1 MATLAB MATLAB MATrix LABoratory 20 Cleve Moler

1 MATLAB  MATLAB  MATrix   LABoratory  20  Cleve Moler

1 MATLAB MATLAB MATrix LABoratory 20 Cleve Moler LINPACK EISPACK FORTRAN MATLAB 1984 Little Moler Steve Bangert MathWorks MATLAB MATLAB C

1997 MATLAB5.0 5.1 5.2 1999 5.3 MATLAB 2 MATLAB 1 FFT 2

GUI 3 MATLAB 3 WAV wavread sound bmp gif pcx tif jpeg 4 SIMULINK COMM DSP SIGNAL 16 5 MATLAB

M EXE MATLAB API MATLAB FORTRAN C MATLAB 6 PDF HTML demo help help elfun help exp help simulink lookfor lookfor 4 fourier MATLAB 1 MATLAB 1 MATLAB

Cell Array Cell 1_2_1 Structure Array Structure 1_2_2 5 . 1. A=[1,2,3;4,5,6;7,8,9]

A= 1 2 3 4 5 6 7 8 9 (:) (:) (ROWS)) (COLUMNS)) A(:,2), 2 ans = 2 5 8 6

1 eye (m,n) eye (m) m*n m*m eye (3,4) eye (3) 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 2 zeros (m,n) zeros (m) m*n m*m zeros (3,4) zeros (3) 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 7 3 ones (m,n) ones (m) m*n m*m 1 ones (3,4) ones(3) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2. 1 d=eig (A) A

[v,d]=eig (A) A [v,d]=eig (A) 8 v= d= 0.2320 0.7858 0.4082 16.1168 0 0 0.5253 0.0868 -0.8165 0 -1.1168 0 0.8187 -0.6123 0.4082 0

0 0.0000 v (:,i) d (i,i) 2 det (A) A det (A) ans = 0 9 3 expm (A) A expm (A) ans = 1.0e+006 * 1.1189 1.3748 1.6307 2.5339 3.1134 3.6929 3.9489 4.8520 5.7552

4 inv (A) A inv (A) Warning: Matrix is close to singular or badly scaled.Results may be inaccurate. RCOND = 2.055969e-018. ans = 1.0e+016 * -0.4504 0.9007 -0.4504 0.9007 -1.8014 0.9007 -0.4504 0.9007 -0.4504 10 5 orth (A) A orth (A) ans = 0.2148 0.8872 0.5206 0.2496

0.8263 -0.3879 6 poly (A) A A poly (A) ans = 1.0000 -15.0000 -18.0000 -0.0000 A A r=[1,2,3]; p= poly (r) p= 1 -6 11 -6 7 rank (A) A r=rank (A) r = 2 11 3. +

* / . b=[1+2i;3+4i] b= 1.0000 + 2.0000i 3.0000 + 4.0000i b' ans = 1.0000 - 2.0000i 3.0000 - 4.0000i b.' ans = 1.0000 + 2.0000i 3.0000 + 4.0000i 12

4. 1 [q,r]=qr (A) A A=q*r q (unitary matrix), norm 1 r [q,r]=qr(A) q= -0.1231 0.9045 0.4082 -0.4924 0.3015 -0.8165 -0.8616 -0.3015 0.4082 r= -8.1240 -9.6011 -11.0782 0 0.9045 1.8091 0 0 -0.0000 norm(q) ans =

1.0000 13 2 [L,U]=lu (A) A A=L*U L lower triangular matrix U (upper triangular matrix) [L,U]=lu(A) L= 0.1429 1.0000 0 0.5714 0.5000 1.0000 1.0000 0 0

U= 7.0000 8.0000 9.0000 0 0.8571 1.7143 0 0 0.0000 14 0 1 4x^3+3x^2+2x+1 [4 3 2 1] 1. 1 conv z=conv (x,y) x=[1 3 5]; y=[2 4 6]; z=conv(x,y)

z= 2 10 28 38 30 15 conv x,y conv(conv(x,y),x) ans = 2 16 68 172 284 280 150 2 1 deconv [z,r]=deconv (x,y) x y z r [z,r]=deconv(z,x) z=

2 4 6 r= 0 0 0 0 0 16 3 roots fx=[1 3 2]; rootoffx=roots(fx) rootoffx = -2 -1 4 polyval (p,x) p x x p = [1 -6 11 -6] x=1; p1=polyval (p,x) p1 = 0 x=[1,2,3]; p2=polyval (p,x)

p2 = 0 0 0 17 x=A; p3=polyval (p,x) p3 = 0 0 0 6 24 60 120 210 336 5 polyder (p) p p=[1 -6 11 -6]; dp=polyder(p) dp = 3 -12 11 18

6 [r,p,k]=residue (x,y) x/y x,y , x/y x/y=r1/(s-p1)+r2/ (s-p2)+...+rn/ (s-pn)+ks residue x/(x^2+3x+2) x=[1 0]; y=[1 3 2]; [r,p,k]=residue(x,y) r= 2 -1 p= -2 -1 k= []

19 r,p,k ?[x,y]=residue(r,p,k) x= 1 0 y= 1 3 2 20 sym x=sym(x) a=sym(alpha) x, alpha

f=sym(a*x^2+b*x+c) f a, b, c, x syms syms a b c x sym f=sym (f(x)) f (x) 21 1. diff Diff (f, x, n) f x n 1). sin (ax), x a ?syms a x ?f=sin(a*x);

?df=diff(f,x) df = cos(a*x)*a ?dfa=diff(f,a) dfa = cos(a*x)*x 22 2 ?syms a x ?A=[-sin(a*x),sin(a*x);cos(a*x),cos(a*x)] A= [ -sin(a*x), sin(a*x)] [ cos(a*x), cos(a*x)] ?dy=diff(A,x) dy =

[ -cos(a*x)*a, cos(a*x)*a] [ -sin(a*x)*a, -sin(a*x)*a] 23 3 jacobian Jacobi ?syms r l f ?x=r*cos(l)*cos(f); ?y=r*cos(l)*sin(f); ?z=r*sin(l); ?J=jacobian([x;y;z],[r l f]) J= [ cos(l)*cos(f), -r*sin(l)*cos(f), -r*cos(l)*sin(f)] [ cos(l)*sin(f), -r*sin(l)*sin(f), r*cos(l)*cos(f)] [ sin(l), r*cos(l), 0 ]

24 2. int int (f, r, x0, x1) f r x0,x1 ?sym x; ?sym k real ?f=exp(-(k*x)^2) f= exp(-k^2*x^2) ?int(f,x,-inf,inf) ans = signum(k)/k*pi^(1/2) 25

3. ?syms k; ?s1=symsum(1/k^2,1,inf) s1 = 1/6*pi^2 26 4. limit limit lim f ( x ) Limit (f ), limit (f , x )

x 0 lim f ( x ) Limit (f , x , a) , limit (f , a ) x a lim f ( x ) Limit (f , x , a , left) x a lim f ( x ) Limit (f , x , a , right) x a

27 5. 1 collect (f ) 2 expand ( f ) 3 horner ( f ) 4 factor ( f ) 5 simplify ( f ) 28

2 2 f ( x) x sin x MATLAB Taylor 29 MATLAB 30 1 M Script File Function File . m 1 1 M

Script file MATLAB M MATLAB MATLAB Base workspace clear MATLAB 31 1 1 1 2 M

MATLAB M function MATLAB Function workspace MATLAB 32 1 2 1 3 M

M functio % lookfor help % % M 33 2 2 1 Local

Global global MATLAB 2 2 MATLAB [ 1, 2,] = ( 1, 2 , ) 34 2 2 3 MATLAB MATLAB nargin

nargout circle .m nargin am1.m nargout varargin varrgout evalin 35 2 3 MATLAB

2 3 1 MATLAB forend while---end ifelseend switch---case try---catch 2 3 2 return echo input pause keyboard break error warning 36 2 3 MATLAB

2 3 3 GUI MATLAB Callback Callback Callback M MATLAB Callback Callback Callback M MATLAB Callback Callback 37

2 4 M M Bug Syntax Run-time M 38 2 4 M 1

M M disp echo echo on M echo FunNsme on FunNsme M M keyboard keyboard M M M 39

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