = [ 1.0 2.0 3.0 4.0 ]
 *     y     = [ 5.0 2.0 4.0 1.0 ]
 *     z     = [ 6.0 4.0 7.0 5.0 ]
 *   10z     = [ 60.0 40.0 70.0 50.0 ]
 *    |x|    = 5.477225575051661
 *   <x, y>  = 25.0
 *
 *
 *  Note that Vector is also the name of an unrelated Java library class.
 *
 *************************************************************************/

public class Vector {

  private final int N;               // length of the vector
  private final double[] data;       // array of vector's components


  // create the zero vector of length n
  public Vector(int n) {
    N = n;
    data = new double[N];
  }

  // create a vector from either an array or a vararg list
  // this constructor uses Java's vararg syntax to support
  // a constructor that takes a variable number of arguments, such as
  // Vector x = new Vector(1.0, 2.0, 3.0, 4.0);
  // Vector y = new Vector(5.0, 2.0, 4.0, 1.0);
  public Vector(double... d) {
    N = d.length;

    // defensive copy so that client can't alter our copy of data[]
    data = new double[N];
    for (int i = 0; i < N; i++)
      data[i] = d[i];
  }
  // return the length of the vector
  public int length() {
    return N;
  }

  // return the inner product of this Vector a and b
  public double dot(Vector that) {
    if (this.N != that.N) throw new Error("Dimensions don't agree");
    double sum = 0.0;
    for (int i = 0; i < N; i++)
      sum = sum + (this.data[i] * that.data[i]);
    return sum;
  }

  // return the Euclidean norm of this Vector
  public double magnitude() {
    return Math.sqrt(this.dot(this));
  }

  // return the Euclidean distance between this and that
  public double distanceTo(Vector that) {
    if (this.N != that.N) throw new Error("Dimensions don't agree");
    return this.minus(that).magnitude();
  }

  // return this + that
  public Vector plus(Vector that) {
    if (this.N != that.N) throw new Error("Dimensions don't agree");
    Vector c = new Vector(N);
    for (int i = 0; i < N; i++)
      c.data[i] = this.data[i] + that.data[i];
    return c;
  }

  // return this + that
  public Vector minus(Vector that) {
    if (this.N != that.N) throw new Error("Dimensions don't agree");
    Vector c = new Vector(N);
    for (int i = 0; i < N; i++)
      c.data[i] = this.data[i] - that.data[i];
    return c;
  }

  // return the corresponding coordinate
  public double cartesian(int i) {
    return data[i];
  }

  // create and return a new object whose value is (this * factor)
  public Vector times(double factor) {
    Vector c = new Vector(N);
    for (int i = 0; i < N; i++)
      c.data[i] = factor * data[i];
    return c;
  }


  // return the corresponding unit vector
  public Vector direction() {
    if (this.magnitude() == 0.0) throw new Error("Zero-vector has no direction");
    return this.times(1.0 / this.magnitude());
  }


  // return a string representation of the vector
  public String toString() {
    String s = "";
    for (int i = 0; i < N; i++)
      s = s + data[i] + " ";
    return s;
  }




  // test client
  public static void main(String[] args) {
    double[] xdata = { 1.0, 2.0, 3.0, 4.0 };
    double[] ydata = { 5.0, 2.0, 4.0, 1.0 };
    Vector x = new Vector(xdata);
    Vector y = new Vector(ydata);

    StdOut.println("   x       = " + x);
    StdOut.println("   y       = " + y);

    Vector z = x.plus(y);
    StdOut.println("   z       = " + z);

    z = z.times(10.0);
    StdOut.println(" 10z       = " + z);

    StdOut.println("  |x|      = " + x.magnitude());
    StdOut.println(" <x, y>    = " + x.dot(y));
    StdOut.println("dist(x, y) = " + x.distanceTo(y));
    StdOut.println("dir(x)     = " + x.direction());

  }
}