sympref FloatingPointOutput adds roundoff error

Question

Max Murtaugh 2020-10-18

2
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/617383-sympref-floatingpointoutput-adds-roundoff-error

回答： Walter Roberson 2023-11-29

I was trying to use symunit to keep track of units for my thermodynamics class and I set symbolic values to floating point output so it was easier to keep track of values. However, I found that it introduces significant round off error for some reason. I was led to believe that it would only affect the displayed values not the calculations but can't seem to figure out how to get the unrounded value back. I have the calculation where I realized this below.

clear
format short e
u = symunit;
baseUnits('SI');
sympref('FloatingPointOutput', false);
P = 100*u.kPa;
P_w = 3.1698*u.kPa;
w = 0.622*P_w/(P - P_w)

4929039/242075500

val_1 = double(separateUnits(w))

val_1 = 2.0362e-02

sympref('FloatingPointOutput', true);
w

w=0.0204

val_2 = double(separateUnits(w))

val_2 = 2.0400e-02

val_3 = double(w)

val_3 = 2.0400e-02

for reference here are the values without symunit (since the units cancel out anyway)

P = 100;
P_w = 3.1698;
w = 0.622*P_w/(P - P_w)

w = 2.0362e-02

How do I prevent this round-off error? Also, is there anyway to display symbolic results the same way as "format short g/e" where it gives 5 significant figures? 5 significant figures is often the minimum I need for my classes.