Informatics2-2018/Lab11
(Új oldal, tartalma: „=Exercises= ==Introduction== Some exercises to bet used to numpy # Make a vector of length 10 with elements all zero! Then modify its 4th element to 1 ''(zeros)'' # Ma…”) |
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(egy szerkesztő 2 közbeeső változata nincs mutatva) | |||
1. sor: | 1. sor: | ||
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=Exercises= | =Exercises= | ||
==Introduction== | ==Introduction== | ||
− | Some exercises to | + | Some exercises to get used to numpy |
# Make a vector of length 10 with elements all zero! Then modify its 4th element to 1 ''(zeros)'' | # Make a vector of length 10 with elements all zero! Then modify its 4th element to 1 ''(zeros)'' | ||
# Make a 3-by-3 matrix with elements ranging from 0 up to 8 ''(reshape)'' | # Make a 3-by-3 matrix with elements ranging from 0 up to 8 ''(reshape)'' | ||
− | # Make a random vector of length 30 containing random number between 0 to 1! Calculate its | + | # Make a random vector of length 30 containing random number between 0 to 1! Calculate its average and standard deviation! ''(rand, mean, std)'' |
## Make a random vector of the same length with elements between -3 and 2! | ## Make a random vector of the same length with elements between -3 and 2! | ||
# Make a random unit vector in 5 dimensions! First make a random vector in 5 dimensions and then normalize it to unit length! | # Make a random unit vector in 5 dimensions! First make a random vector in 5 dimensions and then normalize it to unit length! | ||
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==Monte-Carlo== | ==Monte-Carlo== | ||
Generate 500000 random points in the rectangle <math>[0,2]\times[0,4]</math>. Count how many of the points <math>(x,y)</math> have the property that <math>x^2>y</math>. Use this to approximate the integral <math>\int_0^2x^2 d x</math> Like in the end of the lecture. | Generate 500000 random points in the rectangle <math>[0,2]\times[0,4]</math>. Count how many of the points <math>(x,y)</math> have the property that <math>x^2>y</math>. Use this to approximate the integral <math>\int_0^2x^2 d x</math> Like in the end of the lecture. | ||
22. sor: | 25. sor: | ||
Plot the function <math>\sin(x)</math> and its derivative on the interval <math>[-\pi, \pi]</math>. | Plot the function <math>\sin(x)</math> and its derivative on the interval <math>[-\pi, \pi]</math>. | ||
Calculate the derivative with [https://en.wikipedia.org/wiki/Finite_difference finite difference] method! | Calculate the derivative with [https://en.wikipedia.org/wiki/Finite_difference finite difference] method! | ||
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A lap jelenlegi, 2018. május 10., 11:23-kori változata
Tartalomjegyzék |
Exercises
Introduction
Some exercises to get used to numpy
- Make a vector of length 10 with elements all zero! Then modify its 4th element to 1 (zeros)
- Make a 3-by-3 matrix with elements ranging from 0 up to 8 (reshape)
- Make a random vector of length 30 containing random number between 0 to 1! Calculate its average and standard deviation! (rand, mean, std)
- Make a random vector of the same length with elements between -3 and 2!
- Make a random unit vector in 5 dimensions! First make a random vector in 5 dimensions and then normalize it to unit length!
Monte-Carlo
Generate 500000 random points in the rectangle . Count how many of the points (x,y) have the property that x2 > y. Use this to approximate the integral Like in the end of the lecture.
Numeric integral
Estimate the integral of on the interval [ − 2,5] with the left Riemann sum!
Gradient descent
Let's have a vector-to-scalar function f(x,y) = x2 + y2. Starting from (x0,y0) = ( − 1, − 1) we will wind the minimum of the function. A gradient step is when you subtract the from the (x,y) point. If you do this for small ε many times then the point will converge a point where you cannot increase the function value any more, i.e. the gradient is zero. This way you can find the minimum of the function (it will be (x,y) = (0,0)).
- Store each step along the way, and plot them with matplotlib!
Numeric derivative
Plot the function sin(x) and its derivative on the interval [ − π,π]. Calculate the derivative with finite difference method!