A __matlab of the practice of MATLAB introduction

Provide a few introductory miscellaneous examples for the first time to touch matlab people pondering. The beauty of Matlab lies in the simplicity of its code and its use in various industries. tiredness and product and upper and lower triangles

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Clear
a=magic (9)
cumsum (a)
prod (a,2)% by line Triu (
a)% upper triangular 
tril (ones (4,4), -1)
a=[2 1-1;2 1 0;1-1 1]
b=[1-1 3;4 3 2]
x=b/a x*a a*b
'

Factoring, character definition, determinant, simplification, Tong, etc brief Operation

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Clear
syms percent x defines variable
f=factor (x^9-1)% factorization
x=sym (' x ')
m=sym (' [a,b;c,d] ')
det ( Magic (3))
det (M)
%simple% simplify
simplify (cos (x) ^2+sin (x) ^2) Simple
(cos (x) ^2+sin (x) ^2)
[N, D]=numden (f)% Tong
factor (sym (' 239239893849832 '))
% expand%  expand
% collect
% similar terms Find variables

a small exploration of t distribution

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Clear
syms y
syms n x H
f=exp ((-(n+x^2) *y^2)/2 *y^ (n)
pretty (y)
h=int (F,y,0,inf)
Simplify (Y)

a=n^ (N/2)/(2^ (N/2-1/2)) y=h*a P=gamma


((n+1)/2)/SQRT (n) * (1+x^2/n) ^ ((n+1)/2)
pretty (f)
y-p
Simplify (p)

determination of Planck constant in the experiment of large objects

x1=[4.57 3.96 3.58 2.94 1.90 0.86 0.12-0.73-1.24-1.73-1.91-1.95-2.00-2.05-2.10-2.15-2.40-2.50-2.55-2.65] Y1=[ 42.6*10^-9 38.0*10^-9 33.5*10^-9 30.0*10^-9 18.5*10^-9 10.7*10^-9 61.4*10^-10 23.5*10^-10 70.1*10^-11 38.0*10^-12-20*10 ^-12-21.5*10^-12-25.5*10^-12-26.5*10^-12-30.4*10^-12-30*10^-12-37.5*10^-12-40*10^-12-40.7*10^-12-40*10^-12] X2= [4.5 3.5 2.51 1.50 0.50-0.17-0.7-1.14-1.36-1.40-1.44-1.50-1.58-1.68-1.77-1.78-1.86-1.95-2.09-2.17-2.27-2. 30-2.42-2.52-2.63-2.74-2.80-2.74-2.85] y2=[13.4*10^-9 11.1*10^-9 85.1*10^-10 58.3*10^-10 29.1*10^-10 13.8*10^-10 4 4*10^-11 37.6*10^-12 27.7*10^-13 4.8*10^-13-26.7*10^-13-59.9*10^-13-81.2*10^-13-98*10^-13-99.5*10^-13-99.6*10^-13 -13.8*10^-13-14.5*10^-13-14.2*10^-13-15.2*10^-13-14.2*10^-13-14.4*10^-13-14.1*10^-13-14.82*10^-13-16.8*10^-13- 13.9*10^-13-14.0*10^-13-14.4*10^-13-14.4*10^-13] x3=[4.64 3.48 2.70 2.01 1.72 1.56 1.15 0.97 0.30-0.03-1.18-1.21-1. 2-1.25-1.33-1.36-1.48-1.53-1.56-1.64-1.72-1.81-1.91] y3=[11.6*10^-9 10.0*10^-9 82.0*10^-10 62.0*10^-10 58.5*10^-10 50.6*10^-10 40.1*10^-10 34.0* 10^-10 17.0*10^-10 10.3*10^-10 57.7*10^-13 9.3*10^-13-6.9*10^-13-20.0*10^-13-55*10^-13-32.8*10^-13-59.5*10^-13- 67.7*10^-13-70.2*10^-13-73.8*10^-13-82.6*10^-13-82.0*10^-13-88.5*10^-13] x4=[4.58 3.98 2.95 2.68 1.96 0.18-0.38-0.5 5-0.65-0.68-0.73-0.78-0.8-0.83-0.87-0.95-1.00-1.08-1.43-1.60-1.75] y4=[14.3*10^-9 12.2*10^-9 10.0*10^-9 88.3* 10^-10 71.7*10^-10 16.3*10^-10 16.7*10^-11 31.7*10^-12 90.0*10^-13 68.0*10^-13 15.0*10^-13-13.0*10^-13-30.9*10^-13-34 *10^-13-42*10^-13-50.5*10^-13-60*10^-13-66.7*10^-13-72.3*10^-13-70.0*10^-13-74.2*10^-13] X5=[4.07 3.72 1.97 1.28 0. 0.21-0.29-0.53-0.58-0.61-0.66-0.68-0.75-0.78-0.83-0.90-1.00-1.13-1.23-1.38-1.47] Y5=[62.1*10^-10 53.3*1 0^-10 40.3*10^-10 24.4*10^-10 14.7*10^-10 69.2*10^-11 84.8*10^-12 60.2*10^-13 33.9*10^-13-9.6*10^-13-7.3*10^-13-11.3* 10^-13-18.4*10^-13-21.9*10^-13-24.7*10^-13-26.6*10^-13-30.0*10^-13-29.5*10^-13-28.7*10^-13-28.0*10^-13-31.5*10^-13] X6=[4.51 3.97 3.61 2.41 1.99 0  .65 0.02-0.48-0.57-0.60-0.64-0.67-0.74-0.82-0.86-0.89-0.96-1.03-1.07-1.35-1.43-1.65-1.82-2.02-2.26-2.61 -2.82-3.2] y6=[11.4*10^-10 10.0*10^-10 85.9*10^-11 65.2*10^-11 57.0*10^-11 23.5*10^-11 73.8*10^-12 33.6*10^-13 10.0*10 ^-13 6.0*10^-13 3.7*10^-13 1.9*10^-13-0.4*10^-13-1.1*10^-13-1.5*10^-13-2.0*10^-13-2.3*10^-13-2.3*10^-13-2.3*10^- 13-2.4*10^-13-1.7*10^-13-2.2*10^-13-2.5*10^-13-3.2*10^-13-3.2*10^-13-3.0*10^-13-3.1*10^-13-3.5*10^-13] X7=[4.50 3.11 1.81 1.16 0.25-0.20-0.44-0.48-0.54-0.62-0.65-0.68-0.71-0.74-0.77-0.78-0.97-1.21] y7=[14.9*10^-9 11.2*10^ -9 77.6*10^-10 60.0*10^-10 17.2*10^-10 32.5*10^-11 35.8*10^-12 21.0*10^-12 89.8*10^-13-10.2*10^-13-28.0*10^-13-58.0* 10^-13-63.0*10^-13-72.0*10^-13-67.4*10^-13-82.2*10^-13-92.0*10^-13-90.2*10^-13] Plot (X1,Y1) plot (X2,Y2) plot (X3, Y3) plot (x4,y4) plot (x5,y5) hold on

Plot (X6,Y6) hold on plot (X7,Y7) 

the use of ksdensity

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Clear
X=[randn (30,1); 5+randn (30,1)];% produces 60 sample values
[F,xi]=ksdensity (x);% returns XI more than X quantity
subplot ( 2,2,1);
Plot (x);
Title (' Sample Data ');
Subplot (2,2,2);
Plot (xi,f);
Title (' Probability density distribution (PDF) ');
Subplot (2,2,3);
f= ksdensity (x,xi); 
Plot (xi,f); 
Subplot (2,2,4);
f= ksdensity (x,xi, ' function ', ' CDF '); 
Plot (xi,f); 

- use of Gplot

x=[0,0;1,0</