CoCalc Public Filesoctave.ipynbOpen with one click!
Author: Harald Schilly
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Compute Environment: Ubuntu 20.04 (Default)
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version()
ans = 6.2.0
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function sqs = squares(n) # Compute the squares of the numbers from 1 to n. ### BEGIN SOLUTION # Put correct code here. This code is removed for the student version, but is # used to confirm that your tests are valid. if (n <= 0) error("n must be positive") endif sqs = (1:n).^2; ### END SOLUTION endfunction
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# [Modify the tests below for your own problem] # Check that squares returns the correct output for several inputs: assert(squares(1), [1]) assert(squares(2), [1 4]) # Check that squares raises an error for invalid input: number_of_errors = 0; for n = [0 -1] try squares(n); catch number_of_errors++; end_try_catch endfor assert(number_of_errors, 2) ### BEGIN HIDDEN TESTS # students will NOT see these extra tests assert(squares(10), [1 4 9 16 25 36 49 64 81 100]) ### END HIDDEN TESTS
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function s = foo(a, b) # Compute the sum of a and b. ### BEGIN SOLUTION s = a + b; ### END SOLUTION endfunction
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foo(23,23)
ans = 46
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[2 3 4]' * [4 3 -1]
ans = 8 6 -2 12 9 -3 16 12 -4
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x = rand(3,3)^3
x = 0.3198 1.3850 1.0445 0.2527 0.9548 0.8514 0.1623 0.8323 0.5163
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save r-octave.mat x -7
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scatter(sort(rand(1000, 1)), sort(randn(1000, 1)))
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i = 0:.1:2*pi; plot(i, sin(i))
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pkg load dicom
error: package dicom is not installed error: called from load_packages at line 47 column 7 pkg at line 588 column 7
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dicomuid()
error: 'dicomuid' undefined near line 1, column 1 The 'dicomuid' function belongs to the dicom package from Octave Forge which seems to not be installed in your system. Please read <https://www.octave.org/missing.html> to learn how you can contribute missing functionality.
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pkg load symbolic; syms x; f = sin(x); diff(f,x)
Symbolic pkg v2.9.0: /usr/local/lib/python3.8/dist-packages/sympy/__init__.py:672: SymPyDeprecationWarning: importing sympy.core.compatibility with 'from sympy import *' has been deprecated since SymPy 1.6. Use import sympy.core.compatibility instead. See https://github.com/sympy/sympy/issues/18245 for more info. self.Warn( Traceback (most recent call last): File "<stdin>", line 1, in <module> File "<stdin>", line 12, in octoutput_drv File "<stdin>", line 54, in octoutput File "<stdin>", line 55, in octoutput File "/usr/local/lib/python3.8/dist-packages/sympy/__init__.py", line 677, in __getattr__ return getattr(self.mod, name) AttributeError: module 'sympy.core.compatibility' has no attribute 'integer_types' Waiting......... Waiting.........
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pkg load symbolic; syms x f = 2 * (cos(x) + sin(x)^2) f1 = diff(f, x)
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xx = -10:0.1:10; plot(xx, f(xx))
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pkg load image
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a = ones(100, 100); b = ones(100, 100); b(3, 1) = .5; psnr(a, b)

This plot shows the famous 3D sombrero.

A quadratic meshgrid of xx and yy coordinates is evaluated via x2+y2+ϵ\sqrt{x^2 + y^2} + \epsilon and the value rr is then the value plotted along the third dimension.

Reference: 3d plots

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tx = ty = linspace (-8, 8, 41)'; [xx, yy] = meshgrid (tx, ty); r = sqrt (xx .^ 2 + yy .^ 2) + eps; tz = sin (r) ./ r; mesh (tx, ty, tz); xlabel ("tx"); ylabel ("ty"); zlabel ("tz"); title ("3-D Sombrero plot");
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[x,y] = meshgrid(-16:0.5:16); r = hypot(x,y)/2 + eps; figure; surf(sin(r)./r); colormap(jet);
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This draws the set of points, where the given equation is satisfied. Here, it shows a tilted ellipse.

x2+3(y1)2+xy2=6x^2 + 3 (y-1)^2 + \frac{x y}{2} = 6

Reference: ezplot

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ezplot (@(x, y) x.^2 + 3 * (y - 1).^2 + .5 * x .* y - 6)

Imagine you want to evaluate a binary function f(x,y):=x+2yf(x,\,y) := x + 2 y.

For evaluating it in vectorized notation, you need a grid for the cartesian product of all xx and yy.

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x = 0:3; y = 0:4; [xx, yy] = meshgrid(x, y); xx + 2*yy
ans = 0 1 2 3 2 3 4 5 4 5 6 7 6 7 8 9 8 9 10 11

dsolve and sympy in symbolic

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pkg load symbolic syms y(x) de = diff(y) == x; f = dsolve(de, y(1) == 1)
/usr/local/lib/python3.8/dist-packages/sympy/__init__.py:672: SymPyDeprecationWarning: importing sympy.core.compatibility with 'from sympy import *' has been deprecated since SymPy 1.6. Use import sympy.core.compatibility instead. See https://github.com/sympy/sympy/issues/18245 for more info. self.Warn( Traceback (most recent call last): File "<stdin>", line 4, in <module> File "<stdin>", line 12, in octoutput_drv File "<stdin>", line 55, in octoutput File "/usr/local/lib/python3.8/dist-packages/sympy/__init__.py", line 677, in __getattr__ return getattr(self.mod, name) AttributeError: module 'sympy.core.compatibility' has no attribute 'integer_types' error: Python exception: AttributeError: module 'sympy.core.compatibility' has no attribute 'integer_types' occurred while copying variables to Python. Try "sympref reset" and repeat your command? (consider filing an issue at https://github.com/cbm755/octsympy/issues) error: called from pycall_sympy__ at line 191 column 5 valid_sym_assumptions at line 38 column 10 assumptions at line 82 column 7 syms at line 97 column 13 error: 'dsolve' undefined near line 1, column 1 'dsolve' is a method of class 'sym'; it must be called with a 'sym' argument (see 'help @sym/dsolve'). Please read <https://www.octave.org/missing.html> to learn how you can contribute missing functionality.

Octave's ODE PKG in Action

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pkg load odepkg;
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dxdt = @(t, x) - 0.24 * x.^2 + t; tsteps = [0:0.1:5]; [t, x] = ode45(dxdt, tsteps, [-1:0.5:3]); plot(t, x)
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You can run numerical optimizations via the optim package.

In this example we minimize the classical Rosenbrock function in 20 dimensions using BFGS.

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pkg load optim; function [obj_value, gradient] = objective(theta, location) x = theta - location + ones(rows(theta),1); # move minimizer to "location" [obj_value, gradient] = rosenbrock(x); endfunction dim = 20; # dimension of Rosenbrock function theta0 = zeros(dim+1,1); # starting values location = (0:dim)/dim; # true values location = location'; control = {Inf,1}; # maxiters, verbosity bfgsmin("objective", {theta0, location}, control);
------------------------------------------------ bfgsmin final results: 65 iterations function value: 2.17563e-16 STRONG CONVERGENCE Function conv 1 Param conv 1 Gradient conv 1 used numeric gradient param gradient (n) change 0.00000 0.00000 -0.00000 0.05000 -0.00000 0.00000 0.10000 0.00000 0.00000 0.15000 -0.00000 0.00000 0.20000 -0.00000 0.00000 0.25000 0.00000 0.00000 0.30000 -0.00000 0.00000 0.35000 -0.00000 0.00000 0.40000 -0.00000 0.00000 0.45000 0.00000 -0.00000 0.50000 0.00000 -0.00000 0.55000 -0.00000 0.00000 0.60000 0.00000 -0.00000 0.65000 0.00000 -0.00000 0.70000 -0.00000 0.00000 0.75000 -0.00000 0.00000 0.80000 0.00000 0.00000 0.85000 0.00000 0.00000 0.90000 0.00000 0.00000 0.95000 -0.00000 0.00000 1.00000 0.00000 0.00000
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