F# for Scientists. Jon Harrop Flying Frog Consultancy Ltd. Foreword by Don Syme A JOHN WILEY & SONS, INC., PUBLICATION WILEY

Transcription

1 F# for Scientists Jon Harrop Flying Frog Consultancy Ltd. Foreword by Don Syme WILEY A JOHN WILEY & SONS, INC., PUBLICATION

2 Preface Acknowledgments List of Figi ares List of Tables Acronyms 1 Introduction Programming guidelines A brief history of F# Benefits of F# Introducing F# Language overview Pattern matching Equality Sequence expressions 4 XIX xxi xxiii xxv xxxi ХХХШ ix

3 X Exceptions Imperative programming Functional programming Immutability Recursion Curried functions Higher-order functions 35 Program Structure 37 2.,1 Nesting Factormg Factoring out common subexpressions Factoring out higher-order functions Modules Objects Augmentations Classes Functional design patterns Combinators Maps and folds F# development Creating an F# project Building executables Debugging Interactive mode C# interoperability 58 Data Structures Algorithmic complexity Primitive operations Complexity Arrays А ТТ'ЯЛ/'С 69 r\.l I ay a Array literals Array indexing Array concatenation Aliasing Subarrays Creation

4 XI Lists Sets Hash tables Maps Iteration Map Folds Sorting Pattern matching Sorting Searching Filtering Maps and folds Pattern matching Creation Insertion Cardinality Set-theoretic operations Comparison Creation Searching Insertion, replacement a Higher-order functions Creation Searching Higher-order functions Choosing a data structure Sequen ces Heterogeneous containers Trees Balanced trees Unbalanced trees Abstract syntax trees Numerical Analysis 4.1 Number representation Machine-precision integers Machine-precision floating-point numbers

5 XII 4.2 Algebra Interpolation Quadratic solutions Mean and variance Other forms of arithmetic Arbitrary-precision integer arithmetic Arbitrary-precision rational arithmetic Adaptive precision 125 Input and Output Printiflg Generating strings Generic printing Reading from and writing to files Serialization Lexing and parsing Lexing Parsing Simple Examples Functional Nest Fixed point Within Memoize Binary search Numerical Heaviside step Kronecker ^-function Gaussian Binomial coefficients Root finding Grad Function minimization Gamma function Discrete wavelet transform String related Transcribing DNA

6 6.3.2 Word frequency 6.4 List related count positions fold_to insert chop dice apply_at sub extract shuffle transpose combinations distribute permute Power set 6.5 Array related rotate swap except shuffle 6.6 Higher-order functions Tuple related Generalized products Visualization 7.1 Windows Forms Forms Controls Events Bitmaps Example: Cellular automata Running an application 7.2 Managed DirectX Handling DirectX devices Programmatic rendering Rendering an icosahedron

7 XIV Declarative rendering Spawning visualizations from the F# interactive mode Tesselating objects into triangles Spheres D function plotting 196 Optimization Libraries Timing % Absolute time CPU time Looping Example timing Profilin j queens problem Algorithmic optimizations Lower-level optimizations Benchmarking data structures Compiler flags Tail-recursion Avoiding allocation Terminating early Avoiding higher-order functions Use mutable Specialized functions Unboxing data structures Eliminate needless closures Inlining Serializing Loading I.NET libraries Charting and graphing Threads Thread safety Basic use Locks The thread pool Asynchronous delegates

8 XV Background threads Random numbers Regular expressions Vectors and matrices Downloading from the Web Compression Handling XML Reading Writing Declarative representation Calling native libraries Fourier transform Native-code bindings Interface in F# Pretty printing complex numbers Example use Metaprogramming Emitting IL code Compiling with LINQ Databases Protein data bank Interrogating the PDB Pretty printing XML in F# interactive sessions Deconstructing XML using active patterns Visualization in a GUI Web services US temperature by zip code Interrogating the NCBI Relational databases Connection to a database Executing SQL statements Evaluating SQL expressions Interrogating the database programmatically Filling the database from a data structure Visualizing the result Cleaning up 264 ч

9 XVi 11 Interoperability Excel Referencing the Excel interface Loading an existing spreadsheet Creating a new spreadsheet Referring to a worksheet Writing cell values into a worksheet Reading cell values from a worksheet MATLAB Creating a.net interface from a COM interface % Using the interface Remote execution of MATLAB commands Reading and writing MATLAB variables Mathematica Using.NET-link Example Complete Examples Fast Fourier transform Discrete Fourier transform Danielson-Lanczos algorithm Bluestein's convolution algorithm Testing and performance Semi-circle law Eigenvalue computation Injecting results into Excel Results Finding n -nearest neighbors Formulation Representing an atomic configuration Parser Lexer Main program Visualization Logistic map Real-time particle dynamics Appendix A: Troubleshooting 311

10 XVII АЛ A.2 А.З А.4 A.5 А.6 А.7 А.8 Glossary Value restriction Mutable array contents Negative literals Accidental capture Local and non-local variable definitions Merging lines Applications that do not die Beware of "it" Bibliography 325 Index 329