1 basic matlab ผศ. ดร. อนันต์ ผลเพิ่ม anan phonphoem anan...
TRANSCRIPT
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Outline
History of MATLAB(modified from Prof. James Brucker’s slide)
Elements Operators
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Fortran and Scientific Computing
Engineering and scientific need numerical computing In the past, main language was FORTRAN
First "high level" programming language Here's a Fortran code to solve a x2 + b x + c = 0:
C Solve a quadratic equation (this is a comment). DESC = B*B - 4*A*C IF ( DESC .LT. 0.0 ) GOTO 10 DESC = SQRT(DESC) X1 = (-B + DESC)/(2.0*A) X2 = (-B - DESC)/(2.0*A) WRITE(6,*) "SOLUTIONS ARE ",X1," AND ", X2 RETURN 10 WRITE(6,*) "EQUATION HAS COMPLEX ROOTS" RETURN
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Problems using FORTRAN
loss of precision and inaccurate results:X = 0.1Y = 1.0 - 10*X Y "should" equal 0, but probably does not!
underflow and overflow: X = 1.0E20, X*X --> too big!
efficient coding of algorithms not always obvious DO 10 N=1,100000 10 Y(N) = SQRT(2.0)*X(N) <-- inefficient!
programming errors!
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Solving a Linear System in Fortran
From equation: b = A*x, solve for x It doesn't check for degeneracy or zeros.C Solve B = A*X for X. C N is dimension of vectors and matrixC Does not use row interchange, scaling. SUBROUTINE LINSYS(N, A, X, B, TMP) INTEGER N DOUBLE PRECISION A(N,N), X(N), B(N) DOUBLE PRECISION TMP(N), RATIOC... Forward elimination DO 13 J=1,N-1 DO 12 I=J+1,N RATIO = -A(I,J)/A(J,J) A(I,*) = A(I,*) +RATIO*ROW(J,*) DO 11 K=J+1,N 11 A(I,K) = A(I,K) + RATIO*A(J,K) A(I,J) = 0.0 X(I) = X(I) + RATIO*X(J) 12 CONTINUE 11 CONTINUE Continued...
C... Backwards substitution X(N) = X(N)/A(N,N) DO 21 I=N-1,1,-1 TMP = X(I) DO 20 J=I+1,N 20 TMP = TMP - A(I,J)*X(J) X(I) = TMP/A(I,I) 21 CONTINUE RETURN END
This is just a small example.
A full program may be 1000's of lines long.
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Need for Numerical Libraries
The U.S. government notices that many engineers write the same algorithms.
Need a good quality algorithms for common tasks.
Make it as "libraries" of subroutines Libraries are available at: www.netlib.org
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Examples of Numerical Libraries
BLAS (Basic Linear Algebra Subroutines): Vector operation (adding vectors, dot product)
LINPACK: linear algebra subroutines Vector-matrix operations (factoring, inverting a matrix) replaced by LAPACK.
EISPACK: compute eigenvalues and eigenvectors of matrices.
Example: solve A*x = b using LINPACKC.... factor the A matrix CALL SGEFA(A, N, N, IPVT, INFO)C.... copy B vector into X vector CALL SCOPY(N, B, 1, X, 1)C.... solve the system of equations CALL SGESL(A, N, N, IPVT, X, 0)
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Still Not Easy Enough!
Cleve Moler (mathematician, C.S. Professor, Co-author of LINPACK) thought this is still too much work: write FORTRAN, compile, debug, compile, run...
He wrote MATLAB ("Matrix Laboratory"). interactive easy input, output operations on a whole vector or matrix at once
Example: solve b = A*x in Matlab...x = A \ b
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Immediate Popularity!
MATLAB quickly became quite popular and used for both teaching and research. It was also free.
An engineer, Jack Little, saw Matlab during a lecture by Cleve Moler at Stanford University.
He saw the commercial potential and (with permission) rewrote Matlab in C added "M-files" (stored programs) many new features and libraries founded The Mathworks to market it.
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Software principles...
Matlab illustrates some useful design concepts for software.
FORTRAN Compiler
Linear Algebra Libraries
Matlab
Matlab "Toolkits"Matlab "M-Files"
Standard base platform
Modular, reusable software components
Extensible using "Toolkits" or user-contributed programs called M-files.
Interactive user interface; hides boring details
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Matlab Today
Millions of users! A standard tool in both professional and academic use "Toolboxes" providing functions for many
applications: control systems identification neural networks bio-informatics statistics and time-series analysis
Can do symbolic mathematics, too. Simulink: GUI based simulation tool
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Pascal Programming
Program Calculate;{ This program calculates how much you need to pay }const
Unit_Price = 20;var
cost, total : integer;begin
write (‘How many pieces do you want ? ’);readln(total); { read total number that you want }
cost := total * Unit_Price;writeln (‘It costs ’,
cost, ‘ Baht’);end.
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MATLAB Programming
% Basic Matrix Operations% Show how easy MATLAB isa = [1 2 3 4 6 4 3 4 5];b = a + 2;plot(b);grid on;xlabel('Sample #');ylabel('Pounds');
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Outline
History of MATLAB(modified from Prof. James Brucker’s slide)
Elements Operators
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Elements
Letter (A…Z, a…z) Digit (0…9) Special character (+ - * / _ = ! <> []{}) Number (1, 1.1, -1.1212, 23e+2) String (‘Hello’, ‘Today is Monday’, etc.) Matrix and Vector Operator
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Matrix
1 2 3 4 2 3 4 9 12 0 2 7
row 1row 2row 3
col 1 col 2 col 3col 4
4 x 3 Matrix
Scalar
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Vector
1 9 0 3
Vector A4 X 1
13 -2 8
Vector B1 X 3
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Symbols
Symbol Description
. Decimal point
.. Parent directory
... Continuation
( ) Parentheses and subscripting
[ ] Brackets
{ } Braces and subscripting
: Colon
, Separator
; Semicolon
% Comment
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Operators
Arithmetic operators Relational operators Logical operators
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Arithmetic OperatorsOperator Description Example
+ Plus S + T
+ Unary plus +3
- Minus S – T
- Unary minus -C
* Matrix Multiply S * T
.* Array Multiply (member) S .* T
/ Left Matrix Divide (S* INV(T))
S / T
./ Left Array Divide S ./ T
\ Right Matrix Divide
(INV(S *) T) S \ T
.\ Right Array Divide S .\ T
^ Matrix Power S ^ 2
.^ Array Power S .^ 3
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Relational Operators
Operator Description Example
== Equal S == T
~= Not Equal S ~= T
< Less than S < T
> Greater than S > T
<= Less than or equal S <= T
>= Greater than or equal S >= T
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Logical Operators
Operator Description Example
&& Logical AND S && T
|| Logical OR S || T
& Element-wise logical AND S & T
| Element-wise logical OR S | T
~ Logical NOT ~S
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Arithmetic Expression
45.00 (width + length) (12*(top – bottom)) 4 – 2 = ? 2+15/3*2 = ? (2+15)/(3*2) (2 + (15/3)) * 2 2 + ((15/3) * 2)
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Precedence rules for arithmetic operators
1. ( ) parentheses2. Unary + and –3. *, /4. + –5. If equal precedence, left to rightExamples
-a+k/-w = (-a) + (k / (-w))
C*23/6+23*2 = ((C*23)/6) + (23*2)
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Assignment statement
A = 12 C = A + B Ans = width + length Result = 2+15/3*2