Interactive Computing

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1 Interactive Computing 1 Input/Output and Complex Arithmetic interactive Python scripts complex arithmetic 2 Python Coding Style and pylint coding style static code checking with pylint 3 Programming with Sound sampling sine functions numpy arrays in Python PyAudio: PortAudio v19 Python Bindings MCS 507 Lecture 3 Mathematical, Statistical and Scientific Software Jan Verschelde, 30 August 2013 Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

2 Interactive Computing 1 Input/Output and Complex Arithmetic interactive Python scripts complex arithmetic 2 Python Coding Style and pylint coding style static code checking with pylint 3 Programming with Sound sampling sine functions numpy arrays in Python PyAudio: PortAudio v19 Python Bindings Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

3 running a script We run the script hellothere.py at the command line prompt $: $ python hellothere.py Welcome to our interactive Python script! who is there? me How are you, me? type some number : 3.4 -> your number 3.4 : <type float > $ Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

4 input statements Two ways to enter data: 1 raw_input() returns a string, example: NAME = raw_input( who is there? ) After displaying who is there?, the characters typed in by the user are returned in a string are assigned to the variable NAME. 2 input() interprets the input of the user, e.g.: NUMB = input( type some number : ) After displaying type a number : and taking the user input, this input is interpreted and, if successful, is then assigned to the variable NUMB. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

5 parsing input strings The statement x = input( type some number : ) is equivalent to s = raw_input( type some number : ) x = eval(s) Test in an interactive Python session: >>> s = 1.2 >>> x = eval(s) >>> type(x) <type float > >>> x 1.2 Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

6 output statements The basic output is print some string. Some examples: print How are you, + NAME +? The + signs are for string concatenation. First the strings How are you,, the string in NAME, and? are added to one string before printing. print -> your number, NUMB, :, NUMBTYPE What is printed is separated by commas. The type of NUMB is not restricted to string. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

7 formatted output Often we want to format the output of floats: limit the number of decimal places >>> import math >>> print %.5f % math.pi display in scientific format >>> print %.4e % (100*math.pi) e+02 Observe that % is used twice differently: The % inside the string defines the format. The % after the format string is an operator. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

8 hellothere.py # L-3 MCS 507 Fri 30 Aug 2013 : hellothere.py """ Execute this script by typing at the command prompt $: python hellothere.py """ print Welcome to our interactive Python script! NAME = raw_input( who is there? ) print How are you, + NAME +? NUMB = input( type some number : ) NUMBTYPE = type(numb) print -> your number, NUMB, :, NUMBTYPE To explicitly check on the type, use isinstance. For example, in an interactive Python session: >>> x = 4.3 >>> isinstance(x,float) True Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

9 an alternative way to run a script #!/Library/Frameworks/Python.framework/Versions/2.7/bin/python # L-3 MCS 507 Fri 30 Aug 2013 : hellothere2.py """ Execute this script by typing at the command prompt $: hellothere2.py """ print Welcome to our interactive Python script! NAME = raw_input( who is there? ) print How are you, + NAME +? NUMB = input( type some number : ) NUMBTYPE = type(numb) print -> your number, NUMB, :, NUMBTYPE At the command prompt $, just type $./hellothere2.py Note that one must have permissions to execute the file, if necessary do chmod +x hellothere2.py (on Unix-like systems). Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

10 Interactive Computing 1 Input/Output and Complex Arithmetic interactive Python scripts complex arithmetic 2 Python Coding Style and pylint coding style static code checking with pylint 3 Programming with Sound sampling sine functions numpy arrays in Python PyAudio: PortAudio v19 Python Bindings Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

11 math and cmath The operations in math are restricted to floats: >>> import math >>> math.sqrt(-1) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: math domain error The c in cmath stands for complex: >>> import cmath >>> cmath.sqrt(-1) 1j The imaginary unit 1 is displayed as 1j. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

12 defining complex numbers The type complex is a builtin Python type: >>> z = complex(2,3) >>> type(z) <type complex > >>> z.real 2.0 >>> z.imag 3.0 >>> type(z.real) <type float > >>> z.conjugate() (2-3j) Python is object oriented: z.conjugate() is the application of the method conjugate to the object z. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

13 polar representation Session continued, with z = 2 + 3j: >>> import cmath >>> cmath.polar(z) ( , ) On returns is a tuple with absolute value and angle: >>> abs(z) >>> cmath.phase(z) From polar to rectangular representation: >>> (r,t) = cmath.polar(z) >>> r*cmath.exp(t*complex(0,1)) ( j) Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

14 unified treatment with numpy >>> import cmath >>> cmath.sqrt(2) ( j) We want a floating-point approximation for 2. >>> import numpy.lib >>> numpy.lib.scimath.sqrt(2) >>> type(_) <type numpy.float64 > >>> numpy.lib.scimath.sqrt(-2) j >>> type(_) <type numpy.complex128 > Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

15 Interactive Computing 1 Input/Output and Complex Arithmetic interactive Python scripts complex arithmetic 2 Python Coding Style and pylint coding style static code checking with pylint 3 Programming with Sound sampling sine functions numpy arrays in Python PyAudio: PortAudio v19 Python Bindings Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

16 Python coding style PEP 8 Style Guide for Python PEP = Python Enhancement Proposal available at This document gives coding conventions for Python code. The guidelines are intended to improve readability of the code. For example in Names to Avoid: Never use the characters l (lowercase letter el), O (uppercase letter oh), or I (uppercase letter eye) as single character variable names. In some fonts, these characters are indistinguishable from the numerals one and zero. When tempted to use l, use L instead. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

17 Interactive Computing 1 Input/Output and Complex Arithmetic interactive Python scripts complex arithmetic 2 Python Coding Style and pylint coding style static code checking with pylint 3 Programming with Sound sampling sine functions numpy arrays in Python PyAudio: PortAudio v19 Python Bindings Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

18 a Python code static checker pylint is a static checker of Python code. Copied from Pylint is a Python source code analyzer which looks for programming errors, helps enforcing a coding standard and sniffs for some code smells (as defined in Martin Fowler s Refactoring book). Pylint has many rules enabled by default, way too much to silence them all on a minimally sized program. It s highly configurable and handle pragmas to control it from within your code. Additionally, it is possible to write plugins to add your own checks. It s a free software distributed under the GNU Public Licence. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

19 running pylint $ pylint hellothere.py No config file found, using default configuration ************* Module hellothere W: 11, 7: Used builtin function input (bad-builtin) Report ====== 7 statements analysed.... output omitted... Global evaluation Your code has been rated at 8.57/10 (previous run: 8.57/10, Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

20 Interactive Computing 1 Input/Output and Complex Arithmetic interactive Python scripts complex arithmetic 2 Python Coding Style and pylint coding style static code checking with pylint 3 Programming with Sound sampling sine functions numpy arrays in Python PyAudio: PortAudio v19 Python Bindings Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

21 modeling sound A sound is a wave describe by sine function s(t) = A sin(2πf t), t is time in seconds, where the amplitude A is the strength of the sound and f is the frequency expressed in Hertz. An f Hz tone lasting for m seconds with sample rate r is defined by the sequence ( s n = A sin 2πf n ), n = 0, 1,..., m r. r For CD quality, the rate r is samples per second. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

22 playing sounds Sounds on a computer are stored in a WAV file. The package scitools available from the web site of the text book has a module sound.py. The script playsounds.py contains f = raw_input( give file name : ) print playing, f,... import scitools.sound scitools.sound.play(f) We run at the command prompt $ as $ python playsounds.py On MacOS X, scitools.sound.play(f) is equivalent to typing open f at the command line prompt. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

23 playing a tone We create a sound at 440 Hz for 6 seconds: import numpy, scitools.sound ATONE = scitools.sound.note(440, 6) calling note() of the module sound in the package scitools; note() returns a numpy array of floats and we must convert this array to two bytes integers: AMPLITUDE = 2**15-1 ATONE = AMPLITUDE*ATONE ATONE = ATONE.astype(numpy.int16) scitools.sound.write(atone, atone.wav ) scitools.sound.play( atone.wav ) Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

24 Interactive Computing 1 Input/Output and Complex Arithmetic interactive Python scripts complex arithmetic 2 Python Coding Style and pylint coding style static code checking with pylint 3 Programming with Sound sampling sine functions numpy arrays in Python PyAudio: PortAudio v19 Python Bindings Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

25 arrays in Python Python has no array type, but there is numpy, an abbreviation for the package Numerical Python. >>> import numpy as np >>> t = np.linspace(0,2*np.pi,5) >>> t array([ 0., , , , ]) linspace(a,b,n) creates an array of n equidistant points in the interval [a,b]. We sample at those points: >>> s = np.sin(2*np.pi*t) The array s contains the values of sin(2πt) at the points in the array of 5 equidistant points in t. No loop is needed! Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

26 vectorization Difference between math.sin() and numpy.sin()? numpy.sin() applies to numbers, arrays + is efficient >>> import numpy >>> x = numpy.linspace(0,1,100) >>> y = numpy.sin(x) the y = numpy.sin(x) is equivalent to >>> y = numpy.zeros(len(x)) >>> for i in range(0,len(x)):... y[i] = math.sin(x[i])... but the loop is not efficient. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

27 computing a sound Computing r = samples of a f = 440 Hz sound lasting for m = 6 seconds of amplitude A = 1 via ( s n = A sin 2πf n ), n = 0, 1,..., m r. r A couple of lines at the Python prompt: >>> import numpy as np >>> r = 44100; f = 440; m = 6; A = 1 >>> t = np.linspace(0,m,m*r) >>> s = A*np.sin(2*np.pi*f*t) Values for r, f, m, and A are the parameters for the note() in the sound module of the package scitools. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

28 creating an echo With a sound defined in the array s, we compute an echo: with a delay of one second, play a sound of half the original strength, for half of the original length. Using r as the sampling rate: delay = np.zeros(r) echo = 0.5*s[0:len(s)/2] sound = np.concatenate((s,delay,echo)) Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

29 the script compute_sound.py # L-3 MCS 507 Fri 30 Aug 2013 : compute_sound.py """ This script creates a.wav file with a sound at a prescribed frequency, using numpy and scitools. """ import numpy as np RATE = FREQ = 440 RANGE = 6 TIME = np.linspace(0, RANGE, RANGE*RATE) SINE = np.sin(2*np.pi*freq*time) DELAY = np.zeros(rate) ECHO = 0.5*SINE[0:len(SINE)/2] SOUND = np.concatenate((sine, DELAY, ECHO)) AMPLITUDE = 2**15-1 SOUND = AMPLITUDE*SOUND SOUND = SOUND.astype(np.int16) import scitools.sound scitools.sound.write(sound, atone.wav ) scitools.sound.play( atone.wav ) Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

30 Interactive Computing 1 Input/Output and Complex Arithmetic interactive Python scripts complex arithmetic 2 Python Coding Style and pylint coding style static code checking with pylint 3 Programming with Sound sampling sine functions numpy arrays in Python PyAudio: PortAudio v19 Python Bindings Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

31 PyAudio With PyAudio, you can use Python to play and record audio on a variety of platforms. Written by Hubert Phan, available at Download the scripts record.py and play.py: python record.py records a few sounds and saves to output.wav. python play.py output.wav plays the recorded sounds in output.wav. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

32 Summary + Exercises We covered chapter 1 of the text book. Exercises: (1 is exercise 1.13 how to cook the perfect egg) 1 The time t in seconds it takes for the center of the yolk to reach the temperature T y in Celsius is given by the formula t = M2/3 cρ 1/3 [ Kπ 2 ln 0.76 T ] o T w (4π/3) 2/3 T y T w where M is the mass, ρ the density, c is the specific heat capacity, and K is the thermal conductivity of the egg. Typical values for a large egg are M = 67 g, ρ = g cm 3, c = 3.7 J g 1 K 1, and K = W cm 1 K 1. The original temperature in Celsius is T o and T w = 100 C is the temperature of the boiling water. Write a script egg.py using the formula to compute the time t it takes for T y = 70 C. Prompt the user for the value of T o, for example: T o = 4 C (fridge), T o = 20 C (room temperature). Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

33 more exercises b 2 Consider the quadratic formula x = b± 2 4ac 2a for the roots of ax 2 + bx + c. Write an interactive Python script that prompts the user for a, b, c and prints the roots. Use numpy.lib.scimath to compute the roots. 3 Make a sound composed of two frequencies, e.g.: one at 440 Hz and the other at 300 Hz, where the first has twice the amplitude of the other, lasting for ten seconds. The first homework collection is on Monday 9 September, at 9AM. Bring to class your answers to exercise 3 of Lecture 1; exercises 1, 2 of Lecture 2; and exercises 1, 3 of Lecture 3. Along with a paper version, also me your scripts. Scientific Software (MCS 507 L-3) Interactive Computing 30 August / 33

List Comprehensions and Simulations

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