E77: INTRODUCTION TO COMPUTER PROGRAMMING FOR SCIENTISTS AND ENGINEERS

1
E77 INTRODUCTION TO COMPUTER PROGRAMMING FOR
SCIENTISTS AND ENGINEERS

• Lecture Outline
• 1. Introduction to arrays
• 2. One-dimensional arrays
• 3. Character strings

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Introduction to arrays

• A simple array is an ordered collection of real
  numbers.
• MATLAB treats arrays very efficiently
• Input/output, indexing and addressing
• Arithmetic operations
• Other manipulations (e.g., sizing, reshaping,
  etc.)
• Arrays are the primary building blocks in MATLAB.

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Introduction to arrays

• Examples
• 
  (1 row, 1 column)
• 
  (1 row,4 columns)
• 
  (3 rows, 1 column)

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Introduction to arrays

• Examples 2-dimensional arrays
• 
  (2 rows, 3 columns)
• (3 rows, 3 columns)

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One-dimensional arrays

• Those that have one row or one column.
• Construction
• Manual
• Incremental
• linspace
• transpose
• zeros
• ones
• rand/randn

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One-dimensional arrays manual construction

• Row vectors
• Syntax element1 , element2 ,
  

gtgtr 3,7,9 r 3 7 9
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One-dimensional arrays manual construction

• Row vectors
• Syntax element1 element2
  

gtgtr 3 7 9 r 3 7 9
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One-dimensional arrays manual construction

• Column vectors
• Syntax element1
  element2

gtgtc 379 c 3 7 9
starts the array
separates rows of an array
ends the array
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Row vectors incremental construction

gtgt r 3 2 10 r 3 5 7 9
Syntax first element increment limit
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Row vectors incremental construction

gtgt r 3 2 10 r 3 5 7 9
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Examples incremental construction

first element increment limit

• gtgt A 1110
• A
• 1 2 3 4 5 6 7 8
  9 10

• gtgt B 110
• B
• 1 2 3 4 5 6 7 8
  9 10

(first element limit)
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Examples incremental construction

first element negative increment limit

• gtgt C 10 -2 -5
• C
• 10 8 6 4 2 0 -2 -4

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Linspace command

• also creates a linearly spaced row vector
• number of elements are specified instead of
  increment
• Syntax linspace(x1,x2,n)
• x1 lower limit
• x2 upper limit
• n - number of evenly-spaced elements

gtgt A linspace(3,9,4) A 3 5 7
9
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Linspace command

• also creates a linearly spaced row vector
• number of elements are specified instead of
  increment
• Syntax linspace(x1,x2,n)
• x1 lower limit
• x2 upper limit
• n - number of evenly-spaced elements

gtgt A linspace(3,9,5) A 3 4.5 6
7.5 9
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The transpose operator
'

• The transpose operator converts
• (row vector) (column vector)
• (column vector) (row vector)

gtgtr 3,7,9 r 3 7 9
gtgt c r' c 3 7 9
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zeros

• Syntax zeros(n,m)
• Create an array of zeros that has
• n rows
• m - columns

gtgt r zeros(1,3) r 0 0 0
gtgt c zeros(3,1) c 0 0
0
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ones

• Syntax ones(n,m)
• Create an array of ones that has
• n rows
• m - columns

gtgt r ones(1,3) r 1 1 1
gtgt c ones(3,1) c 1 1
1
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rand

• Syntax rand(n,m)
• Create an array of random numbers
• n rows
• m - columns

gtgt r rand(1,3) r 0.9501 0.2311
0.6068
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randn

• Syntax randn(n,m)
• Create an array of Gaussian random numbers
• n rows
• m - columns

gtgt r randn(1,3) r -0.4326 -1.6656
0.1253
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Length, and Absolute Value of a Vector

• length
• gives the number of elements in the vector.
• abs
• gives a vector whose elements are the absolute
  values of the original vector
• Commands apply to both row and column vectors
• Neither command gives the magnitude of the vector

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Length, and Absolute Value of a Vector

• Example

gtgt r -3 2 1 5 r -3 2 1 5 gtgt
length(r) ans 4 gtgt abs(r) ans 3
2 1 5
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Accessing single elements of a vector

• If A is a vector (i.e., a row or column vector),
  then
• A(1) is its first element,
• A(2) is its second element,
• A(end) is its last element
• Example

gtgt r -3 2 1 5 gtgt r(3) ans 1
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Accessing single elements of a vector

• This syntax can be used to assign an entry of A
• Syntax VariableName(Index) Expression
• Example

gtgt r -3 2 1 5 gtgt r(end) 2 r -3
2 1 2
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Accessing multiple elements of a vector

• If A is a vector (i.e., a row or column vector),
  then
• A(i,j,k) is a vector with i,j,k elements of A
• Example

gtgt r -3 2 1 5 gtgt r(2,3) ans 2 1
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Assigning multiple elements of a vector

• If A is a vector, then we can assign multiple
  elements
• A(i,j,k,) expression
• (must have consistent dimensions)
• Example

gtgt r -3 2 1 5 gtgt r(2,3) 1 2 ans
-3 1 2 5
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Unary Numeric Operations on Arrays

• Unary operations involve one input argument.
  Examples
• Negation, (using the - sign), abs
• Trig functions, sin, cos, tan, asin, acos, atan,
• General rounding functions, floor, ceil, fix,
  round
• Exponential and logs, exp, log, log10, sqrt
• Complex, abs, angle, real, imag

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Unary Operation Examples

• Trigonometric sin
• (arguments are assumed to be in radians)

gtgt r pi -1 gtgt sin(r) ans 0.0
-0.8415
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Binary (two argument) operations on Arrays

• Addition (and subtraction)
• If A and B are arrays of the same size,
• A B is the array A(i) B(i)
• Example

gtgt A B ans -1 3 gtgt A - B ans -5
1
gtgt A -3 2 gtgt B 2 1
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Binary (two argument) operations on Arrays

• Addition (and subtraction)
• If A is an array, and b is a scalar
• A b b A is the same size as A
• A(i) b
• Example

gtgt A b ans -1 4 gtgt A - b ans -5
0
gtgt A -3 2 gtgt b 2
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Binary (two argument) operations on Arrays

• Scalar-Array Multiplication
• If A is an array, and b is a scalar
• A b b A the same size as A
• A(i) b
• Example

gtgt A b ans -6 4 gtgt b A ans -6
4
gtgt A -3 2 gtgt b 2
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Binary (two argument) operations on Arrays

• Array Element-by-Element Multiplication .
• If A and B are arrays of the same size,
• A . B B . A is the array
• A(i) B(i)
• Example

gtgt A . B ans -6 2 gtgt B . B ans
4 1
gtgt A -3 2 gtgt B 2 1
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Binary (two argument) operations on Arrays

• Matrix Multiplication ()
• If A and B are arrays of consistent dimensions,
• A B the matrix multiplication of the two
  arrays (more later)
• Example

gtgt r c ans -4 gtgt c r ans -6
3 4 2
gtgt r -3 2 gtgt c 2 1
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Binary (two argument) operations on Arrays

• Matrix Multiplication ()
• If A and B are arrays of consistent dimensions,
• A B the matrix multiplication of the two
  arrays (more later)
• Example

gtgt r1 r2 ??? Error using gt Inner matrix
dimensions must agree.
gtgt r1 -3 2 gtgt r2 2 1
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Computing the magnitude of a vector

• Example
• How do we compute the magnitude of c ?

gtgt c -3 2 1 5 gtgt sqrt(c c) ans
6.2450
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Character strings

• In addition to numbers, many computer programs
  also
• need to deal with text data, e.g.,
• Names and addresses
• Input and output prompts
• Labels
• Text files
• Character strings in MATLAB are special arrays
  displayed
• in text format, but stored and manipulated in
  numerical
• format.

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Strings construction

• Use the single quote to create basic character
  arrays

gtgt s 'Roberto is the teacher' s Roberto is
the teacher
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Strings manipulation

• Strings are special kinds of vectors
• Each character in the string is an element of the
  array
• Matlab converts characters using ASCII code
• E.g. b is the ASCII code 98

gtgt s 'Roberto is the teacher' gtgt
length(s) ans 22
gtgt s(end) ans r
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Strings manipulation

gtgt s 'Roberto is the teacher' gtgt s(1 4
6) ans Ret
gtgt s(end-11) ans rehcaet eht si otreboR
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Strings to double conversion

gtgt s 'Roberto '
gtgt v double(s) v 82 111 98 101 114
116 111 32
gtgt char(v) ans Roberto
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Finding a string with findstr

• Syntax k findstr(str1,str2)
• finds index of first occurrence of str1 in str2

gtgt s 'Roberto is the teacher' gtgt
findstr(the,s) ans 12
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Summary

• What did we learn today?
• Arrays are important data structures and can be
• treated with great efficiency in MATLAB.
• Many different MATLAB built-in functions can be
• employed to input, manipulate and output arrays.
• Strings are numerical arrays in disguise and are
• employed to treat text data.
• Many different MATLAB built-in functions can be
• employed to input, manipulate and output strings
  and
• string arrays.