メインコンテンツ
結果:
t=0.2:0.01:3*pi;
hold on
plot(t,cos(t)./(1+t),'LineWidth',4)
plot(t,sin(t)./(1+t),'LineWidth',4)
plot(t,cos(t+pi/2)./(1+t+pi/2),'LineWidth',4)
plot(t,cos(t+pi)./(1+t+pi),'LineWidth',4)
ax=gca;
hLegend=legend();
pause(1e-16)
colorData = uint8([255, 150, 200, 100; ...
255, 100, 50, 200; ...
0, 50, 100, 150; ...
102, 150, 200, 50]);
set(ax.Backdrop.Face, 'ColorBinding','interpolated','ColorData',colorData);
set(hLegend.BoxFace,'ColorBinding','interpolated','ColorData',colorData)
I have written two tools and uploaded fileexchange, which allows us to easily draw chord diagrams：
chord chart 弦图
download:
demo:
dataMat=[2 0 1 2 5 1 2;
3 5 1 4 2 0 1;
4 0 5 5 2 4 3];
dataMat=dataMat+rand(3,7);
dataMat(dataMat<1)=0;
colName={'G1','G2','G3','G4','G5','G6','G7'};
rowName={'S1','S2','S3'};
CC=chordChart(dataMat,'rowName',rowName,'colName',colName);
CC=CC.draw();
CC.setFont('FontSize',17,'FontName','Cambria')
% 显示刻度和数值
% Displays scales and numeric values
CC.tickState('on')
CC.tickLabelState('on')
% 调节标签半径
% Adjustable Label radius
CC.setLabelRadius(1.4);
Digraph chord chart 有向弦图
download:
demo:
dataMat=randi([0,8],[6,6]);
% 添加标签名称
NameList={'CHORD','CHART','MADE','BY','SLANDARER','MATLAB'};
BCC=biChordChart(dataMat,'Label',NameList,'Arrow','on');
BCC=BCC.draw();
% 添加刻度
BCC.tickState('on')
% 修改字体，字号及颜色
BCC.setFont('FontName','Cambria','FontSize',17,'Color',[.2,.2,.2])
BCC.setLabelRadius(1.3);
BCC.tickLabelState('on')
How to create a legend as follows?
Principle Explanation - Graphic Objects
Hidden Properties of Legend are laid as follows
In most cases, legends are drawn using LineLoop and Quadrilateral:
Both of these basic graphic objects are drawn in groups of four points, and the general principle is as follows:
Of course, you can arrange the points in order, or set VertexIndices whitch means the vertex order to obtain the desired quadrilateral shape:
Other objects
Compared to objects that can only be grouped into four points, we also need to introduce more flexible objects. Firstly, LineStrip, a graphical object that draws lines in groups of two points:
And TriangleStrip is a set of three points that draw objects to fill triangles, for example, complex polygons can be filled with multiple triangles:
Principle Explanation - Create and Replace
Let's talk about how to construct basic graphic objects, which are all constructed using undisclosed and very low-level functions, such as LineStrip, not through:
- LineStrip()
It is built through:
- matlab.graphics.primitive.world.LineStrip()
After building the object, the following properties must be set to make the hidden object visible:
- Layer
- ColorBinding
- ColorData
- VertexData
- PickableParts
The settings of these properties can refer to the original legend to form the object, which will not be elaborated here. You can also refer to the code I wrote.
Afterwards, set the newly constructed object's parent class as the Group parent class of the original component, and then hide the original component
newBoxEdgeHdl.Parent=oriBoxEdgeHdl.Parent;
oriBoxEdgeHdl.Visible='off';
The above is the entire process of component replacement, with two example codes written:
Semi transparent legend
function SPrettyLegend(lgd)
% Semitransparent rounded rectangle legend
% Copyright (c) 2023, Zhaoxu Liu / slandarer
% -------------------------------------------------------------------------
% Zhaoxu Liu / slandarer (2023). pretty legend
% (https://www.mathworks.com/matlabcentral/fileexchange/132128-pretty-legend),
% MATLAB Central File Exchange. 检索来源 2023/7/9.
% =========================================================================
if nargin<1
ax = gca;
lgd = get(ax,'Legend');
end
pause(1e-6)
Ratio = .1;
t1 = linspace(0,pi/2,4); t1 = t1([1,2,2,3,3,4]);
t2 = linspace(pi/2,pi,4); t2 = t2([1,2,2,3,3,4]);
t3 = linspace(pi,3*pi/2,4); t3 = t3([1,2,2,3,3,4]);
t4 = linspace(3*pi/2,2*pi,4); t4 = t4([1,2,2,3,3,4]);
XX = [1,1,1-Ratio+cos(t1).*Ratio,1-Ratio,Ratio,Ratio+cos(t2).*Ratio,...
0,0,Ratio+cos(t3).*Ratio,Ratio,1-Ratio,1-Ratio+cos(t4).*Ratio];
YY = [Ratio,1-Ratio,1-Ratio+sin(t1).*Ratio,1,1,1-Ratio+sin(t2).*Ratio,...
1-Ratio,Ratio,Ratio+sin(t3).*Ratio,0,0,Ratio+sin(t4).*Ratio];
% 圆角边框(border-radius)
oriBoxEdgeHdl = lgd.BoxEdge;
newBoxEdgeHdl = matlab.graphics.primitive.world.LineStrip();
newBoxEdgeHdl.AlignVertexCenters = 'off';
newBoxEdgeHdl.Layer = 'front';
newBoxEdgeHdl.ColorBinding = 'object';
newBoxEdgeHdl.LineWidth = 1;
newBoxEdgeHdl.LineJoin = 'miter';
newBoxEdgeHdl.WideLineRenderingHint = 'software';
newBoxEdgeHdl.ColorData = uint8([38;38;38;0]);
newBoxEdgeHdl.VertexData = single([XX;YY;XX.*0]);
newBoxEdgeHdl.Parent=oriBoxEdgeHdl.Parent;
oriBoxEdgeHdl.Visible='off';
% 半透明圆角背景(Semitransparent rounded background)
oriBoxFaceHdl = lgd.BoxFace;
newBoxFaceHdl = matlab.graphics.primitive.world.TriangleStrip();
Ind = [1:(length(XX)-1);ones(1,length(XX)-1).*(length(XX)+1);2:length(XX)];
Ind = Ind(:).';
newBoxFaceHdl.PickableParts = 'all';
newBoxFaceHdl.Layer = 'back';
newBoxFaceHdl.ColorBinding = 'object';
newBoxFaceHdl.ColorType = 'truecoloralpha';
newBoxFaceHdl.ColorData = uint8(255*[1;1;1;.6]);
newBoxFaceHdl.VertexData = single([XX,.5;YY,.5;XX.*0,0]);
newBoxFaceHdl.VertexIndices = uint32(Ind);
newBoxFaceHdl.Parent = oriBoxFaceHdl.Parent;
oriBoxFaceHdl.Visible = 'off';
end
Usage examples
clc; clear; close all
rng(12)
% 生成随机点(Generate random points)
mu = [2 3; 6 7; 8 9];
S = cat(3,[1 0; 0 2],[1 0; 0 2],[1 0; 0 1]);
r1 = abs(mvnrnd(mu(1,:),S(:,:,1),100));
r2 = abs(mvnrnd(mu(2,:),S(:,:,2),100));
r3 = abs(mvnrnd(mu(3,:),S(:,:,3),100));
% 绘制散点图(Draw scatter chart)
hold on
propCell = {'LineWidth',1.2,'MarkerEdgeColor',[.3,.3,.3],'SizeData',60};
scatter(r1(:,1),r1(:,2),'filled','CData',[0.40 0.76 0.60],propCell{:});
scatter(r2(:,1),r2(:,2),'filled','CData',[0.99 0.55 0.38],propCell{:});
scatter(r3(:,1),r3(:,2),'filled','CData',[0.55 0.63 0.80],propCell{:});
% 增添图例(Draw legend)
lgd = legend('scatter1','scatter2','scatter3');
lgd.Location = 'northwest';
lgd.FontSize = 14;
% 坐标区域基础修饰(Axes basic decoration)
ax=gca; grid on
ax.FontName = 'Cambria';
ax.Color = [0.9,0.9,0.9];
ax.Box = 'off';
ax.TickDir = 'out';
ax.GridColor = [1 1 1];
ax.GridAlpha = 1;
ax.LineWidth = 1;
ax.XColor = [0.2,0.2,0.2];
ax.YColor = [0.2,0.2,0.2];
ax.TickLength = [0.015 0.025];
% 隐藏轴线(Hide XY-Ruler)
pause(1e-6)
ax.XRuler.Axle.LineStyle = 'none';
ax.YRuler.Axle.LineStyle = 'none';
SPrettyLegend(lgd)
Heart shaped legend (exclusive to pie charts)
function pie2HeartLegend(lgd)
% Heart shaped legend for pie chart
% Copyright (c) 2023, Zhaoxu Liu / slandarer
% -------------------------------------------------------------------------
% Zhaoxu Liu / slandarer (2023). pretty legend
% (https://www.mathworks.com/matlabcentral/fileexchange/132128-pretty-legend),
% MATLAB Central File Exchange. 检索来源 2023/7/9.
% =========================================================================
if nargin<1
ax = gca;
lgd = get(ax,'Legend');
end
pause(1e-6)
% 心形曲线(Heart curve)
x = -1:1/100:1;
y1 = 0.6 * abs(x) .^ 0.5 + ((1 - x .^ 2) / 2) .^ 0.5;
y2 = 0.6 * abs(x) .^ 0.5 - ((1 - x .^ 2) / 2) .^ 0.5;
XX = [x, flip(x),x(1)]./3.4+.5;
YY = ([y1, y2,y1(1)]-.2)./2+.5;
Ind = [1:(length(XX)-1);2:length(XX)];
Ind = Ind(:).';
% 获取图例图标(Get Legend Icon)
lgdEntryChild = lgd.EntryContainer.NodeChildren;
iconSet = arrayfun(@(lgdEntryChild)lgdEntryChild.Icon.Transform.Children.Children,lgdEntryChild,UniformOutput=false);
% 基础边框句柄(Base Border Handle)
newEdgeHdl = matlab.graphics.primitive.world.LineStrip();
newEdgeHdl.AlignVertexCenters = 'off';
newEdgeHdl.Layer = 'front';
newEdgeHdl.ColorBinding = 'object';
newEdgeHdl.LineWidth = .8;
newEdgeHdl.LineJoin = 'miter';
newEdgeHdl.WideLineRenderingHint = 'software';
newEdgeHdl.ColorData = uint8([38;38;38;0]);
newEdgeHdl.VertexData = single([XX;YY;XX.*0]);
newEdgeHdl.VertexIndices = uint32(Ind);
% 基础多边形面句柄(Base Patch Handle)
newFaceHdl = matlab.graphics.primitive.world.TriangleStrip();
Ind = [1:(length(XX)-1);ones(1,length(XX)-1).*(length(XX)+1);2:length(XX)];
Ind = Ind(:).';
newFaceHdl.PickableParts = 'all';
newFaceHdl.Layer = 'middle';
newFaceHdl.ColorBinding = 'object';
newFaceHdl.ColorType = 'truecoloralpha';
newFaceHdl.ColorData = uint8(255*[1;1;1;.6]);
newFaceHdl.VertexData = single([XX,.5;YY,.5;XX.*0,0]);
newFaceHdl.VertexIndices = uint32(Ind);
% 替换图例图标(Replace Legend Icon)
for i = 1:length(iconSet)
oriEdgeHdl = iconSet{i}(1);
tNewEdgeHdl = copy(newEdgeHdl);
tNewEdgeHdl.ColorData = oriEdgeHdl.ColorData;
tNewEdgeHdl.Parent = oriEdgeHdl.Parent;
oriEdgeHdl.Visible = 'off';
oriFaceHdl = iconSet{i}(2);
tNewFaceHdl = copy(newFaceHdl);
tNewFaceHdl.ColorData = oriFaceHdl.ColorData;
tNewFaceHdl.Parent = oriFaceHdl.Parent;
oriFaceHdl.Visible = 'off';
end
end
Usage examples
clc; clear; close all
% 生成随机点(Generate random points)
X = [1 3 0.5 2.5 2];
pieHdl = pie(X);
% 修饰饼状图(Decorate pie chart)
colorList=[0.4941 0.5490 0.4118
0.9059 0.6510 0.3333
0.8980 0.6157 0.4980
0.8902 0.5137 0.4667
0.4275 0.2824 0.2784];
for i = 1:2:length(pieHdl)
pieHdl(i).FaceColor=colorList((i+1)/2,:);
pieHdl(i).EdgeColor=colorList((i+1)/2,:);
pieHdl(i).LineWidth=1;
pieHdl(i).FaceAlpha=.6;
end
for i = 2:2:length(pieHdl)
pieHdl(i).FontSize=13;
pieHdl(i).FontName='Times New Roman';
end
lgd=legend('FontSize',13,'FontName','Times New Roman','TextColor',[1,1,1].*.3);
pie2HeartLegend(lgd)
I found this list on Book Authority about the top MATLAB books: https://bookauthority.org/books/best-matlab-books
My favorite book is Accelerating MATLAB Performance - 1001 tips to speed up MATLAB programs. I always pick something up from the book that helps me out.
A key aspect to masting MATLAB Graphics is getting a hang of the MATLAB Graphics Object Hierarchy which is essentially the structure of MATLAB figures that is used in the rendering pipeline. The base object is the Graphics Root (see groot) which contains the Figure. The Figure contains Axes or other containers such as a Tiled Chart Layout (see tiledlayout). Then these Axes can contain graphics primatives (the objects that contain data and get rendered) such as Lines or Patches.
Every graphics object has two important properties, the "Parent" and "Children" properties which can be used to access other objects in the tree. This can be very useful when trying to customize a pre-built chart (such as adding grid lines to both axes in an eye diagram chart) or when trying to access the axes of a non-current figure via a primative (so "gca" doesn't help out).
One last Tip and Trick with this is that you can declare graphics primatives without putting them on or creating an Axes by setting the first input argument to "gobjects(0)" which is an empty array of placeholder graphics objects. Then, when you have an Axes to plot the primitive on and are ready to render it, you can set the "Parent" of the object to your new Axes.
For Example:
l = line(gobjects(0), 1:10, 1:10);
...
...
...
l.Parent = gca;
Practicing navigating and exploring this tree will help propel your understanding of plotting in MATLAB.
spy
Over at Reddit, a MATLAB user asked about when to use a script vs. a live script. How would you answer this?
Starting with MATLAB can be daunting, but the right resources make all the difference. In my experience, the combination of MATLAB Onramp and Cody offers an engaging start.
MATLAB Onramp introduces you to MATLAB's basic features and workflows. Then practice your coding skill on Cody. Challenge yourself to solve 1 basic problem every day for a month! This consistent practice can significantly enhance your proficiency.
What other resources have helped you on your MATLAB journey? Share your recommendations and let's create a comprehensive learning path for beginners!
I would tell myself to understand vectorization. MATLAB is designed for operating on whole arrays and matrices at once. This is often more efficient than using loops.
how can I do to get those informations?
Explore all the capabilities for Modeling Dynamic Systems while keeping them handy with this Cheat Sheet - Download Now.
Here's a MATLAB class I wrote that leverages the MATLAB Central Interface for MATLAB toolbox, which in turn uses the publicy available Community API. Using this class, I've created a few Favorites that show me what's going on in MATLAB Central - without having to leave MATLAB 🙂
The class has a few convenient queries:
- Results for the last 7 days
- Results for the last 30 days
- Results for the current month
- Results for today
And supporting a bunch of different content scopes:
- All MATLAB Central
- MATLAB Answers
- Blogs
- Cody
- Contests
- File Exchange
- Exclude Answers content
The results are displayed in the command window (which worked best for me) and link to each post. Here's what that looks like for this command
>> CommunityFeed.thisMonth("app designer", CommunityFeed.Scope.ExcludeAnswers)
Let me know if you find this class useful and feel free to suggest changes.
New Cheat Sheet Alert!
Level up your data organization and access skills in MATLAB with our latest cheat sheet! Download the full cheat sheet on MATLAB GitHub for Students here.
Calling all students! New to MATLAB or need helpful resources? Check out our MATLAB GitHub for Students repository! Find MATLAB examples, videos, cheat sheets, and more!
Visit the repository here: MATLAB GitHub for Students
Imagine x is a large vector and you want the smallest 10 elements. How might you do it?
I've now seen linear programming questions pop up on Answers recently, with some common failure modes for linprog that people seem not to understand.
One basic failure mode is an infeasible problem. What does this mean, and can it be resolved?
The most common failure mode seems to be a unbounded problem. What does this mean? How can it be avoided/solved/fixed? Is there some direction I can move where the objective obviously grows without bounds towards +/- inf?
Finally, I also see questions where someone wants the tool to produce all possible solutions.
A truly good exposition about linear programming would probably result in a complete course on the subject, and Aswers is limited in how much I can write (plus I'll only have a finite amount of energy to keep writing.) I'll try to answer each sub-question as separate answers, but if someone else would like to offer their own take, feel free to do so as an answer, since it has been many years for me since I learned linear programming.
Introduction
Comma-separated lists are really very simple. You use them all the time. Here is one:
a,b,c,d
That is a comma-separated list containing four variables, the variables a, b, c, and d. Every time you write a list separated by commas then you are writing a comma-separated list. Most commonly you would write a comma-separated list as inputs when calling a function:
fun(a,b,c,d)
or as arguments to the concatenation operator or cell construction operator:
[a,b,c,d]
{a,b,c,d}
or as function outputs:
[a,b,c,d] = fun();
It is very important to understand that in general a comma-separated list is NOT one variable (but it could be). However, sometimes it is useful to create a comma-separated list from one variable (or define one variable from a comma-separated list), and MATLAB has several ways of doing this from various container array types:
struct_array.field % all elements
struct_array(idx).field % selected elements
cell_array{:} % all elements
cell_array{idx} % selected elements
string_array{:} % all elements
string_array{idx} % selected elements
Note that in all cases, the comma-separated list consists of the content of the container array, not subsets (or "slices") of the container array itself (use parentheses to "slice" any array). In other words, they will be equivalent to writing this comma-separated list of the container array content:
content1, content2, content3, .. , contentN
and will return as many content arrays as the original container array has elements (or that you select using indexing, in the requested order). A comma-separated list of one element is just one array, but in general there can be any number of separate arrays in the comma-separated list (zero, one, two, three, four, or more). Here is an example showing that a comma-separated list generated from the content of a cell array is the same as a comma-separated list written explicitly:
>> C = {1,0,Inf};
>> C{:}
ans =
1
ans =
0
ans =
Inf
>> 1,0,Inf
ans =
1
ans =
0
ans =
Inf
How to Use Comma-Separated Lists
Function Inputs: Remember that every time you call a function with multiple input arguments you are using a comma-separated list:
fun(a,b,c,d)
and this is exactly why they are useful: because you can specify the arguments for a function or operator without knowing anything about the arguments (even how many there are). Using the example cell array from above:
>> vertcat(C{:})
ans =
1
0
Inf
which, as we should know by now, is exactly equivalent to writing the same comma-separated list directly into the function call:
>> vertcat(1,0,Inf)
ans =
1
0
Inf
How can we use this? Commonly these are used to generate vectors of values from a structure or cell array, e.g. to concatenate the filenames which are in the output structure of dir:
S = dir(..);
F = {S.name}
which is simply equivalent to
F = {S(1).name, S(2).name, S(3).name, .. , S(end).name}
Or, consider a function with multiple optional input arguments:
opt = {'HeaderLines',2, 'Delimiter',',', 'CollectOutputs',true);
fid = fopen(..);
C = textscan(fid,'%f%f',opt{:});
fclose(fid);
Note how we can pass the optional arguments as a comma-separated list. Remember how a comma-separated list is equivalent to writing var1,var2,var3,..., then the above example is really just this:
C = textscan(fid,'%f%f', 'HeaderLines',2, 'Delimiter',',', 'CollectOutputs',true)
with the added advantage that we can specify all of the optional arguments elsewhere and handle them as one cell array (e.g. as a function input, or at the top of the file). Or we could select which options we want simply by using indexing on that cell array. Note that varargin and varargout can also be useful here.
Function Outputs: In much the same way that the input arguments can be specified, so can an arbitrary number of output arguments. This is commonly used for functions which return a variable number of output arguments, specifically ind2sub and gradient and ndgrid. For example we can easily get all outputs of ndgrid, for any number of inputs (in this example three inputs and three outputs, determined by the number of elements in the cell array):
C = {1:3,4:7,8:9};
[C{:}] = ndgrid(C{:});
which is thus equivalent to:
[C{1},C{2},C{3}] = ndgrid(C{1},C{2},C{3});
Further Topics:
MATLAB documentation:
Click on these links to jump to relevant comments below:
Dynamic Indexing (indexing into arrays with arbitrary numbers of dimensions)
Summary
Just remember that in general a comma-separated list is not one variable (although they can be), and that they are exactly what they say: a list (of arrays) separated with commas. You use them all the time without even realizing it, every time you write this:
fun(a,b,c,d)
There are multiple ways to create a graphical user interface (GUI) in Matlab. Which method is the best depends on multiple factors: the complexity of the project, to what extent it should be a long-term solution, on what releases your GUI should work, your available time, your skill level, and probably other factors I'm forgetting.
To keep the thread clear I'll attempt to provide a short outline a few ways in this question, and leave the details for the answers. (@anyone with editing privileges: feel free to update the section below if I missed something important and am slow in editing this question)
---------------------------------------------------------------------------------------------------
GUIDE
GUIDE is probably the first tool new users will encounter. It is very useful for quickly putting something together, but it is otherwise fairly limited. It requires maintaining (and distributing) both a .m and a .fig file. Note that the GUIDE environment will be removed in a future release. After GUIDE is removed, existing GUIDE apps will continue to run in Matlab but they will not be editable in GUIDE. If you're starting a new GUI, don't use GUIDE. If you're updating an existing GUIDE GUI, migrate it to AppDesigner. In R2021a the first step for this removal was taken: all templates except the blank template have been removed.
GUILT
Although I haven't had a detailed look myself, it seems a list like this is not complete without at least mentioning the GUI Layout Toolbox, which is available on the file exchange and offers a lot of customization options.
Programmatic GUIs
You can bypass GUIDE and use the normal figures and functions like uicontrol to build GUIs from code. This makes the design less visual, but more flexible for future additions.
App Designer
The official successor to GUIDE, AppDesigner is not based on functions, but works similar to a class. It uses uifigure and mostly uses graphical elements that are incompatible with 'normal' GUIs that are created with a figure (or .fig).
Summary:
Dynamically accessing variable names can negatively impact the readability of your code and can cause it to run slower by preventing MATLAB from optimizing it as well as it could if you used alternate techniques. The most common alternative is to use simple and efficient indexing.
Explanation:
Sometimes beginners (and some self-taught professors) think it would be a good idea to dynamically create or access variable names, the variables are often named something like these:
- matrix1, matrix2, matrix3, matrix4, ...
- test_20kmh, test_50kmh, test_80kmh, ...
- nameA, nameB, nameC, nameD,...
Good reasons why dynamic variable names should be avoided:
- Slow
- Buggy
- Security Risk
- Difficult to Work With
- Obfuscated Code Intent
- Confuses Data with Code
- Code Helper Tools do not Work
- Magically Making Variables Appear in a Workspace is Risky
There are much better alternatives to accessing dynamic variable names:
- Indexing into Cell Array or ND-Array
- Non-scalar Structures (with Indexing)
- Dynamic Field-Names in a Structure
- load into a Structure, not into the Workspace
- save the Fields of a Scalar Structure
- Use a table or timetable Array
- Use more Efficient Ways to Pass Variables Between Workspaces
Note that avoiding eval (and assignin, etc.) is not some esoteric MATLAB restriction, it also applies to many other programming languages as well:
MATLAB Documentation:
If you are not interested in reading the answers below then at least read MATLAB's own documentation on this topic Alternatives to the eval Function, which states "A frequent use of the eval function is to create sets of variables such as A1, A2, ..., An, but this approach does not use the array processing power of MATLAB and is not recommended. The preferred method is to store related data in a single array." Data in a single array can be accessed very efficiently using indexing.
Note that all of these problems and disadvantages also apply to functions load (without an output variable), assignin, evalin, and evalc, and the MATLAB documentation explicitly recommends to "Avoid functions such as eval, evalc, evalin, and feval(fname)".
The official MATLAB blogs explain why eval should be avoided, the better alternatives to eval, and clearly recommend against magically creating variables. Using eval comes out at position number one on this list of Top 10 MATLAB Code Practices That Make Me Cry. Experienced MATLAB users recommend avoiding using eval for trivial code, and have written extensively on this topic.
The community is very helpful, yet I feel really powerless that I cannot find the appropriate way to code, nor find the problems with the codes I have written. I have read numerous books on MATLAB, mostly related with science and engineering applications. Any advice to improve would be greatly appreciated. Thanks.
また、以下のリストから Web サイトを選択することもできます。
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