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Polcz Péter honlapja

Tartalomjegyzék

TELJES MATLAB SCRIPT KIEGÉSZÍTŐ FÜGGVÉNYEKKEL

file:   vectorfield_Coulombs_law.m
author: Polcz Péter <ppolcz@gmail.com>
Created on 2016.09.06. Tuesday, 10:56:21
Reviewed on 2017. August 25. [Vagó tanárnőnek képek generálása]
Output:
┌vectorfield_Coulombs_law
│   - Persistence for `vectorfield_Coulombs_law` initialized [run ID: 3492, 2017.08.27. Sunday, 04:04:57]
│   - Script `vectorfield_Coulombs_law` backuped

Pozitív és negatív ponttöltések töltések elektromos tere (normalizálva)

% Coulomb's constant
ke = 8.99e9;

e = -1.6e-19;

q = 10000 * e;

Qn = [ -2 -0.5 ];
Qp = [ 2 0.7 0.9 ];

rn = [
    -5 0
    0  9
    ];

rp = [
    5  2 -8
    0 -9 -8
    ];

Qs = [Qp Qn];
rs = [rp rn];

resolution = 20;
[x,y] = meshgrid(linspace(-10,10,resolution));
Fx = zeros(size(x));
Fy = Fx;

for i = 1:size(rs,2)
    square_distance = (x-rs(1,i)).^2 + (y-rs(2,i)).^2;
    Fx = Fx + ke * Qs(i) * q * (x - rs(1,i)) ./ (square_distance.^(3/2));
    Fy = Fy + ke * Qs(i) * q * (y - rs(2,i)) ./ (square_distance.^(3/2));
end

Fr = (Fx.^2 + Fy.^2).^(1/2);

fig = figure('Units','normalized', 'Position', [0.3474 0.3611 0.4359 0.5389]);
hold on;
% quiver(x,y,Fx,Fy);
quiver(x,y,Fx./Fr,Fy./Fr,0.5);

s = {'' '' '+'};
R_divider = 3;
for i = 1:numel(Qs)
    if Qs(i) > 0
        color = 'r';
    else
        color = 'b';
    end
    R = abs(Qs(i))/R_divider;
    rectangle('Position',[rs(1,i)-R,rs(2,i)-R,2*R,2*R],'Curvature',[1,1],...
        'FaceColor',color,'EdgeColor',color);
end


axis equal tight
% title 'Normalized vector field between some electric point charge' interpreter latex

set(gca,'YTick',[-10 -5 0 5 10],'XTick',[-10 -5 0 5 10],persist.font.axis18{:});

plabel x '$x$'
plabel y '$y$'
set(get(gca,'ylabel'),'rotation',0)

% title 'Elektromos t\"{o}lt\''esek \''altal keltett (normaliz\''alt) elektromos t\''er' interpreter latex
% title 'Normalized vector field between some electric point charge' interpreter latex
% legend([h1 h2], {'negative','positive'},'Position',[0.85,0.8,0.1,0.1],'Box','off')

persist.png('ponttoltesek')

title 'T\"olt\''esek norm\''alt elektromos tere' interpreter latex

persist.png('ponttoltesek-szoveg')
Output:
│   - File saved to:
/home/ppolcz/Repositories/Bitbucket/control-systems/zygote/dropbox_link/oktatas/anal3/1_vekanal/vectorfield_Coulombs_law/media/17_08_27_Time040457_runID3492_ponttoltesek.png
│   - File saved to:
/home/ppolcz/Repositories/Bitbucket/control-systems/zygote/dropbox_link/oktatas/anal3/1_vekanal/vectorfield_Coulombs_law/media/17_08_27_Time040457_runID3492_ponttoltesek-szoveg.png

Ponttöltések elektromos tere véletlenszerű pontokban (normalizálva)

Reviewed on 2017.08.25. Friday, 14:35:51
% Coulomb's constant
ke = 8.99e9;

e = -1.6e-19;

Nr = 5;

q = 10000 * e;
Q = randn(1,Nr);

Q_pos = (rand(2,Nr)-0.5)*20;

[x,y] = meshgrid(linspace(min(min(min(Q_pos)),-10),max(max(max(Q_pos)),10),30));
Fx = zeros(size(x));
Fy = Fx;

for i = 1:size(Q_pos,2)
    square_distance = (x-Q_pos(1,i)).^2 + (y-Q_pos(2,i)).^2;
    Fx = Fx + ke * Q(i) * q * (x - Q_pos(1,i)) ./ (square_distance.^(3/2));
    Fy = Fy + ke * Q(i) * q * (y - Q_pos(2,i)) ./ (square_distance.^(3/2));
end

Fr = (Fx.^2 + Fy.^2).^(1/2);

fig = figure('Units','normalized', 'Position', [0.3474 0.3611 0.4359 0.5389]);
% quiver(x,y,Fx,Fy);
quiver(x,y,Fx./Fr,Fy./Fr, 0.5), hold on;
for i = 1:size(Q_pos,2)
    if Q(i) < 0
        h1 = plot(Q_pos(1,i), Q_pos(2,i), '.r', 'linewidth', 10, 'markersize', 20);
    else
        h2 = plot(Q_pos(1,i), Q_pos(2,i), '.b', 'linewidth', 10, 'markersize', 20);
    end
end
axis equal tight
set(gca,'YTick',[-10 -5 0 5 10],'XTick',[-10 -5 0 5 10],persist.font.axis18{:});

plabel x '$x$'
plabel y '$y$'
set(get(gca,'ylabel'),'rotation',0)

% title 'Elektromos t\"{o}lt\''esek \''altal keltett (normaliz\''alt) elektromos t\''er' interpreter latex
% title 'Normalized vector field between some electric point charge' interpreter latex
% legend([h1 h2], {'negative','positive'},'Position',[0.85,0.8,0.1,0.1],'Box','off')

persist.png('ponttoltesek')

title 'T\"olt\''esek norm\''alt elektromos tere' interpreter latex

persist.png('ponttoltesek-szoveg')
Output:
│   - File saved to:
/home/ppolcz/Repositories/Bitbucket/control-systems/zygote/dropbox_link/oktatas/anal3/1_vekanal/vectorfield_Coulombs_law/media/17_08_27_Time040457_runID3492_ponttoltesek.png
│   - File saved to:
/home/ppolcz/Repositories/Bitbucket/control-systems/zygote/dropbox_link/oktatas/anal3/1_vekanal/vectorfield_Coulombs_law/media/17_08_27_Time040457_runID3492_ponttoltesek-szoveg.png

Anod és katód elektromos tere (ponttöltésekkel közelítve)

Reviewed on 2017.08.25. Friday, 14:36:01
% Coulomb's constant
ke = 8.99e9;

e = -1.6e-19;

q = 10000 * e;

Nr_anode = 100;
Nr_cathode = 70;

Q = [ 0.01*ones(1,Nr_anode) -0.01*ones(1,Nr_cathode) ];

Q_pos = [
    linspace(-7,7,Nr_anode) linspace(-3,3,Nr_cathode)
    5*ones(1,Nr_anode) -5*ones(1,Nr_cathode)
    ];

[x,y] = meshgrid(linspace(-10,10,20));
Fx = zeros(size(x));
Fy = Fx;

for i = 1:size(Q_pos,2)
    square_distance = (x-Q_pos(1,i)).^2 + (y-Q_pos(2,i)).^2;
    Fx = Fx + ke * Q(i) * q * (x - Q_pos(1,i)) ./ (square_distance.^(3/2));
    Fy = Fy + ke * Q(i) * q * (y - Q_pos(2,i)) ./ (square_distance.^(3/2));
end

Fr = (Fx.^2 + Fy.^2).^(1/2);

fig = figure();
% quiver(x,y,Fx,Fy);
quiver(x,y,Fx./Fr,Fy./Fr, 0.5), hold on;
for i = 1:size(Q_pos,2)
    if Q(i) < 0
        h1 = plot(Q_pos(1,i), Q_pos(2,i), '.r', 'linewidth', 10, 'markersize', 20);
    else
        h2 = plot(Q_pos(1,i), Q_pos(2,i), '.b', 'linewidth', 10, 'markersize', 20);
    end
end
axis equal tight
set(gca,'YTick',[-10 -5 0 5 10],'XTick',[-10 -5 0 5 10],persist.font.axis18{:});

plabel x '$x$'
plabel y '$y$'
set(get(gca,'ylabel'),'rotation',0)

% title 'Normalized electric field between two electrically charged nodes' interpreter latex
% title 'Elektromosan felt\"olt\"ott fegyverzetek (elektr\''od\''ak) \''altal keltett (normaliz\''alt) elektromos t\''er' interpreter latex
% legend([h1 h2], {'negative','positive'},'Position',[0.85,0.8,0.1,0.1])


persist.png('kondenzator')

text(0,6.3,['$Q_1 = -' num2str(Nr_anode/100) 'C$'],persist.font.latex18c{:})
text(0,-6.3,['$Q_2 = +' num2str(Nr_cathode/100) 'C$'],persist.font.latex18c{:})
title 'Elektr\''odok norm\''alt elektromos tere' interpreter latex

persist.png('kondenzator-szoveg')
Output:
│   - File saved to:
/home/ppolcz/Repositories/Bitbucket/control-systems/zygote/dropbox_link/oktatas/anal3/1_vekanal/vectorfield_Coulombs_law/media/17_08_27_Time040457_runID3492_kondenzator.png
│   - File saved to:
/home/ppolcz/Repositories/Bitbucket/control-systems/zygote/dropbox_link/oktatas/anal3/1_vekanal/vectorfield_Coulombs_law/media/17_08_27_Time040457_runID3492_kondenzator-szoveg.png

Komplex számos megközelítés - NAGYON SZÉP ('Bruno' megoldása)

n = 5; % number of charges
% locations
x = rand(n,1)-0.5;
y = rand(n,1)-0.5;
% charge
q = rand(n,1);
q = q - mean(q);

% Coulumb's number
ke = 8.9875517873681764e9;

xi = linspace(-1,1,33);
yi = linspace(-1,1,33);
[XI YI] = meshgrid(xi,yi);
zi = complex(XI,YI);
z = complex(x,y);

[ZI Z]=ndgrid(zi(:),z(:));

dZ = ZI-Z;
Zn = abs(dZ);

% http://en.wikipedia.org/wiki/Electric_field
E = (dZ./Zn.^3)*(q(:)*e*ke);
E = reshape(E, size(XI));
En = abs(E);
Ex = real(E);
Ey = imag(E);

figure
quiver(XI,YI,Ex./En,Ey./En);
hold on
plot(x, y, 'or')
axis equal

Próba: divergenciája az r/|r|^3 fuggvenynek

syms x y z t real
r = [x;y];

E = r / norm(r)^(3)

divE = trace(jacobian(E));
divE_fh = matlabFunction(divE, 'vars', {x,y});

[xx,yy] = meshgrid(linspace(-1,1,31));
divE_num = divE_fh(xx,yy)
surf(xx,yy,divE_num)
Output:
E =
 x/(abs(x)^2 + abs(y)^2)^(3/2)
 y/(abs(x)^2 + abs(y)^2)^(3/2)
divE_num =
   1.0e+03 *
  Columns 1 through 7
   -0.0004   -0.0004   -0.0004   -0.0005   -0.0005   -0.0006   -0.0006
   -0.0004   -0.0004   -0.0005   -0.0005   -0.0006   -0.0007   -0.0007
   -0.0004   -0.0005   -0.0005   -0.0006   -0.0007   -0.0008   -0.0009
   -0.0005   -0.0005   -0.0006   -0.0007   -0.0008   -0.0009   -0.0010
   -0.0005   -0.0006   -0.0007   -0.0008   -0.0009   -0.0010   -0.0012
   -0.0006   -0.0007   -0.0008   -0.0009   -0.0010   -0.0012   -0.0014
   -0.0006   -0.0007   -0.0009   -0.0010   -0.0012   -0.0014   -0.0016
   -0.0007   -0.0008   -0.0009   -0.0011   -0.0013   -0.0016   -0.0019
   -0.0007   -0.0009   -0.0010   -0.0013   -0.0015   -0.0019   -0.0023
   -0.0008   -0.0010   -0.0011   -0.0014   -0.0017   -0.0021   -0.0027
   -0.0009   -0.0010   -0.0012   -0.0015   -0.0019   -0.0024   -0.0031
   -0.0009   -0.0011   -0.0013   -0.0017   -0.0021   -0.0027   -0.0035
   -0.0009   -0.0011   -0.0014   -0.0018   -0.0023   -0.0030   -0.0040
   -0.0010   -0.0012   -0.0015   -0.0019   -0.0024   -0.0032   -0.0043
   -0.0010   -0.0012   -0.0015   -0.0019   -0.0025   -0.0033   -0.0045
   -0.0010   -0.0012   -0.0015   -0.0020   -0.0025   -0.0034   -0.0046
   -0.0010   -0.0012   -0.0015   -0.0019   -0.0025   -0.0033   -0.0045
   -0.0010   -0.0012   -0.0015   -0.0019   -0.0024   -0.0032   -0.0043
   -0.0009   -0.0011   -0.0014   -0.0018   -0.0023   -0.0030   -0.0040
   -0.0009   -0.0011   -0.0013   -0.0017   -0.0021   -0.0027   -0.0035
   -0.0009   -0.0010   -0.0012   -0.0015   -0.0019   -0.0024   -0.0031
   -0.0008   -0.0010   -0.0011   -0.0014   -0.0017   -0.0021   -0.0027
   -0.0007   -0.0009   -0.0010   -0.0013   -0.0015   -0.0019   -0.0023
   -0.0007   -0.0008   -0.0009   -0.0011   -0.0013   -0.0016   -0.0019
   -0.0006   -0.0007   -0.0009   -0.0010   -0.0012   -0.0014   -0.0016
   -0.0006   -0.0007   -0.0008   -0.0009   -0.0010   -0.0012   -0.0014
   -0.0005   -0.0006   -0.0007   -0.0008   -0.0009   -0.0010   -0.0012
   -0.0005   -0.0005   -0.0006   -0.0007   -0.0008   -0.0009   -0.0010
   -0.0004   -0.0005   -0.0005   -0.0006   -0.0007   -0.0008   -0.0009
   -0.0004   -0.0004   -0.0005   -0.0005   -0.0006   -0.0007   -0.0007
   -0.0004   -0.0004   -0.0004   -0.0005   -0.0005   -0.0006   -0.0006
  Columns 8 through 14
   -0.0007   -0.0007   -0.0008   -0.0009   -0.0009   -0.0009   -0.0010
   -0.0008   -0.0009   -0.0010   -0.0010   -0.0011   -0.0011   -0.0012
   -0.0009   -0.0010   -0.0011   -0.0012   -0.0013   -0.0014   -0.0015
   -0.0011   -0.0013   -0.0014   -0.0015   -0.0017   -0.0018   -0.0019
   -0.0013   -0.0015   -0.0017   -0.0019   -0.0021   -0.0023   -0.0024
   -0.0016   -0.0019   -0.0021   -0.0024   -0.0027   -0.0030   -0.0032
   -0.0019   -0.0023   -0.0027   -0.0031   -0.0035   -0.0040   -0.0043
   -0.0023   -0.0028   -0.0034   -0.0040   -0.0047   -0.0054   -0.0060
   -0.0028   -0.0035   -0.0043   -0.0053   -0.0064   -0.0076   -0.0087
   -0.0034   -0.0043   -0.0055   -0.0071   -0.0090   -0.0112   -0.0133
   -0.0040   -0.0053   -0.0071   -0.0095   -0.0129   -0.0170   -0.0216
   -0.0047   -0.0064   -0.0090   -0.0129   -0.0186   -0.0270   -0.0377
   -0.0054   -0.0076   -0.0112   -0.0170   -0.0270   -0.0442   -0.0720
   -0.0060   -0.0087   -0.0133   -0.0216   -0.0377   -0.0720   -0.1492
   -0.0064   -0.0095   -0.0150   -0.0255   -0.0482   -0.1067   -0.3019
   -0.0066   -0.0098   -0.0156   -0.0270   -0.0527   -0.1250   -0.4219
   -0.0064   -0.0095   -0.0150   -0.0255   -0.0482   -0.1067   -0.3019
   -0.0060   -0.0087   -0.0133   -0.0216   -0.0377   -0.0720   -0.1492
   -0.0054   -0.0076   -0.0112   -0.0170   -0.0270   -0.0442   -0.0720
   -0.0047   -0.0064   -0.0090   -0.0129   -0.0186   -0.0270   -0.0377
   -0.0040   -0.0053   -0.0071   -0.0095   -0.0129   -0.0170   -0.0216
   -0.0034   -0.0043   -0.0055   -0.0071   -0.0090   -0.0112   -0.0133
   -0.0028   -0.0035   -0.0043   -0.0053   -0.0064   -0.0076   -0.0087
   -0.0023   -0.0028   -0.0034   -0.0040   -0.0047   -0.0054   -0.0060
   -0.0019   -0.0023   -0.0027   -0.0031   -0.0035   -0.0040   -0.0043
   -0.0016   -0.0019   -0.0021   -0.0024   -0.0027   -0.0030   -0.0032
   -0.0013   -0.0015   -0.0017   -0.0019   -0.0021   -0.0023   -0.0024
   -0.0011   -0.0013   -0.0014   -0.0015   -0.0017   -0.0018   -0.0019
   -0.0009   -0.0010   -0.0011   -0.0012   -0.0013   -0.0014   -0.0015
   -0.0008   -0.0009   -0.0010   -0.0010   -0.0011   -0.0011   -0.0012
   -0.0007   -0.0007   -0.0008   -0.0009   -0.0009   -0.0009   -0.0010
  Columns 15 through 21
   -0.0010   -0.0010   -0.0010   -0.0010   -0.0009   -0.0009   -0.0009
   -0.0012   -0.0012   -0.0012   -0.0012   -0.0011   -0.0011   -0.0010
   -0.0015   -0.0015   -0.0015   -0.0015   -0.0014   -0.0013   -0.0012
   -0.0019   -0.0020   -0.0019   -0.0019   -0.0018   -0.0017   -0.0015
   -0.0025   -0.0025   -0.0025   -0.0024   -0.0023   -0.0021   -0.0019
   -0.0033   -0.0034   -0.0033   -0.0032   -0.0030   -0.0027   -0.0024
   -0.0045   -0.0046   -0.0045   -0.0043   -0.0040   -0.0035   -0.0031
   -0.0064   -0.0066   -0.0064   -0.0060   -0.0054   -0.0047   -0.0040
   -0.0095   -0.0098   -0.0095   -0.0087   -0.0076   -0.0064   -0.0053
   -0.0150   -0.0156   -0.0150   -0.0133   -0.0112   -0.0090   -0.0071
   -0.0255   -0.0270   -0.0255   -0.0216   -0.0170   -0.0129   -0.0095
   -0.0482   -0.0527   -0.0482   -0.0377   -0.0270   -0.0186   -0.0129
   -0.1067   -0.1250   -0.1067   -0.0720   -0.0442   -0.0270   -0.0170
   -0.3019   -0.4219   -0.3019   -0.1492   -0.0720   -0.0377   -0.0216
   -1.1932   -3.3750   -1.1932   -0.3019   -0.1067   -0.0482   -0.0255
   -3.3750       NaN   -3.3750   -0.4219   -0.1250   -0.0527   -0.0270
   -1.1932   -3.3750   -1.1932   -0.3019   -0.1067   -0.0482   -0.0255
   -0.3019   -0.4219   -0.3019   -0.1492   -0.0720   -0.0377   -0.0216
   -0.1067   -0.1250   -0.1067   -0.0720   -0.0442   -0.0270   -0.0170
   -0.0482   -0.0527   -0.0482   -0.0377   -0.0270   -0.0186   -0.0129
   -0.0255   -0.0270   -0.0255   -0.0216   -0.0170   -0.0129   -0.0095
   -0.0150   -0.0156   -0.0150   -0.0133   -0.0112   -0.0090   -0.0071
   -0.0095   -0.0098   -0.0095   -0.0087   -0.0076   -0.0064   -0.0053
   -0.0064   -0.0066   -0.0064   -0.0060   -0.0054   -0.0047   -0.0040
   -0.0045   -0.0046   -0.0045   -0.0043   -0.0040   -0.0035   -0.0031
   -0.0033   -0.0034   -0.0033   -0.0032   -0.0030   -0.0027   -0.0024
   -0.0025   -0.0025   -0.0025   -0.0024   -0.0023   -0.0021   -0.0019
   -0.0019   -0.0020   -0.0019   -0.0019   -0.0018   -0.0017   -0.0015
   -0.0015   -0.0015   -0.0015   -0.0015   -0.0014   -0.0013   -0.0012
   -0.0012   -0.0012   -0.0012   -0.0012   -0.0011   -0.0011   -0.0010
   -0.0010   -0.0010   -0.0010   -0.0010   -0.0009   -0.0009   -0.0009
  Columns 22 through 28
   -0.0008   -0.0007   -0.0007   -0.0006   -0.0006   -0.0005   -0.0005
   -0.0010   -0.0009   -0.0008   -0.0007   -0.0007   -0.0006   -0.0005
   -0.0011   -0.0010   -0.0009   -0.0009   -0.0008   -0.0007   -0.0006
   -0.0014   -0.0013   -0.0011   -0.0010   -0.0009   -0.0008   -0.0007
   -0.0017   -0.0015   -0.0013   -0.0012   -0.0010   -0.0009   -0.0008
   -0.0021   -0.0019   -0.0016   -0.0014   -0.0012   -0.0010   -0.0009
   -0.0027   -0.0023   -0.0019   -0.0016   -0.0014   -0.0012   -0.0010
   -0.0034   -0.0028   -0.0023   -0.0019   -0.0016   -0.0013   -0.0011
   -0.0043   -0.0035   -0.0028   -0.0023   -0.0019   -0.0015   -0.0013
   -0.0055   -0.0043   -0.0034   -0.0027   -0.0021   -0.0017   -0.0014
   -0.0071   -0.0053   -0.0040   -0.0031   -0.0024   -0.0019   -0.0015
   -0.0090   -0.0064   -0.0047   -0.0035   -0.0027   -0.0021   -0.0017
   -0.0112   -0.0076   -0.0054   -0.0040   -0.0030   -0.0023   -0.0018
   -0.0133   -0.0087   -0.0060   -0.0043   -0.0032   -0.0024   -0.0019
   -0.0150   -0.0095   -0.0064   -0.0045   -0.0033   -0.0025   -0.0019
   -0.0156   -0.0098   -0.0066   -0.0046   -0.0034   -0.0025   -0.0020
   -0.0150   -0.0095   -0.0064   -0.0045   -0.0033   -0.0025   -0.0019
   -0.0133   -0.0087   -0.0060   -0.0043   -0.0032   -0.0024   -0.0019
   -0.0112   -0.0076   -0.0054   -0.0040   -0.0030   -0.0023   -0.0018
   -0.0090   -0.0064   -0.0047   -0.0035   -0.0027   -0.0021   -0.0017
   -0.0071   -0.0053   -0.0040   -0.0031   -0.0024   -0.0019   -0.0015
   -0.0055   -0.0043   -0.0034   -0.0027   -0.0021   -0.0017   -0.0014
   -0.0043   -0.0035   -0.0028   -0.0023   -0.0019   -0.0015   -0.0013
   -0.0034   -0.0028   -0.0023   -0.0019   -0.0016   -0.0013   -0.0011
   -0.0027   -0.0023   -0.0019   -0.0016   -0.0014   -0.0012   -0.0010
   -0.0021   -0.0019   -0.0016   -0.0014   -0.0012   -0.0010   -0.0009
   -0.0017   -0.0015   -0.0013   -0.0012   -0.0010   -0.0009   -0.0008
   -0.0014   -0.0013   -0.0011   -0.0010   -0.0009   -0.0008   -0.0007
   -0.0011   -0.0010   -0.0009   -0.0009   -0.0008   -0.0007   -0.0006
   -0.0010   -0.0009   -0.0008   -0.0007   -0.0007   -0.0006   -0.0005
   -0.0008   -0.0007   -0.0007   -0.0006   -0.0006   -0.0005   -0.0005
  Columns 29 through 31
   -0.0004   -0.0004   -0.0004
   -0.0005   -0.0004   -0.0004
   -0.0005   -0.0005   -0.0004
   -0.0006   -0.0005   -0.0005
   -0.0007   -0.0006   -0.0005
   -0.0008   -0.0007   -0.0006
   -0.0009   -0.0007   -0.0006
   -0.0009   -0.0008   -0.0007
   -0.0010   -0.0009   -0.0007
   -0.0011   -0.0010   -0.0008
   -0.0012   -0.0010   -0.0009
   -0.0013   -0.0011   -0.0009
   -0.0014   -0.0011   -0.0009
   -0.0015   -0.0012   -0.0010
   -0.0015   -0.0012   -0.0010
   -0.0015   -0.0012   -0.0010
   -0.0015   -0.0012   -0.0010
   -0.0015   -0.0012   -0.0010
   -0.0014   -0.0011   -0.0009
   -0.0013   -0.0011   -0.0009
   -0.0012   -0.0010   -0.0009
   -0.0011   -0.0010   -0.0008
   -0.0010   -0.0009   -0.0007
   -0.0009   -0.0008   -0.0007
   -0.0009   -0.0007   -0.0006
   -0.0008   -0.0007   -0.0006
   -0.0007   -0.0006   -0.0005
   -0.0006   -0.0005   -0.0005
   -0.0005   -0.0005   -0.0004
   -0.0005   -0.0004   -0.0004
   -0.0004   -0.0004   -0.0004

end of the scope

Output:
└ 7.8604 [sec]