tutor1.m

很多matlab的源代码

%The colon has another very useful function. The command x=y(:) strings out 
%the elements of y by columns and places them in a column  vector.  Clearly, 
%for a row vector, this is equivalent to a transposition.
%The elements of a matrix z can therefore also  be  addressed  by  a  single 
%argument which represents its position in  the  strung  out  column  vector 

a=[1 2 3;4 5 6;7 8 9]  %A 3x3 matrix
%When strung out, a(1)=1, a(2)=4, a(3)=7, a(4)=2 etc. To see this enter
b=a(4)  %this should equal 2
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%To see the strung out order enter the command
a(:)  %the strung out column vector
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clc
%Here are some useful matrices in MATLAB 
a=zeros(2,3)  %A 2x3 matrix with all elements zero
b=ones(2,3)  %A 2x3 matrix with all elements equal to one
c=eye(3)  %A square 3x3 identity matrix
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%COMPLEX NUMBERS
%Variables may be complex-valued. Complex entries are entered in rectangular 
%form (e.g. 2+i*3). All results are returned in the same form. Either i or j
%may be used for the imaginary unit.  Consider  for example.
j=sqrt(-1);i=j;   %Force i or j to be imaginary unit (not necessary).
zc=2+j*3  %A complex number
%Its real and  imaginary parts may be accessed via
zr=real(zc),zi=imag(zc)  %the real and imaginary parts of zc
%Thus zcomp is in fact the matrix zreal+j*zimag
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%The absolute magnitude and angle may be found as
zabs=abs(zc),zr=angle(zc)  %Magnitude and angle of zc
%NOTE:Angles are returned in radians. To find the angle in degrees, 
%we use the conversion deg=rad*180/pi. Thus
za= 180*angle(zc)/pi  %Angle of zc in degrees
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%The complex conjugate of the matrix is accessed by the command "conj"
zstar=conj(zc)   %the conjugate of zc
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%TRANSPOSE
%The transpose command is an apostrophe ('). Consider
c=[1 5 2;3 4 8]   %a 2x3 matrix
%The transpose of this matrix is
c'   %the transposed 3x2 matrix
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%NOTE:For complex matrices the  operation  '  actually 
%results in the COMPLEX CONJUGATE TRANSPOSE. For example
a=[2+i -1+5*i;6 4+i*3]  %A matrix of complex numbers
b=a'      %Its complex conjugate transpose
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%The non-conjugated transpose is obtained by using the command  .' instead 
%(a period followed by the apostrophe)

c=a.'  %the non-conjugated transpose the way we normally visualize it
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%Consider the following commands
a1=[1 2 3 ; 5,6 7]      %A 3x2 matrix
b=[1+2*i  5 -j*7 9]    %A 4-element row vector
c=[2 4 6 8]'            %A 4-element column vector
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d=(2:2:8)'              %Same as vector c
e=a1(:)                 %An 6-element column vector

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%COMPUTATIONAL ASPECTS
%MATLAB is an extremely powerful computational tool. The greatest advantage
%of this computational aspect is the host of  built in or supplied operations
%and  functions  which  obviates  the  need  for  any  extensive programming

%OPERATIONS ON MATRICES AND THE "DOT" CONVENTION
%Let us choose two matrices a  and  b  and  define  the  various  operations 
%allowed by MATLAB. These seemingly innocuous operations can actually  prove 
%both powerful or disastrous depending on how they are used or misused.
a=[1 2;3 4],b=[4 5;6 7],
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%ADDITION AND SUBTRACTION:
%In operations involving a scalar and a matrix, the scalar is treated  as  a 
%matrix with the same dimensions as the matrix with all entries equal to the 
%scalar value. The operations of  addition  and  subtraction  are  performed 
%element by element.
a,c=4-a
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%For two matrices,  addition  and  subtraction  is  also elementwise provided
%the dimensions are identical.
a,b,d=a-b
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%MULTIPLICATION
%The operation a.*b (NOTE THE DOT) denotes elementwise multiplication. Here
%a and b may be matrices of the same size or one or both may be scalar.
a,b,c=a.*b
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%If a is a scalar, each element is of b is multiplied by a
a,d=4 .*a
%NOTE the space between 4 and the dot is important in v3.5, else the dot acts
%as a decimal point following the 4. To avoid confusion enclose numbers in ()
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%For matrices, a*b denotes matrix multiplication. The columns of a must equal
%the rows of b. If not, an error results. If a is scalar, a*b = a.*b.
a,d=4;d1=d.*a,d2=d*a
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%A third form of multiplication yields a*b the so called outer product when
%a is a column matrix and b a row matrix.
a=[1;2;3],b=a',c=a*b
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%DIVISION
%Elementwise division is produced by using a./b. Either a or b may be scalar 
a=[2 4;6 8],b=[1 2;2 4],c=a./b
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%The quantity a/b is not defined in the usual sense. Actually there are  two 
%types of division operators in MATLAB, the left and right division  denoted 
%by the slashes / and \. We shall not discuss these at this time
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%EXPONENTIATION
%Exponentiation can also be elementwise (.^) or matrixwise (^).
a=[1 2;3 4],b=a.^2,c=(2).^a
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%NOTE: Elementwise exponentiation requires  dimensional  consistency
%unless  the variable or exponent is a scalar

%But functions such as  sqrt  (square  root),  exp (raising to the power e)
%are all implemented elementwise.
a=[1 4;9 36],b=sqrt(a)
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%Here are some useful MATLAB OPERATIONS
%round(x): rounds elements of x to nearest integers
x=[2.1 3.6;-3.1 -3.6],y=round(x)
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%fix(x): truncates fractional parts of elements of x
x=[2.1 3.6;-3.1 -3.6],y=fix(x)
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%floor(x), ceil(x): rounds elements of x to lower or upper nearest integers
x=[2.1 3.6;-3.1 -3.6],y=floor(x),z=ceil(x)
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%sign(x): returns 1 if x>1 or -1 if x<1 and 0 if x=0
x=[2.1 3.6;-3.1 0],y=sign(x)
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%rem(x,a): returns remainder left after dividing x by a
x=[2.1 35;-3 0],y=rem(x,3)
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%COLUMNWISE OPERATIONS
%min(x),max(x): returns min or max value for each column of x.
x=[2.1 3.6 1.5;-3.1 1 2.3],ymin=min(x),ymax=max(x)
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%mean(x),median(x): mean or median of each column of x
x=[2 4 3;-3 4 2;3 3 3],y=mean(x),z=median(x)
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%sort(x) returns columns of x in sorted order
x=[2 4 3;-3 4 2;-1 1 -2],y=sort(x)
%[y,k]=sort(x) also returns (columnwise) the indices of x used in the sort

[y,k]=sort(x)
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%sum(x),prod(x) sum or product of columns of x
x=[2 4 3;-3 4 2;2 1 -1],y=sum(x),z=prod(x)
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%cumsum(x),cumprod(x) cumulative sum or product for each column of x
x=[2 4 3;-3 4 2;2 -2 3],y=cumsum(x),z=cumprod(x)
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%diff(x) difference between adjacent values of columns of x
x=[2 4 3;-3 4 2;3 -3 5],y=diff(x)

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%			POLYNOMIALS AND ROOTS

%Consider the polynomial f(x) = x^3 + 5x^2  +3x + 2
%To find its roots, we set up the coefficient array as follows
p=[1 5 3 2]
%Note that the coefficients are in descending powers of x

%To find its roots we use the routine roots as follows
rts=roots(p)
%Note that rts is a column vector!!

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%To reassemble the polynomial from its roots, we use the command poly
pp=poly(rts)
%The array pp should equal p (to within machine roundoff)
[p;pp]

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%To force the coefficients to be real, we could use
rts=real(poly(rts))

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%To evaluate the polynomial f(x) at various values of x
%we first generate an array of values. For example
zz=[0 1 2 -1]

%Then we use the command polyval to evaluate the polynomial as follows
ff=polyval(p,zz)

pause  %STRIKE A KEY TO END THIS PORTION
echo off 
%clear a a1 avar b c d d1 d2 e ff i j k p pp rts s
%clear x y ymax ymin z za zabs zc zi zr zstar zz
clear