matlab fundamentals

Cookbook (M 2)

2014 -10 -18 (V0.7 Revision 98 ) , {oUUID 1.858}

Vincent ISOZ, Daname KOLANI Sciences.ch

MATLAB 2

TABLE OF CONTENTS .................................................................................... 2

TABLES INDEX ............................................................................................... 13

Introduction ....................................................................................................... 14 MATLAB Evolution ................................................................................................. 15

About the writer ................................................................................................ 20 ISOZ Vincent ............................................................................................................ 20

KOLANI Daname ..................................................................................................... 21

Warning .............................................................................................................. 22

Your Opinion Matters! ..................................................................................... 23

Useful Links ....................................................................................................... 24 General ...................................................................................................................... 24

Forums ....................................................................................................................... 25

Non-Mathworks additional powerful Toolboxes and tools ...................................... 25

Bibliography ....................................................................................................... 26

MATLAB core (without Toolbox) ................................................................... 27 New main core features (to be complete) ................................................................. 27

MATLAB 2014a (8.3) ...................................................................................................... 27

MATLAB 2013b (8.2) ..................................................................................................... 27 MATLAB 2013a (8.1) ...................................................................................................... 27

MATLAB 2012b (8.0) ..................................................................................................... 27 MATLAB 2012a (7.14) .................................................................................................... 27 MATLAB 2011b (7.14) ................................................................................................... 28

MATLAB 2011a (7.12) .................................................................................................... 28

MATLAB 2010b (7.11) ................................................................................................... 28 MATLAB 2010a (7.10/2010) .......................................................................................... 28 MATLAB 2009b (7.9/2009) ............................................................................................ 28

MATLAB 2009a (7.9/2009) ............................................................................................ 29 MATLAB 2008b (7.8/2009) ............................................................................................ 29 MATLAB 2008a (7.6/2008) ............................................................................................ 29

MATLAB 2007b (7.5/2007) ............................................................................................ 29 MATLAB 2007a (7.4/2007) ............................................................................................ 30 MATLAB 2006b (7.3/2006) ............................................................................................ 30 MATLAB R14SP3 (7.1/2005) ......................................................................................... 31 MATLAB R14SP2 (7.0.4/2005) ...................................................................................... 31

MATLAB R14SP1 (7.0.1/2004) ...................................................................................... 31

MATLAB R14 (7.0/2004) ................................................................................................ 31

MATLAB R13 (6.5/2000) ................................................................................................ 32 MATLAB R10 (5.2/1998) ................................................................................................ 32

MATLAB R9 (5.1/1997) .................................................................................................. 32 MATLAB R8 (5.0/1996) .................................................................................................. 32

Cite MATLAB .......................................................................................................... 33

User Interface ............................................................................................................ 33

Use Help .................................................................................................................... 46


MATLAB 3

Edit a native function source code (if available) .............................................................. 48

Most asked user preferences ..................................................................................... 50

General commands .................................................................................................... 52 Execute system commands ............................................................................................... 52

Call R from MATLAB ..............................................................................................................................53 Get MATLAB system information .................................................................................. 55 Some dates stuff ............................................................................................................... 60

Manage variables .............................................................................................................. 61 Some Command Window controls .................................................................................. 63 Use the startup.m file ....................................................................................................... 65 Use the clipboard .............................................................................................................. 69

Comments and multiple line commands ................................................................... 69

Save workspace/Use commands diary ...................................................................... 70

Arithmetic operations on scalars ............................................................................... 73

Operators of comparison ........................................................................................... 76

Real numbers manipulations ..................................................................................... 78 Command Windows real numbers formatting and output ............................................... 80

Arithmetic operations on complex numbers ............................................................. 83 Identify the number type .................................................................................................. 86

Rounding results ........................................................................................................ 88

Set (vectors) operations ............................................................................................. 89 Important practical cases .................................................................................................. 96

Counting/Removing NaN in cell arrays .....................................................................................................96 Counting/Removing NaN in (numeric) vectors .........................................................................................97 Finding the closest number in an vector ....................................................................................................98

Arithmetic operations and manipulations of vectors ................................................ 99 Important practical cases ................................................................................................ 108

Build an orthonormal vector base ............................................................................................................108

Arithmetic operations and manipulations of matrices ............................................ 110 Important practical cases ................................................................................................ 125

Removing NaN in matrices (arrays) ........................................................................................................125 Sampling matrix columns ........................................................................................................................126

Creation multiple dimensional matrices .................................................................. 127

Manipulating tables (structure array) ...................................................................... 128

Mathematical functions ........................................................................................... 134

Core (elementary) statistical functions .................................................................... 147

Generate random variable ....................................................................................... 157

Use of constants (permanent variables) .................................................................. 161

Working with strings ............................................................................................... 164

Working with dates ................................................................................................. 171 Important practical cases ................................................................................................ 178

Convert year/month/day matrix as dates ..................................................................................................178 Difference in milliseconds/seconds between 2 dates ...............................................................................179

Simple user interactions .......................................................................................... 182 Message boxes ................................................................................................................ 182 Input ............................................................................................................................... 183

Input Dialog .................................................................................................................... 184 UI set color ..................................................................................................................... 187 UI save ............................................................................................................................ 188


MATLAB 4

UI open ........................................................................................................................... 188

UI get dir ........................................................................................................................ 190 Wait bar .......................................................................................................................... 192 Question dialog .............................................................................................................. 195 Menu ............................................................................................................................... 196 List dialog ....................................................................................................................... 198

Send E-mail .................................................................................................................... 199

Data management .................................................................................................... 200 MATLAB files (*.mat and *.m) ..................................................................................... 200 Manage working paths ................................................................................................... 203 Browse and manage folders and files ............................................................................. 209 Import/Export csv files ................................................................................................... 216

Import very clean local csv files (with comas, without headers, without texts, without dates) ................216 Import clean local csv files (with semi-colons, with headers, without text, without dates) ......................219 Import local csv files (with semi-colons, with headers, with text, with dates) .........................................220 Merge csv files ........................................................................................................................................223 Import web csv files (with semi-colons, with headers, with text, with dates) .........................................225 Import from Yahoo Finance ....................................................................................................................226 Export to csv file .....................................................................................................................................228

Import/Export xls/xlsx (Microsoft Office Excel) files ................................................... 230 Import xls/xlsx local files ........................................................................................................................230 Export to xls/xlsx files .............................................................................................................................234

Import data with the wizard ........................................................................................... 236

Charts....................................................................................................................... 243 Demo .............................................................................................................................. 243 Data sets ......................................................................................................................... 247 Chart wizard ................................................................................................................... 249

Control chart window ..................................................................................................... 280 Pick-up points on chart ................................................................................................... 291

C to R2 plots ................................................................................................................... 293

Analytical based plot ...............................................................................................................................293 Vector based plot with lines and stems ....................................................................................................294 Animated vector based plot .....................................................................................................................297 Vector based plot with various lines, colors and points ...........................................................................299 Vector based multiple plot with legends and titles ..................................................................................301 Horizontal/Vertical lines method .............................................................................................................303 Vector based plot with error bars .............................................................................................................304 Vector based semi-log X plot with custom tick space .............................................................................305 Vector based semi-log Y plot ..................................................................................................................306 Vector based log-log plot with data cursor tip .........................................................................................307 Subplots ...................................................................................................................................................309 Greeks letters in legends and titles (LaTeX style) ...................................................................................312 Plots with dates in axis ............................................................................................................................313 Multiple axis on line plots .......................................................................................................................315 Magnifier on line plot ..............................................................................................................................318 2D vertical/horizontal bar charts..............................................................................................................319

Multiple series bar chart ................................................................................................................... 319 Stacked bar chart ............................................................................................................................... 320 Stacked normalized bar chart ............................................................................................................ 321 Bar chart with error bars .................................................................................................................. 322 Bar chart with bar having a special a color ...................................................................................... 324 Tornado Chart ................................................................................................................................... 325 Bar chart with line and multiple axis ................................................................................................. 326


MATLAB 5

Two series bar chart with multiple axis ............................................................................................. 327 Probability histogram with density curve (pdf) ................................................................................. 329

Correlation 2D Heatmap ................................................................................................ 330 3D vertical bar charts ..................................................................................................... 332 2D/3D sector charts (cheese) .......................................................................................... 334 2D Surface/Area charts .................................................................................................. 337

Radial (rose) bar chart/arrow (compass) chart ............................................................... 339 Pareto chart ..................................................................................................................... 342 Plotmatrix ....................................................................................................................... 343 3D parametric plots ........................................................................................................ 344

Vector based 3D parametric line plot ......................................................................................................344 Animated or non-animated analytic based 3D parametric line plot .........................................................345 Animated vector based 3D parametric line plot .......................................................................................346 Vector based 3D stem parametric line plot ..............................................................................................347 Vector based 3D surface parametric plot .................................................................................................348

3D surface plots .............................................................................................................. 359 ezsurf .......................................................................................................................................................359 ezsurfc .....................................................................................................................................................360 surf ..........................................................................................................................................................361

surf with an explicit or implicit function! .......................................................................................... 369 Animated surf ..........................................................................................................................................370 mesh ........................................................................................................................................................371 surfc.........................................................................................................................................................374 contour3 (3d contours) ............................................................................................................................375 surf with surf projection ..........................................................................................................................378 contour (2d contours) ..............................................................................................................................381 waterfall ..................................................................................................................................................385 2D Gradient (quiver) ...............................................................................................................................386 3D Gradient .............................................................................................................................................387 Perpendicular vectors ..............................................................................................................................390 Surface plots of nonuniformly sampled data ...........................................................................................391

Cubic (triangle base interpolation) ................................................................................................... 391 Delaunay (triangular connections) .................................................................................................... 393 Spline (biharmonic-spline) ................................................................................................................ 393

Image mapping plots ...................................................................................................... 394 Map an image on a 2D plane chart ..........................................................................................................394 Map an image on a 3D surface chart .......................................................................................................395 Sphere plot with data mapping and animated rotation .............................................................................397

Export animated plots as *.avi or *.gif........................................................................... 400 Export to *.avi .........................................................................................................................................400 Export to *.gif .........................................................................................................................................401

Engineering/Simulations ................................................................................................ 402 Vector filed equation analysis .................................................................................................................402 Vector field snapshots analysis ................................................................................................................404

Regression/Interpolation/Extropolation ......................................................................... 423 OLS univariate regression .......................................................................................................................423 Spline univariate interpolation .................................................................................................................425 Spline multivariate interpolation .............................................................................................................426

Fractals ........................................................................................................................... 428 Save chart as image ........................................................................................................ 430

Save on drive ...........................................................................................................................................430 Copy in the clipboard ..............................................................................................................................432

Analysis ................................................................................................................... 433


MATLAB 6

Estimate value of an univariate polynom on various points .......................................... 433

Calculate the roots of an univariate polynom ................................................................. 433 Find the local min/max of an univariate function in a range ......................................... 436 Find the local min/max of a bivariate function .............................................................. 438

1st Method (very old one) ........................................................................................................................438

2nd

Method (modern one).........................................................................................................................440 Discrete convolution ...................................................................................................... 440 Integration ...................................................................................................................... 443

Pseudo-symbolic integration of polynoms ...............................................................................................443 Numeric integration .................................................................................................................................443 Numeric trapezoidal integration ..............................................................................................................444 Double numeric integration .....................................................................................................................445

Derivation ....................................................................................................................... 446 Pseudo-symbolic derivation of polynoms ................................................................................................446 Numeric derivation ..................................................................................................................................447

Differential equations (ODE/PDE) ................................................................................ 450 Pendulum (ODE) .....................................................................................................................................450 Lotka-Volterra (system of ODE) .............................................................................................................453 Lorenz attractor (system of ODE) ...........................................................................................................455 2 body motion (system of ODE) ..............................................................................................................457 Heat equation (parapolic PDE) ................................................................................................................461

Fast Fourier Transform (DFT) ....................................................................................... 465

Image processing ..................................................................................................... 468 Get image properties ...................................................................................................... 468 Show an image properly ................................................................................................. 470 Decompose images alpha layers .................................................................................... 471

Build an image ............................................................................................................... 472 Plot some basic images manipulations and save image ................................................. 473

Filter on luminosity value of a given channel ................................................................ 474

Draw on an image and export the result ......................................................................... 475

Compare images ............................................................................................................. 478 Add (superpose) images ................................................................................................. 480

Video processing ..................................................................................................... 483 Get video properties ....................................................................................................... 483 Play video ....................................................................................................................... 484 Extract a frame ............................................................................................................... 485 Export all video frames in a folder ................................................................................. 486

Build a video from a list of (pre-processed or not) images ............................................ 487

Sound processing ..................................................................................................... 488 Get sound properties ....................................................................................................... 488 Play, Pause (resume), Resume, Stop sound playing ...................................................... 489 Plot a sound spectrum .................................................................................................... 490 Sound FFT (DFT)........................................................................................................... 492

Generate a sound and save it .......................................................................................... 494 Play sounds in sequence or parallel ................................................................................ 495

Scripting .................................................................................................................. 496 Script Editor most asked preferences ............................................................................. 496 Well commented script ................................................................................................... 498 Define help text .............................................................................................................. 500 Autocompletion .............................................................................................................. 501


MATLAB 7

Conditional structure (if/switch) .................................................................................... 503 if statement ..............................................................................................................................................503 switch statement (with if...) .....................................................................................................................506

Iteration structures .......................................................................................................... 507 For...End iteration structure (and optimization) .......................................................................................507 While...End iteration structure .................................................................................................................510

Functions (functions files) .............................................................................................. 511 One input, One output (OIOO) ................................................................................................................511 Multiple inputs, One output (MIOO) .......................................................................................................512 One input, Multiple outputs (OIMO) .......................................................................................................513 Multiple inputs, Multiple outputs (MIMO) ..............................................................................................515 Optional arguments .................................................................................................................................516 Variables scope .......................................................................................................................................517

Global vs Local variables .................................................................................................................. 517 Persistent variables ........................................................................................................................... 520

Anonymous function as input, chart output .............................................................................................521 Recursive functions .................................................................................................................................523 Local functions (multiple functions in one script) ...................................................................................525 Profile a script .........................................................................................................................................526 Catching errors ........................................................................................................................................528 Multiple callable functions in one *.m file ..............................................................................................528

Debugging technics ........................................................................................................ 531 M-lint ......................................................................................................................................................532

M-lint real time analyzer ................................................................................................................... 532 M-lint reports ..................................................................................................................................... 533

Echo on/Echo off .....................................................................................................................................537 For simple scripts .............................................................................................................................. 537 For functions scripts .......................................................................................................................... 541

Manipulations during a run ......................................................................................................................542 Debugging (db...) functions .....................................................................................................................544

Create a more complex wait bar ..................................................................................... 551

Import an XML file ........................................................................................................ 552 Export an XML file ........................................................................................................ 555 MATLAB Automation ................................................................................................... 557

Generate a Microsoft Word report ...........................................................................................................557 Put values into Microsoft Excel ...............................................................................................................559 Get values from a MS Excel VBA function ............................................................................................562

Create a ToolBox (App) ................................................................................................. 564 Install/Uninstall a Toolbox ......................................................................................................................570

Publish a script (documented script) .............................................................................. 574 Optimization tricks ......................................................................................................... 579

Statistically check code efficiency ...........................................................................................................580 linspace vs sequence ................................................................................................................................582 Simple arithmetic operation vs bsxfun ....................................................................................................583 Create userforms .....................................................................................................................................585

Symbolic calculations (Symbolic Toolbox) ................................................... 591 New main core features (to be complete) ............................................................... 591

MATLAB 2014a (8.3) .................................................................................................... 591 MATLAB 2013b (8.2) ................................................................................................... 591

MATLAB 2013a (8.1) .................................................................................................... 591 MATLAB 2012b (8.0) ................................................................................................... 591

Limits....................................................................................................................... 592

Derivate/Partial Derivate ......................................................................................... 593


MATLAB 8

Integration ............................................................................................................... 594

Taylor series ............................................................................................................ 594

Heaviside function ................................................................................................... 596

Matrix determinant .................................................................................................. 598

Jacobien ................................................................................................................... 598

MuPAD ................................................................................................................... 599

Databases (with Database/Datafeed toolbox) ............................................... 601 Connect to mySQL 5.5.36 .............................................................................................. 601 Connect to Microsoft Access 2003/2010 (*.mdb/*.accdb) ............................................ 606 Connect to Oracle Express 11g ...................................................................................... 610

Connect to MS SQL Server Express 2008 ..................................................................... 614 Connect to Yahoo! Finance ............................................................................................ 620

Statistics (with Statistical and Curve Fitting Toolbox) ................................ 621 Datasets ................................................................................................................... 621

Import/Export *.csv files as data set (data frame) .......................................................... 621 Import *.xls/*.xlsx files as data set (data frame) ............................................................ 623

Convert structure array to data sets ................................................................................ 624 Clean messy or missing data in datasets ........................................................................ 626 Select/Remove column (variable) .................................................................................. 628 Create subsets and filter ................................................................................................. 628

Delete rows and clean duplicates ................................................................................... 630 Add variables .................................................................................................................. 630

Change variable name .................................................................................................... 631 Change column order ..................................................................................................... 631 Random sample of a dataset ........................................................................................... 632

Sort a dataset .................................................................................................................. 633 Merge datasets ................................................................................................................ 634

Plots ......................................................................................................................... 635 Histogram/CDF/PDF ...................................................................................................... 635 Box-Whisker plot ........................................................................................................... 638

Scatter Group plot .......................................................................................................... 639 QQ plot ........................................................................................................................... 640 Histogram Scatter ........................................................................................................... 641 Copulas ........................................................................................................................... 642

Gaussian copula .......................................................................................................................................642

Descriptive statistics ................................................................................................ 645 Geometric mean ............................................................................................................. 645 Harmonic mean .............................................................................................................. 646 Trimmed mean (M-statistics) ......................................................................................... 646

CDF/iCDF/Quantile/Centile........................................................................................... 648 Skewness/Kurtosis ......................................................................................................... 649

Hypothesis tests ....................................................................................................... 652 Tests power, sample size and resolution ........................................................................ 652

Power of a Z test ......................................................................................................................................652 Sample size of a one sample Z test ..........................................................................................................653 Difference (resolution) of a one sample Z test .........................................................................................653 Power of a t test .......................................................................................................................................654 Sample size of a one sample t test ...........................................................................................................654 Sample size of a one sample p test ..........................................................................................................655


MATLAB 9

One sample Z-test ........................................................................................................... 655

One sample t-test ............................................................................................................ 656 One sample t-test with explicit target mean ................................................................... 657 Two sample homoscedastic t-test ................................................................................... 658 Two sample heteroscedastic t-test (Welch test) ............................................................. 659 Paired t-test ..................................................................................................................... 660

Chi-square variance test ................................................................................................. 661 Two sample F-test for equality of variances .................................................................. 662 Two sample Levene test for equality of variances ......................................................... 663

Brown-Forsythe (median)........................................................................................................................663 Absolute Levene ......................................................................................................................................665 Quadratic Levene (square) .......................................................................................................................666

Test for the median (one sample sign test) ..................................................................... 667 Binomial signed rank test (dixit: median test paired samples) ....................................... 668 Two unpaired samples Wilcoxon (Mann-Withney) rank sum test ................................ 669

Wilcoxon signed rank test for 1 sample ......................................................................... 670 Wilcoxon signed rank test for two paired samples ........................................................ 671 ANOVA ......................................................................................................................... 672

One-way fixed factor canonical ANOVA ................................................................................................672 Two-way fixed factors canonical ANOVA..............................................................................................675 Friedman's test (canonical non-parametric ANOVA based on ranks) ......................................................677 Kruskal-Wallis test (canonical non-parametric one-way ANOVA ..........................................................679

Adequation tests ............................................................................................................. 682 Chi-square goodness of fit for Poisson distribution .................................................................................682 Kolmogorov-Smirnov (one sample) adequation test ................................................................................682 Anderson-Darling adequation test ...........................................................................................................684

Regression Techniques ............................................................................................ 685 Ordinary Least Squares (parametric) univariate regression ........................................... 685

1st method (coefficient and constant can not be extracted) ......................................................................685

2nd

method (coefficient and constant and others can be extracted) ..........................................................689 3

rd method (using Curve Fitting Toolbox) ...............................................................................................691

Manage outliers .......................................................................................................................................697 Residuals and Leverage (residual diagnosis) ...........................................................................................701 Regression diagnostics wizard .................................................................................................................702

Ordinary Least Squares (parametric) multivariate regression (with/without interactions)

........................................................................................................................................ 704 1

st method (coefficient and constant can not be extracted) ......................................................................704

2nd

method (coefficient and constant and others can be extracted) ..........................................................707 Polynomial multivariate regression using OLS and Curve fit Toolbox ......................... 709 (Forward) Stepwise regression ....................................................................................... 712 General Linear Models (GLM) ...................................................................................... 715

Normal regression ...................................................................................................................................715 Log-linear Poisson regression..................................................................................................................716 Binomial (logistic) regression..................................................................................................................717

Data Mining/Machine Learning .............................................................................. 719 K-means (euclidian full) ................................................................................................. 719

Hierarchical ascendant (CAH) Dendrogram .................................................................. 726 CART Classification trees (Gini index based) ............................................................... 731 k-NN (k-Nearest Neighbors) .......................................................................................... 735 Naive Bayes .................................................................................................................... 737 Parametric Principal Component Analysis .................................................................... 740


MATLAB 10

Linear Discriminant Analysis (Fisher Discriminant) ..................................................... 745

Control charts (CC) ................................................................................................. 752 P attribute CC ................................................................................................................. 754 NP attribute CC .............................................................................................................. 756 C attribute CC ................................................................................................................. 758 U attribute CC ................................................................................................................ 760 Xbar-R continuous CC ................................................................................................... 762

Rbar-R continuous CC ................................................................................................... 763 Sbar-S continuous CC ................................................................................................... 765 I-EM continuous CC ...................................................................................................... 766 Moving Average continuous CC .................................................................................... 769

Design of experiments ............................................................................................. 771 Two-level full factorial design ....................................................................................... 771

Full factorial design ........................................................................................................ 771 Fractional factorial design .............................................................................................. 772

Simulations techniques ............................................................................................ 773 Kernel Smoothing .......................................................................................................... 773

Monte Carlo traditional technique .................................................................................. 775 Monte Carlo antithetic variables technique .................................................................... 777 Monte Carlo with antithetic quasi-random variables technique ..................................... 779 Latin HyperCube ............................................................................................................ 780

Monte Carlo by control variable (variance reduction technique) .................................. 782 Monte Carlo importance sampling ................................................................................. 784

Optimization (with Op timization Toolbox/Global Optimization Toolbox)

........................................................................................................................... 788 Linear optimization using LP Simplex (LPS) ......................................................... 788

LP-S Factory optimization problem (inequality linear system) ..................................... 788

LP-S Naive (without covariance...) Markowitz parametric portfolio optimization

problem (equality linear system without target value) ................................................... 791 LP-S Naive (without covariance...) Markowitz parametric portfolio optimization

problem (equality linear system with target value) ........................................................ 792

Function constrained optimization (FCO) .............................................................. 793 FCO with constraints and without specific target .......................................................... 793 FCO with constraints and specific target ....................................................................... 795 FCO with non linear constraints (and specific target) .................................................... 796

Quadratic optimization (QO) .................................................................................. 798 QO using conjugate gradient method (Q-CG) ............................................................... 798

QO using interior point convex method (Q-IPC) ........................................................... 800

Finance (with Finance/Optimization and Econometrics Toolboxes) ......... 801 Fractional prices ...................................................................................................... 801

Return ...................................................................................................................... 801

Maximum Draw Down ............................................................................................ 802

Box-Cox transformation .......................................................................................... 802

Simple capital calculations ...................................................................................... 804 Composed Interest (fixed future value) .......................................................................... 804 Composed Interest (fixed present value) ........................................................................ 805

Amortization and deprecation ................................................................................. 806 Straight line deprecation (SLN) ..................................................................................... 806


MATLAB 11

Sum of years digit (SYD) ............................................................................................... 806

Fixed declining-balance depreciation schedule (DB) .................................................... 807 Double declining balance (DDB) ................................................................................... 807

Loans and credits ..................................................................................................... 808 Payment for a loan based on constant payments and a constant interest rate (PMT) .... 808 Principal Payment (PPMT) ............................................................................................ 809 Interest Payment (IPMT) ................................................................................................ 810

Payment Present Value (PV) .......................................................................................... 811 Plot resume of loan payment .......................................................................................... 812

Annuities ................................................................................................................. 814 Postnumerando actual annuity value (PV) ..................................................................... 814 Postnumerando forward annuity value (PV) .................................................................. 814 Postnumerando number of periods (NPER) ................................................................... 815

Postnumerando annuity rate (ANNURATE) ................................................................. 815

Corporate finance .................................................................................................... 816 Net Present Value (NPV) ............................................................................................... 816

Periodic NPV ..........................................................................................................................................816 non-Periodic NPV ...................................................................................................................................816

Internal Rate of Return (IRR) ......................................................................................... 817 Periodic IRR ............................................................................................................................................817 non-Periodic IRR .....................................................................................................................................817

Modified Internal Rate of Return (MIRR) ..................................................................... 818

Treasure bonds/securities calculations .................................................................... 819 Clean price of a security (PRICE) .................................................................................. 819 Price of treasury bond/security (TBILLPRICE) ............................................................ 819

Yield of a treasury bond (TBILLYIELD) ...................................................................... 820 Discount rate of a security (DISC) ................................................................................. 821

Annual yield for a discounted security (YIELDDISC) .................................................. 821

Bond duration and Macaulay duration ........................................................................... 822

Naive Markowitz portfolio models ......................................................................... 823 Optimal short-long portfolio (without transaction costs) ............................................... 824

Optimal portfolio with implicit constraints no short sales allowed (without transaction

costs) ............................................................................................................................... 826 Optimal portfolio with implicit constraints no short sales allowed (with transaction costs)

........................................................................................................................................ 831 Get portfolios on the efficient frontier with explicit constraints (without transaction

costs) ............................................................................................................................... 832 Equally weighted portfolio (EWP) (without transaction costs) ..................................... 834 Maximum Sharpe Ratio (max. diversification) portfolio with implicit constraints

(without costs) ................................................................................................................ 836 Optimal portfolios for target returns and CVaR minimization (without transaction costs)

........................................................................................................................................ 838

Optimal portfolios for target risks and CVaR minimization (without transaction costs)

........................................................................................................................................ 839

Values at risk (VaR) ................................................................................................ 840 Parametric relative VaR ................................................................................................. 840

Parametric absolute VaR ................................................................................................ 840 non-Parametric (absolute) VaR ...................................................................................... 840 Condition (absolute) Normal VaR ................................................................................. 840


MATLAB 12

Options Pricing & Monitoring ................................................................................ 843 Pricing European Call & Put .......................................................................................... 843

European Call & Put implied volatiliy ........................................................................... 845 European Call & Put delta .............................................................................................. 845 European Option (call/put) Gamma ............................................................................... 846 European Option (call/put) Vega ................................................................................... 846 Option european lambda ................................................................................................ 846

Option european theta .................................................................................................... 847 Option european rho ....................................................................................................... 847 Implied volatility surface of an European option ........................................................... 847 Volatility smile of an European option .......................................................................... 848 CRR binomial European option pricing model .............................................................. 853

Time series .............................................................................................................. 855 Autocorrelation ............................................................................................................... 855 Partial autocorrelation .................................................................................................... 858

Moving average MM3 (without ARIMA) ..................................................................... 860 Simple Exponential Weighted Moving Average (EWMA) ........................................... 862 Univariate AR(2)/ARIMA(2,0,0) ................................................................................... 865 Univariate ARIMA(0,0,0)/Moving Average .................................................................. 868 Univariate ARIMA(0,1,0) .............................................................................................. 871

Univariate ARIMA(0,1,1)/Simple Exponential Smoothing (EWMA) .......................... 875 Univariate ARIMA(0,2,2)/Holt's double exponential smoothing .................................. 877

Univariate ARMA(1,1)/ARIMA(1,0,1) ......................................................................... 880 Univariate GARCH(1,1) ................................................................................................ 883

Applications (without Financial Toolbox) .............................................................. 888 Bond portfolio with duration/convexity targets ............................................................. 888

Brownian motion and Wiener Process ........................................................................... 889 Risk-return asset pricing models .................................................................................... 891

Capital Asset Pricing Model (CAPM) .....................................................................................................891 Three-factor Fama-French model (FFM) .................................................................................................892 Fama-McBeth ..........................................................................................................................................894

Options Pricing ............................................................................................................... 897 CRR binomial option pricing model without Financial Toolbox .............................................................897 Drifted CRR binomial option pricing model without Financial Toolbox .................................................898 Jarrow-Rudd binomial option pricing model without Financial Toolbox ................................................900 Jarrow-Rudd binomial risk neutral option pricing model without Financial Toolbox ..............................901 Leisen-Reimer binomial option pricing model without Financial Toolbox .............................................903 Tian binomial option pricing model without Financial Toolbox ..............................................................905

Portfolios models ............................................................................................................ 907 Global Minimum Variance Efficient Portfolios (GMVP) without Toolboxes using langrangien multiplier

................................................................................................................................................................907 Global Minimum Variance Efficient Portfolios (GMVP) using only Optimization Toolbox ..................908 Portfolio Performance .............................................................................................................................917 Michaud Optimal Portfolio (bootstrap/resample efficiency) ....................................................................919 CVaR portfolio ........................................................................................................................................923 Black-Litermann portfolio .......................................................................................................................930

Signal processing (Signal processing Toolbox) ............................................. 934

Circuit Analysis (Simulink Toolbox) ............................................................. 938 Create an RLC circuit .............................................................................................. 946

Neural Networks (Neural Network Toolbox) ............................................... 953


MATLAB 13

Image Processing (with Image Processing and Acquisition Toolboxes) .... 965 Play with the image tool wizard .............................................................................. 965

Image as a function ................................................................................................. 969

Image histogram ...................................................................................................... 971

Filters (blur, motion) on an image ........................................................................... 975

Crop an image ......................................................................................................... 979

Convert a *.gif file into an *.avi.............................................................................. 980

Overlay images with masks..................................................................................... 982

Objects recognition and extraction .......................................................................... 986 Without references ......................................................................................................... 986 With reference ................................................................................................................ 987

Image filters (convolution) ...................................................................................... 993 Gaussian (blur) filter ...................................................................................................... 993

1st method using imfilter() .......................................................................................................................993

2nd

method using convn().........................................................................................................................995 3

rd method using conv2() .........................................................................................................................996

External Camera Acquisition .................................................................................. 997

Parallel Computing (with Parallel Computing Toolbox) .......................... 1003 Clusters computing ................................................................................................ 1003

NVidia GPU computing ........................................................................................ 1007

Advanced scripting (C#, C++, Compiler Toolbox) .................................... 1008 Create a *.p (protected script) file (aka "pcode") .................................................. 1008

C MEX file ............................................................................................................ 1009

Create executable (*.exe) ...................................................................................... 1012

Call MATLAB from C# (VS Express 2010) ........................................................ 1016

Call MATLAB from C++ (VS Express 2010 x64) ............................................... 1022

Compile DLL and call from C# ............................................................................ 1048 Passing a scalar ............................................................................................................. 1048 Passing a constant, vector and matrix .......................................................................... 1058

Table 1 Standardized color codes ........................................................................................... 288 Table 2 Common dates format syntaxes ................................................................................ 314 Tableau 3 ODE solvers .......................................................................................................... 451


MATLAB 14

MATLAB is the abbreviation for MAtrix LABoratory and is actually the leading

environment for technical computing. Originally written in Fortran, by C Moler, MATLAB

was designed to facilitate the access to the matrix framework developed for the LINPACK

and EISPACK projects. The current version, written in C by the MathWorks Inc., exist in a

Professional version and a Student version. Its availability is ensured on multiple platforms:

Linux, Mac, Windows and several parallel machines.

MATLAB is a comprehensive and almost easy to use for scientific computing but very

expensive for students or independent/small companies (unlike R, Octave, Scilab or other free

open source equivalent alternatives). It provides to engineers, researchers and any scientific

an interactive system that integrates a lot of scientific numerical computation and

visualization algorithms (but can do much better!). It is a powerful, almost open and

programmable system allowing especially remarkable gains in productivity and creativity.

MATLAB is relatively complete, open and extensible for calculation and visualization

algorithms. It has hundreds (if not thousands, depending on the version and the optional

toolbox around the MATLAB core solution) mathematical, scientific and technical functions.

The matrix approach allows MATLAB to process data without large size variables and

perform numeric and symbolic calculations quickly and reliably. Thanks to the graphics

capabilities of MATLAB , it becomes very easy to interactively change the various graphics

settings and to adapt them according to our wishes.

The fact that the source code of some functions integrated in MATLAB can be inspected

gives sometimes the engineers to develop better custom made solutions (also do Python

Scipy...).

MATLAB has its own language that is very fast and allows time savings for Engineers

compared to other languages like C, Fortran, Python and the TurboPascal even if the language

is horrible to use (non-typed, bad closed lined, etc.). With MATLAB , we can make

connections dynamically, to C, .Net or Fortran programs, exchange data with other

applications (via DDE: MATLAB server or client) or use MATLAB as analysis and

visualization engine.

In terms of development speed, MATLAB is always faster than C/C++. This is to be expected

with a higher-level language, just as C/C++ is faster to develop with than assembler.

But a C/C++ programmer with an infinite amount of development time can beat MATLABs

speed, in the same way an assembly programmer with an infinite time can beat a C/C++

programmer.

MATLAB also includes a set of tools specific to engineering areas called Toolboxes.

Essential for most users, Toolboxes are collections of functions that extend the MATLAB

environment to solve specific types of problems. The areas covered are varied and include

signal processing, automatic control, system identification, neural networks, fuzzy logic,

structure calculation, statistics, database access, etc.

This document can also strongly help you to prepare the following certifications:


MATLAB 15

Like all my e-books you will found here only subjects that are proven and calculated by

hand in the theoretical course.

MATLAB Evolution

MATLAB was Programmed by Cleve Moler as an interface for EISPACK & LINPACK.

1957: Moler goes to Caltech. Studies numerical Analysis

1961: Goes to Stanford. Works with G. Forsythe on Laplacian eigenvalues.

1977: 1st edition of MATLAB ; 2000 lines of Fortran 80 functions (now more than 8'000 functions)

1979: Met with Jack Little in Stanford. Started working on porting it to C

1984: Mathworks is founded

Below is a screen shot from MATLAB 3.13:


MATLAB 16

Here's a screen shot of MATLAB 4.2c (1994):

Here's a screen shot from MATLAB 5.1 in 1997:


MATLAB 17

The last big change was in MATLAB 6.5 in 2002:


MATLAB 18

MATLAB 7:

MATLAB 8:


MATLAB 19


MATLAB 20

ISOZ Vincent

Resident until this date in Lausanne (Switzerland)

Trainer: Physicist Engineer HES (B.Sc.)

Year of birth: 1978

Director of the company Scientific Evolution Srl specialized in consulting and training for

high-potentials especially quantitative analysts in project management, quality, engineering,

finance and decision making. Incidentally, happy freelancer that gathers since young

information from articles everywhere and now addicted to everything related to applied

mathematics in the management of organization (Businesses, States), TQM (Total Quality

Management) with Post-taylorisme and related softwares.

Consultant in applied mathematics tutoring quantitative analysts (graduate and posgraduate)

in French, English and German and author of several French and English eBooks in the

following areas:

- statistical process control (parametric and nonparametric methods)

- predictive modeling / advanced decision (decision trees, Markov chains)

- Operations Research (quasi-Newton, simplex, genetic algorithms, algorithm GRG)

- data mining (neural networks, PCA, CA, regressions, scoring, clustering, etc.)

- risk modeling in project management and corporate finance (monte-carlo, bootstrapping)

- project management (best practices and theoretical models EFQM+Six Sigma, MS Office Project)

- ISO 9001:2008, 5807:1985, 10015:1999, 31000+31010:2009, 8258:1991, 10017:2003

- Adobe Photoshop and Illustrator

- 12 applications of the Microsoft Office System (Project, Visio, SharePoint, Access, etc.)

At this date I made interventions in over 200 companies, including some of to the Fortune 500

according to the 2009 listing and also in three universities and engineering schools in

Switzerland for databases and stochastic risk simulations trainings. I also gave training in

several multinational to executives in one to one. Sometimes I give training on softwares like

MS Project, MS Visio, MS Access and approximately 20 others softwares that I delegated the

training organization to companies specialized in computer softwares trainings (university

degree level and below).

Finally, I would advise anyone wishing to really master the subject to read my e-book on

Applied Mathematics (~ 4'900 pages).


MATLAB 21

KOLANI Daname

I'm currently living in Casablanca (Maroc)

Graduate in Finance from the Business School ENCG-

Casablanca

Born in 1990, I am from Togo.

I am passionate in the field of finance, economics, and other corollary as econometrics, also in

statistics & probabilities. Apart, the theories associated with those fields, I have a great

interest in tools that underpin all of these areas. I am bilingual (French & English) and my

specific competences include:

- Corporate Finance (Investment decision & Financing, Financial Analysis and Diagnosis, Management Control and Company Evaluation...)

- Market finance (financial portfolio management, financial asset valuation, risk management tools ...)

I also have an interest in computational finance skills in R Project, VBA, Excel, MATLAB ,

EViews & SPSS.

I aspire to get into consulting and thereby contribute to the optimization of financial decisions

and the implementation of efficient financial strategy consistent with the business model of

companies.


MATLAB 22

The content of this document is elaborated by a development process by which volunteers

reach a consensus. This process that brings together volunteers, research also the point of

view of people interested in the topic of this document. The person in charge of this document

administers the process and establishes rules to promote fairness in the consensus approach. It

is also responsible for drafting the text, sometime for testing/evaluating or independently

verifying the accuracy or completeness of the presented information.

We decline no responsibility for any injury, damage or any other kind, special, incidental,

consequential or compensatory, arising from the publication, application or reliance on the

content of this document. We make no express or implied warranty on the accuracy or

completeness of any information published in this document, and do not guarantee that the

information contained in this document meet any specific need or goal of the reader. We do

not guarantee the performance of products or services of one manufacturer or vendor solely

by virtue of the document content.

By publishing texts, it is not the intention of this document to provide services on behalf of

any person or entity or performing any task to be accomplished by any person or entity for the

benefit of a third party. Anyone using this document should rely on its own independent

judgment or, where that is appropriate, seek the advice of a qualified expert to determine how

to exercise reasonable care under all circumstances. The information and standards on the

topic covered by this document may be available from other sources that the reader may wish

to visit in search of points of view or additional information not covered by the contents of

this document.

We have no power in order to enforce compliance with the contents of this document, and we

do not undertake to monitor or enforce such compliance. We have no certification, testing or

inspection activity of products, designs or installations for safety or health of persons and

property. Any certification or other statement of compliance regarding information relating to

health or safety of persons and property, mentioned in this document, can not possibly be

attributed to the content of this document and remains under the responsibility of the

certification center or the concerned reporter.


MATLAB 23

As a reader of this document, you are the critic and the most important commentator. Your

opinion counts and it is very interesting for us to know what is good, what can be better and

topics that you would like to see be treated.

You can send me an e-mail to share what you liked or disliked in this document to ensure

continuous improvement.

If you want to complete this support with a subject that is important to you and for which you

have the mathematical proof please do not hesitate to contact me. I will integrate the subject

specifying your name and surname.

Note that unfortunately I can not answer to technical engineering questions or business issues

for free by email for obvious professional reasons.

E-mail: [email protected]

With that, I want to say a huge "THANK YOU" to all of my customers, partners,

colleagues, students and friends who with their feedback, return on experience helped

me write this e-book.
mailto:[email protected]


MATLAB 24

General

http://ww.sciences.ch (the companion website containing mathematical proofs)

http://ww.google.com

http://www.youtube.com

http://www.scribd.com

http://www.mathworks.com/products/

http://www.mathworks.ch/ch/help/matlab/release-notes.html

http://www.mathworks.com/matlabcentral/fileexchange/

http://www.mathworks.ch/discovery/

http://www.mathworks.ch/discovery/gallery.html

http://www.mathworks.com/matlabcentral/newsreader/

http://www.undocumentedmatlab.com

http://www.imageprocessingblog.com

http://www.alphorm.com (for people that want a part of this eBook as a video training):

z
www.sciences.chwww.google.comwww.youtube.comwww.scribd.comwww.mathworks.com/products/www.mathworks.ch/ch/help/matlab/release-notes.htmlwww.mathworks.com/matlabcentral/fileexchange/www.mathworks.ch/discovery/www.mathworks.ch/discovery/gallery.htmlwww.mathworks.com/matlabcentral/newsreader/www.undocumentedmatlab.comwww.imageprocessingblog.comhttp://www.alphorm.com/


MATLAB 25

Forums

http://ww.mathworks.ch/matlabcentral/answers/

http://www.talkstats.com

http://matlab.developpez.com

Non

matlab fundamentals

Documents

matlab core

matlab evolution

daname kolani

kolani daname

vincent isoz

isoz vincent

new main core features

table of contents