Basic MATLAB

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Basic MATLAB

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• Anan Phonphoem
• http//www.cpe.ku.ac.th/anan
• anan_at_cpe.ku.ac.th

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Outline

• History of MATLAB
• (modified from Prof. James Bruckers 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 BB - 4AC IF (
DESC .LT. 0.0 ) GOTO 10 DESC
SQRT(DESC) X1 (-B DESC)/(2.0A)
X2 (-B - DESC)/(2.0A) 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 resultsX
  0.1Y 1.0 - 10X
• Y "should" equal 0, but probably does not!
• underflow and overflow X 1.0E20, XX --gt too
  big!
• efficient coding of algorithms not always
  obvious DO 10 N1,100000 10 Y(N)
  SQRT(2.0)X(N) lt-- inefficient!
• programming errors!

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Solving a Linear System in Fortran

• From equation b Ax, solve for x
• It doesn't check for degeneracy or zeros.

C Solve B AX for X. C N is dimension of
vectors and matrix C 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), RATIO C... Forward elimination
DO 13 J1,N-1 DO 12 IJ1,N
RATIO -A(I,J)/A(J,J) A(I,) A(I,)
RATIOROW(J,) DO 11 KJ1,N 11
A(I,K) A(I,K) RATIOA(J,K) A(I,J)
0.0 X(I) X(I) RATIOX(J) 12
CONTINUE 11 CONTINUE Continued...
C... Backwards substitution X(N)
X(N)/A(N,N) DO 21 IN-1,1,-1 TMP
X(I) DO 20 JI1,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 Ax b using LINPACK

C.... 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 Ax 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.

Extensible using "Toolkits" or user-contributed
programs called M-files.
Matlab "Toolkits"
Matlab "M-Files"
Interactive user interface hides boring details
Matlab
Linear Algebra Libraries
Modular, reusable software components
FORTRAN Compiler
Standard base platform
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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 is
• a 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 Bruckers slide)
• Elements
• Operators

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Elements

• Letter (AZ, az)
• Digit (09)
• Special character ( - / _ ! ltgt )
• Number (1, 1.1, -1.1212, 23e2)
• String (Hello, Today is Monday, etc.)
• Matrix and Vector
• Operator

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Matrix
4 x 3 Matrix
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Vector
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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 Operators
Operator 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 (SINV(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
lt Less than S lt T
gt Greater than S gt T
lt Less than or equal S lt T
gt Greater than or equal S gt 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 ?
• 215/32 ?
• (215)/(32)
• (2 (15/3)) 2
• 2 ((15/3) 2)

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Precedence rules for arithmetic operators

• ( ) parentheses
• Unary and
• , /
• If equal precedence, left to right
• Examples

-ak/-w (-a) (k / (-w)) C23/6232
((C23)/6) (232)
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Assignment statement

• A 12
• C A B
• Ans width length
• Result 215/32