gibson:teaching:fall-2013:math445:lecture2
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gibson:teaching:fall-2013:math445:lecture2 [2013/09/04 18:47] gibson created |
gibson:teaching:fall-2013:math445:lecture2 [2013/09/04 18:47] (current) gibson |
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| - | <code> | + | <code>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| - | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | + | % How to evaluate wind chill formula in Matlab |
| - | % Linear algebra | + | |
| - | % Assign matrix A | + | % Approach 1: Set variables T and V, then evaluate formula |
| - | A = [ 1 3 ; 5 -2] | + | T = 45 |
| - | A = | + | T = |
| - | 1 3 | + | 45 |
| - | 5 -2 | + | V = 10 |
| - | % Assign vector b | + | V = |
| - | b = [3 ; 32] | + | 10 |
| - | b = | + | WCF = 35.7 + 0.6*T - 35.7*V^0.16 + 0.43*T*V^0.16 |
| + | WCF = | ||
| + | 39.0671 | ||
| + | |||
| + | % Approach 2: evaluate formula with embedded values of T,V | ||
| + | WCF = 35.7 + 0.6*45- 35.7*10^0.16 + 0.43*45*10^0.16 | ||
| + | WCF = | ||
| + | 39.0671 | ||
| + | |||
| + | % Approach 1 is better because you can easily modify T,V, e.g. | ||
| + | T=45; V=0; WCF = 35.7 + 0.6*T - 35.7*V^0.16 + 0.43*T*V^0.16 | ||
| + | WCF = | ||
| + | 62.7000 | ||
| + | |||
| + | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| + | % Random numbers | ||
| + | |||
| + | % The rand function produces a random real number between 0 and 1 | ||
| + | rand | ||
| + | ans = | ||
| + | 0.9649 | ||
| + | |||
| + | % So 20*rand produces a random real number between 0 and 20 | ||
| + | 20*rand | ||
| + | ans = | ||
| + | 3.1523 | ||
| + | |||
| + | 20*rand | ||
| + | ans = | ||
| + | 19.4119 | ||
| + | |||
| + | % and 20 + 30*rand produces and random real between 20 and 50 | ||
| + | 20+30*rand | ||
| + | ans = | ||
| + | 42.7322 | ||
| + | |||
| + | 20+30*rand | ||
| + | ans = | ||
| + | 31.7668 | ||
| + | |||
| + | 20+30*rand | ||
| + | ans = | ||
| + | 20.9550 | ||
| + | |||
| + | % randi(N) produces a random integer between 1 and N | ||
| + | randi(4) | ||
| + | ans = | ||
| 3 | 3 | ||
| - | 32 | + | randi(4) |
| + | ans = | ||
| + | 1 | ||
| - | % Solve Ax=b for x | + | % so 100 + randi(10) |
| - | x = A\b; | + | 100 + randi(11) % gives rnadom numbers btwn 101 and 110 |
| - | x = A\b | + | ans = |
| - | x = | + | 107 |
| - | 6.0000 | + | 100 + randi(11) % gives rnadom numbers btwn 101 and 111 |
| - | -1.0000 | + | ans = |
| + | 106 | ||
| + | |||
| + | % round(10*rand) will produce random integers between 0 and 10, | ||
| + | % but it's not as efficient as using the randi() function | ||
| + | round(10*rand) | ||
| + | ans = | ||
| + | 8 | ||
| + | round(10*rand) | ||
| + | ans = | ||
| + | 4 | ||
| + | |||
| + | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| + | % Boolean expressions, also known as logical expressions | ||
| + | |||
| + | % double equals signs means evaluate whether both sides are equal | ||
| + | % return true or false accordingly | ||
| + | |||
| + | 3 == 2 + 1 % remember 1 == true ; 0 == false | ||
| + | ans = | ||
| + | 1 | ||
| + | |||
| + | 3 == 2 - 1 % remember 1 == true ; 0 == false | ||
| + | ans = | ||
| + | 0 | ||
| + | |||
| + | % here (3 == 2) evaluates to 0, which is then added to 1 | ||
| + | (3 == 2) + 1 | ||
| + | ans = | ||
| + | 1 | ||
| + | |||
| + | % variables b and c are undefined | ||
| + | b > c + 1 | ||
| + | Undefined function or variable 'b'. | ||
| + | |||
| + | % but 'b' is the character b | ||
| + | 'b' | ||
| + | ans = | ||
| + | b | ||
| + | |||
| + | 'c' | ||
| + | ans = | ||
| + | c | ||
| + | |||
| + | class('b') | ||
| + | ans = | ||
| + | char | ||
| + | |||
| + | % cast char 'b' to an integer | ||
| + | uint32 | ||
| + | uint32('b') | ||
| + | ans = | ||
| + | 98 | ||
| + | |||
| + | % cast char 'c' to an integer | ||
| + | uint32('c') | ||
| + | ans = | ||
| + | 99 | ||
| - | % Verify that Ax equals b | + | % to evaluate this expression, Matlab casts 'b' and 'c' to their |
| - | A*x | + | % integer values and then evaluates the integer equation |
| + | 'b' >= 'c' + 1 | ||
| ans = | ans = | ||
| - | 3.0000 | + | 0 |
| - | 32.0000 | + | |
| - | A*x-b | + | 'b' >= 'c' - 1 |
| ans = | ans = | ||
| - | -8.8818e-16 | + | 1 |
| - | 0.0000e+00 | + | |
| - | % pretty darn close | ||
| </code> | </code> | ||
gibson/teaching/fall-2013/math445/lecture2.1378345633.txt.gz · Last modified: 2013/09/04 18:47 by gibson
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