Programming with MATLAB for Scientists : A Beginner’s Introduction

265 Pages·2018·7.09 MB·English

by  Mikhailov

Programming with
MATLAB for Scientists
A Beginner’s Introduction

Programming with
MATLAB for Scientists
A Beginner’s Introduction
Eugeniy E. Mikhailov
MATLAB®andSimulink®aretrademarksoftheMathWorks,Inc.andareusedwithpermission.The
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Title:ProgrammingwithMATLABforscientists:abeginner’sintroduction/EugeniyE.Mikhailov.
Description:BocaRaton,FL:CRCPress,Taylor&FrancisGroup,[2017]
Identifiers:LCCN2017031570|ISBN9781498738286|ISBN1498738281
Subjects:LCSH:MATLAB.|Science–Dataprocessing.|Engineeringmathematics–Dataprocessing.
|Numericalanalysis–Dataprocessing.
Classification:LCCQ183.9.M552017|DDC510.285/53–dc23
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Contents
Preface ................................................................. xi
I ComputingEssentials ............................................ 1
1 ComputersandProgrammingLanguages:AnIntroduction ............ 3
1.1 EarlyHistoryofComputing .................................... 3
1.2 ModernComputers............................................ 4
1.2.1 Commonfeaturesofamoderncomputer.................. 4
1.3 WhatIsProgramming? ........................................ 5
1.4 ProgrammingLanguagesOverview............................. 5
1.5 NumbersRepresentationinComputersandIts
PotentialProblems............................................. 7
1.5.1 Discretization—themainweaknessofcomputers .......... 7
1.5.2 Binaryrepresentation.................................... 8
1.5.3 Floating-pointnumberrepresentation..................... 8
1.5.4 Conclusion ............................................. 9
1.6 Self-Study .................................................... 10
2 MATLABBasics .................................................... 11
2.1 MATLAB’sGraphicalUserInterface ............................ 11
2.2 MATLABasaPowerfulCalculator.............................. 14
2.2.1 MATLAB’svariabletypes................................ 14
2.2.2 Somebuilt-infunctionsandoperators..................... 15
2.2.3 Operatorprecedence .................................... 16
2.2.4 Comments.............................................. 17
2.3 EfficientEditing ............................................... 17
2.4 UsingDocumentation.......................................... 18
2.5 Matrices ...................................................... 19
2.5.1 Creatingandaccessingmatrixelements ................... 19
2.5.2 Nativematrixoperations................................. 21
2.5.3 Stringsasmatrices....................................... 24
2.6 Colon(:)Operator ............................................. 25
2.6.1 Slicingmatrices ......................................... 25
2.7 Plotting....................................................... 26
2.7.1 Savingplotstofiles...................................... 28
2.8 Self-Study .................................................... 29
v
vi Contents
3 BooleanAlgebra,ConditionalStatements,Loops ...................... 31
3.1 BooleanAlgebra............................................... 31
3.1.1 BooleanoperatorsprecedenceinMATLAB ................ 32
3.1.2 MATLABBooleanlogicexamples......................... 32
3.2 ComparisonOperators......................................... 33
3.2.1 Comparisonwithvectors ................................ 34
3.2.2 Comparisonwithmatrices ............................... 34
3.3 ConditionalStatements ........................................ 35
3.3.1 Theif-else-endstatement ................................ 35
3.3.2 Shortformofthe“if”statement .......................... 36
3.4 CommonMistakewiththeEqualityStatement................... 36
3.5 Loops ........................................................ 36
3.5.1 The“while”loop........................................ 36
3.5.2 Specialcommands“break”and“continue”................ 38
3.5.3 The“for”loop .......................................... 38
3.6 Self-Study .................................................... 40
4 Functions,Scripts,andGoodProgrammingPractice ................... 41
4.1 MotivationalExamples......................................... 41
4.1.1 Bankinterestrateproblem ............................... 41
4.1.2 Timeofflightproblem ................................... 42
4.2 Scripts ........................................................ 43
4.2.1 Quadraticequationsolverscript.......................... 43
4.3 Functions ..................................................... 45
4.3.1 Quadraticequationsolverfunction ....................... 46
4.4 GoodProgrammingPractice.................................... 47
4.4.1 Simplifythecode........................................ 47
4.4.2 Trytoforeseeunexpectedbehavior ....................... 48
4.4.3 Runtestcases ........................................... 48
4.4.4 Checkandsanitizeinputarguments ...................... 49
4.4.5 Isthesolutionrealistic? .................................. 50
4.4.6 Summaryofgoodprogrammingpractice.................. 51
4.5 RecursiveandAnonymousFunctions ........................... 51
4.5.1 Recursivefunctions...................................... 51
4.5.2 Anonymousfunctions ................................... 52
4.6 Self-Study .................................................... 54
II SolvingEverydayProblemswithMATLAB ...................... 57
5 SolvingSystemsofLinearAlgebraicEquations........................ 59
5.1 TheMobileProblem ........................................... 59
5.2 Built-InMATLABSolvers ...................................... 61
5.2.1 Theinversematrixmethod............................... 61
Contents vii
5.2.2 Solutionwithoutinversematrixcalculation ............... 62
5.2.3 Whichmethodtouse .................................... 62
5.3 SolutionoftheMobileProblemwithMATLAB................... 63
5.3.1 Solutioncheck .......................................... 64
5.4 Example:WheatstoneBridgeProblem........................... 65
5.5 Self-Study .................................................... 66
6 FittingandDataReduction .......................................... 69
6.1 NecessityforDataReductionandFitting ........................ 69
6.2 FormalDefinitionforFitting.................................... 70
6.2.1 Goodnessofthefit ...................................... 70
6.3 FittingExample ............................................... 71
6.4 ParameterUncertaintyEstimations ............................. 73
6.5 EvaluationoftheResultingFit.................................. 74
6.6 HowtoFindtheOptimalFit.................................... 75
6.6.1 Example:Lightdiffractiononasingleslit ................. 77
6.6.2 Plottingthedata ........................................ 77
6.6.3 Choosingthefitmodel................................... 78
6.6.4 Makinganinitialguessforthefitparameters .............. 79
6.6.5 Plottingdataandthemodelbasedonthe
initialguess............................................. 80
6.6.6 Fittingthedata.......................................... 81
6.6.7 Evaluatinguncertaintiesforthefitparameters ............. 82
6.7 Self-Study .................................................... 84
7 NumericalDerivatives .............................................. 87
7.1 EstimateoftheDerivativeviatheForwardDifference ............ 87
7.2 AlgorithmicErrorEstimateforNumericalDerivative............. 88
7.3 EstimateoftheDerivativeviatheCentralDifference ............. 89
7.4 Self-Study .................................................... 91
8 RootFindingAlgorithms ............................................ 93
8.1 RootFindingProblem.......................................... 93
8.2 TrialandErrorMethod......................................... 94
8.3 BisectionMethod .............................................. 95
8.3.1 Bisectionuseexampleandtestcase ....................... 97
8.3.2 Possibleimprovementofthebisectioncode ............... 100
8.4 AlgorithmConvergence........................................ 100
8.5 FalsePosition(RegulaFalsi)Method............................. 101
8.6 SecantMethod ................................................ 102
8.7 Newton–RaphsonMethod ..................................... 103
8.7.1 UsingNewton–Raphsonalgorithmwiththeanalytical
derivative .............................................. 105
8.7.2 UsingNewton–Raphsonalgorithmwiththenumerical
derivative .............................................. 106
viii Contents
8.8 Ridders’Method .............................................. 106
8.9 RootFindingAlgorithmsGotchas............................... 108
8.10 RootFindingAlgorithmsSummary ............................. 109
8.11 MATLAB’sRootFindingBuilt-inCommand..................... 110
8.12 Self-Study .................................................... 110
9 NumericalIntegrationMethods...................................... 113
9.1 IntegrationProblemStatement.................................. 113
9.2 TheRectangleMethod ......................................... 114
9.2.1 Rectanglemethodalgorithmicerror....................... 116
9.3 TrapezoidalMethod ........................................... 116
9.3.1 Trapezoidalmethodalgorithmicerror..................... 117
9.4 Simpson’sMethod............................................. 118
9.4.1 Simpson’smethodalgorithmicerror ...................... 118
9.5 GeneralizedFormulaforIntegration ............................ 119
9.6 MonteCarloIntegration........................................ 119
9.6.1 Toyexample:findingtheareaofapond................... 119
9.6.2 NaiveMonteCarlointegration ........................... 120
9.6.3 MonteCarlointegrationderived.......................... 120
9.6.4 TheMonteCarlomethodalgorithmicerror................ 121
9.7 MultidimensionalIntegration................................... 122
9.7.1 Minimalexampleforintegrationin
twodimensions ......................................... 122
9.8 MultidimensionalIntegrationwithMonteCarlo ................. 123
9.8.1 MonteCarlomethoddemonstration ...................... 124
9.9 NumericalIntegrationGotchas ................................. 124
9.9.1 Usingaverylargenumberofpoints ...................... 124
9.9.2 Usingtoofewpoints .................................... 124
9.10 MATLABFunctionsforIntegration ............................. 125
9.11 Self-Study .................................................... 126
10 DataInterpolation .................................................. 129
10.1 TheNearestNeighborInterpolation............................. 129
10.2 LinearInterpolation ........................................... 130
10.3 PolynomialInterpolation....................................... 132
10.4 CriteriaforaGoodInterpolationRoutine........................ 134
10.5 CubicSplineInterpolation...................................... 134
10.6 MATLABBuilt-InInterpolationMethods ........................ 135
10.7 Extrapolation ................................................. 136
10.8 UnconventionalUseofInterpolation ............................ 136
=
10.8.1 Findingthelocationofthedatacrossingy 0............. 136
10.9 Self-Study .................................................... 138
Contents ix
III GoingDeeperandExpandingtheScientist’sToolbox ............ 139
11 RandomNumberGeneratorsandRandomProcesses .................. 141
11.1 StatisticsandProbabilityIntroduction........................... 141
11.1.1 Discreteeventprobability................................ 141
11.1.2 Probabilitydensityfunction.............................. 142
11.2 UniformRandomDistribution.................................. 142
11.3 RandomNumberGeneratorsandComputers.................... 143
11.3.1 Linearcongruentialgenerator ............................ 144
11.3.2 Randomnumbergeneratorperiod........................ 145
11.4 HowtoCheckaRandomGenerator............................. 145
11.4.1 SimpleRNGtestwithMonteCarlointegration ............ 146
11.5 MATLAB’sBuilt-InRNGs ...................................... 148
11.6 Self-Study .................................................... 148
12 MonteCarloSimulations ............................................ 149
12.1 PegBoard..................................................... 149
12.2 CoinFlippingGame ........................................... 151
12.3 One-DimensionalInfectionSpread.............................. 152
12.4 Self-Study .................................................... 160
13 TheOptimizationProblem .......................................... 161
13.1 IntroductiontoOptimization ................................... 161
13.2 One-DimensionalOptimization................................. 162
13.2.1 Thegoldensectionoptimumsearchalgorithm............. 163
13.2.2 MATLAB’sbuilt-infunctionfortheone-dimension
optimization ............................................ 165
13.2.3 One-dimensionaloptimizationexamples .................. 165
13.3 MultidimensionalOptimization ................................ 167
13.3.1 Examplesofmultidimensionaloptimization............... 168
13.4 CombinatorialOptimization.................................... 174
13.4.1 Backpackproblem....................................... 174
13.4.2 Travelingsalesmanproblem.............................. 178
13.5 SimulatedAnnealingAlgorithm ................................ 183
13.5.1 Thebackpackproblemsolutionwiththe
annealingalgorithm ..................................... 185
13.6 GeneticAlgorithm............................................. 192
13.7 Self-Study .................................................... 193
14 OrdinaryDifferentialEquations...................................... 195
14.1 IntroductiontoOrdinaryDifferentialEquation................... 195
14.2 BoundaryConditions .......................................... 197
14.3 NumericalMethodtoSolveODEs .............................. 197
14.3.1 Euler’smethod.......................................... 197
14.3.2 Thesecond-orderRunge–Kuttamethod(RK2) ............. 199