I'm trying to have a textbox in MATLAB on a spinning plot, but I don't want the textbox to change its position relative to the figure. I thought that 'units','normalized' in the text function would do it, but it's not quite working, as the example below illustrates. I suppose I could use uicontrol but I'd like to use Greek letters and I can't get uicontrol looking quite as good as text. The following example recreates my problem. You'll notice the text box moves as the plot spins, but I'd like it to just stay in the top left region where it starts. Thank you!
part_x = rand(1000,3)-.5; %generate random 3D coordinates to scatter
fig1 = figure;
scatter3(part_x(:,1), part_x(:,2), part_x(:,3))
axis equal vis3d
axis([-1 1 -1 1 -1 1])
set(fig1,'color','w')
for tau = 1:150
view(tau+20,30); %spin the plot
pause(.01)
if tau~=1; delete(tau_text); end; %delete the previous text if it exists
tau_text = text(.1,.7,...
['\tau = ',num2str(tau)],...
'units','normalized',... %text coordinates relative to figure?
'Margin',3,... %these last 3 lines make it look nice
'edgecolor','k',...
'backgroundcolor','w');
end
Several things:
1) As you found out - using an annotation object instead of text object is the way to go. The difference is explained very nicely here.
2) You should only create the annotation once and then modify its string instead of deleting and recreating it on every iteration.
Finally:
part_x = rand(1000,3)-.5;
fig1 = figure;
scatter3(part_x(:,1), part_x(:,2), part_x(:,3))
axis equal vis3d
axis([-1 1 -1 1 -1 1])
set(fig1,'color','w')
%// Create the text outside the loop:
tau_text = annotation('textbox',[0.2 0.8 0.1 0.05],...
'string','\tau = NaN',...
'Margin',4,...
'edgecolor','k',...
'backgroundcolor','w',...
'LineWidth',1);
for tau = 1:150
view(tau+20,30);
pause(.01)
set(tau_text,'String',['\tau = ',num2str(tau)]); %// Modify the string
end
Notes:
1) It is interesting to note that #Otto's suggestion of using legend results in the creation of an axes (because this is what a legend object is - an axes with annotation children). You could then position the legend manually, and get its location using either get(gco,'position') (assuming it was the last thing you clicked) or more generally get(findobj('tag','legend'),'position'). Afterwards, whenever you create the legend, you can just set its position to the one you previously got. You could also get rid of the line\marker inside the legend by deleting the appropriate child of type line from the legend, e.g.:
ezplot('sin(x)');
hLeg = legend('\tauex\tau');
delete(findobj(findobj('Tag','legend'),'Type','line'));
hA1 = findobj(findobj('Tag','legend'),'Type','text');
set(hA1,'Position',[0.5,0.5,0],'HorizontalAlignment','center');
It is of course also possible to manipulate the legend's String using its handle (hA1) directly.
2) This post on UndocumentedMatlab discusses the behavior of annotation objects and some undocumented ways to manipulate them.
You could use
legend(['\tau = ',num2str(tau)],'Location','NorthWestOutside')
Thank you Dev-iL! annotation works much better for this purpose than text and the implementation is very similar. And thank you for the advice on modifying the string rather than deleting an recreating it.
Here is the code now, working much better:
part_x = rand(1000,3)-.5; %generate random 3D coordinates to scatter
fig1 = figure;
scatter3(part_x(:,1), part_x(:,2), part_x(:,3))
axis equal vis3d
axis([-1 1 -1 1 -1 1])
set(fig1,'color','w')
tau_text = annotation('textbox',[0.2 0.8 0.1 0.05],...
'string','',...
'Margin',4,... %these last 4 lines make it look nice
'edgecolor','k',...
'backgroundcolor','w',...
'LineWidth',1);
for tau = 1:150
view(tau+20,30); %spin the plot
pause(.01)
set(tau_text,'String',['\tau = ',num2str(tau)]);
end
Related
I want to add something to make my phase portrait more understandable. Nevertheless, I can't find anything (I found this
https://se.mathworks.com/help/matlab/ref/colorspec.html
https://se.mathworks.com/matlabcentral/fileexchange/11611-linear-2d-plot-with-rainbow-color
https://se.mathworks.com/help/symbolic/mupad_ref/linecolortype.html
) but it is not what I need.
I would really like to see the color of the line of the phase portrait changing depending of if it is at the beginning or at the end of the simulation.
I found this idea which seems great :
I don't understand at all what he has done (the code is I suppose written here:
https://blogs.mathworks.com/pick/2008/08/15/colors-for-your-multi-line-plots/ )
but It would be great if I can plot a one line function which color varies depending of the time. If moreover, like on the picture, I can have have a scale on the right: it would be awesome.
So for now, I have that :
data = readtable('test.txt');
figure('Name','Phase' , 'units','normalized','outerposition',[(8/100) (0.3- 16/100) 0.5 0.7]);
hold on
plot(data{:,2},data{:,3}, 'k.', 'LineWidth',1.5 );
plot(data{:,4},data{:,5}, 'r.', 'LineWidth',1.5 );
xL = xlim;
yL = ylim;
line([0 0], yL); %x-axis
line(xL, [0 0]); %y-axis
title(['Phase portrait'])
xlabel('f')
ylabel('f '' ')
hold off
I read the values of the function in a .txt file, and then I plot the 2nd/3rd columns and 4/5th columns. The first column is the time evoluting.
Do you have any idea :)?
Thank you!
There are several ways to go about this to be honest.
However it makes a bit easier if you let us know what your time data is.
Do you plot your time data on the x (or y) axis or is it a different additional data set. Should it be an additional data set then you can consider it like z-data, plotted on the Z-axis or/and as a color.
Below is an example of what you can do by making a 3D plot but displaying it in 2D, this allows you to add the colorbar without too many problems.
x=0:5;
y=0:5;
z=rand(1,6); %random data to simulate your time
xx=[x' x']; %this allows you to plot the data using surf in 3d
yy=[y' y']; %same as for xx
z1=zeros(size(xx)); % we don't need z-data so we're making it a matrix of zeros
zc=[z' z']; %input here your time data values, if x/y then you can just use those instead of z
hs=surf(xx,yy,z1,zc,'EdgeColor','interp') %// color binded to "z" values, choose interp for interpolated/gradual color changes, flat makes it sudden
colormap('hsv') %choose your colormap or make it yourself
view(2) %// view(0,90)
hcb=colorbar; %add a colorbar
I found this, thanks to another user on stackoverflaw.
data = readtable('4ressorspendule.txt');
n = numel(data.Var1);
c = size(data,2);
figure('Name','Phase' , 'units','normalized','outerposition',[(8/100) (0.3 - 16/100) 0.5 0.7]);
for i=1:n
hold on
plot(data{i,2},data{i,3},'.','Color',[1 (1-i/n) 0] ,'MarkerSize',4);
plot(data{i,4},data{i,5},'.','Color',[0 (i/n) (1-i/n)],'MarkerSize',4);
end
xL = xlim;
yL = ylim;
line([0 0], yL); %x-axis
line(xL, [0 0]); %y-axis
title(['Phase portrait'])
xlabel('f')
ylabel('f '' ')
hold off
Situation: change Position of a single subplot with imagesc
%% Matlab recommends this structure if axes(); in loop
a1 = subplot(1,2,1);
a2 = subplot(1,2,2);
while 1
plot(a1, rand(3))
plot(a2, rand(3))
drawnow
end
%% Test code
unitsPerInches=[0 0 15 15];
figure('Units', 'inches');
a1 = subplot(1,2,1);
a2 = subplot(1,2,2);
while 1
set(a1, 'Position', unitsPerInches); % TODO how to affect a1's Position here only?
imagesc(a1, rand(3))
imagesc(a2, rand(3))
drawnow
end
Open
What is imagesc corresponding structure to plot(a1,rand(3))?
How to change Position of figure inside the loop?
Forward in Q1 - almost done
%% Extension to imagesc
figure
a1=subplot(1,2,1);
a2=subplot(1,2,2);
for counter=1:2;
imagesc(a1,rand(3))
imagesc(a2,rand(3))
drawnow
end
Fig. 1 Output of Docs example, Fig. 2 Output of Imagesc, Fig. 3 about Q2 where Position affects both subplots
Q1 is almost done; I have just forgotten how to get corresponding plot in imagesc; x-values should be put there but pseudocode imagesc(a1,XDATA,rand(3)) is unsuccessfuly.
Backward in Q2
Code
%% Extension to imagesc
unitsPerInches=[0 0 15 15];
figure
a1=subplot(1,2,1);
a2=subplot(1,2,2);
for counter=1:2;
set(a1, 'Position', unitsPerInches); % TODO how to affect a1's Position here only?
imagesc(a1,rand(3))
imagesc(a1,rand(3))
drawnow
end
Output: position affects both images in Fig. 3.
I think I have misunderstood the meaning of Position here because so strange output.
Testing EBH's proposal for Q2
The implicit assignments cause problems when having two figures where subplots
unitsPerInches=[0 0 15 15];
aFig=figure();
a1=subplot(1,2,1);
a2=subplot(1,2,2);
bFig=figure();
b1=subplot(1,2,1);
b2=subplot(1,2,2);
for counter=1:2;
if counter==1
set(a1, 'Position', unitsPerInches); % affect only position of a1
end
subplot(1,2,counter);
imagesc(rand(3));
drawnow
subplot(1,2,counter);
imagesc(rand(3));
drawnow
end
Output: second figure of subplots fails.
System: Linux Ubuntu 16.04 64 bit
Linux kernel 4.6
Matlab: 2016a
Related threads: Matlab7 'bug' when using "subplot" + "imagesc"?
I'm not 100% sure what you're asking, but I think it's about combining multiple imagesc statements while in a loop. I'd do something more direct -- use gca and put the subplot inside the loop. Quite often, if you want to programmatically address multiple images, it makes sense to put them in some sort of structure other than creating lots of differently named variables. Note also that while 1 is probably not really what you want -- it will hammer your graphics device drivers -- and that pause can take an argument to act as a wait function, for some fraction of a second if required.
testImages{1}=double(imread('coins.png'));
testImages{2}=double(imread('cameraman.tif'));
h=figure;
set(h,'color','w'); %This handle refers to the background window
for ix=1:2
subplot(1,2,ix);
imagesc(testImages{ix});
axis equal;
colormap gray;
%Change, for example, axis position
curPoss=get(gca,'Position'); %gca stands for 'get current axis'
set(gca,'Position',curPoss+1e-2*ix^2); %Move one image up a bit
end
Does that help?
If you want to jump between figures, make an array of them, and use it within a loop:
unitsPerInches = [0.1 0.1 0.15 0.15];
figs = [figure(1) figure(2)];
for f = 1:numel(figs)
figure(figs(f));
for counter = 1:2;
subplot(1,2,counter);
imagesc(rand(3));
drawnow
end
figs(f).Children(1).Position = unitsPerInches;
figs(f).Children(2).Position = unitsPerInches+0.3;
end
Your original values for unitsPerInches was wrong, since the 'Position' property of an axes takes values between 0 to 1 by default. You can change this using the 'Units' property, like:
figs(f).Children(1).Units = 'inches';
The output from this example is two figures that looks like this:
Where there is a small axes on the down-left and a big one on the top-right.
So, back to your original questions:
What is imagesc corresponding structure to plot(a1,rand(3))?
Instead of passing the axes to imagesc, set the focus on the relevant figure, and subplot with:
figure(h)
subplot(x,y,c)
imagesc(data)
where h is a handle to the relevant figure, c is the place of the subplot within h where you want to plot the image (a number between 1 to x*y), and after these two line you call imagesc.
How to change 'Position' of figure inside the loop?
In this question it is not clear if you want to change the 'Position' of the figure or the axes, they have different units and meaning, but both are accessible in the same way:
h.Position = [left bottom width height]; % for the position of the figure
h.Children(c).Position = [left bottom width height]; % for the position of the axes
where h is as before, but c may be numbered differently, so subplot(x,y,c) may not refer to the same axes as h.Children(c). However, you can always use gca to get the current axes handle:
ax = gca;
ax.Position = [left bottom width height];
Hope it's all clear now, and if there are further questions, let me know ;)
I am using the matlab to plot some project figures, see the blow figure. Now I am trying to cut the legend width so that the line won't look so wide. I tried these command as suggest by Benoit_11:
[~,icons,~,~] = legend(leg,'location','northwest');
hline = icons(2);
linedata = get(hline,'xdata');
newdata = [linedata(1)+0.2 linedata(2)];
set(hline,'xdata',newdata,'linewidth',1)
I am using the for loop to plot these figures because I have multiple figures to analysis at the same time. Now I can change the length of the legend line right now. But I got another problem: if I have different length of legend text, even if I set the same starting point and end point, I will get different length for the line in the end (you can see that from the figures). I tried to modify icon(1) but always got the error. Any suggestions?
There are 2 things you are not doing right with your code (aside the fact that you use size as the handles to the legend...that's risky because size is a built-in function):
1) Calling legend with only 1 argument returns a handle to the legend object and getting its position actually gives you the position of the box enclosing the legend, i.e. the text + the line.
2) Using this line:
p(3) = p(3) - 0.06;
does modify the position, however you would need to set the new position of the legend with something like the following for the changes to be effective:
set(HandleToLegend,'Position',p)
To come back to your question, the trick is to assign many outputs during the call to legend; you can then modify specific elements of the legend object.
Actually we only need 1 of the 4 output arguments, called icons in the docs so I'll stick with the notation. Then, we can get the XData property of the line and modify it as we want. The XData is actually a 2-element vector:
[StartingPoint EndingPoint]
so changing one or the other (or both) will change the length of the line displayed in the legend box.
Here is the whole code with comments; I changed the length and linewidth of the line in the 2nd plot to highlight the changes.
clear
clc
close all
x = 1:10;
y = rand(1,10);
figure;
%// Default case
subplot(1,2,1)
plot(x,y);
legend('First plot','Location','NorthWest');
title('Before','FontSize',18);
%// With modifications
subplot(1,2,2)
plot(x,y);
title('After','FontSize',18);
%//========================
%// Change the legend here
%//========================
%// The "icons" output is what you want
[~,icons,~,~] = legend('First plot','Location','NorthWest');
%// icons(1) is the text of the current element in the legend Here its 'First plot'
i_1 = get(icons(1)); %// access the properties with this command.
%// icons(2) is the line associated with that text. Here the blue line.
i_2 = get(icons(2));
%// Mhh I don't know what icons(3) represents haha sorry about that.
i_3 = get(icons(3));
%// Get the actual line
hline = icons(2);
%// Fetch its XData property
LineData = get(hline,'XData')
%// Play with those 2 elements to see the output change.
NewData = [LineData(1)+.2 LineData(2)-.01];
%// Apply the changes
set(hline,'XData',NewData,'LineWidth',3)
Which gives the following:
You need to set the value of the Position property, you can just change the vector p. p does not affect the plot at all, it's just a vector of numbers. You have to modify it, then apply it back to the plot, using
set(size,'Position',p)
There does seem to be a minimum width of the legend however.
Imagine I have function myPlot which creates a simple plot and returns figure and axes handle:
function [ fig_handle, axes_handle ] = myPlot( myTitle )
x = linspace(-10,10,100);
y = x.^2;
fig_handle = figure;
plot(x,y,'Color','b')
ylim([0,42]); xlim([-42/10,42/10]);
ylabel('y'); xlabel('x');
title(myTitle);
grid on;
axes_handle = gca;
end
Now I want to call that function multiple times with different input parameters and concatenate them into an array of subplots. The solution I came up with is
[f1,a1] = myPlot('Plot #1');
[f2,a2] = myPlot('Plot #2');
figure(3)
s221 = subplot(211);
s222 = subplot(212);
copyobj(get(a1,'children'),s221)
copyobj(get(a2,'children'),s222)
it gives me
so the new 2-part plot does not keep any property of the two plots before. Of course I am aware that I can just do:
set(s221,'Ylabel',get(a1,'Ylabel'))
with all properties. But I try to avoid this. Is there something easier I am missing?
Another workaround is to copy the full axes object (so all the properties come along) into a new figure. The only property you have left to set yourself is the position according to the rules of subplot(xyz).
To start with your example :
[f1,a1] = myPlot('Plot #1');
[f2,a2] = myPlot('Plot #2');
Then copy the axis of each figure into the new figure
h4 = figure(4)
copyobj(get(f1,'children'),h4)
copyobj(get(f2,'children'),h4)
They are both here, but they are still superimposed. You just have to reposition them now.
For a quick workaround I use an intermediate figure to let subplot calculate the position for me but these positions (axes arrangement) could probably be calculated by yourself with a helper function (rip some code from subplot.m if you need).
%// Just to get some position calculated for me
figure(3)
s221 = subplot(211);
s222 = subplot(212);
Then I apply the positions to axes in the figure:
hl = flipud( get(h4,'Children') ) ;
set( hl(1),'Position', get(s221,'Position') )
set( hl(2),'Position', get(s222,'Position') )
Just be careful, the axes/children list is upside down (so the use of the flipud function), but if you put that in a loop, you could just run the loop backward.
Edit
If you are going to discard the original figure (f1 and f2), then you can also simply move the axes to the new figure (instead of copying them) by assigning the Parent property of the axes, then close the figure (to keep things tidy). Just use :
set(a1,'Parent',h4) ; close(f1)
set(a2,'Parent',h4) ; close(f2)
instead of the 2 lines with copyobj. The rest of the solution is identical. Not sure if there is a performance gain by moving an object instead of replicating it (Matlab may do a copy in the background anyway ... or not) but if it involve many figures with heavy data sets it may at least save some memory during the process.
One possible workaround could be the following, not really generic though. Would be interested in a solution solving the original problem.
If it is possible to modify the myPlot function one could pass the figure handle and subplot specifier and plot everything correctly from the beginning.
function [ fig_handle, axes_handle ] = myPlot(fig_handle, sub, myTitle )
figure(fig_handle); subplot(sub)
....
end
called by
f = figure(3);
[f,a1] = myPlot(f, 221,'Plot #1');
[f,a2] = myPlot(f, 222,'Plot #2');
I'm trying to find a way to nicely plot my measurement data of digital signals.
So I have my data available as csv and mat file, exported from an Agilent Oscilloscope. The reason I'm not just taking a screen shot of the Oscilloscope screen is that I need to be more flexible (make several plots with one set of data, only showing some of the lines). Also I need to be able to change the plot in a month or two so my only option is creating a plot from the data with a computer.
What I'm trying to achieve is something similar to this picture:
The only thing missing on that pic is a yaxis with 0 and 1 lines.
My first try was to make a similar plot with Matlab. Here's what I got:
What's definitely missing is that the signal names are right next to the actual line and also 0 and 1 ticks on the y-axis.
I'm not even sure if Matlab is the right tool for this and I hope you guys can give me some hints/a solution on how to make my plots :-)
Here's my Matlab code:
clear;
close all;
clc;
MD.RAW = load('Daten/UVLOT1 debounced 0.mat'); % get MeasurementData
MD.N(1) = {'INIT\_DONE'};
MD.N(2) = {'CONF\_DONE'};
MD.N(3) = {'NSDN'};
MD.N(4) = {'NRST'};
MD.N(5) = {'1V2GD'};
MD.N(6) = {'2V5GD'};
MD.N(7) = {'3V3GD'};
MD.N(8) = {'5VGD'};
MD.N(9) = {'NERR'};
MD.N(10) = {'PGD'};
MD.N(11) = {'FGD'};
MD.N(12) = {'IGAGD'};
MD.N(13) = {'GT1'};
MD.N(14) = {'NERRA'};
MD.N(15) = {'GT1D'};
MD.N(16) = {'GB1D'};
% concat vectors into one matrix
MD.D = [MD.RAW.Trace_D0, MD.RAW.Trace_D1(:,2), MD.RAW.Trace_D2(:,2), MD.RAW.Trace_D3(:,2), ...
MD.RAW.Trace_D4(:,2), MD.RAW.Trace_D5(:,2), MD.RAW.Trace_D6(:,2), MD.RAW.Trace_D7(:,2), ...
MD.RAW.Trace_D8(:,2), MD.RAW.Trace_D9(:,2), MD.RAW.Trace_D10(:,2), MD.RAW.Trace_D11(:,2), ...
MD.RAW.Trace_D12(:,2), MD.RAW.Trace_D13(:,2), MD.RAW.Trace_D14(:,2), MD.RAW.Trace_D15(:,2)];
cm = hsv(size(MD.D,2)); % make colormap for plot
figure;
hold on;
% change timebase to ns
MD.D(:,1) = MD.D(:,1) * 1e9;
% plot lines
for i=2:1:size(MD.D,2)
plot(MD.D(:,1), MD.D(:,i)+(i-2)*1.5, 'color', cm(i-1,:));
end
hold off;
legend(MD.N, 'Location', 'EastOutside');
xlabel('Zeit [ns]'); % x axis label
title('Messwerte'); % title
set(gca, 'ytick', []); % hide y axis
Thank you guys for your help!
Dan
EDIT:
Here's a pic what I basically want. I added the signal names via text now the only thing that's missing are the 0, 1 ticks. They are correct for the init done signal. Now I just need them repeated instead of the other numbers on the y axis (sorry, kinda hard to explain :-)
So as written in my comment to the question. For appending Names to each signal I would recommend searching the documentation of how to append text to graph. There you get many different ways how to do it. You can change the position (above, below) and the exact point of data. As an example you could use:
text(x_data, y_data, Var_Name,'VerticalAlignment','top');
Here (x_data, y_data) is the data point where you want to append the text and Var_Name is the name you want to append.
For the second question of how to get a y-data which contains 0 and 1 values for each signal. I would do it by creating your signal the way, that your first signal has values of 0 and 1. The next signal is drawn about 2 higher. Thus it changes from 2 to 3 and so on. That way when you turn on y-axis (grid on) you get values at each integer (obviously you can change that to other values if you prefer less distance between 2 signals). Then you can relabel the y-axis using the documentation of axes (check the last part, because the documentation is quite long) and the set() function:
set(gca, 'YTick',0:1:last_entry, 'YTickLabel',new_y_label(0:1:last_entry))
Here last_entry is 2*No_Signals-1 and new_y_label is an array which is constructed of 0,1,0,1,0,....
For viewing y axis, you can turn the grid('on') option. However, you cannot chage the way the legends appear unless you resize it in the matlab figure. If you really want you can insert separate textboxes below each of the signal plots by using the insert ->Textbox option and then change the property (linestyle) of the textbox to none to get the exact same plot as above.
This is the end result and all my code, in case anybody else wants to use the good old ctrl-v ;-)
Code:
clear;
close all;
clc;
MD.RAW = load('Daten/UVLOT1 debounced 0.mat'); % get MeasurementData
MD.N(1) = {'INIT\_DONE'};
MD.N(2) = {'CONF\_DONE'};
MD.N(3) = {'NSDN'};
MD.N(4) = {'NRST'};
MD.N(5) = {'1V2GD'};
MD.N(6) = {'2V5GD'};
MD.N(7) = {'3V3GD'};
MD.N(8) = {'5VGD'};
MD.N(9) = {'NERR'};
MD.N(10) = {'PGD'};
MD.N(11) = {'FGD'};
MD.N(12) = {'IGAGD'};
MD.N(13) = {'GT1'};
MD.N(14) = {'NERRA'};
MD.N(15) = {'GT1D'};
MD.N(16) = {'GB1D'};
% concat vectors into one matrix
MD.D = [MD.RAW.Trace_D0, MD.RAW.Trace_D1(:,2), MD.RAW.Trace_D2(:,2), MD.RAW.Trace_D3(:,2), ...
MD.RAW.Trace_D4(:,2), MD.RAW.Trace_D5(:,2), MD.RAW.Trace_D6(:,2), MD.RAW.Trace_D7(:,2), ...
MD.RAW.Trace_D8(:,2), MD.RAW.Trace_D9(:,2), MD.RAW.Trace_D10(:,2), MD.RAW.Trace_D11(:,2), ...
MD.RAW.Trace_D12(:,2), MD.RAW.Trace_D13(:,2), MD.RAW.Trace_D14(:,2), MD.RAW.Trace_D15(:,2)];
cm = hsv(size(MD.D,2)); % make colormap for plot
figure;
hold on;
% change timebase to ns
MD.D(:,1) = MD.D(:,1) * 1e9;
% plot lines
for i=2:1:size(MD.D,2)
plot(MD.D(:,1), MD.D(:,i)+(i-2)*2, 'color', cm(i-1,:));
text(MD.D(2,1), (i-2)*2+.5, MD.N(i-1));
end
hold off;
%legend(MD.N, 'Location', 'EastOutside');
xlabel('Zeit [ns]'); % x axis label
title('Messwerte'); % title
% make y axis and grid the way I want it
set(gca, 'ytick', 0:size(MD.D,2)*2-3);
grid off;
set(gca,'ygrid','on');
set(gca, 'YTickLabel', {'0'; '1'});
ylim([-1,(size(MD.D,2)-1)*2]);