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https://issues.apache.org/jira/browse/MATH-1289?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Luc Maisonobe resolved MATH-1289.
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Resolution: Invalid
The expressions used in the library are correct.
With your expressions, computing I^2 would give +1 instead of -1. and
multiplication would not be commutative (for example I * 1 would be the
opposite of 1 * I).
Remember that in the complex class, the imaginary field is a *real* value
holding the multiplicative factor to be applied to I (the square root of -1).
In other words z = real + I * imaginary.
So
{noformat}
z1 * z2 = (r1 + I * i1) * (r2 + I * i2)
= (r1 * r2 + I * r1 * i2 + I * i1 * r2 + I * I * i1 * i2)
= (r1 * r2 + I * I * i1 * i1) + I * (r1 * i2 + i1 * r2)
= (r1 * r2 - i1 * i2) + I * (r1 * i2 + i1 * r2)
{noformat}
which is exactly the expression in the library.
> Incorrect calculation in org.apache.commons.math3.complex.Complex#multiply
> --------------------------------------------------------------------------
>
> Key: MATH-1289
> URL: https://issues.apache.org/jira/browse/MATH-1289
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.5
> Environment: Linux 3.16.0-44-generic #59-Ubuntu SMP Tue Jul 7
> 02:07:39 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux
> java version "1.8.0_45"
> Java(TM) SE Runtime Environment (build 1.8.0_45-b14)
> Java HotSpot(TM) 64-Bit Server VM (build 25.45-b02, mixed mode)
> Reporter: Detaille Octave
> Labels: easyfix
>
> Hello guys!
> If think there is a bug in the
> org.apache.commons.math3.complex.Complex#multiply method
> Line 536 & 537 below are not correct
> {code:title=Complex.java|borderStyle=solid}
> return createComplex(real * factor.real - imaginary * factor.imaginary, real
> * factor.imaginary + imaginary * factor.real);
> {code}
> It should be
> {code:title=Complex.java|borderStyle=solid}
> return createComplex(real * factor.real + imaginary * factor.imaginary,
> imaginary * factor.real-real * factor.imaginary);
> {code}
> Can you confirm that? Or do I miss something?
> Thanks a lot (also, for this excellent library).
> Best,
> Octave
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