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## Newest Discussions

Several of the colormaps are great for a 256 color surface plot, but aren't well optimized for extracting m colors for plotting several independent lines. The issue is that many colormaps have start/end colors that are too similar or are suboptimal colors for lines. There are certainly many workarounds for this, but it would be a great quality of life to adjust that directly when calling this.

Example:

x = linspace(0,2*pi,101)';

y = [1:6].*cos(x);

figure; plot(x,y,'LineWidth',2); grid on; axis tight;

And now if I wanted to color these lines, I could use something like turbo(6) or gray(6) and then apply it using colororder.

colororder(turbo(6))

But my issue is that the ends of the colormap are too similar. For other colormaps, you may get lines that are too light to be visible against the white background. There are plenty of workarounds, with my preference being to create extra colors and truncate that before using colororder.

cmap = turbo(8); cmap = cmap(2:end-1,:); % Truncate the end colors

figure; plot(x,y,'LineWidth',2); grid on; axis tight;

colororder(cmap)

I think it would be really awesome to add some name-argument input pair to these colormaps that can specify the range you want so this could even be done inside the colororder calling if desired. An example of my proposed solution would look something like this:

cmap = turbo(6,'Range',[0.1 0.8]); % Proposed idea to add functionality

Where in this scenario, the resulting colormap would be 6 equally spaced colors that range from 10% to 80% of the total color range. This would be especially nice because you could more quickly modify the range of colors, or you could set the limits regardless of whether you need to plot 3, 6, or 20 lines.

I asked my question in the general forum and a few minutes later it was deleted. Perhaps this is a better place?

Rather than using my German regional forum (as I do not speak German), I want to ask questions in an international English-speaking forum. Presumably there should be an international English forum for everyone around the world, as English is the first or second language of everyone who has gone to school. Where is it?

Big congratulations to @VBBV for achieving the remarkable milestone of 3,000 reputation points, earning the prestigious title of Editor within our community.

This achievement is a testament to @VBBV's exceptional contributions and steadfast commitment to the community. These efforts have also been endorsed by fellow top contributors, underscoring the value and impact of @VBBV's expertise.

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eye(3) - diag(ones(1,3))

9%

0 ./ ones(3)

8%

cos(repmat(pi/2, [3,3]))

18%

zeros(3)

21%

A(3, 3) = 0

33%

mtimes([1;1;0], [0,0,0])

12%

559 Stimmen

MATLAB O/X Quiz

Answer BEFORE Googling!

- An infinite loop can be made using "for".
- "A == A" is always true.
- "round(2.5)" is 3.
- "round(-0.5)" is 0.

MATLAB Support Package for Quantum Computing lets you build, simulate, and run quantum algorithms.

Check out the Cheat Sheet here!

2 x 2 행렬의 행렬식은

- 행렬의 두 row 벡터로 정의되는 평행사변형의 면적입니다.
- 물론 두 column 벡터로 정의되는 평행사변형의 면적이기도 합니다.
- 좀 더 정확히는 signed area입니다. 면적이 음수가 될 수도 있다는 뜻이죠.
- 행렬의 두 행(또는 두 열)을 맞바꾸면 행렬식의 부호도 바뀌고 면적의 부호도 바뀌어야합니다.

일반적으로 n x n 행렬의 행렬식은

- 각 row 벡터(또는 각 column 벡터)로 정의되는 N차원 공간의 평행면체(?)의 signed area입니다.
- 제대로 이해하려면 대수학의 개념을 많이 가지고 와야 하는데 자세한 설명은 생략합니다.(=저도 모른다는 뜻)
- 더 자세히 알고 싶으시면 수학하는 만화의 '넓이 이야기' 편을 추천합니다.
- 수학적인 정의를 알고 싶으시면 위키피디아를 보시면 됩니다.
- 이렇게 생겼습니다. 좀 무섭습니다.

아래 코드는...

- 2 x 2 행렬에 대해서 이것을 수식 없이 그림만으로 증명하는 과정입니다.
- gif 생성에는 ScreenToGif를 사용했습니다. (gif 만들기엔 이게 킹왕짱인듯)

Determinant of 2 x 2 matrix is...

- An area of a parallelogram defined by two row vectors.
- Of course, same one defined by two column vectors.
- Precisely, a signed area, which means area can be negative.
- If two rows (or columns) are swapped, both the sign of determinant and area change.

More generally, determinant of n x n matrix is...

- Signed area of parallelepiped defined by rows (or columns) of the matrix in n-dim space.
- For a full understanding, a lot of concepts from abstract algebra should be brought, which I will not write here. (Cuz I don't know them.)
- For a mathematical definition of determinant, visit wikipedia.
- A little scary, isn't it?

The code below is...

- A process to prove the equality of the determinant of 2 x 2 matrix and the area of parallelogram.
- ScreenToGif is used to generate gif animation (which is, to me, the easiest way to make gif).

% 두 점 (a, b), (c, d)의 좌표

a = 4;

b = 1;

c = 1;

d = 3;

% patch 색 pre-define

lightgreen = [144, 238, 144]/255;

lightblue = [169, 190, 228]/255;

lightorange = [247, 195, 160]/255;

% animation params.

anim_Nsteps = 30;

% create window

figure('WindowStyle','docked')

ax = axes;

ax.XAxisLocation = 'origin';

ax.YAxisLocation = 'origin';

ax.XTick = [];

ax.YTick = [];

hold on

ax.XLim = [-.4, a+c+1];

ax.YLim = [-.4, b+d+1];

% create ad-bc patch

area = patch([0, a, a+c, c], [0, b, b+d, d], lightgreen);

p_ab = plot(a, b, 'ko', 'MarkerFaceColor', 'k');

p_cd = plot(c, d, 'ko', 'MarkerFaceColor', 'k');

p_ab.UserData = text(a+0.1, b, '(a, b)', 'FontSize',16);

p_cd.UserData = text(c+0.1, d-0.2, '(c, d)', 'FontSize',16);

area.UserData = text((a+c)/2-0.5, (b+d)/2, 'ad-bc', 'FontSize', 18);

pause

%% Is this really ad-bc?

area.UserData.String = 'ad-bc...?';

pause

%% fade out ad-bc

fadeinout(area, 0)

area.UserData.Visible = 'off';

pause

%% fade in ad block

rect_ad = patch([0, a, a, 0], [0, 0, d, d], lightblue, 'EdgeAlpha', 0, 'FaceAlpha', 0);

uistack(rect_ad, 'bottom');

fadeinout(rect_ad, 1, t_pause=0.003)

draw_gridline(rect_ad, ["23", "34"])

rect_ad.UserData = text(mean(rect_ad.XData), mean(rect_ad.YData), 'ad', 'FontSize', 20, 'HorizontalAlignment', 'center');

pause

%% fade-in bc block

rect_bc = patch([0, c, c, 0], [0, 0, b, b], lightorange, 'EdgeAlpha', 0, 'FaceAlpha', 0);

fadeinout(rect_bc, 1, t_pause=0.0035)

draw_gridline(rect_bc, ["23", "34"])

rect_bc.UserData = text(b/2, c/2, 'bc', 'FontSize', 20, 'HorizontalAlignment', 'center');

pause

%% slide ad block

patch_slide(rect_ad, ...

[0, 0, 0, 0], [0, b, b, 0], t_pause=0.004)

draw_gridline(rect_ad, ["12", "34"])

pause

%% slide ad block

patch_slide(rect_ad, ...

[0, 0, d/(d/c-b/a), d/(d/c-b/a)],...

[0, 0, b/a*d/(d/c-b/a), b/a*d/(d/c-b/a)], t_pause=0.004)

draw_gridline(rect_ad, ["14", "23"])

pause

%% slide bc block

uistack(p_cd, 'top')

patch_slide(rect_bc, ...

[0, 0, 0, 0], [d, d, d, d], t_pause=0.004)

draw_gridline(rect_bc, "34")

pause

%% slide bc block

patch_slide(rect_bc, ...

[0, 0, a, a], [0, 0, 0, 0], t_pause=0.004)

draw_gridline(rect_bc, "23")

pause

%% slide bc block

patch_slide(rect_bc, ...

[d/(d/c-b/a), 0, 0, d/(d/c-b/a)], ...

[b/a*d/(d/c-b/a), 0, 0, b/a*d/(d/c-b/a)], t_pause=0.004)

pause

%% finalize: fade out ad, bc, and fade in ad-bc

rect_ad.UserData.Visible = 'off';

rect_bc.UserData.Visible = 'off';

fadeinout([rect_ad, rect_bc, area], [0, 0, 1])

area.UserData.String = 'ad-bc';

area.UserData.Visible = 'on';

%% functions

function fadeinout(objs, inout, options)

arguments

objs

inout % 1이면 fade-in, 0이면 fade-out

options.anim_Nsteps = 30

options.t_pause = 0.003

end

for alpha = linspace(0, 1, options.anim_Nsteps)

for i = 1:length(objs)

switch objs(i).Type

case 'patch'

objs(i).FaceAlpha = (inout(i)==1)*alpha + (inout(i)==0)*(1-alpha);

objs(i).EdgeAlpha = (inout(i)==1)*alpha + (inout(i)==0)*(1-alpha);

case 'constantline'

objs(i).Alpha = (inout(i)==1)*alpha + (inout(i)==0)*(1-alpha);

end

pause(options.t_pause)

end

end

end

function patch_slide(obj, x_dist, y_dist, options)

arguments

obj

x_dist

y_dist

options.anim_Nsteps = 30

options.t_pause = 0.003

end

dx = x_dist/options.anim_Nsteps;

dy = y_dist/options.anim_Nsteps;

for i=1:options.anim_Nsteps

obj.XData = obj.XData + dx(:);

obj.YData = obj.YData + dy(:);

obj.UserData.Position(1) = mean(obj.XData);

obj.UserData.Position(2) = mean(obj.YData);

pause(options.t_pause)

end

end

function draw_gridline(patch, where)

ax = patch.Parent;

for i=1:length(where)

v1 = str2double(where{i}(1));

v2 = str2double(where{i}(2));

x1 = patch.XData(v1);

x2 = patch.XData(v2);

y1 = patch.YData(v1);

y2 = patch.YData(v2);

if x1==x2

xline(x1, 'k--')

else

fplot(@(x) (y2-y1)/(x2-x1)*(x-x1)+y1, [ax.XLim(1), ax.XLim(2)], 'k--')

end

end

end

and immeditaely everyone wanted the code! It turns out that this is the result of my remix of @Zhaoxu Liu / slandarer's entry on the MATLAB Flipbook Mini Hack.

I pointed people to the Flipbook entry but, of course, that just gave the code to render a single frame and people wanted the full code to render the animated gif. That way, they could make personalised versions

I just published a blog post that gives the code used by the team behind the Mini Hack to produce the animated .gifs https://blogs.mathworks.com/matlab/2024/02/16/producing-animated-gifs-from-matlab-flipbook-mini-hack-entries/

Thanks again to @Zhaoxu Liu / slandarer for a great entry that seems like it will live for a long time :)

If you've dabbled in "procedural generation," (algorithmically generating natural features), you may have come across the problem of sphere texturing. How to seamlessly texture a sphere is not immediately obvious. Watch what happens, for example, if you try adding power law noise to an evenly sampled grid of spherical angle coordinates (i.e. a "UV sphere" in Blender-speak):

% Example: how [not] to texture a sphere:

rng(2, 'twister'); % Make what I have here repeatable for you

% Make our radial noise, mapped onto an equal spaced longitude and latitude

% grid.

N = 51;

b = linspace(-1, 1, N).^2;

r = abs(ifft2(exp(6i*rand(N))./(b'+b+1e-5))); % Power law noise

r = rescale(r, 0, 1) + 5;

[lon, lat] = meshgrid(linspace(0, 2*pi, N), linspace(-pi/2, pi/2, N));

[x2, y2, z2] = sph2cart(lon, lat, r);

r2d = @(x)x*180/pi;

% Radial surface texture

subplot(1, 3, 1);

imagesc(r, 'Xdata', r2d(lon(1,:)), 'Ydata', r2d(lat(:, 1)));

xlabel('Longitude (Deg)');

ylabel('Latitude (Deg)');

title('Texture (radial variation)');

% View from z axis

subplot(1, 3, 2);

surf(x2, y2, z2, r);

axis equal

view([0, 90]);

title('Top view');

% Side view

subplot(1, 3, 3);

surf(x2, y2, z2, r);

axis equal

view([-90, 0]);

title('Side view');

The created surface shows "pinching" at the poles due to different radial values mapping to the same location. Furthermore, the noise statistics change based on the density of the sampling on the surface.

How can this be avoided? One standard method is to create a textured volume and sample the volume at points on a sphere. Code for doing this is quite simple:

rng default % Make our noise realization repeatable

% Create our 3D power-law noise

N = 201;

b = linspace(-1, 1, N);

[x3, y3, z3] = meshgrid(b, b, b);

b3 = x3.^2 + y3.^2 + z3.^2;

r = abs(ifftn(ifftshift(exp(6i*randn(size(b3)))./(b3.^1.2 + 1e-6))));

% Modify it - make it more interesting

r = rescale(r);

r = r./(abs(r - 0.5) + .1);

% Sample on a sphere

[x, y, z] = sphere(500);

% Plot

ir = interp3(x3, y3, z3, r, x, y, z, 'linear', 0);

surf(x, y, z, ir);

shading flat

axis equal off

set(gcf, 'color', 'k');

colormap(gray);

The result of evaluating this code is a seamless, textured sphere with no discontinuities at the poles or variation in the spatial statistics of the noise texture:

But what if you want to smooth it or perform some other local texture modification? Smoothing the volume and resampling is not equivalent to smoothing the surficial features shown on the map above.

A more flexible alternative is to treat the samples on the sphere surface as a set of interconnected nodes that are influenced by adjacent values. Using this approach we can start by defining the set of nodes on a sphere surface. These can be sampled almost arbitrarily, though the noise statistics will vary depending on the sampling strategy.

One noise realisation I find attractive can be had by randomly sampling a sphere. Normalizing a point in N-dimensional space by its 2-norm projects it to the surface of an N-dimensional unit sphere, so randomly sampling a sphere can be done very easily using randn() and vecnorm():

N = 5e3; % Number of nodes on our sphere

g=randn(3,N); % Random 3D points around origin

p=g./vecnorm(g); % Projected to unit sphere

The next step is to find each point's "neighbors." The first step is to find the convex hull. Since each point is on the sphere, the convex hull will include each point as a vertex in the triangulation:

k=convhull(p');

In the above, k is an N x 3 set of indices where each row represents a unique triangle formed by a triplicate of points on the sphere surface. The vertices of the full set of triangles containing a point describe the list of neighbors to that point.

What we want now is a large, sparse symmetric matrix where the indices of the columns & rows represent the indices of the points on the sphere and the nth row (and/or column) contains non-zero entries at the indices corresponding to the neighbors of the nth point.

How to do this? You could set up a tiresome nested for-loop searching for all rows (triangles) in k that contain some index n, or you could directly index via:

c=@(x)sparse(k(:,x)*[1,1,1],k,1,N,N);

t=c(1)|c(2)|c(3);

The result is the desired sparse connectivity matrix: a matrix with non-zero entries defining neighboring points.

So how do we create a textured sphere with this connectivity matrix? We will use it to form a set of equations that, when combined with the concept of "regularization," will allow us to determine the properties of the randomness on the surface. Our regularizer will penalize the difference of the radial distance of a point and the average of its neighbors. To do this we replace the main diagonal with the negative of the sum of the off-diagonal components so that the rows and columns are zero-mean. This can be done via:

w=spdiags(-sum(t,2)+1,0,double(t));

Now we invoke a bit of linear algebra. Pretend x is an N-length vector representing the radial distance of each point on our sphere with the noise realization we desire. Y will be an N-length vector of "observations" we are going to generate randomly, in this case using a uniform distribution (because it has a bias and we want a non-zero average radius, but you can play around with different distributions than uniform to get different effects):

Y=rand(N,1);

and A is going to be our "transformation" matrix mapping x to our noisy observations:

Ax = Y

In this case both x and Y are N length vectors and A is just the identity matrix:

A = speye(N);

Y, however, doesn't create the noise realization we want. So in the equation above, when solving for x we are going to introduce a regularizer which is going to penalize unwanted behavior of x by some amount. That behavior is defined by the point-neighbor radial differences represented in matrix w. Our estimate of x can then be found using one of my favorite Matlab assets, the "\" operator:

smoothness = 10; % Smoothness penalty: higher is smoother

x = (A+smoothness*w'*w)\Y; % Solving for radii

The vector x now contains the radii with the specified noise realization for the sphere which can be created simply by multiplying x by p and plotting using trisurf:

p2 = p.*x';

trisurf(k,p2(1,:),p2(2,:),p2(3,:),'FaceC', 'w', 'EdgeC', 'none','AmbientS',0,'DiffuseS',0.6,'SpecularS',1);

light;

set(gca, 'color', 'k');

axis equal

The following images show what happens as you change the smoothness parameter using values [.1, 1, 10, 100] (left to right):

Now you know a couple ways to make a textured sphere: that's the starting point for having a lot of fun with basic procedural planet, moon, or astroid generation! Here's some examples of things you can create based on these general ideas:

The MATLAB command window isn't just for commands and outputs—it can also host interactive hyperlinks. These can serve as powerful shortcuts, enhancing the feedback you provide during code execution. Here are some hyperlinks I frequently use in fprintf statements, warnings, or error messages.

1. Open a website.

msg = "Could not download data from website.";

url = "https://blogs.mathworks.com/graphics-and-apps/";

hypertext = "Go to website"

fprintf(1,'%s <a href="matlab: web(''%s'') ">%s</a>\n',msg,url,hypertext);

Could not download data from website. Go to website

2. Open a folder in file explorer (Windows)

msg = "File saved to current directory.";

directory = cd();

hypertext = "[Open directory]";

fprintf(1,'%s <a href="matlab: winopen(''%s'') ">%s</a>\n',msg,directory,hypertext)

File saved to current directory. [Open directory]

3. Open a document (Windows)

msg = "Created database.csv.";

filepath = fullfile(cd,'database.csv');

hypertext = "[Open file]";

fprintf(1,'%s <a href="matlab: winopen(''%s'') ">%s</a>\n',msg,filepath,hypertext)

Created database.csv. [Open file]

4. Open an m-file and go to a specific line

msg = 'Go to';

file = 'streamline.m';

line = 51;

fprintf(1,'%s <a href="matlab: matlab.desktop.editor.openAndGoToLine(which(''%s''), %d); ">%s line %d</a>', msg, file, line, file, line);

Go to streamline.m line 51

5. Display more text

msg = 'Incomplete data detected.';

extendedInfo = '\tFilename: m32c4r28\n\tDate: 12/20/2014\n\tElectrode: (3,7)\n\tDepth: ???\n';

hypertext = '[Click for more info]';

warning('%s <a href="matlab: fprintf(''%s'') ">%s</a>', msg,extendedInfo,hypertext);

<click>

- Filename: m32c4r28
- Date: 12/20/2014
- Electrode: (3,7)
- Depth: ???

6. Run a function

Similarly, you can also add hyperlinks in figures and apps

And what do you do for Valentine's Day?

which technical support should I contact/ask for the published Simscape example?

Happy year of the dragon.

To enlarge an array with more rows and/or columns, you can set the lower right index to zero. This will pad the matrix with zeros.

m = rand(2, 3) % Initial matrix is 2 rows by 3 columns

mCopy = m;

% Now make it 2 rows by 5 columns

m(2, 5) = 0

m = mCopy; % Go back to original matrix.

% Now make it 3 rows by 3 columns

m(3, 3) = 0

m = mCopy; % Go back to original matrix.

% Now make it 3 rows by 7 columns

m(3, 7) = 0

Can you see them?

It is easy to obtain sankey plot like that using my tool: