CoCalc Public Filesoctave.ipynbOpen with one click!
Author: Harald Schilly
Views : 327
License: Apache License 2.0
Description: octave 5.2.0
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version()
ans = 5.2.0
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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 = 1.06801 0.90711 1.08065 1.64741 1.47672 1.82312 1.73806 1.64319 2.03286
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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
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dicomuid()
ans = 1.2.826.0.1.3680043.2.1143.2148357442172746621572640965233790846
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pkg load symbolic; syms x; f = sin(x); diff(f,x)
Symbolic pkg v2.9.0: Python communication link active, SymPy v1.5.1. ans = (sym) cos(x)
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pkg load symbolic; syms x f = 2 * (cos(x) + sin(x)^2) f1 = diff(f, x)
f = (sym) 2 2⋅sin (x) + 2⋅cos(x) f1 = (sym) 4⋅sin(x)⋅cos(x) - 2⋅sin(x)
In [11]:
xx = -10:0.1:10; plot(xx, f(xx))
error: invalid indices: should be integers or boolean error: called from subsref at line 65 column 11
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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)
ans = 46.021

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

In [14]:
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");
In [1]:
[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

In [15]:
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.

In [16]:
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

In [1]:
pkg load symbolic syms y(x) de = diff(y) == x; f = dsolve(de, y(1) == 1)
Symbolic pkg v2.9.0: Python communication link active, SymPy v1.5.1. f = (sym) 2 x 1 y(x) = ── + ─ 2 2

Octave's ODE PKG in Action

In [17]:
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.

In [20]:
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: 3.42399e-16 STRONG CONVERGENCE Function conv 1 Param conv 1 Gradient conv 1 used analytic 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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