Using for loop to generate and store matrix array and plot each cell

mpz
5 Dec 2022
1 Answer
Answer Accepted
Updated 6 Dec 2022
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Hi,
I am trying to generate the data for each cell and store it for the time history then plot it.
I = identity matrix (4 by 4), A = matrix (4 by 4).
I want to calculate the phi_2 for each time and store it. Then when all is complete, plot each cell history versus time. So essentially, I will have 16 plots on one figure. Below is how I attempted to code that but struggling to save the data
% Analytical
clear all;clc;close all
I = eye(4);
A = [0 1 0 0;0 0 -4.91 0;0 0 0 1;0 0 73.55 0];
t0=0;
tf=2;
for t=0:0.01:2
Phi_2 = I + A.*(t-t0) + (((t-t0)^2)/2).*A^2; % I want to be able to store the result of each cell and plot it wrt time
end

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 Accepted Answer

Voss
Voss on 5 Dec 2022
Ran in:

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Ran in:
% Analytical
clear all;clc;close all
I = eye(4);
A = [0 1 0 0;0 0 -4.91 0;0 0 0 1;0 0 73.55 0];
t0=0;
tf=2;
t = t0:0.01:tf;
Nt = numel(t);
Phi_2 = zeros(4,4,Nt); % Phi_2 is a 3d array, 4-by-4-by-Nt
for ii = 1:Nt
Phi_2(:,:,ii) = I + A.*(t(ii)-t0) + (((t(ii)-t0)^2)/2).*A^2;
end
Phi_2
Phi_2 =
Phi_2(:,:,1) = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 Phi_2(:,:,2) = 1.0000 0.0100 -0.0002 0 0 1.0000 -0.0491 -0.0002 0 0 1.0037 0.0100 0 0 0.7355 1.0037 Phi_2(:,:,3) = 1.0000 0.0200 -0.0010 0 0 1.0000 -0.0982 -0.0010 0 0 1.0147 0.0200 0 0 1.4710 1.0147 Phi_2(:,:,4) = 1.0000 0.0300 -0.0022 0 0 1.0000 -0.1473 -0.0022 0 0 1.0331 0.0300 0 0 2.2065 1.0331 Phi_2(:,:,5) = 1.0000 0.0400 -0.0039 0 0 1.0000 -0.1964 -0.0039 0 0 1.0588 0.0400 0 0 2.9420 1.0588 Phi_2(:,:,6) = 1.0000 0.0500 -0.0061 0 0 1.0000 -0.2455 -0.0061 0 0 1.0919 0.0500 0 0 3.6775 1.0919 Phi_2(:,:,7) = 1.0000 0.0600 -0.0088 0 0 1.0000 -0.2946 -0.0088 0 0 1.1324 0.0600 0 0 4.4130 1.1324 Phi_2(:,:,8) = 1.0000 0.0700 -0.0120 0 0 1.0000 -0.3437 -0.0120 0 0 1.1802 0.0700 0 0 5.1485 1.1802 Phi_2(:,:,9) = 1.0000 0.0800 -0.0157 0 0 1.0000 -0.3928 -0.0157 0 0 1.2354 0.0800 0 0 5.8840 1.2354 Phi_2(:,:,10) = 1.0000 0.0900 -0.0199 0 0 1.0000 -0.4419 -0.0199 0 0 1.2979 0.0900 0 0 6.6195 1.2979 Phi_2(:,:,11) = 1.0000 0.1000 -0.0246 0 0 1.0000 -0.4910 -0.0246 0 0 1.3678 0.1000 0 0 7.3550 1.3678 Phi_2(:,:,12) = 1.0000 0.1100 -0.0297 0 0 1.0000 -0.5401 -0.0297 0 0 1.4450 0.1100 0 0 8.0905 1.4450 Phi_2(:,:,13) = 1.0000 0.1200 -0.0354 0 0 1.0000 -0.5892 -0.0354 0 0 1.5296 0.1200 0 0 8.8260 1.5296 Phi_2(:,:,14) = 1.0000 0.1300 -0.0415 0 0 1.0000 -0.6383 -0.0415 0 0 1.6215 0.1300 0 0 9.5615 1.6215 Phi_2(:,:,15) = 1.0000 0.1400 -0.0481 0 0 1.0000 -0.6874 -0.0481 0 0 1.7208 0.1400 0 0 10.2970 1.7208 Phi_2(:,:,16) = 1.0000 0.1500 -0.0552 0 0 1.0000 -0.7365 -0.0552 0 0 1.8274 0.1500 0 0 11.0325 1.8274 Phi_2(:,:,17) = 1.0000 0.1600 -0.0628 0 0 1.0000 -0.7856 -0.0628 0 0 1.9414 0.1600 0 0 11.7680 1.9414 Phi_2(:,:,18) = 1.0000 0.1700 -0.0709 0 0 1.0000 -0.8347 -0.0709 0 0 2.0628 0.1700 0 0 12.5035 2.0628 Phi_2(:,:,19) = 1.0000 0.1800 -0.0795 0 0 1.0000 -0.8838 -0.0795 0 0 2.1915 0.1800 0 0 13.2390 2.1915 Phi_2(:,:,20) = 1.0000 0.1900 -0.0886 0 0 1.0000 -0.9329 -0.0886 0 0 2.3276 0.1900 0 0 13.9745 2.3276 Phi_2(:,:,21) = 1.0000 0.2000 -0.0982 0 0 1.0000 -0.9820 -0.0982 0 0 2.4710 0.2000 0 0 14.7100 2.4710 Phi_2(:,:,22) = 1.0000 0.2100 -0.1083 0 0 1.0000 -1.0311 -0.1083 0 0 2.6218 0.2100 0 0 15.4455 2.6218 Phi_2(:,:,23) = 1.0000 0.2200 -0.1188 0 0 1.0000 -1.0802 -0.1188 0 0 2.7799 0.2200 0 0 16.1810 2.7799 Phi_2(:,:,24) = 1.0000 0.2300 -0.1299 0 0 1.0000 -1.1293 -0.1299 0 0 2.9454 0.2300 0 0 16.9165 2.9454 Phi_2(:,:,25) = 1.0000 0.2400 -0.1414 0 0 1.0000 -1.1784 -0.1414 0 0 3.1182 0.2400 0 0 17.6520 3.1182 Phi_2(:,:,26) = 1.0000 0.2500 -0.1534 0 0 1.0000 -1.2275 -0.1534 0 0 3.2984 0.2500 0 0 18.3875 3.2984 Phi_2(:,:,27) = 1.0000 0.2600 -0.1660 0 0 1.0000 -1.2766 -0.1660 0 0 3.4860 0.2600 0 0 19.1230 3.4860 Phi_2(:,:,28) = 1.0000 0.2700 -0.1790 0 0 1.0000 -1.3257 -0.1790 0 0 3.6809 0.2700 0 0 19.8585 3.6809 Phi_2(:,:,29) = 1.0000 0.2800 -0.1925 0 0 1.0000 -1.3748 -0.1925 0 0 3.8832 0.2800 0 0 20.5940 3.8832 Phi_2(:,:,30) = 1.0000 0.2900 -0.2065 0 0 1.0000 -1.4239 -0.2065 0 0 4.0928 0.2900 0 0 21.3295 4.0928 Phi_2(:,:,31) = 1.0000 0.3000 -0.2210 0 0 1.0000 -1.4730 -0.2210 0 0 4.3097 0.3000 0 0 22.0650 4.3097 Phi_2(:,:,32) = 1.0000 0.3100 -0.2359 0 0 1.0000 -1.5221 -0.2359 0 0 4.5341 0.3100 0 0 22.8005 4.5341 Phi_2(:,:,33) = 1.0000 0.3200 -0.2514 0 0 1.0000 -1.5712 -0.2514 0 0 4.7658 0.3200 0 0 23.5360 4.7658 Phi_2(:,:,34) = 1.0000 0.3300 -0.2673 0 0 1.0000 -1.6203 -0.2673 0 0 5.0048 0.3300 0 0 24.2715 5.0048 Phi_2(:,:,35) = 1.0000 0.3400 -0.2838 0 0 1.0000 -1.6694 -0.2838 0 0 5.2512 0.3400 0 0 25.0070 5.2512 Phi_2(:,:,36) = 1.0000 0.3500 -0.3007 0 0 1.0000 -1.7185 -0.3007 0 0 5.5049 0.3500 0 0 25.7425 5.5049 Phi_2(:,:,37) = 1.0000 0.3600 -0.3182 0 0 1.0000 -1.7676 -0.3182 0 0 5.7660 0.3600 0 0 26.4780 5.7660 Phi_2(:,:,38) = 1.0000 0.3700 -0.3361 0 0 1.0000 -1.8167 -0.3361 0 0 6.0345 0.3700 0 0 27.2135 6.0345 Phi_2(:,:,39) = 1.0000 0.3800 -0.3545 0 0 1.0000 -1.8658 -0.3545 0 0 6.3103 0.3800 0 0 27.9490 6.3103 Phi_2(:,:,40) = 1.0000 0.3900 -0.3734 0 0 1.0000 -1.9149 -0.3734 0 0 6.5935 0.3900 0 0 28.6845 6.5935 Phi_2(:,:,41) = 1.0000 0.4000 -0.3928 0 0 1.0000 -1.9640 -0.3928 0 0 6.8840 0.4000 0 0 29.4200 6.8840 Phi_2(:,:,42) = 1.0000 0.4100 -0.4127 0 0 1.0000 -2.0131 -0.4127 0 0 7.1819 0.4100 0 0 30.1555 7.1819 Phi_2(:,:,43) = 1.0000 0.4200 -0.4331 0 0 1.0000 -2.0622 -0.4331 0 0 7.4871 0.4200 0 0 30.8910 7.4871 Phi_2(:,:,44) = 1.0000 0.4300 -0.4539 0 0 1.0000 -2.1113 -0.4539 0 0 7.7997 0.4300 0 0 31.6265 7.7997 Phi_2(:,:,45) = 1.0000 0.4400 -0.4753 0 0 1.0000 -2.1604 -0.4753 0 0 8.1196 0.4400 0 0 32.3620 8.1196 Phi_2(:,:,46) = 1.0000 0.4500 -0.4971 0 0 1.0000 -2.2095 -0.4971 0 0 8.4469 0.4500 0 0 33.0975 8.4469 Phi_2(:,:,47) = 1.0000 0.4600 -0.5195 0 0 1.0000 -2.2586 -0.5195 0 0 8.7816 0.4600 0 0 33.8330 8.7816 Phi_2(:,:,48) = 1.0000 0.4700 -0.5423 0 0 1.0000 -2.3077 -0.5423 0 0 9.1236 0.4700 0 0 34.5685 9.1236 Phi_2(:,:,49) = 1.0000 0.4800 -0.5656 0 0 1.0000 -2.3568 -0.5656 0 0 9.4730 0.4800 0 0 35.3040 9.4730 Phi_2(:,:,50) = 1.0000 0.4900 -0.5894 0 0 1.0000 -2.4059 -0.5894 0 0 9.8297 0.4900 0 0 36.0395 9.8297 Phi_2(:,:,51) = 1.0000 0.5000 -0.6138 0 0 1.0000 -2.4550 -0.6138 0 0 10.1937 0.5000 0 0 36.7750 10.1937 Phi_2(:,:,52) = 1.0000 0.5100 -0.6385 0 0 1.0000 -2.5041 -0.6385 0 0 10.5652 0.5100 0 0 37.5105 10.5652 Phi_2(:,:,53) = 1.0000 0.5200 -0.6638 0 0 1.0000 -2.5532 -0.6638 0 0 10.9440 0.5200 0 0 38.2460 10.9440 Phi_2(:,:,54) = 1.0000 0.5300 -0.6896 0 0 1.0000 -2.6023 -0.6896 0 0 11.3301 0.5300 0 0 38.9815 11.3301 Phi_2(:,:,55) = 1.0000 0.5400 -0.7159 0 0 1.0000 -2.6514 -0.7159 0 0 11.7236 0.5400 0 0 39.7170 11.7236 Phi_2(:,:,56) = 1.0000 0.5500 -0.7426 0 0 1.0000 -2.7005 -0.7426 0 0 12.1244 0.5500 0 0 40.4525 12.1244 Phi_2(:,:,57) = 1.0000 0.5600 -0.7699 0 0 1.0000 -2.7496 -0.7699 0 0 12.5326 0.5600 0 0 41.1880 12.5326 Phi_2(:,:,58) = 1.0000 0.5700 -0.7976 0 0 1.0000 -2.7987 -0.7976 0 0 12.9482 0.5700 0 0 41.9235 12.9482 Phi_2(:,:,59) = 1.0000 0.5800 -0.8259 0 0 1.0000 -2.8478 -0.8259 0 0 13.3711 0.5800 0 0 42.6590 13.3711 Phi_2(:,:,60) = 1.0000 0.5900 -0.8546 0 0 1.0000 -2.8969 -0.8546 0 0 13.8014 0.5900 0 0 43.3945 13.8014 Phi_2(:,:,61) = 1.0000 0.6000 -0.8838 0 0 1.0000 -2.9460 -0.8838 0 0 14.2390 0.6000 0 0 44.1300 14.2390 Phi_2(:,:,62) = 1.0000 0.6100 -0.9135 0 0 1.0000 -2.9951 -0.9135 0 0 14.6840 0.6100 0 0 44.8655 14.6840 Phi_2(:,:,63) = 1.0000 0.6200 -0.9437 0 0 1.0000 -3.0442 -0.9437 0 0 15.1363 0.6200 0 0 45.6010 15.1363 Phi_2(:,:,64) = 1.0000 0.6300 -0.9744 0 0 1.0000 -3.0933 -0.9744 0 0 15.5960 0.6300 0 0 46.3365 15.5960 Phi_2(:,:,65) = 1.0000 0.6400 -1.0056 0 0 1.0000 -3.1424 -1.0056 0 0 16.0630 0.6400 0 0 47.0720 16.0630 Phi_2(:,:,66) = 1.0000 0.6500 -1.0372 0 0 1.0000 -3.1915 -1.0372 0 0 16.5374 0.6500 0 0 47.8075 16.5374 Phi_2(:,:,67) = 1.0000 0.6600 -1.0694 0 0 1.0000 -3.2406 -1.0694 0 0 17.0192 0.6600 0 0 48.5430 17.0192 Phi_2(:,:,68) = 1.0000 0.6700 -1.1020 0 0 1.0000 -3.2897 -1.1020 0 0 17.5083 0.6700 0 0 49.2785 17.5083 Phi_2(:,:,69) = 1.0000 0.6800 -1.1352 0 0 1.0000 -3.3388 -1.1352 0 0 18.0048 0.6800 0 0 50.0140 18.0048 Phi_2(:,:,70) = 1.0000 0.6900 -1.1688 0 0 1.0000 -3.3879 -1.1688 0 0 18.5086 0.6900 0 0 50.7495 18.5086 Phi_2(:,:,71) = 1.0000 0.7000 -1.2030 0 0 1.0000 -3.4370 -1.2030 0 0 19.0198 0.7000 0 0 51.4850 19.0198 Phi_2(:,:,72) = 1.0000 0.7100 -1.2376 0 0 1.0000 -3.4861 -1.2376 0 0 19.5383 0.7100 0 0 52.2205 19.5383 Phi_2(:,:,73) = 1.0000 0.7200 -1.2727 0 0 1.0000 -3.5352 -1.2727 0 0 20.0642 0.7200 0 0 52.9560 20.0642 Phi_2(:,:,74) = 1.0000 0.7300 -1.3083 0 0 1.0000 -3.5843 -1.3083 0 0 20.5974 0.7300 0 0 53.6915 20.5974 Phi_2(:,:,75) = 1.0000 0.7400 -1.3444 0 0 1.0000 -3.6334 -1.3444 0 0 21.1380 0.7400 0 0 54.4270 21.1380 Phi_2(:,:,76) = 1.0000 0.7500 -1.3809 0 0 1.0000 -3.6825 -1.3809 0 0 21.6859 0.7500 0 0 55.1625 21.6859 Phi_2(:,:,77) = 1.0000 0.7600 -1.4180 0 0 1.0000 -3.7316 -1.4180 0 0 22.2412 0.7600 0 0 55.8980 22.2412 Phi_2(:,:,78) = 1.0000 0.7700 -1.4556 0 0 1.0000 -3.7807 -1.4556 0 0 22.8039 0.7700 0 0 56.6335 22.8039 Phi_2(:,:,79) = 1.0000 0.7800 -1.4936 0 0 1.0000 -3.8298 -1.4936 0 0 23.3739 0.7800 0 0 57.3690 23.3739 Phi_2(:,:,80) = 1.0000 0.7900 -1.5322 0 0 1.0000 -3.8789 -1.5322 0 0 23.9513 0.7900 0 0 58.1045 23.9513 Phi_2(:,:,81) = 1.0000 0.8000 -1.5712 0 0 1.0000 -3.9280 -1.5712 0 0 24.5360 0.8000 0 0 58.8400 24.5360 Phi_2(:,:,82) = 1.0000 0.8100 -1.6107 0 0 1.0000 -3.9771 -1.6107 0 0 25.1281 0.8100 0 0 59.5755 25.1281 Phi_2(:,:,83) = 1.0000 0.8200 -1.6507 0 0 1.0000 -4.0262 -1.6507 0 0 25.7275 0.8200 0 0 60.3110 25.7275 Phi_2(:,:,84) = 1.0000 0.8300 -1.6912 0 0 1.0000 -4.0753 -1.6912 0 0 26.3343 0.8300 0 0 61.0465 26.3343 Phi_2(:,:,85) = 1.0000 0.8400 -1.7322 0 0 1.0000 -4.1244 -1.7322 0 0 26.9484 0.8400 0 0 61.7820 26.9484 Phi_2(:,:,86) = 1.0000 0.8500 -1.7737 0 0 1.0000 -4.1735 -1.7737 0 0 27.5699 0.8500 0 0 62.5175 27.5699 Phi_2(:,:,87) = 1.0000 0.8600 -1.8157 0 0 1.0000 -4.2226 -1.8157 0 0 28.1988 0.8600 0 0 63.2530 28.1988 Phi_2(:,:,88) = 1.0000 0.8700 -1.8582 0 0 1.0000 -4.2717 -1.8582 0 0 28.8350 0.8700 0 0 63.9885 28.8350 Phi_2(:,:,89) = 1.0000 0.8800 -1.9012 0 0 1.0000 -4.3208 -1.9012 0 0 29.4786 0.8800 0 0 64.7240 29.4786 Phi_2(:,:,90) = 1.0000 0.8900 -1.9446 0 0 1.0000 -4.3699 -1.9446 0 0 30.1295 0.8900 0 0 65.4595 30.1295 Phi_2(:,:,91) = 1.0000 0.9000 -1.9886 0 0 1.0000 -4.4190 -1.9886 0 0 30.7877 0.9000 0 0 66.1950 30.7877 Phi_2(:,:,92) = 1.0000 0.9100 -2.0330 0 0 1.0000 -4.4681 -2.0330 0 0 31.4534 0.9100 0 0 66.9305 31.4534 Phi_2(:,:,93) = 1.0000 0.9200 -2.0779 0 0 1.0000 -4.5172 -2.0779 0 0 32.1264 0.9200 0 0 67.6660 32.1264 Phi_2(:,:,94) = 1.0000 0.9300 -2.1233 0 0 1.0000 -4.5663 -2.1233 0 0 32.8067 0.9300 0 0 68.4015 32.8067 Phi_2(:,:,95) = 1.0000 0.9400 -2.1692 0 0 1.0000 -4.6154 -2.1692 0 0 33.4944 0.9400 0 0 69.1370 33.4944 Phi_2(:,:,96) = 1.0000 0.9500 -2.2156 0 0 1.0000 -4.6645 -2.2156 0 0 34.1894 0.9500 0 0 69.8725 34.1894 Phi_2(:,:,97) = 1.0000 0.9600 -2.2625 0 0 1.0000 -4.7136 -2.2625 0 0 34.8918 0.9600 0 0 70.6080 34.8918 Phi_2(:,:,98) = 1.0000 0.9700 -2.3099 0 0 1.0000 -4.7627 -2.3099 0 0 35.6016 0.9700 0 0 71.3435 35.6016 Phi_2(:,:,99) = 1.0000 0.9800 -2.3578 0 0 1.0000 -4.8118 -2.3578 0 0 36.3187 0.9800 0 0 72.0790 36.3187 Phi_2(:,:,100) = 1.0000 0.9900 -2.4061 0 0 1.0000 -4.8609 -2.4061 0 0 37.0432 0.9900 0 0 72.8145 37.0432 Phi_2(:,:,101) = 1.0000 1.0000 -2.4550 0 0 1.0000 -4.9100 -2.4550 0 0 37.7750 1.0000 0 0 73.5500 37.7750 Phi_2(:,:,102) = 1.0000 1.0100 -2.5043 0 0 1.0000 -4.9591 -2.5043 0 0 38.5142 1.0100 0 0 74.2855 38.5142 Phi_2(:,:,103) = 1.0000 1.0200 -2.5542 0 0 1.0000 -5.0082 -2.5542 0 0 39.2607 1.0200 0 0 75.0210 39.2607 Phi_2(:,:,104) = 1.0000 1.0300 -2.6045 0 0 1.0000 -5.0573 -2.6045 0 0 40.0146 1.0300 0 0 75.7565 40.0146 Phi_2(:,:,105) = 1.0000 1.0400 -2.6553 0 0 1.0000 -5.1064 -2.6553 0 0 40.7758 1.0400 0 0 76.4920 40.7758 Phi_2(:,:,106) = 1.0000 1.0500 -2.7066 0 0 1.0000 -5.1555 -2.7066 0 0 41.5444 1.0500 0 0 77.2275 41.5444 Phi_2(:,:,107) = 1.0000 1.0600 -2.7584 0 0 1.0000 -5.2046 -2.7584 0 0 42.3204 1.0600 0 0 77.9630 42.3204 Phi_2(:,:,108) = 1.0000 1.0700 -2.8107 0 0 1.0000 -5.2537 -2.8107 0 0 43.1037 1.0700 0 0 78.6985 43.1037 Phi_2(:,:,109) = 1.0000 1.0800 -2.8635 0 0 1.0000 -5.3028 -2.8635 0 0 43.8944 1.0800 0 0 79.4340 43.8944 Phi_2(:,:,110) = 1.0000 1.0900 -2.9168 0 0 1.0000 -5.3519 -2.9168 0 0 44.6924 1.0900 0 0 80.1695 44.6924 Phi_2(:,:,111) = 1.0000 1.1000 -2.9706 0 0 1.0000 -5.4010 -2.9706 0 0 45.4978 1.1000 0 0 80.9050 45.4978 Phi_2(:,:,112) = 1.0000 1.1100 -3.0248 0 0 1.0000 -5.4501 -3.0248 0 0 46.3105 1.1100 0 0 81.6405 46.3105 Phi_2(:,:,113) = 1.0000 1.1200 -3.0796 0 0 1.0000 -5.4992 -3.0796 0 0 47.1306 1.1200 0 0 82.3760 47.1306 Phi_2(:,:,114) = 1.0000 1.1300 -3.1348 0 0 1.0000 -5.5483 -3.1348 0 0 47.9580 1.1300 0 0 83.1115 47.9580 Phi_2(:,:,115) = 1.0000 1.1400 -3.1905 0 0 1.0000 -5.5974 -3.1905 0 0 48.7928 1.1400 0 0 83.8470 48.7928 Phi_2(:,:,116) = 1.0000 1.1500 -3.2467 0 0 1.0000 -5.6465 -3.2467 0 0 49.6349 1.1500 0 0 84.5825 49.6349 Phi_2(:,:,117) = 1.0000 1.1600 -3.3034 0 0 1.0000 -5.6956 -3.3034 0 0 50.4844 1.1600 0 0 85.3180 50.4844 Phi_2(:,:,118) = 1.0000 1.1700 -3.3606 0 0 1.0000 -5.7447 -3.3606 0 0 51.3413 1.1700 0 0 86.0535 51.3413 Phi_2(:,:,119) = 1.0000 1.1800 -3.4183 0 0 1.0000 -5.7938 -3.4183 0 0 52.2055 1.1800 0 0 86.7890 52.2055 Phi_2(:,:,120) = 1.0000 1.1900 -3.4765 0 0 1.0000 -5.8429 -3.4765 0 0 53.0771 1.1900 0 0 87.5245 53.0771 Phi_2(:,:,121) = 1.0000 1.2000 -3.5352 0 0 1.0000 -5.8920 -3.5352 0 0 53.9560 1.2000 0 0 88.2600 53.9560 Phi_2(:,:,122) = 1.0000 1.2100 -3.5944 0 0 1.0000 -5.9411 -3.5944 0 0 54.8423 1.2100 0 0 88.9955 54.8423 Phi_2(:,:,123) = 1.0000 1.2200 -3.6540 0 0 1.0000 -5.9902 -3.6540 0 0 55.7359 1.2200 0 0 89.7310 55.7359 Phi_2(:,:,124) = 1.0000 1.2300 -3.7142 0 0 1.0000 -6.0393 -3.7142 0 0 56.6369 1.2300 0 0 90.4665 56.6369 Phi_2(:,:,125) = 1.0000 1.2400 -3.7748 0 0 1.0000 -6.0884 -3.7748 0 0 57.5452 1.2400 0 0 91.2020 57.5452 Phi_2(:,:,126) = 1.0000 1.2500 -3.8359 0 0 1.0000 -6.1375 -3.8359 0 0 58.4609 1.2500 0 0 91.9375 58.4609 Phi_2(:,:,127) = 1.0000 1.2600 -3.8976 0 0 1.0000 -6.1866 -3.8976 0 0 59.3840 1.2600 0 0 92.6730 59.3840 Phi_2(:,:,128) = 1.0000 1.2700 -3.9597 0 0 1.0000 -6.2357 -3.9597 0 0 60.3144 1.2700 0 0 93.4085 60.3144 Phi_2(:,:,129) = 1.0000 1.2800 -4.0223 0 0 1.0000 -6.2848 -4.0223 0 0 61.2522 1.2800 0 0 94.1440 61.2522 Phi_2(:,:,130) = 1.0000 1.2900 -4.0854 0 0 1.0000 -6.3339 -4.0854 0 0 62.1973 1.2900 0 0 94.8795 62.1973 Phi_2(:,:,131) = 1.0000 1.3000 -4.1489 0 0 1.0000 -6.3830 -4.1489 0 0 63.1497 1.3000 0 0 95.6150 63.1497 Phi_2(:,:,132) = 1.0000 1.3100 -4.2130 0 0 1.0000 -6.4321 -4.2130 0 0 64.1096 1.3100 0 0 96.3505 64.1096 Phi_2(:,:,133) = 1.0000 1.3200 -4.2776 0 0 1.0000 -6.4812 -4.2776 0 0 65.0768 1.3200 0 0 97.0860 65.0768 Phi_2(:,:,134) = 1.0000 1.3300 -4.3426 0 0 1.0000 -6.5303 -4.3426 0 0 66.0513 1.3300 0 0 97.8215 66.0513 Phi_2(:,:,135) = 1.0000 1.3400 -4.4082 0 0 1.0000 -6.5794 -4.4082 0 0 67.0332 1.3400 0 0 98.5570 67.0332 Phi_2(:,:,136) = 1.0000 1.3500 -4.4742 0 0 1.0000 -6.6285 -4.4742 0 0 68.0224 1.3500 0 0 99.2925 68.0224 Phi_2(:,:,137) = 1.0000 1.3600 -4.5408 0 0 1.0000 -6.6776 -4.5408 0 0 69.0190 1.3600 0 0 100.0280 69.0190 Phi_2(:,:,138) = 1.0000 1.3700 -4.6078 0 0 1.0000 -6.7267 -4.6078 0 0 70.0230 1.3700 0 0 100.7635 70.0230 Phi_2(:,:,139) = 1.0000 1.3800 -4.6753 0 0 1.0000 -6.7758 -4.6753 0 0 71.0343 1.3800 0 0 101.4990 71.0343 Phi_2(:,:,140) = 1.0000 1.3900 -4.7433 0 0 1.0000 -6.8249 -4.7433 0 0 72.0530 1.3900 0 0 102.2345 72.0530 Phi_2(:,:,141) = 1.0000 1.4000 -4.8118 0 0 1.0000 -6.8740 -4.8118 0 0 73.0790 1.4000 0 0 102.9700 73.0790 Phi_2(:,:,142) = 1.0000 1.4100 -4.8808 0 0 1.0000 -6.9231 -4.8808 0 0 74.1124 1.4100 0 0 103.7055 74.1124 Phi_2(:,:,143) = 1.0000 1.4200 -4.9503 0 0 1.0000 -6.9722 -4.9503 0 0 75.1531 1.4200 0 0 104.4410 75.1531 Phi_2(:,:,144) = 1.0000 1.4300 -5.0202 0 0 1.0000 -7.0213 -5.0202 0 0 76.2012 1.4300 0 0 105.1765 76.2012 Phi_2(:,:,145) = 1.0000 1.4400 -5.0907 0 0 1.0000 -7.0704 -5.0907 0 0 77.2566 1.4400 0 0 105.9120 77.2566 Phi_2(:,:,146) = 1.0000 1.4500 -5.1616 0 0 1.0000 -7.1195 -5.1616 0 0 78.3194 1.4500 0 0 106.6475 78.3194 Phi_2(:,:,147) = 1.0000 1.4600 -5.2331 0 0 1.0000 -7.1686 -5.2331 0 0 79.3896 1.4600 0 0 107.3830 79.3896 Phi_2(:,:,148) = 1.0000 1.4700 -5.3050 0 0 1.0000 -7.2177 -5.3050 0 0 80.4671 1.4700 0 0 108.1185 80.4671 Phi_2(:,:,149) = 1.0000 1.4800 -5.3774 0 0 1.0000 -7.2668 -5.3774 0 0 81.5520 1.4800 0 0 108.8540 81.5520 Phi_2(:,:,150) = 1.0000 1.4900 -5.4503 0 0 1.0000 -7.3159 -5.4503 0 0 82.6442 1.4900 0 0 109.5895 82.6442 Phi_2(:,:,151) = 1.0000 1.5000 -5.5237 0 0 1.0000 -7.3650 -5.5237 0 0 83.7437 1.5000 0 0 110.3250 83.7437 Phi_2(:,:,152) = 1.0000 1.5100 -5.5976 0 0 1.0000 -7.4141 -5.5976 0 0 84.8507 1.5100 0 0 111.0605 84.8507 Phi_2(:,:,153) = 1.0000 1.5200 -5.6720 0 0 1.0000 -7.4632 -5.6720 0 0 85.9650 1.5200 0 0 111.7960 85.9650 Phi_2(:,:,154) = 1.0000 1.5300 -5.7469 0 0 1.0000 -7.5123 -5.7469 0 0 87.0866 1.5300 0 0 112.5315 87.0866 Phi_2(:,:,155) = 1.0000 1.5400 -5.8223 0 0 1.0000 -7.5614 -5.8223 0 0 88.2156 1.5400 0 0 113.2670 88.2156 Phi_2(:,:,156) = 1.0000 1.5500 -5.8981 0 0 1.0000 -7.6105 -5.8981 0 0 89.3519 1.5500 0 0 114.0025 89.3519 Phi_2(:,:,157) = 1.0000 1.5600 -5.9745 0 0 1.0000 -7.6596 -5.9745 0 0 90.4956 1.5600 0 0 114.7380 90.4956 Phi_2(:,:,158) = 1.0000 1.5700 -6.0513 0 0 1.0000 -7.7087 -6.0513 0 0 91.6467 1.5700 0 0 115.4735 91.6467 Phi_2(:,:,159) = 1.0000 1.5800 -6.1287 0 0 1.0000 -7.7578 -6.1287 0 0 92.8051 1.5800 0 0 116.2090 92.8051 Phi_2(:,:,160) = 1.0000 1.5900 -6.2065 0 0 1.0000 -7.8069 -6.2065 0 0 93.9709 1.5900 0 0 116.9445 93.9709 Phi_2(:,:,161) = 1.0000 1.6000 -6.2848 0 0 1.0000 -7.8560 -6.2848 0 0 95.1440 1.6000 0 0 117.6800 95.1440 Phi_2(:,:,162) = 1.0000 1.6100 -6.3636 0 0 1.0000 -7.9051 -6.3636 0 0 96.3245 1.6100 0 0 118.4155 96.3245 Phi_2(:,:,163) = 1.0000 1.6200 -6.4429 0 0 1.0000 -7.9542 -6.4429 0 0 97.5123 1.6200 0 0 119.1510 97.5123 Phi_2(:,:,164) = 1.0000 1.6300 -6.5227 0 0 1.0000 -8.0033 -6.5227 0 0 98.7075 1.6300 0 0 119.8865 98.7075 Phi_2(:,:,165) = 1.0000 1.6400 -6.6030 0 0 1.0000 -8.0524 -6.6030 0 0 99.9100 1.6400 0 0 120.6220 99.9100 Phi_2(:,:,166) = 1.0000 1.6500 -6.6837 0 0 1.0000 -8.1015 -6.6837 0 0 101.1199 1.6500 0 0 121.3575 101.1199 Phi_2(:,:,167) = 1.0000 1.6600 -6.7650 0 0 1.0000 -8.1506 -6.7650 0 0 102.3372 1.6600 0 0 122.0930 102.3372 Phi_2(:,:,168) = 1.0000 1.6700 -6.8467 0 0 1.0000 -8.1997 -6.8467 0 0 103.5618 1.6700 0 0 122.8285 103.5618 Phi_2(:,:,169) = 1.0000 1.6800 -6.9290 0 0 1.0000 -8.2488 -6.9290 0 0 104.7938 1.6800 0 0 123.5640 104.7938 Phi_2(:,:,170) = 1.0000 1.6900 -7.0117 0 0 1.0000 -8.2979 -7.0117 0 0 106.0331 1.6900 0 0 124.2995 106.0331 Phi_2(:,:,171) = 1.0000 1.7000 -7.0949 0 0 1.0000 -8.3470 -7.0949 0 0 107.2797 1.7000 0 0 125.0350 107.2797 Phi_2(:,:,172) = 1.0000 1.7100 -7.1787 0 0 1.0000 -8.3961 -7.1787 0 0 108.5338 1.7100 0 0 125.7705 108.5338 Phi_2(:,:,173) = 1.0000 1.7200 -7.2629 0 0 1.0000 -8.4452 -7.2629 0 0 109.7952 1.7200 0 0 126.5060 109.7952 Phi_2(:,:,174) = 1.0000 1.7300 -7.3476 0 0 1.0000 -8.4943 -7.3476 0 0 111.0639 1.7300 0 0 127.2415 111.0639 Phi_2(:,:,175) = 1.0000 1.7400 -7.4328 0 0 1.0000 -8.5434 -7.4328 0 0 112.3400 1.7400 0 0 127.9770 112.3400 Phi_2(:,:,176) = 1.0000 1.7500 -7.5184 0 0 1.0000 -8.5925 -7.5184 0 0 113.6234 1.7500 0 0 128.7125 113.6234 Phi_2(:,:,177) = 1.0000 1.7600 -7.6046 0 0 1.0000 -8.6416 -7.6046 0 0 114.9142 1.7600 0 0 129.4480 114.9142 Phi_2(:,:,178) = 1.0000 1.7700 -7.6913 0 0 1.0000 -8.6907 -7.6913 0 0 116.2124 1.7700 0 0 130.1835 116.2124 Phi_2(:,:,179) = 1.0000 1.7800 -7.7784 0 0 1.0000 -8.7398 -7.7784 0 0 117.5179 1.7800 0 0 130.9190 117.5179 Phi_2(:,:,180) = 1.0000 1.7900 -7.8661 0 0 1.0000 -8.7889 -7.8661 0 0 118.8308 1.7900 0 0 131.6545 118.8308 Phi_2(:,:,181) = 1.0000 1.8000 -7.9542 0 0 1.0000 -8.8380 -7.9542 0 0 120.1510 1.8000 0 0 132.3900 120.1510 Phi_2(:,:,182) = 1.0000 1.8100 -8.0428 0 0 1.0000 -8.8871 -8.0428 0 0 121.4786 1.8100 0 0 133.1255 121.4786 Phi_2(:,:,183) = 1.0000 1.8200 -8.1319 0 0 1.0000 -8.9362 -8.1319 0 0 122.8135 1.8200 0 0 133.8610 122.8135 Phi_2(:,:,184) = 1.0000 1.8300 -8.2215 0 0 1.0000 -8.9853 -8.2215 0 0 124.1558 1.8300 0 0 134.5965 124.1558 Phi_2(:,:,185) = 1.0000 1.8400 -8.3116 0 0 1.0000 -9.0344 -8.3116 0 0 125.5054 1.8400 0 0 135.3320 125.5054 Phi_2(:,:,186) = 1.0000 1.8500 -8.4022 0 0 1.0000 -9.0835 -8.4022 0 0 126.8624 1.8500 0 0 136.0675 126.8624 Phi_2(:,:,187) = 1.0000 1.8600 -8.4933 0 0 1.0000 -9.1326 -8.4933 0 0 128.2268 1.8600 0 0 136.8030 128.2268 Phi_2(:,:,188) = 1.0000 1.8700 -8.5849 0 0 1.0000 -9.1817 -8.5849 0 0 129.5985 1.8700 0 0 137.5385 129.5985 Phi_2(:,:,189) = 1.0000 1.8800 -8.6770 0 0 1.0000 -9.2308 -8.6770 0 0 130.9776 1.8800 0 0 138.2740 130.9776 Phi_2(:,:,190) = 1.0000 1.8900 -8.7695 0 0 1.0000 -9.2799 -8.7695 0 0 132.3640 1.8900 0 0 139.0095 132.3640 Phi_2(:,:,191) = 1.0000 1.9000 -8.8626 0 0 1.0000 -9.3290 -8.8626 0 0 133.7577 1.9000 0 0 139.7450 133.7577 Phi_2(:,:,192) = 1.0000 1.9100 -8.9561 0 0 1.0000 -9.3781 -8.9561 0 0 135.1589 1.9100 0 0 140.4805 135.1589 Phi_2(:,:,193) = 1.0000 1.9200 -9.0501 0 0 1.0000 -9.4272 -9.0501 0 0 136.5674 1.9200 0 0 141.2160 136.5674 Phi_2(:,:,194) = 1.0000 1.9300 -9.1446 0 0 1.0000 -9.4763 -9.1446 0 0 137.9832 1.9300 0 0 141.9515 137.9832 Phi_2(:,:,195) = 1.0000 1.9400 -9.2396 0 0 1.0000 -9.5254 -9.2396 0 0 139.4064 1.9400 0 0 142.6870 139.4064 Phi_2(:,:,196) = 1.0000 1.9500 -9.3351 0 0 1.0000 -9.5745 -9.3351 0 0 140.8369 1.9500 0 0 143.4225 140.8369 Phi_2(:,:,197) = 1.0000 1.9600 -9.4311 0 0 1.0000 -9.6236 -9.4311 0 0 142.2748 1.9600 0 0 144.1580 142.2748 Phi_2(:,:,198) = 1.0000 1.9700 -9.5276 0 0 1.0000 -9.6727 -9.5276 0 0 143.7201 1.9700 0 0 144.8935 143.7201 Phi_2(:,:,199) = 1.0000 1.9800 -9.6246 0 0 1.0000 -9.7218 -9.6246 0 0 145.1727 1.9800 0 0 145.6290 145.1727 Phi_2(:,:,200) = 1.0000 1.9900 -9.7220 0 0 1.0000 -9.7709 -9.7220 0 0 146.6327 1.9900 0 0 146.3645 146.6327 Phi_2(:,:,201) = 1.0000 2.0000 -9.8200 0 0 1.0000 -9.8200 -9.8200 0 0 148.1000 2.0000 0 0 147.1000 148.1000
% plot Phi_2(1,1,:), Phi_2(2,1,:), etc.
figure()
for ii = 1:16
subplot(4,4,ii)
[r,c] = ind2sub([4 4],ii);
plot(t,squeeze(Phi_2(c,r,:))) % swap c and r because the way subplot counts is the opposite of everything else in MATLAB
end

2 Comments
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mpz
mpz on 6 Dec 2022
Thank you @Voss. Appreciate the help.
I tried to plot all the graphs on one figure with a legend but couldn't. Could you please show how.
Voss
Voss on 6 Dec 2022
Ran in:
Ran in:
Maybe a title on each subplot is better than a legend (all the lines are the same color, so a legend wouldn't be useful to distingiush them):
% Analytical
clear all;clc;close all
I = eye(4);
A = [0 1 0 0;0 0 -4.91 0;0 0 0 1;0 0 73.55 0];
t0=0;
tf=2;
t = t0:0.01:tf;
Nt = numel(t);
Phi_2 = zeros(4,4,Nt); % Phi_2 is a 3d array, 4-by-4-by-Nt
for ii = 1:Nt
Phi_2(:,:,ii) = I + A.*(t(ii)-t0) + (((t(ii)-t0)^2)/2).*A^2;
end
% plot Phi_2(1,1,:), Phi_2(2,1,:), etc.
figure()
for ii = 1:16
subplot(4,4,ii)
[r,c] = ind2sub([4 4],ii);
plot(t,squeeze(Phi_2(c,r,:)))
title(sprintf('%d, %d',c,r))
end

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Asked:

mpz
mpz
on 5 Dec 2022

Commented:

Voss
Voss
on 6 Dec 2022

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