1. Other Kinds of Arrays Chapter 11

2. Objectives After studying this chapter, you should be able to:
Understand the different kinds of data used in MATLAB
Create and use both numeric and character arrays
Create multidimensional arrays, and access data in those arrays
Create and use cell and structure arrays

3. Section 11.1 Data Types
The primary data type (also called a class) in MATLAB is the array or matrix
Within the array, MATLAB supports a number of different secondary data types (classes)
The default is a double precision floating point number

4. MATLAB’s arrays can store different types of data
Kinds of Data Stored in MATLAB Matrices
Numeric
Character
Logical
Symbolic Objects - Symbolic Toolbox
Integer
Floating Point
multiple signed integer types
multiple unsigned integer types
single precision
double precision
complex
real

5. There are a variety of array types to store the data
MATLAB Array Types
Character Arrays
Logical Arrays
Numeric Arrays
Symbolic Arrays
Cell Arrays
Structure Arrays
Most of these arrays can only hold information of one data type
Integer
multiple signed integer types
multiple unsigned integer types
Floating Point
single precision
double precision
Cell and Structure arrays can store different types of data in the same array
Other types, including user defined and JAVA types

6. The difference between array types and data types may be confusing
Consider the following analogy

7. There are lots of different places you could store your wealth
They correspond to the array types

8. There are lots of different kinds of wealth you might store in a bank
They correspond to the data types

9. Numeric Data Types Numeric data is stored in numeric arrays
The default data type is double precision floating point
Every time you enter a number into MATLAB, the program assumes you’ve entered a double
MATLAB conforms to the IEEE standards that specify the meaning of the double data type

10. When you define numeric values they default to doubles
Each value in a double array needs 8 bytes of memory to store

11. There are 6 values in the C array – therefore it requires 6 x 8 = 48 bytes of memory

12. Value limitations
The biggest number you can store in a double can be found using the realmax function
The smallest number you can store in a double can be found using the realmin function

13. Single Precision floating point numbers
This data type is a new feature in MATLAB 7
Uses half the storage space of a double
Each value requires
4 bytes = 32 bits

14. The grid symbol indicates a numeric array – double, single or integer
It’s necessary to use the single function to change the value of 5 (which is a double by default) into a single

15. Value limitations
Since single precision numbers are allocated only half as much storage space, they can not cover as large a range of values as double numbers
The biggest number you can store in a single can be found using the realmax(‘single’) function
The smallest number you can store in a double can be found using the realmin(‘single’) function

16. Engineers will rarely need to convert to single precision numbers, because
today’s computers have plenty of storage space for most applications,
and will execute most of the problems we pose in extremely short amounts of time

17. When would you use the short data type instead of double values?
In some numerical analysis applications you may be able to improve the run time of a long problem by changing from double to single precision
However, round off error becomes more of a problem.

18. Consider the harmonic series
Shorthand for the harmonic series
This series diverges -it just keeps getting bigger the more terms you add

19. For large numbers of steps the results are different using double and single data types

20. Why?
When the series gets big enough the value of 1/n is so small that the computer can’t distinguish it from 0
This occurs at the value of realmin
Since doubles can differentiate between smaller numbers than singles the summation is valid for more steps

21. Integers Integer arrays are new to MATLAB 7
Each of these types require a different amount of storage
Integer arrays are new to MATLAB 7
Integers are stored in integer arrays
MATLAB Integer Types
8-bit signed integer
int8
8-bit unsigned integer
uint8
16-bit signed integer
int16
16-bit unsigned integer
uint16
32-bit signed integer
int32
32-bit unsigned integer
uint32
64-bit signed integer
int64
64-bit unsigned integer
uint64
Remember that 8 bits = 1 byte

22. Determine the size range using
You can determine the number of possible values allowed in the integer data type
Each of the integer types uses a different amount of storage, and can thus save different ranges of values
Determine the size range using
intmax and intmin

24. When do we use integers
Integer arrays can be used to store image information
These arrays are often very large, but there are a limited number of colors used in many of these images to create the picture.
Storing them as unsigned integer arrays reduces the storage requirement dramatically.

25. Complex numbers Default is double
Twice as much storage is needed because the real and imaginary components must be stored
Could also be stored as a single or integer

26. Character and String Data
Character arrays store character information
A character array is produced from a string

27. Each character is a separate element in the array

28. The fifth element of the H array is the letter y

29. Any string represents a character array in MATLAB
Each character requires 2 bytes of storage

30. The ‘ab’ symbol indicates a character array
Spaces are characters too

31. How are characters stored in MATLAB?
All information in computers is stored using a series of zeros and ones
ASCII – Used in small computers
EBCDIC – Used in mainframes and super computers
You can think of this list of 0’s and 1’s as a base two number

32. Comparison between base 2 and base 10
Base 2 ”binary”
Base 10 ”decimal” 1 10 2 11 3
100 4
101 5
110 6
111 7
1000 8

33. Every character stored using ASCII or EBCDIC code has both a binary representation and a decimal equivalent
When we ask MATLAB to change a character to a double, the number we get is the decimal equivalent in the ASCII coding system

34. MATLAB includes functions to change data types
Use the double function to convert to a double precision floating point number
Use char to convert a number to a character

35. You shouldn’t mix data types in calculations or in arrays
Notice that the ans array has two characters
If you attempt to create an array with both character and numeric data, the array defaults to all characters
There is no character equivalent to 3, so MATLAB adds a space to the array

36. If you try to perform arithmetic with a combination of character and numeric data, MATLAB converts the character to its decimal equivalent
Remember that a has a decimal equivalent of 97

37. Symbolic Data Covered in more detail in a separate chapter
The symbolic toolbox uses symbolic data to perform symbolic algebraic calculations
Create a symbolic variable using the sym function

38. Storage requirements for symbolics vary, depending on how big the expression is.

39. The cube symbol indicates a symbolic array
Symbolic variables can be grouped into arrays, just like other data types

40. Logical Data Types Logical data can have only one of two values
True
False
MATLAB uses
0 to represent false and
1 to represent true

41. The check mark indicates a logical array
Although a logical array contains the information true and false, MATLAB represents it as 0 and 1
We don’t usually create logical arrays by entering true and false values. Usually they are the result of logical operations

42. Notice that x and y are numeric arrays and z is a logical array
We can interpret this result to mean that x>y is false for elements 1 and 3, and true for elements 2,3 and 5
These arrays are used in logical functions, and are not usually even seen by the user.

43. In this example the find command used the result of the comparison x>y to determine that elements 2, 3, and 4 met the criteria

44. Sparse Arrays
Both double precision arrays and logical arrays can be stored in either full matrices, or as sparse matrices.
Sparse matrices are “sparsely populated”, meaning many or most of the values in the array are zero
Identity matrices are examples of sparse matrices

45. Sparse matrices require less space than the corresponding numeric or logical matrices
If we store sparse arrays in the full matrix format, it takes 8 bytes of storage for every data value, whether they are zeros or not
The sparse matrix format only stores the non-zero values, and remembers where they are
this strategy saves a lot of space

46. Compare the size of N and P
N is a 1000x1000 identity matrix
P is the same matrix, stored using the sparse strategy

47. Section 11.2 Multidimensional Arrays
Sometimes you may want to store data in multidimensional arrays
Rows
Columns
Pages
Additional dimensions are possible

48. Multidimensional arrays are grouped into pages
rows
columns
pages

49. Page 1
Page 2
Page 3
Page 4
Imagine that you would like to store each of these 4 two-dimensional arrays into 1 three-dimensional array with four pages.

50. You must define each page separately
You must define each page separately. Read the first definition statement as
“all the rows, all the columns, in page 1”

52. Section 11.3 Creating Character Arrays
We can create two dimensional character arrays only if the number of elements in each row is the same

53. This statement doesn’t work, because the number of characters in each line is different

54. The char functions “pads” the array with blanks
The char functions “pads” the array with blanks. Notice that the array size is 6 rows by 7 columns
Character arrays can store any of the characters defined in the ASCII coding scheme – including the symbols for numbers

55. Character arrays can only hold character data
We can take advantage of this to create tables that look like they include both character and numeric information, but really are composed of just characters
The number 1 is different from the character 1

56. Let’s combine an array of test scores and names98 84 73 88 95
100
Names
Holly
Steven
Meagan
David
Michael
Heidi
Numeric information
Character information

57. Notice that table is a character array
When we tried to store the two different data types into the same array, MATLAB interpreted the numbers as the ASCII equivalent of characters

58. num2str
In order to store the two different data types in the same array, we’ll need to convert the numbers into the corresponding characters
num2str

59. The num2str function converted the array of scores into the corresponding characters

60. Creation of file names
A useful application of character arrays and the num2str function is the creation of file names
There are occasions when you may want to save data into .dat or .mat files, but you don’t know ahead of time how many files will be required
my_data1.dat
my_data2.dat
my_data3.dat
Etc.

61. For example…. Load a file of unknown size called some_data
Create a number of new files, one for each column from the input file

62. Input and Output
Output files
Data from input file
Data in File1
Data in File2 1 2 3 4 5 6 7 8 9 10 11 12 1 4 7 10 2 5 8 11
Data in File3 3 6 9 12

63. Load the input file
Determine the number of rows and columns
Create the file names
Extract the data
Save the data into the new files

65. Section 11.4 Cell Arrays
The cell array can store different types of data inside the same array
Each element in the array is also an array

66. These three arrays all store different data types

67. Create a cell array using curly braces

68. Indexing
The indexing system used for cell arrays is the same as that used in other arrays.
You may either use a single index, or a row and column indexing scheme.
There are two approaches to retrieving information from cell arrays.
Parentheses – results in a description
Curly braces – results in the values

70. To access a particular element inside an array stored in a cell array, you must use a combination of curly braces and parentheses

71. Section 11.5 Structure Arrays
Similar to Cell Arrays
Multiple arrays of differing data types can be stored in structure arrays
Instead of using content indexing each of the matrices is given a location called a field

72. This is still a 1x1 structure array – however it has three fields
This structure array (struct) contains three fields

73. We can add more content to the structure, and expand its size, by adding more matrices to the fields we’ve defined.

74. You can access the information using…
Matrix name
Field name
Index numbers

75. Just calling the matrix name returns a description of the array

76. You can access the actual arrays you’ve stored in the structure by using an index number to identify which set of data you’re interested in

77. You can use the field name to access just the data in certain fields
You can use the field name to access just the data in certain fields. This example returns the arrays in the first field of each member of the structure

78. Combining an index number and the field name allows you to access one particular array

79. Finally, if you want to know the content of one particular element in a field you must specify the element index number after the field name.

80. Variable Editor
You can use the variable editor to access the content of a structure array
Double click the structure array name in the workspace window

81. If you double click on one of the elements of the structure in the variable editor, the editor expands to show you the contents of that element

82. Summary MATLAB’s primary data structure is the array
MATLAB supports a number of different array types, each of which can store a particular type of data
Cell and structure arrays can store more than one data type in the same array

83. Summary-Data Type MATLAB supports the following data types Numeric
double
single
8 different types of integers
Character
Symbolic
Logical

84. Summary - Array Types Numeric Character Symbolic Logical Sparse Cell
double
single
8 different integer arrays
Character
Symbolic
Logical
Sparse
Cell
Structure

85. Summary – Multidimensional Arrays
Additional dimensions can be stored in MATLAB arrays
The third dimension is called a page
Each page must be entered separately as a two-dimensional array