diary on x=5 x = 5 a=[4;7;9] a = 4 7 9 a=[4,7,9] a = 4 7 9 a=[4,7,9]' a = 4 7 9 A=[5,7,3;1,4,2] A = 5 7 3 1 4 2 size A ans = 1 1 size(A) ans = 2 3 A*a ans = 96 50 A A = 5 7 3 1 4 2 a a = 4 7 9 b=[1 2 3]' b = 1 2 3 a.*b ans = 4 14 27 a.^2 ans = 16 49 81 a*b' ans = 4 8 12 7 14 21 9 18 27 a(2) ans = 7 A(2,1) ans = 1 A A = 5 7 3 1 4 2 A(2,:) ans = 1 4 2 t=0:1:5 t = 0 1 2 3 4 5 t t = 0 1 2 3 4 5 x=0:0.01:2*pi; size(x) ans = 1 629 y=sin(x); size(y) ans = 1 629 plot(x,y,'r') x=rand(1) x = 0.9501 x=rand(1) x = 0.2311 x=rand(1) x = 0.6068 x=rand(1) x = 0.4860 help rand RAND Uniformly distributed random numbers. RAND(N) is an N-by-N matrix with random entries, chosen from a uniform distribution on the interval (0.0,1.0). RAND(M,N) and RAND([M,N]) are M-by-N matrices with random entries. RAND(M,N,P,...) or RAND([M,N,P,...]) generate random arrays. RAND with no arguments is a scalar whose value changes each time it is referenced. RAND(SIZE(A)) is the same size as A. RAND produces pseudo-random numbers. The sequence of numbers generated is determined by the state of the generator. Since MATLAB resets the state at start-up, the sequence of numbers generated will be the same unless the state is changed. S = RAND('state') is a 35-element vector containing the current state of the uniform generator. RAND('state',S) resets the state to S. RAND('state',0) resets the generator to its initial state. RAND('state',J), for integer J, resets the generator to its J-th state. RAND('state',sum(100*clock)) resets it to a different state each time. This generator can generate all the floating point numbers in the closed interval [2^(-53), 1-2^(-53)]. Theoretically, it can generate over 2^1492 values before repeating itself. MATLAB Version 4.x used random number generators with a single seed. RAND('seed',0) and RAND('seed',J) cause the MATLAB 4 generator to be used. RAND('seed') returns the current seed of the MATLAB 4 uniform generator. RAND('state',J) and RAND('state',S) cause the MATLAB 5 generator to be used. See also randn, sprand, sprandn, randperm. Reference page in Help browser doc rand RAND('state',sum(100*clock)) ??? Undefined command/function 'RAND'. rand('state',sum(100*clock)) N=100 N = 100 rand('state',0) x=rand(1) x = 0.9501 rand('state',sum(100*clock)) u=rand(N,1) u = 0.3250 0.9595 0.5752 0.6019 0.0368 0.0535 0.7024 0.1529 0.2807 0.0190 0.0913 0.1062 0.2731 0.8910 0.8698 0.4291 0.0011 0.0851 0.8930 0.2801 0.7188 0.2144 0.6345 0.8828 0.1944 0.6847 0.9401 0.8732 0.0652 0.4065 0.1675 0.2269 0.9032 0.5564 0.9745 0.3697 0.1898 0.6875 0.2666 0.4922 0.6408 0.7112 0.7089 0.1435 0.2797 0.6847 0.4707 0.6151 0.0335 0.8417 0.6013 0.1376 0.5921 0.0659 0.0261 0.2089 0.0372 0.5595 0.2472 0.1864 0.9742 0.0905 0.0650 0.8781 0.0207 0.8663 0.7499 0.5524 0.4918 0.8430 0.5247 0.6971 0.5345 0.5861 0.1417 0.7805 0.4370 0.0494 0.4809 0.9186 0.3103 0.5612 0.6379 0.8677 0.0791 0.7735 0.0028 0.2895 0.1415 0.6640 0.4791 0.6084 0.8112 0.0836 0.1360 0.4025 0.4342 0.9787 0.3784 0.6737 u=(1:10) u = 1 2 3 4 5 6 7 8 9 10 u=rand(N,1); u=1:10 u = 1 2 3 4 5 6 7 8 9 10 u=rand(N,1); u1:10 ??? Undefined function or variable 'u1'. u(1:10) ans = 0.1833 0.2888 0.3446 0.5622 0.6186 0.2811 0.8350 0.6241 0.4263 0.8080 fa = hist(u,10) fa = 13 8 11 8 13 10 10 7 8 12 f=fa/N f = Columns 1 through 7 0.1300 0.0800 0.1100 0.0800 0.1300 0.1000 0.1000 Columns 8 through 10 0.0700 0.0800 0.1200 delta=0.1 delta = 0.1000 h=f/delta h = Columns 1 through 7 1.3000 0.8000 1.1000 0.8000 1.3000 1.0000 1.0000 Columns 8 through 10 0.7000 0.8000 1.2000 bar(h) uc=0.05:0.1:0.95 uc = Columns 1 through 7 0.0500 0.1500 0.2500 0.3500 0.4500 0.5500 0.6500 Columns 8 through 10 0.7500 0.8500 0.9500 bar(uc,h) N=1000 N = 1000 u=rand(N,1); fa = hist(u,10) fa = 102 107 117 81 104 103 92 91 116 87 f=fa/N f = Columns 1 through 7 0.1020 0.1070 0.1170 0.0810 0.1040 0.1030 0.0920 Columns 8 through 10 0.0910 0.1160 0.0870 h=f/delta h = Columns 1 through 7 1.0200 1.0700 1.1700 0.8100 1.0400 1.0300 0.9200 Columns 8 through 10 0.9100 1.1600 0.8700 bar(uc,h) figure bar(uc,h,1) figure bar(uc,h,1) N=100000 N = 100000 u=rand(N,1); fa = hist(u,10) fa = Columns 1 through 6 10116 9923 10154 10220 9812 9885 Columns 7 through 10 10073 9965 9889 9963 f=fa/N f = Columns 1 through 7 0.1012 0.0992 0.1015 0.1022 0.0981 0.0988 0.1007 Columns 8 through 10 0.0997 0.0989 0.0996 h=f/delta h = Columns 1 through 7 1.0116 0.9923 1.0154 1.0220 0.9812 0.9885 1.0073 Columns 8 through 10 0.9965 0.9889 0.9963 figure bar(uc,h,1) N=5 N = 5 N=10 N = 10 M=10000 M = 10000 u=rand(N,M); size(u) ans = 10 10000 %Ho ripetuto 10000 volte le 10 estrazioni %Devo fare la media per colonne m=mean(u,1); size(m) ans = 1 10000 %Media = mean close all hist(m,50) 1/12 ans = 0.0833 (1/12)/10 ans = 0.0083 sqrt((1/12)/10) ans = 0.0913 %Media dell'uniforme é 0.5, la varianza é 1/12 N=100 N = 100 u=rand(N,M); figure m=mean(u,1); hist(m,50) N=10000 N = 10000 u=rand(N,M); N=100 N = 100 u=rand(N,M); m=mean(u,1); hist(m,50) s2=var(u,1); figure hist(s2,50) 1/12 ans = 0.0833 mean(s2) ans = 0.0823 N=10 N = 10 u=rand(N,M); m=mean(u,1); hist(s2,50) N=5 N = 5 u=rand(N,M); s2=var(u,1); figure hist(s2,50) mean(s2)*5/4 ans = 0.0836 mean(s2) ans = 0.0668 clear alla clear all clc clear clc x=1,1 x = 1 ans = 1 x=[1;1] x = 1 1 t=(0:1:4)' t = 0 1 2 3 4 A = [t ones (5,1)] ??? A = [t ones (5,1)] | Error: Incomplete or misformed expression or statement. A = [t ones(5,1)] A = 0 1 1 1 2 1 3 1 4 1 y=A*x y = 1 2 3 4 5 figure plot(x,y) ??? Error using ==> plot Vectors must be the same lengths. plot(t,y) plot(t,y,'-o') %Supponiamo che siano medie di VC ai diversi tempi v=randn(5,1) v = -0.4326 -1.6656 0.1253 0.2877 -1.1465 Y0=y+v Y0 = 0.5674 0.3344 3.1253 4.2877 3.8535 hold on plot(t,Y0,'or') plot(t,y,'-o') plot(t,Y0,'or') hold on plot(t,y,'-o') grid on %Ho sommato alla retta le estrazioni da una NORMALE N=A'*A N = 30 10 10 5 Tn=A'*Y0 Tn = 34.8622 12.1684 xst = N^(-1)*tn ??? Undefined function or variable 'tn'. xst = N^(-1)*Tn xst = 1.0525 0.3286 yst=A*xst; hold on plot(t,yst,'o-g') vst=Y0-yst vst = 0.2388 -1.0467 0.6917 0.8015 -0.6852 sigma02st=(vst' * vst)/(5-2) sigma02st = 0.9143 Cxxst=sigma02st*N^(-1) Cxxst = 0.0914 -0.1829 -0.1829 0.5486 N^(-1) ans = 0.1000 -0.2000 -0.2000 0.6000 diary off