Exercise Sheet 1 - Solutions

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1 Exercise Sheet 1 - Solutions Alessandro Gnoatto October 23, Exercise 1 / 2 4 package de. lmu. firstclass ; 6 Alessandro Gnoatto 8 10 public class ComplexNumber { //fields 12 private double real ; private double imag ; //specify a constructor public ComplexNumber (double real, double imag ){ 18 this. real = real ; this. imag = imag ; //get methods public double getreal (){ 24 return this. real ; 26 public double getimag (){ 28 return this. real ; 30 //set methods 32 public void setreal (double real ){ this. real = real ; public void setimag (double imag ){ this. imag = imag ; //some methods public s t a t i c ComplexNumber add ( ComplexNumber a, ComplexNumber b){ 42 return new ComplexNumber (a. real +b.real,a. imag +b. imag ); 44 1

2 public s t a t i c ComplexNumber subtract ( ComplexNumber a, ComplexNumber b){ 46 return new ComplexNumber (a.real -b.real,a.imag -b. imag ); 48 public s t a t i c ComplexNumber multiply ( ComplexNumber a, ComplexNumber b){ 50 return new ComplexNumber ( a. real * b. real - a. imag * b. imag,a. imag * b. real + a. real * b. imag ); public s t a t i c ComplexNumber divide ( ComplexNumber a, ComplexNumber b){ return new ComplexNumber (( a. real * b. real + a. imag * b. imag ) 56 /(b. real * b. real - b. imag * b. imag ), (a. imag * b. real - a. real * b. imag ) 58 /(b. real * b. real - b. imag * b. imag )); 60 public s t a t i c double abs ( ComplexNumber a){ 62 return Math. sqrt (a. real *a. real +a. imag *a. imag ); Exercise Interface / 2 (c) Copyright Christian P. Fries, Germany. All rights reserved. Contact: @christian fries.de. 4 Created on package net. finmath. time ; 8 import java. util. ArrayList ; 10 Christian Fries 12 public interface TimeDiscretizationInterface extends Iterable < Double > { 14 / Returns the number of time discretization points. 18 int getnumberoftimes (); 20 Returns the number of time steps (= number of discretization points 1). 22 int getnumberoftimesteps (); 24 / 26 Returns the time for the given time index. 2

3 timeindex Time Returns the time for a given time index. 30 double gettime ( int timeindex ); 32 / 34 Returns the time step from the given time index to the next one. timeindex Time Returns the time step 38 double gettimestep ( int timeindex ); 40 / 42 Returns the time index for the given time. If the given time is not in the time discretization the method returns a negative number being ( insertionpoint 1). time The time. Returns the time index for a given time. 48 int gettimeindex (double time ); 50 / Returns the time index for the time in the time discretization which is the nearest 52 to the given time, being less or equal (i.e. max(i : timediscretization[i] time where timediscretization[i] timediscretization[j]). time Given time. Returns a time index 58 int gettimeindexnearestlessorequal (double time ); 60 / Returns the time index for the time in the time discretization which is the nearest 62 to the given time, being greater or equal (i.e. min(i : timediscretization[i] time where timediscretization[i] timediscretization[j]). time Given time. Returns a time index 68 int gettimeindexnearestgreaterorequal (double time ); 70 / Return a clone of this time discretization as <code> double[]</code>. The time discretization as <code>double[]</code> 74 double[] getasdoublearray (); 76 / Return a clone of this time discretization as <code> ArrayList<Double></code>. 78 Note that this method is costly in terms of performance. 3

4 The time discretization as <code>arraylist< Double></code> 82 ArrayList < Double > getasarraylist (); 84 / 86 Return a new time discretization where all time points have been shifted by a given time shift. timeshift A time shift applied to all discretization points. A new time discretization where all time points have been shifted by the given time shift. 92 TimeDiscretizationInterface gettimeshiftedtimediscretization (double timeshift ); 2.2 Class / 2 (c) Copyright Christian P. Fries, Germany. All rights reserved. Contact: @christian fries.de. 4 Created on package net. finmath. time ; 8 import java. io. Serializable ; import java. util. ArrayList ; 10 import java. util. Arrays ; import java. util. Iterator ; 12 / 14 This class represents a set of discrete points in time. <br> 16 It handles the mapping from time indices to time points and back. It uses a time tick size ("quantum") of 1.0 / ( ) (which corresponds to one hour if 1.0 is a non leap year): 18 Times are rounded to the nearest multiple of 1.0 / ( ). 20 Objects of this class are immutable. Christian public class TimeDiscretization implements Serializable, TimeDiscretizationInterface { private s t a t i c f i n a l long serialversionuid = L; private f i n a l double[] timediscretization ; 30 private f i n a l double timeticksize = 1.0 / (365.0 * 24.0) ; 32 public enum ShortPeriodLocation { 4

5 SHORT_PERIOD_AT_START, 34 SHORT_PERIOD_AT_END 36 / 38 Constructs a time discretization from a given set of doubles. times Given array or arguments list of discretization points. 42 public TimeDiscretization (double... times ) { super(); 44 this. timediscretization = times. clone (); java. util. Arrays. sort ( this. timediscretization ); / Constructs a time discretization from a given set of Doubles. times Given array or arguments list of discretization points 52 public TimeDiscretization ( Double [] times ) { 54 super(); this. timediscretization = new double[ times. length ]; 56 for ( int timeindex =0; timeindex < timediscretization. length ; timeindex ++) this. timediscretization [ timeindex ] = roundtotimeticksize ( times [ timeindex ]); java. util. Arrays. sort ( this. timediscretization ); / Constructs a time discretization from a given ArrayList of Doubles. timediscretization Given ArrayList of discretization points 64 public TimeDiscretization ( ArrayList < Double > timediscretization ) { 66 super(); this. timediscretization = new double[ timediscretization. size () ]; 68 for ( int timeindex =0; timeindex < timediscretization. size (); timeindex ++) this. timediscretization [ timeindex ] = roundtotimeticksize ( timediscretization. get ( timeindex )) ; java. util. Arrays. sort ( this. timediscretization ); / Constructs an equi distant time discretization with points timediscretization[i] being 74 <code>for(i=0; i timesteps; i++) timediscretization[ i] = initial + i deltat;</code> initial First discretization numberoftimesteps Number of time steps. deltat Time step size. 5

6 80 public TimeDiscretization (double initial, int numberoftimesteps, double deltat ) { super(); 82 timediscretization = new double[ numberoftimesteps +1]; for ( int timeindex =0; timeindex < timediscretization. length ; timeindex ++) timediscretization [ timeindex ] = roundtotimeticksize ( initial + timeindex * deltat ); / Constructs an equi distant time discretization with stub periods at start or end. initial First discretization point. last Last time deltat Time step size. shortperiodlocation Placement of the stub period. 94 public TimeDiscretization (double initial, double last, double deltat, ShortPeriodLocation shortperiodlocation ) { super(); 96 int numberoftimesteps = ( int )(( last - initial )/ deltat + 0.5) ; 98 // Adjust for short period, if any i f ( roundtotimeticksize ( initial + numberoftimesteps * deltat ) < roundtotimeticksize ( last )) numberoftimesteps ++; 100 timediscretization = new double[ numberoftimesteps +1]; 102 i f ( shortperiodlocation == ShortPeriodLocation. SHORT_PERIOD_AT_END ) { for ( int timeindex =0; timeindex < timediscretization. length ; timeindex ++) timediscretization [ timeindex ] = roundtotimeticksize ( initial + timeindex * deltat ); 104 timediscretization [ timediscretization. length -1] = last ; 106 else { for ( int timeindex =0; timeindex < timediscretization. length ; timeindex ++) timediscretization [ timeindex ] = roundtotimeticksize ( last - ( numberoftimesteps - timeindex ) * deltat ); 108 timediscretization [0] = initial ; 110 public int getnumberoftimes () { 114 return timediscretization. length ; 118 public int getnumberoftimesteps () { return timediscretization. length -1; 120 public double gettime ( int timeindex ) { 124 return timediscretization [ timeindex ]; 126 6

7 @Override 128 public double gettimestep ( int timeindex ) { return timediscretization [ timeindex +1] - timediscretization [ timeindex ]; 130 public int gettimeindex (double time ) { 134 int index = java. util. Arrays. binarysearch ( timediscretization, roundtotimeticksize ( time )); return index ; 136 public int gettimeindexnearestlessorequal (double time ) { 140 int index = java. util. Arrays. binarysearch ( timediscretization, roundtotimeticksize ( time )); i f ( index < 0) index = - index -2; 142 return index ; 146 public int gettimeindexnearestgreaterorequal (double time ) { int index = java. util. Arrays. binarysearch ( timediscretization, time ); 148 i f ( index < 0) index = - index -1; return index ; 150 public double[] getasdoublearray () { 154 // Note: This is a deep copy return timediscretization. clone (); 156 public ArrayList < Double > getasarraylist () { 160 ArrayList < Double > times = new ArrayList < Double >( timediscretization. length ); for (double atimediscretization : timediscretization ) times. add ( atimediscretization ); 162 return times ; 166 public TimeDiscretizationInterface gettimeshiftedtimediscretization (double timeshift ) { double[] newtimediscretization = new double[ timediscretization. length ]; 168 for ( int timeindex =0; timeindex < timediscretization. length ; timeindex ++) newtimediscretization [ timeindex ] = roundtotimeticksize ( timediscretization [ timeindex ]+ timeshift ); 170 java. util. Arrays. sort ( this. timediscretization ); return new TimeDiscretization ( newtimediscretization ); 172 public Iterator < Double > iterator () { 176 return this. getasarraylist (). iterator (); 178 7

8 @Override 180 public String tostring () { return " TimeDiscretization [ timediscretization =" Arrays. tostring ( timediscretization ) + ", timeticksize =" + timeticksize + "]"; private double roundtotimeticksize (double time ) { return Math. rint ( time / timeticksize )* timeticksize ; 188 8

Object Oriented Programming: In this course we began an introduction to programming from an object-oriented approach.

CMSC 131: Chapter 28 Final Review: What you learned this semester The Big Picture Object Oriented Programming: In this course we began an introduction to programming from an object-oriented approach. Java