When creating a vector why does the size change when using a variable vs using a value?

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Matt Thelen
Matt Thelen 2021-4-10
回答： Stephen23 2021-4-10
I am trying to create the time vector that starts at 0, has a step size of variable predefined (stepsize) and ends at predefined variable (fin_time).
In this case I calculated stepsize=0.0990 and fin_step=14.256
It would look like this time=[0:stepsize:fin_time]. When I type this I get a 144x1 vector.
When I type the value of stepsize manually. time=[0:0.0990:fin_time] I get a 145x1 vector. This is what I want.
How come the variable is exactly the same value but gives a different answer?

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Stephen23
Stephen23 2021-4-10
"How come the variable is exactly the same value but gives a different answer?"
No, the values are not exactly the same.
In one case you calculate the value, in the other case you write it explicitly. These are not the same value, but you forgot to actually check this using any reliable method (e.g. num2strexact, format hex, etc).
Read more about binary floating point numbers:
https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero
https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal
http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug
http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab
This is worth reading as well:
https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf

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