Matlab入门（英文）

晓夜寒风 · 发表于 2010-1-20 15:01:24

Branching
Branching is the construction

if <condition>, <program> end

The condition is a MATLAB function usually, but not necessarily with values 0 or 1 (later I will discuss when we can vary from this requirement), and the entire construction allows the execution of the program just in case the value of condition is not 0. If that value is 0, the control moves on to the next program construction. You should keep in mind that MATLAB regards a==b and a<=b as functions with values 0 or 1.
Frequently, this construction is elaborated with

if <condition1>, <program1> else <program2> end

In this case if condition is 0, then program2 is executed.
Another variation is

if <condition1>, <program1>
elseif <condition2>, <program2>
end

Now if condition1 is not 0, then program1 is executed, if condition1 is 0 and if condition2 is not 0, then program2 is executed, and otherwise control is passed on to the next construction. Here is a short program to illustrate branching.

function b=even(n)

% b=even(n). If n is an even integer, then b=1
% otherwise, b=0.

if mod(n,2)==0,
b=1;
else b=0;
end

晓夜寒风 · 发表于 2010-1-21 09:56:20

Branching is the construction

if <condition>, <program> end

The condition is a MATLAB function usually, but not necessarily with values 0 or 1 (later I will discuss when we can vary from this requirement), and the entire construction allows the execution of the program just in case the value of condition is not 0. If that value is 0, the control moves on to the next program construction. You should keep in mind that MATLAB regards a==b and a<=b as functions with values 0 or 1.
Frequently, this construction is elaborated with

if <condition1>, <program1> else <program2> end

In this case if condition is 0, then program2 is executed.
Another variation is

if <condition1>, <program1>
elseif <condition2>, <program2>
end

Now if condition1 is not 0, then program1 is executed, if condition1 is 0 and if condition2 is not 0, then program2 is executed, and otherwise control is passed on to the next construction. Here is a short program to illustrate branching.

function b=even(n)

% b=even(n). If n is an even integer, then b=1
% otherwise, b=0.

if mod(n,2)==0,
b=1;
else b=0;
end

晓夜寒风 · 发表于 2010-1-21 09:56:55

A for loop is a construction of the form

for i=1:n, <program>, end

Here we will repeat program once for each index value i. Here are some sample programs. The first is matrix addition.

function c=add(a,b)

% c=add(a,b). This is the function which adds
% the matrices a and b. It duplicates the MATLAB
% function a+b.

[m,n]=size(a);
[k,l]=size(b);
if m~=k | n~=l,
r='ERROR using add: matrices are not the same size';
return,
end
c=zeros(m,n);
for i=1:m,
for j=1:n,
   c(i,j)=a(i,j)+b(i,j);
end
end

The next program is matrix multiplication.

function c=mult(a,b)

% c=mult(a,b). This is the matrix product of
% the matrices a and b. It duplicates the MATLAB
% function c=a*b.

[m,n]=size(a);
[k,l]=size(b);
if n~=k,
c='ERROR using mult: matrices are not compatible
   for multiplication',
return,
end,
c=zeros(m,l);
for i=1:m,
for j=1:l,
   for p=1:n,
      c(i,j)=c(i,j)+a(i,p)*b(p,j);
   end
end
end

For both of these programs you should notice the branch construction which follows the size statements. This is included as an error message. In the case of add, an error is made if we attempt to add matrices of different sizes, and in the case of mult it is an error to multiply if the matrix on the left does not have the same number of columns as the number of rows of the the matrix on the right. Had these messages not been included and the error was made, MATLAB would have delivered another error message saying that the index exceeds the matrix dimensions. You will notice in the error message the use of single quotes. The words surrounded by the quotes will be treated as text and sent to the screen as the value of the variable c. Following the message is the command return, which is the directive to send the control back to the function which called add or return to the prompt. I usually only recommend using the return command in the context of an error message. Most MATLAB implementations have an error message function, either errmsg or error, which you might prefer to use.

In the construction

for i=1:n, <program>, end

the index i may (in fact usually does) occur in some essential way inside the program. MATLAB will allow you to put any vector in place of the vector 1:n in this construction.
Thus the construction

for i=[2,4,5,6,10], <program>, end

is perfectly legitimate. In this case program will execute 5 times and the values for the variable i during execution are successively, 2,4,5,6,10. The MATLAB developers went one step further. If you can put a vector in, why not put a matrix in? So, for example,
for i=magic(7), <program>, end

is also legal. Now the program will execute 7 (=number of columns) times, and the values of i used in program will be successively the columns of magic(7).

晓夜寒风 · 发表于 2010-1-21 09:57:15

A while loop is a construction of the form

while <condition>, <program>, end

where condition is a MATLAB function, as with the branching construction. The program program will execute successively as long as the value of condition is not 0. While loops carry an implicit danger in that there is no guarantee in general that you will exit a while loop. Here is a sample program using a while loop.

function l=twolog(n)

% l=twolog(n). l is the floor of the base 2
% logarithm of n.

l=0;
m=2;
while m<=n
l=l+1;
m=2*m;
end

晓夜寒风 · 发表于 2010-1-21 09:57:35

Recursion
Recursion is a devious construction which allows a function to call itself. Here is a simple example of recursion

function y=twoexp(n)

% y=twoexp(n). This is a recursive program for computing
% y=2^n. The program halts only if n is a nonnegative integer.

if n==0, y=1;
else y=2*twoexp(n-1);
end

The program has a branching construction built in. Many recursive programs do. The condition n==0 is the base of the recursion. This is the only way to get the program to stop calling itself. The "else" part is the recursion. Notice how the twoexp(n-1) occurs right there in the program which is defining twoexp(n)! The secret is that it is calling a lower value, n-1, and it will continue to do so until it gets down to n=0. A successful recursion is calling a lower value.

There are several dangers using recursion. The first is that, like while loops, it is possible for the function to call itself forever and never return an answer. The second is that recursion can lead to redundant calculations which, though they may terminate, can be time consuming. The third danger is that while a recursive program is running it needs extra space to accomodate the overhead of the recursion. In numerical calculations on very large systems of equations memory space is frequently at a premium, and it should not be wasted on program overhead. With all of these bad possibilities why use recursion? It is not always bad; only in the hands of an inexperienced user. Recursive programs can be easier to write and read than nonrecursive programs. Some of the future projects illustrate good and poor uses of recursion.

晓夜寒风 · 发表于 2010-1-21 09:58:01

Miscellaneous Programming Items
It is possible to place a matrix valued function as the condition of a branching construction or a while loop. Thus the condition might be a matrix like ones(2),zeros(2), or eye(2). How would a construction like

if <condition>, < program1>,
else <program2>, end

behave if condition=eye(2)? The program1 will execute if all of the entries of condition are not 0. Thus if condition=magic(2), program1 will execute while if condition=eye(2) control will pass to the "else" part and program2 will execute.
A problematic construction occurs when you have

if A ~= B, <program>, end.

You would like program to execute if the matrices A and B differ on some entry. Under the convention, program will only execute when they differ on all entries. There are various ways around this. One is the construction
if A ==B  else <program>, end

which will pass control to the "else" part if A and B differ on at least one entry. Another is to convert A==B into a binary valued function by using all(all(A==B)). The inside all creates a binary vector whose i--th entry is 1 only if the i--th column of A is the same as the i--th column of B. The outside all produces a 1 if all the entries of the vector are 1. Thus if A and B differ on at least one entry, then all(all(A==B))=0. The construction
if ~ all(all(A==B)), <program>, end

then behaves in the desired way.
Essentially, the same convention holds for the while construction.

while <condition>, <program>, end.

The program program will execute successively as long as every entry in condition is not 0, and the control passes out of the loop when at least one entry of condition is 0.
Another problem occurs when you have a conjunction of conditions, as in

if  <condition1> & < condition2>,
<program>,  end

Of course, program will execute if both condition1 and condition2 are nonzero. Suppose that condition1=0 and condition2 causes an error message. This might happen for
i<=m &  A(i,j)==0

where m is the number of columns of A. If i>m, then you would like to pass the control, but since A(i,j) makes no sense if i>m an error message will be dished up. Here you can nest the conditions.

if i<=m,
if A(i,j)==0,
   <program>
end
end

晓夜寒风 · 发表于 2010-1-21 09:58:21

Scripts
A script is an m-file without the function declaration at the top. A script behaves differently. When you type who you are given a list of the variables which are in force during the current session. Suppose that x is one of those variables. When you write a program using a function file and you use the variable x inside the program, the program will not use the value of x from your session (unless x was one of the input values in the function), rather x will have the value appropriate to the program. Furthermore, unless you declare a new value for x, the program will not change the value of x from the session. This is very convenient since it means that you do not have to worry too much about the session variables while your program is running. All this has happened because of the function declaration. If you do not make that function declaration, then the variables in your session can be altered. Sometimes this is quite useful, but I usually recommend that you use function files.

晓夜寒风 · 发表于 2010-1-21 09:58:47

Suggestions
These are a few pointers about programming and programming in MATLAB in particular.

1) I urge you to use the indented style that you have seen in the above programs. It makes the programs easier to read, the program syntax is easier to check, and it forces you to think in terms of building your programs in blocks.

2) Put lots of comments in your program to tell the reader in plain English what is going on. Some day that reader will be you, and you will wonder what you did.

3) Put error messages in your programs like the ones above. As you go through this manual, your programs will build on each other. Error messages will help you debug future programs.

4) Always structure your output as if it will be the input of another function. For example, if your program has "yes-no" type output, do not have it return the words "yes" and "no," rather return 1 or 0, so that it can be used as a condition for a branch or while loop construction in the future.

5) In MATLAB, try to avoid loops in your programs. MATLAB is optimized to run the built-in functions. For a comparison, see how much faster A*B is over mult(A,B). You will be amazed at how much economy can be achieved with MATLAB functions.

6) If you are having trouble writing a program, get a small part of it running and try to build on that. With reference to 5), write the program first with loops, if necessary, then go back and improve it.

晓夜寒风 · 发表于 2010-1-21 09:59:02

MATLAB demonstrations
Matlab is shipped with a number of demonstration programs. Use help demos to find out more about these (the number of demos will depend upon the version of Matlab you have).

Some of the standard demos may be especially useful to users who are beginners in linear algebra:

demo - Demonstrate some of MATLAB's capabilities.

matdemo - Introduction to matrix computation in MATLAB.

rrefmovie - Computation of Reduced Row Echelon Form

晓夜寒风 · 发表于 2010-1-21 09:59:19

Some MATLAB built-in functions
This is a list of functions available in Matlab as of 1984, which should be taken as a quick reminder of the most basic tools available. See the Matlab help screens and excerpts from those screens reprinted in section Some MATLAB function descriptions. In any case, your version of Matlab may vary slightly.

intro <       chol    end    function lu    quit    sprintf
help    >       clc    eps    global macro qz    sqrt
demo    =       clear error grid    magic rand    startup
[       &       clg    eval    hess    max    rcond string
]       |       clock exist hold    memory real    subplot
(       ~       conj    exit    home    mesh    relop sum
)       abs    contour  exp    ident meta    rem    svd
.       all    cos    expm    if    min    return tan
,       ans    cumprod  eye    imag    nan    round text
;       any    cumsum feval inf    nargin save    title
%       acos    delete fft    input norm    schur type
!       asin    det    filter inv    ones    script what
:       atan    diag    find    isnan pack    semilogx while
'       atan2 diary finite keyboard pause semilogy who
+       axis    dir    fix    load    pi    setstr xlabel
-       balance  disp    floor log    plot    shg    ylabel
*       break echo    flops loglog polar sign    zeros
\       casesen  eig    for    logop prod    sin
/       ceil    else    format ltifr prtsc size
^       chdir elseif fprintf  ltitr qr    sort

acosh       demo       hankel    membrane    print       table1
angle       demolist    hds       menu       quad       table2
asinh       dft       hilb       meshdemo    quaddemo    tanh
atanh       diff       hist       meshdom    quadstep    tek
bar       eigmovie    histogram mkpp       rank       tek4100
bench       ergo       hp2647    movies    rat       terminal
bessel    etime       humps       nademo    ratmovie    toeplitz
bessela    expm1       idft       nelder    readme    trace
besselh    expm2       ieee       neldstep    residue    translate
besseln    expm3       ifft       nnls       retro       tril
blanks    feval       ifft2       null       roots       triu
cdf2rdf    fft2       info       num2str    rot90       unmkpp
census    fftshift    inquire    ode23       rratref    vdpol
citoh       fitdemo    int2str    ode45       rratrefmovie versa
cla       fitfun    invhilb    odedemo    rref       vt100
compan    flipx       isempty    orth       rsf2csf    vt240
computer    flipy       kron       pinv       sc2dc       why
cond       funm       length    plotdemo    sg100       wow
conv       gallery    log10       poly       sg200       xterm
conv2       gamma       logm       polyfit    sinh       zerodemo
corr       getenv    logspace    polyline    spline    zeroin
cosh       ginput    matdemo    polymark    sqrtm
ctheorem    gpp       matlab    polyval    square
dc2sc       graphon    mean       polyvalm    std
deconv    hadamard    median    ppval       sun

addtwopi buttap cov    fftdemo  freqz kaiser specplot
bartlett butter decimate filtdemo fstab numf    spectrum
bilinear chebap denf    fir1    hamming  readme2  triang
blackman chebwin  detrend  fir2    hanning  remez xcorr
boxcar cheby eqnerr2  freqs interp remezdd  xcorr2
                                                   yulewalk

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Matlab入门（英文）

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