- 6.1.1 - 6.1.13 A concrete example
- Lots of examples using the colon operator to create matrices and create matrices from other matrices.
- 6.1.15 Vectorizing nested fors: loan repayment tables
-
- loanfors.m conventional
>> ls errortrap1.m loanfors.m errortrap2.m loaninnervect.m >> tic >> loanfors 10 10.75 9.65 9.09 11 11.37 10.32 9.80 12 12.00 11.01 10.53 13 12.65 11.72 11.28 14 13.32 12.44 12.04 15 14.00 13.17 12.81 16 14.69 13.91 13.59 17 15.39 14.67 14.38 18 16.10 15.43 15.17 19 16.83 16.21 15.98 20 17.56 16.99 16.78 >> toc Elapsed time is 5.374843 seconds.
- loaninnervect.m vectorized for
>> tic >> loaninnervect 10.0000 10.7461 9.6502 9.0870 11.0000 11.3660 10.3219 9.8011 12.0000 12.0017 11.0109 10.5322 13.0000 12.6524 11.7158 11.2784 14.0000 13.3174 12.4352 12.0376 15.0000 13.9959 13.1679 12.8083 16.0000 14.6870 13.9126 13.5889 17.0000 15.3900 14.6680 14.3780 18.0000 16.1042 15.4331 15.1743 19.0000 16.8288 16.2068 15.9768 20.0000 17.5630 16.9882 16.7845 >> toc Elapsed time is 22.090842 seconds.
Note: Stewart deleted some blank lines in the output of loaninnervect.m above.Do you notice something odd in the run-times above?
Analyzing Your Program's Performance from online MATLAB documentation Open this is a new window. Then Select Index; Select "the letter p"; and scroll down to Performance to find Analyzing your Program's Performance
- loanfors.m conventional
Matrix operations, fundamental to MATLAB, are defined in the mathematical sense where if C = A B, and number of columns in A is the same as the number of rows in B
ci,j = SUM ai,k bk,j.
Lecture will highlight many of these examples.
- det determinant
- eig eigenvalue decomposition
- expm matrix exponential, i.e. eA where A is a matrix.
- eig eigenvalue decomposition
- matrix exponential is useful in solving linear ordinary differential equations
- inv inverse
- lu LU factorization into lower and upper triangular matrices
- qr QR orthogonal factorization
- svd singular value decompostion
- lu LU factorization into lower and upper triangular matrices
- 6.4.1 assignment
- s1 = 'Hi There';
s2 = ' 10 o''clock'; need to use double apostrophe (note this is NOT " the double-quote character) - 6.4.2 Input
- strings may be entered in response to the input statement in 2 ways
- prompt the user to use apostrophe, e.g. s = input ('enter a string - using the apostrophe to enclose where you type it');
- or you can indicate in the input statement that a string is expected , e.g. s = input (' enter a string ','s');
- 6.4.3 Strings are arrays
- a MATLAB string is an array with each element representing one character
in the string. If
s = 'Napoleon';
then whos>> s = 'napoleon'; >> whos Name Size Bytes Class Attributes s 1x8 16 char
showing s is a 1x8 char vector. The statement s(8:1:-1) will display the string backwards>> s(8:-1:1) ans = noelopan >>
If a string must contain an apostrophe, the apostrophe must be repeated when entering the string. However, only one apostrophe is actually stored in the string. For example, in
name = 'M''kombe'
name(3) is 'k'Why is this done? The computer system (MATLAB) needs to distinguish the string delimiter (') from the character (').
>> name = 'M''kombe' name = M'kombe >> name(3) ans = k >> whos Name Size Bytes Class Attributes ans 1x1 2 char name 1x7 14 char s 1x8 16 char
We can exploit the vector nature of strings in many ways. For example, to remove all the blanks from the string s. This use a logical vector (nonblanks) too.
>> s = 'Twas brillig and the sithy toves'; >> nonblanks = s ~= ' '; >> s (nonblanks) ans = Twasbrilligandthesithytoves >> whos Name Size Bytes Class Attributes ans 1x26 52 char name 1x7 14 char nonblanks 1x32 32 logical s 1x32 64 char
- 6.4.4 Concatenation of strings
- Treating strings as vectors, we use square brackets to catenate.
>> king = 'Henry'; >> king = [king, ' VIII'] king = Henry VIII >> whos Name Size Bytes Class Attributes ans 1x26 52 char king 1x10 20 char name 1x7 14 char nonblanks 1x31 31 logical s 1x31 62 char
- 6.4.5 ASCII codes, double and char
- A MATLAB character is represented internally by a 16-bit numerical value.
The character codes start at 1; the first 127 such codes are the
ASCII codes. the letters 'A' to 'Z' are the consecutive integers
from 65 to 90, while the codes for 'a' to 'z' are 97 to 122. This is
Appendix D of our text, or you can check online,
http://www.asciitable.com/ for
an ASCII table.
>> double ('napoleon') ans = 110 97 112 111 108 101 111 110 >>or use the char function to convert integers to ASCII codes>> char(65:70) ans = ABCDEF >>
Use char and double to generate rows of identical characters
>> x = char(ones(4,20)*double('#')) x = #################### #################### #################### #################### >>ones(4,20) generates 4 rows and 20 columns of 1's (or true). Multiplying by double('#') replaces the 1's with ASCII code for '#' and char converts the ASCII codes back to text.If a character variable is involved in an arithmetic expression, MATLAB uses the ASCII code of the character in the calculation.
>> s = 'a'; >> s+1 ans = 98 >>
Array operations can be performed on string. If s is a string of letters, the expression char(s+1) returns each letter in the string advanced by one place in the alphabet.The relationship between characters and their ASCII codes means you can do neat things
>> alpha = double ('a'):double('z') alpha = Columns 1 through 11 97 98 99 100 101 102 103 104 105 106 107 Columns 12 through 22 108 109 110 111 112 113 114 115 116 117 118 Columns 23 through 26 119 120 121 122 >> - 6.5.4 fprintf of strings
-
>> fprintf (' %8sVIII\n', 'Henry') HenryVIII >> fprintf ('%-8sVIII\n', 'Henry') Henry VIII >> fprintf ('%.3sVIII\n', 'Henry') HenVIII >> - 6.4.7 Comparing strings
-
>> s1 = 'ann'; >> s2 = 'ban'; >> s1 < s2 ans = 1 0 0 >>the result of the logical comparison, element by element, of the two character vectors, s1 and s2. NOTE: strings must have the same length.The function strcmp(s1,s2) compares the two strings s1 and s2, returning 1 if they are identical and 0 otherwise. In this case, the strings DO NOT have to be the same length.
- 6.4.8 other string functions
- blanks, deblank, int2str, num2str, ischar, lower, upper, sprintf
- 6.5 Two-dimensional strings
-
>> nameAndAddress = ['Adam B Carr '; '21 Barkly Ave'; 'Discovery '] ??? Error using ==> vertcat CAT arguments dimensions are not consistent.
What generated this Error message? We needed to ensure the same number of characters (13) in each column of the array nameAndAddress.>> nameAndAddress = char('Adam B Carr', '21 Barkly Ave', 'Discovery') nameAndAddress = Adam B Carr 21 Barkly Ave Discovery >> whos Name Size Bytes Class Attributes nameAndAddress 3x13 78 char >>It is easier to let MATLAB do the padding of the data for you. Also, remember that if you use single-subscript notation the array is referenced by column, so>> nameAndAddress(1:3) ans = A2D >>
the first letter of each row.
s = 'x = -b / (2*a);'
is made, eval(s) makes MATLAB interpet the text in s as the
statement
x = -b / (2*a);
which is carried out with the current values of a and b.
Another use of eval could be as a "user-friendly" way of inputting
a function from the Command Window. Consideer the following script:
We will see in Chapter 10: Function handles that we will prefer to use
feval rather than eval whenever possible, since feval
is faster and the code using it can be compiled with the MATLAB
compiler.
the function eval can take a second (string) argument, representing an
expression to be executed if an error is encountered in the first argument.
We demonstrate this with errortrap1.m below.
errortrap1.m
errortrap2.m
f = input ('Enter function (of x) to be plotted: ', 's');
x = 0 : 0.01 : 10;
plot(x,eval(f)),grid
This was created and called p165eval.m and is available to you.
