Difference between revisions of "CompSciHW5"
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(Created page with "Homework 6 - Due Friday, March 4, 2016 <pre> 1) Create a function that parses the following files: a) mat33 = """ 1.0 2.0 3.0 -2.0 0.0 1.0 1.0 1.1 1.2 """ b) csv = """ # ti...") |
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| − | Homework |
+ | Homework 5 - Due Friday, March 4, 2016 |
<pre> |
<pre> |
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| − | 1) |
+ | 1) Use numpy and pyplot to plot the following functions: |
| − | + | (remember to start by choosing an appropriate range for x) |
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| − | + | a) f(x) = sin(x) cos(2x) |
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| − | + | b) g(x) = x (if x is in 0,1), 2-x (if x is in 1,2), 0 otherwise |
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| − | + | c) h(x) = exp(-x*x/(2*sigma)), for sigma = 1, 2, and 3 |
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| − | + | d) w(x) = g(x) - 4*g(x-2.0) |
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| + | e) u(x, y) = sin(x)*cos(3*y) - cos(2*x)*sin(y) [Hint: use pylab.imshow()] |
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| − | b) csv = """ |
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| + | 2) Name the type of the following functions: |
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| − | # time temperature sea_level |
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| + | (remember that *a means a list is input and **a means a dictionary) |
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| − | 0.0, 300.0, 44.5 |
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| + | a) def joinwith(space, *a): |
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| − | 1.5, 299.5, 44.0 |
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| + | return space.join(a) |
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| − | 3.0, 299.8, 44.2 |
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| + | b) def map_on_n(f, n): |
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| − | 4.5, 301.0, 43.9 |
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| + | return [f(i) for i in range(n)] |
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| − | """ |
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| + | c) def get_elem(k="default", **d): |
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| + | return d[k] + 2.0 |
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| + | d) def chaos(*a, **b): |
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| + | return random.random()*random.random() |
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| + | e) def sliceof(st, stop, step, *a): |
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| + | return a[st:stop:step] |
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| + | </pre> |
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| − | c) name_val = """ |
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| + | Hint: Try defining x as an array of x-values, and f,g,h, etc. as a python function with type float -> float. |
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| − | seed = 1553 |
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| + | Then plot(x, f(x)) |
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| − | name = "test name" |
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| + | or calculate the values using vals = map(f, x) |
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| − | trials = 10 |
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| + | The first one tricks the function into the type (array -> array), and the second computes 1 float at a time. |
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| − | tolerance = 1e-8 |
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| − | """ |
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| − | d) group_data = """ |
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| + | <source lang="python"> |
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| − | [Group 1] |
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| + | import numpy as np |
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| − | 1 2 3 4 5 6 |
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| + | from pylab import plot, show, imshow |
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| + | N = 100 |
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| + | x = np.linspace(-3.0, 3.0, N) # plotting 1D functions |
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| + | y = np.linspace(-2.0, 2.0, N) |
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| − | [Group 2] |
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| + | X, Y = np.meshgrid(x, y) # plotting 2D functions (1.e) |
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| − | 4 5 11 14 1 |
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| + | </source> |
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| − | |||
| − | [Group 3] |
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| − | 7 8 9 10 11 |
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| − | """ |
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| − | |||
| − | 2) Write code to carry out matrix multiplication manually |
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| − | and test it against the result of numpy.dot. |
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| − | |||
| − | 3) Write code to multiply every column of matrix, A, |
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| − | with every other column. Use this to find the set of angles |
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| − | between the column vectors. |
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| − | </pre> |
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Latest revision as of 15:47, 4 March 2016
Homework 5 - Due Friday, March 4, 2016
1) Use numpy and pyplot to plot the following functions:
(remember to start by choosing an appropriate range for x)
a) f(x) = sin(x) cos(2x)
b) g(x) = x (if x is in 0,1), 2-x (if x is in 1,2), 0 otherwise
c) h(x) = exp(-x*x/(2*sigma)), for sigma = 1, 2, and 3
d) w(x) = g(x) - 4*g(x-2.0)
e) u(x, y) = sin(x)*cos(3*y) - cos(2*x)*sin(y) [Hint: use pylab.imshow()]
2) Name the type of the following functions:
(remember that *a means a list is input and **a means a dictionary)
a) def joinwith(space, *a):
return space.join(a)
b) def map_on_n(f, n):
return [f(i) for i in range(n)]
c) def get_elem(k="default", **d):
return d[k] + 2.0
d) def chaos(*a, **b):
return random.random()*random.random()
e) def sliceof(st, stop, step, *a):
return a[st:stop:step]
Hint: Try defining x as an array of x-values, and f,g,h, etc. as a python function with type float -> float. Then plot(x, f(x)) or calculate the values using vals = map(f, x) The first one tricks the function into the type (array -> array), and the second computes 1 float at a time.
<source lang="python"> import numpy as np from pylab import plot, show, imshow N = 100 x = np.linspace(-3.0, 3.0, N) # plotting 1D functions y = np.linspace(-2.0, 2.0, N)
X, Y = np.meshgrid(x, y) # plotting 2D functions (1.e) </source>
