1. Other Kinds of Arrays Chapter 11

2. 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

3. 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

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

5. 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

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

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

8. 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

9. 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

10. 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

11. 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

12. 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.

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

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

15. 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

16. 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

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

18. Each character is a separate element in the array

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

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

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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

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

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

31. 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

32. 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

33. 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 4, and true for elements 2,3 and 5
These arrays are used in logical functions, and are not usually even seen by the user.

34. In this example the find command used the result of the comparison x>y to determine that elements 2, 3, and 5 met the criteria

35. 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

36. 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

37. Compare the size of N and P (8,000,000 vs. 24,008)
N is a 1000x1000 identity matrix
P is the same matrix, stored using the sparse strategy

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

39. Multidimensional arrays are grouped into pages
rows
columns
pages

40. 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.

41. 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”

43. 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

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

45. 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

46. 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

47. 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

48. 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

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

50. 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.

51. 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

52. 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

53. 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

55. 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

56. These three arrays all store different data types

57. Create a cell array using curly braces

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