Scientific Computing Using. Atriya Sen

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1 Scientific Computing Using Atriya Sen

2 Broad Outline Part I, in which I discuss several aspects of the Python programming language Part II, in which I talk about some Python modules for scientific computing Part III, in which I show you how Python can be integrated with other languages

3 Broad Outline Part I, in which I discuss several aspects of the Python programming language Part II, in which I talk about some Python modules for scientific computing Part III, in which I show you how Python can be integrated with other languages

4 #1: Readable & Compact Code Shorter and more readable programs Higher programmer productivity E F = open(filename, r ); F.read().split()

5 #2: Dynamic typing Types are decided at run-time, as opposed to static typing, where types are decided at compile-time Procedure to dump a data structure with a debugging message: def debug(leading_text, variable): if os.environ.get( MYDEBUG, 0 ) == 1 : print leading_text, variable Dynamic typing extends elegantly to nested heterogeneous data structures!

6 The Same Code In C++... template <class T> void debug(std::ostream& o, const std::string& leading_text, const T& variable) { } char* c = getenv("mydebug"); bool defined = false; if (c!= NULL) // if MYDEBUG is defined... if (std::string(c) == "1") // if MYDEBUG is true... defined = true; if (defined) o << leading_text << " " << variable << std::endl;

7 #3: Interactive Computing

8 #4: Easy GUI Programming A graphical Hello World program: #!/usr/bin/env python from Tkinter import * root = Tk() Label(root, text= Hello, World!, foreground="white", background="black").pack() root.mainloop() C + X11: 176 lines of ugly code Things get even worse for C when it comes to web development!

9 #5: Create Code At Runtime! Code can be constructed and executed at run-time: a = 1.2 no of iterations = 100 solution strategy = implicit c1 = 0 c2 = 0.1 A = 4 c3 = StringFunction( A*sin(x) ) Can we read this file and define a, no_of_iterations, solution_strategy, c1, c2, c3, A with the specified values? Yes!

10 #5: Create Code At Runtime (2) file = open( inputfile.dat, r ) for line in file: variable, value = line.split( = ).strip() variable = re.sub(, _, variable) exec(variable + = + value) # magic :D This cannot be done in C, C++, FORTRAN, or Java!

11 Python Compared To MATLAB Python modules provide functionality comparable to MATLAB Python can be as fast as MATLAB (and faster than Octave) The Python language is more flexible and powerful Object oriented programming is more convenient in Python Transferring functions as arguments to functions is simpler Nested, variable-type data structures are simpler to construct and use Interfacing with other languages and tools is simpler in Python MATLAB is more self-contained Python respects your freedom; Python runs on more platforms

12 Broad Outline Part I, in which I discuss several aspects of the Python programming language Part II, in which I talk about some Python modules for scientific computing Part III, in which I show you how Python can be integrated with other languages

13 numpy.scipy.or g numpy = Numeric + numarray Efficient array computations using a fixed-size, fixed-type multi-dimensional array type; also offers a matrix type Trigonometric and other functions don't use these on scalars! Basic random number generation and linear algebra capabilities More functionality in the numpyutils module

14 NumPy Example: Just How Fast Are We Talking? from numpy import * import time a = linspace(0, 1, 1E+07) t0 = time.clock() b = 3*a -1 t1 = time.clock() for i in xrange(a.size): b[i] = 3*a[i] - 1 t2 = time.clock() print '3*a-1: %g sec, loop: %g sec' % (t1-t0, t2- t1)

16 SciPy ( Builds on NumPy to provide a rapidly developing environment for scientific computing Special mathematical functions Integration ODE solvers Random variables and statistics Linear algebra calls up LAPACK Optimization and root-finding Interpolation An alternative is ScientificPython (dirac.cnrsorleans.fr/plone/software/scientificpython) A short digression: matplotlib and gnuplot

17 SciPy Examples Finding the first four zeroes of the Bessel function J3: from scipy.special import jn_zeros jn_zeros(3, 4) Simple integration: from scipy import integrate def myfunc(x): return sin(x) result, error = integrate.quad(myfunc, 0, pi) print result, error

19 Biopython (biopython.org) Parse bioinformatics files Use NCBI Blast, Entrez, PubMed and ExPASy data Interfaces to common bioinformatics programs A standard sequence class Tools for performing common operations on sequences Code to perform classification of data Code for dealing with alignments Split up parallelizable tasks into separate processes GUI-based programs Extensive documentation Integration with BioSQL

21 SymPy (sympy.org) Aims to become a fullfeatured computer algebra system Written in pure Python An alternative is Swiginac (SWIGbased interface to GiNaC, which is written in C++) Limits Symbolic matrices Quantum physics Differential equations Pattern matching Geometric algebra Complex numbers Expansions

22 SymPy Example def make_symbols(*args): return [Symbol(s) for s in args] x, a, A, omega, sigma, m, t = \ make_symbols('x', 'a', 'A', 'omega', 'sigma', 'm', 't') f = A*exp(-((x-m)/(2*sigma))**2)*exp(- a*t)*sin(2*pi*omega*x) Prms = {'A': 1, 'a': 0.1, 'm': 1, 'sigma': 1, 'omega': 1, 't': 0.2} print diff(f, x, 2)

23 More Python Modules! PyPI The Python Package Index (pypi.python.org/pypi)

24 Broad Outline Part I, in which I discuss several aspects of the Python programming language Part II, in which I talk about some Python modules for scientific computing Part III, in which I show you how Python can be integrated with other languages

25 Python and C Migration of performancecritical code to C Access existing C code Python is written in C and designed to be extended with C functions C has strong typing rules; variables in Python are typeless So, we need a wrapper function written in C extern double hw1(double r1, double r2); from hw import hw1 r1 = 1.2; r2 = -1.2 s = hw1(r1, r2) Python C API Extending and Embedding the Python Interpreter (official documentation) Needed to manipulate Python data structures in C

26 The Wrapper Function static PyObject *_wrap_hw1(pyobject *self, PyObject *args) { double arg1, arg2, result; if (! PyArg_ParseTuple(args, "dd:hw1", &arg1, &arg2)) { } return NULL; result = hw1(arg1, arg2); return Py_BuildValue("d", result); } Compile the wrapper function Compile the hw1 function Link their object codes to form a shared library module This is called an extension module and can be imported into Python code There is no way to tell between a C module and a Python module

27 Generation of Wrapper Code SWIG (Simplified Wrapper Interface Generator) for C and C++ F2PY for FORTRAN Instant has support for inline C code. Uses SWIG Pysco is a JIT for Python Pyrex and Cython convert pseudo-python code to C Many other tools available CXX, SCXX, Boost.Python, Weave, Pyrex, Pysco

28 Python, Java,.NET Seamless implementation of Python on.net Python tools for MS Visual Studio Implementation on Python on the JVM Seamless - any Java class can be used in a Jython script

29 Python, MATLAB, Mathematica The pymat module sends NumPy arrays to MATLAB. It only has the functions open, close, eval, put, get The mlabwrap module makes MATLAB command available directly in Python PYML is a Python- Mathematica interface import pymat x = linspace(0, 4*math.pi, 401) m = pymat.open() pymat.put(m, x, x); pymat.eval(m, y = sin(x) ) pymat.eval(m, plot(x,y) ) y = pymat.get(m, y ) import time; time.sleep(4) pymat.close(m)

30 Where To Go For More or even Both by Mark Pilgrim Python Scripting For Computational Science by H. P. Langtangen The password for the 3 rd edition is 'Clicking' (for MATLAB users)

Slides from INF Course intro

Slides from INF Course intro Slides from INF3331- Course intro p. 1/38 Slides from INF3331 - Course intro Ola Skavhaug, Joakim Sundnes and Hans Petter Langtangen Dept. of Informatics, Univ. of Oslo & Simula Research Laboratory August