The heat index HI, calculated from the air temperature and relative humidity, is
ID: 2258184 • Letter: T
Question
The heat index HI, calculated from the air temperature and relative humidity, is the apparent temperature felt by the body. An equation used by the National Weather Service for calculating the HI is given by: HI = C1 + C2T + C3R + C4TR + C5T 2 + C6R 2 + C7T 2R + C8TR2 + C9T 2R 2 Where T is the temperature in °F, and R is the relative humidity in integer percentage. Write a MATLAB program that reads a file having the following format:
Temperature 80 82 84 86 88 90 92 94
Relative Humidity 50 55 60 65 70 75
Coefficients -42.379 2.04901523 10.14333127 -0.22475541 -6.83783e-3 - 5.481717e-2 1.22874e-3 8.5282e-4 -1.99e-06
In the file above, it is unknown ahead of time how many numbers will be on the Temperature and Relative Humidity lines. There will be exactly nine numbers on the Coefficients line. In the example above, the numbers wrapped to the next line, but in reality, all the Coefficient numbers will be on the same line. All the numbers will likely be different than shown in the file above. Next, compute HI for each combination of T and R. Your results should be written to a file as shown below:
Temperature (F)
1 80 82 84 86 88 90 92 94
Relative Humidity (%)
50 81 83 85 88 91 95 99 103
55 81 84 86 89 93 97 101 106
60 82 84 88 91 95 100 105 110
65 82 85 89 93 98 103 108 114
70 83 86 90 95 100 106 112 119
75 84 88 92 97 103 109 116 124
Each of the columns above is 10 characters wide. Here is a printout of what the user should see while running your program at the command window:
>> miniproject input filename : input.txt
output filename : output.txt
Hints One of the sticky problems that you must deal with is not knowing how many temperatures or relative humidities will be in the input file. An elegant solution to this problem is the built-in MATLAB function repmat. For the numbers shown in the example above, I recommend using repmat to build a Tmat matrix like this:
Tmat =
80 82 84 86 88 90 92 94
80 82 84 86 88 90 92 94
80 82 84 86 88 90 92 94
80 82 84 86 88 90 92 94
80 82 84 86 88 90 92 94
80 82 84 86 88 90 92 94
Notice that Tmat above has as many rows as there are relative humidity numbers, and this number can be found with the built-in function length. Also use repmat to build an Rmat matrix, having as many columns as you have temperature numbers:
Rmat =
50 50 50 50 50 50 50 50
55 55 55 55 55 55 55 55
60 60 60 60 60 60 60 60
65 65 65 65 65 65 65 65
70 70 70 70 70 70 70 70
75 75 75 75 75 75 75 75
Now it’s easy to do an element-by-element calculation and calculate all the HI numbers, using just one line of code. A final problem is constructing the call to fprintf, not knowing how many numbers you will be printing ahead of time. Repmat is, again, an elegant solution to this problem. For example, the following line of code will create a format string, suitable for using in fprintf, that will print n numbers per row:
format_string = [repmat('%10.0f',1,n) ' '];
Explanation / Answer
fid = fopen('inputFile.txt');
T = str2num(fgetl(fid));
R = str2num(fgetl(fid));
C = str2num(fgetl(fid));
fclose(fid);
T = repmat(T,length(R),1);
R = repmat(R',1,length(T));
HI = C(1) + C(2)*T + C(3)*R + C(4)*(T.*R) + C(5)*(T.^2) + ...
C(6)*(R.^2) + C(7)*(T.^2).*R + C(8)*T.*(R.^2) + C(9)*(T.^2).*(R.^2);
fid1 = fopen('outputFile.txt','wt');
format_string = [repmat('%10.4f',1,8) ' '];
fprintf(fid1,format_string,HI);
fclose(fid1);
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