Introductory Scientific Computing with Python Exercises FOSSEE - - PowerPoint PPT Presentation

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Introductory Scientific Computing with Python Exercises FOSSEE - - PowerPoint PPT Presentation

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Introductory Scientific Computing with Python Exercises FOSSEE Department of Aerospace Engineering IIT Bombay Mumbai, India FOSSEE (FOSSEE IIT Bombay) Exercises 1 / 21 Problem 1 Example code In []: l, t = loadtxt(pendulum.txt,

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Introductory Scientific Computing with Python

Exercises FOSSEE

Department of Aerospace Engineering IIT Bombay

Mumbai, India

FOSSEE (FOSSEE – IIT Bombay) Exercises 1 / 21

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Problem 1

Example code

In []: l, t = loadtxt(’pendulum.txt’, unpack=True) In []: plot(l, t, ’.’)

Problem Statement Tweak above code to plot data in file pos.txt.

FOSSEE (FOSSEE – IIT Bombay) Exercises 2 / 21

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Problem 1 cont...

Label both the axes. What kind of motion is this? Title the graph accordingly. Annotate the position where vertical velocity is zero.

FOSSEE (FOSSEE – IIT Bombay) Exercises 3 / 21

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Solution

x, y = loadtxt(’pos.txt’, unpack=True) plot(x, y) xlabel(’x’) ylabel(’y’) title(’Projectile motion’) annotate(’v = 0’, xy=(5, 4.75)) # Or annotate(r’$v_y = 0$’, xy=(5, 4.75))

Note the L

A

T EX syntax Note the raw strings: r’$v_y = 0$’

FOSSEE (FOSSEE – IIT Bombay) Exercises 4 / 21

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Problem 2

Plot points given x and y coordinates

In []: x = [3, 2, -2, 3] In []: y = [1, -3, 4, 1] In []: plot(x, y)

Line can be plotted using arrays of coordinates. Problem statement Write a Program that plots a regular n-gon(Let n = 5).

FOSSEE (FOSSEE – IIT Bombay) Exercises 5 / 21

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Problem 2

Plot points given x and y coordinates

In []: x = [3, 2, -2, 3] In []: y = [1, -3, 4, 1] In []: plot(x, y)

Line can be plotted using arrays of coordinates. Problem statement Write a Program that plots a regular n-gon(Let n = 5).

FOSSEE (FOSSEE – IIT Bombay) Exercises 5 / 21

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Solution

n = 5 t = linspace(0, 2*pi, n+1) x = cos(t) y = sin(t) plot(x, y) axis(’equal’)

FOSSEE (FOSSEE – IIT Bombay) Exercises 6 / 21

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Better Solution

def plot_ngon(n): t = linspace(0, 2*pi, n+1) x = cos(t) y = sin(t) plot(x, y) axis(’equal’) plot_ngon(5) clf() plot_ngon(10)

FOSSEE (FOSSEE – IIT Bombay) Exercises 7 / 21

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Problem 3

Damped Oscillation

In []: t = linspace(0, 4*pi) In []: plot(t, exp(-t/10)*sin(t)) FOSSEE (FOSSEE – IIT Bombay) Exercises 8 / 21

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Problem 3 cont...

Create a sequence of images (say 10) in which the damped oscillator(e−t/10sin(t)) slowly evolves over time t. Hint

savefig(’plot’+str(i)+’.png’) #i is some int

FOSSEE (FOSSEE – IIT Bombay) Exercises 9 / 21

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Naive Solution

for i in range(1, 11): t = linspace(0, 0.5*pi*i, 50*i) clf() plot(t, exp(-t/10)*sin(t)) savefig(’plot’ + str(i) + ’.png’)

FOSSEE (FOSSEE – IIT Bombay) Exercises 10 / 21

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Better Solution

for i in range(1, 11): t = linspace(0, 0.5*pi*i, 50*i) clf() plot(t, exp(-t/10)*sin(t)) xlim(0, 5*pi) ylim(-1, 1) savefig(’plot’ + str(i) + ’.png’)

FOSSEE (FOSSEE – IIT Bombay) Exercises 11 / 21

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Problem 4

In []: x = imread(’smoothing.gif’) In []: x.shape Out[]: (256, 256) In []: imshow(x,cmap=cm.gray) In []: colorbar()

Replace each pixel with mean of neighboring pixels

FOSSEE (FOSSEE – IIT Bombay) Exercises 12 / 21

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FOSSEE (FOSSEE – IIT Bombay) Exercises 13 / 21

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Problem 4: Approach

For y being resultant image:

y[1, 1] = x[0, 1]/4 + x[1, 0]/4 + x[2, 1]/4 + x[1, 2]/4

Hint: Use array Slicing.

FOSSEE (FOSSEE – IIT Bombay) Exercises 14 / 21

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Solution

In []: y = zeros_like(x) In []: y[1:-1,1:-1] = x[:-2,1:-1]/4 + x[2:,1:-1]/4 + x[1:-1,2:]/4 + x[1:-1,:-2]/4 In []: imshow(y,cmap=cm.gray)

FOSSEE (FOSSEE – IIT Bombay) Exercises 15 / 21

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Problem 4 cont. . .

Apply the smoothing operation repeatedly to the

  • riginal image

Subtract the smoothed image from the original to

  • btain the edges

FOSSEE (FOSSEE – IIT Bombay) Exercises 16 / 21

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Problem 5

What if you did the following in problem 4?

In []: y1 = zeros_like(x) In []: y1[1:-1,1:-1] = (x[:-2,1:-1] + x[2:,1:-1] + x[1:-1,2:] + x[1:-1,:-2])/4

Are the answers different?

FOSSEE (FOSSEE – IIT Bombay) Exercises 17 / 21

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Problem 5 cont. . .

Why? The answer lies in the following:

In []: x.dtype Out[]: dtype(’uint8’) In []: print(x.itemsize) 1 In []: z = x/4.0 In []: print(z.dtype) float64

FOSSEE (FOSSEE – IIT Bombay) Exercises 18 / 21

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Problem 5 cont. . .

What if you did this?

x = imread(’smoothing.gif’) y2 = zeros_like(x) y2[1:-1,1:-1] = x[:-2,1:-1]/4. + \ x[2:,1:-1]/4. + \ x[1:-1,2:]/4. + \ x[1:-1,:-2]/4.

Will the answer be any different from y? What will the dtype of y2 be? Discuss what is going on!

FOSSEE (FOSSEE – IIT Bombay) Exercises 19 / 21

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Problem 5 cont. . .

Did you do the right thing to find the edges earlier in problem 4? If not, fix it! Note that:

In []: print(x.dtype) uint8 In []: x1 = x.astype(’float64’) In []: print(x1.dtype) float64 In []: print(x.dtype.char) d In []: x.dtype.<TAB> # Explore!

FOSSEE (FOSSEE – IIT Bombay) Exercises 20 / 21

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Problem 6

Edge detection looks much nicer with lena.png, try it! The caveat is that it is a 4 component RGBA image with elements in the range [0.0, 1.0].

In []: x = imread(’lena.png’) In []: print(x.shape) (512, 512, 4) In []: print(x.min(), x.max()) (0.0, 1.0)

Repeat the edge detection with this image.

FOSSEE (FOSSEE – IIT Bombay) Exercises 21 / 21