regRootAnti-symmetric square root approximation with finite derivative in the origin |
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This function approximates sqrt(abs(x))*sgn(x), such that the derivative is finite and smooth in x=0.
Function | Approximation | Range |
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y = regRoot(x) | y ~= sqrt(abs(x))*sgn(x) | abs(x) >>delta |
y = regRoot(x) | y ~= x/sqrt(delta) | abs(x) << delta |
With the default value of delta=0.01, the difference between sqrt(x) and regRoot(x) is 16% around x=0.01, 0.25% around x=0.1 and 0.0025% around x=1.
x |
Type: Real |
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delta |
Default Value: 0.01 Type: Real Description: Range of significant deviation from sqrt(abs(x))*sgn(x) |
y |
Type: Real |
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