how to reduce symbolic calculation precision?

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EngM
EngM 2024-1-18
评论： Walter Roberson 2024-1-18
The answer of the symbolic calculations may results in extermely small values, of the order of -33! Fo my use, I don't need such precision and would like any value lower than 1.e-6 (or anything else) to be round it to zero.
One solution suggested is to use vpa command. That didn't do anything to my calculations, matrices with entries of the order of 1.e-33 are still present decpite setting vpa('var',3) for example.
can you please help.
thanks.
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Dyuman Joshi
Dyuman Joshi 2024-1-18
编辑：Dyuman Joshi 2024-1-18
You can set the those values to 0 as well.
What is the value of x3? or what values can be used for x3, which can be used for an example?
EngM
EngM 2024-1-18
well, it's cos(x3), so, the function is [-1,1] and the whole term should vanish when using lower precision calculation.

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Walter Roberson
Walter Roberson 2024-1-18
编辑：Walter Roberson 2024-1-18
Ran in:
The below code was developed to specifically search for a small constant multiplied by something
%create some demonstration data
syms nu
M = exp(randn(2,2) - 12) * nu + randn(2,2);
disp(char(vpa(M, 10)))
[0.000005657295524*nu + 1.201796311, 0.00001356942815*nu + 0.1714788358; 0.000003171547516*nu + 0.3197498794, 0.000003738587304*nu + 0.8981736893]
%now do the work
%constant times variable is always stored with the variable first (I thought it was the other way around!)
threshold = 1e-5;
op1 = @(expr) children(expr,1);
op2 = @(expr) children(expr,2);
ZapSmall = @(num, threshold) piecewise(num > -threshold & num < threshold, 0, num);
MM = simplify(mapSymType(M, 'times', @(expr) ZapSmall(op2(expr),threshold)*op1(expr)));
disp(char(vpa(MM, 10)))
[1.201796311, 0.00001356942815*nu + 0.1714788358; 0.3197498794, 0.8981736893]
There is a much more compact version for the case that vpa() has already been applied and all symbolic constants are to be examined.
mapSymType(M, 'vpareal', @(x) piecewise(abs(x)<=threshold, 0, x))
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Walter Roberson
Walter Roberson 2024-1-18
You have to be very careful when using this facility. If you have done a simplify() at any point then simplify() tends to rewrite A*x + B*y in terms of A*(x + B/A*y) where the leading coefficient can be quite large and the B/A coefficient can be quite small. This happens especially if you are working with bessel functions.

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