forked from M-Labs/nalgebra
Correct typos, move doc portion to comment and fix borrow to clone
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@ -181,7 +181,7 @@ where
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/// Calculates the generalized eigenvectors (left and right) associated with the generalized eigenvalues
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/// Outputs two matrices.
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/// The first output matix contains the left eigenvectors of the generalized eigenvalues
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/// The first output matrix contains the left eigenvectors of the generalized eigenvalues
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/// as columns.
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/// The second matrix contains the right eigenvectors of the generalized eigenvalues
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/// as columns.
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@ -196,46 +196,45 @@ where
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///
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/// u(j)**H * A = lambda(j) * u(j)**H * B
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/// where u(j)**H is the conjugate-transpose of u(j).
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///
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/// How the eigenvectors are build up:
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///
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/// Since the input entries are all real, the generalized eigenvalues if complex come in pairs
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/// as a consequence of <https://en.wikipedia.org/wiki/Complex_conjugate_root_theorem>
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/// The Lapack routine output reflects this by expecting the user to unpack the complex eigenvalues associated
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/// eigenvectors from the real matrix output via the following procedure
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///
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/// (Note: VL stands for the lapack real matrix output containing the left eigenvectors as columns,
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/// VR stands for the lapack real matrix output containing the right eigenvectors as columns)
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///
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/// If the j-th and (j+1)-th eigenvalues form a complex conjugate pair,
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/// then
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///
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/// u(j) = VL(:,j)+i*VL(:,j+1)
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/// u(j+1) = VL(:,j)-i*VL(:,j+1)
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///
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/// and
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///
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/// u(j) = VR(:,j)+i*VR(:,j+1)
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/// v(j+1) = VR(:,j)-i*VR(:,j+1).
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///
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pub fn eigenvectors(self) -> (OMatrix<Complex<T>, D, D>, OMatrix<Complex<T>, D, D>)
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pub fn eigenvectors(&self) -> (OMatrix<Complex<T>, D, D>, OMatrix<Complex<T>, D, D>)
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where
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DefaultAllocator:
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Allocator<Complex<T>, D, D> + Allocator<Complex<T>, D> + Allocator<(Complex<T>, T), D>,
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{
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/*
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How the eigenvectors are built up:
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Since the input entries are all real, the generalized eigenvalues if complex come in pairs
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as a consequence of the [complex conjugate root thorem](https://en.wikipedia.org/wiki/Complex_conjugate_root_theorem)
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The Lapack routine output reflects this by expecting the user to unpack the complex eigenvalues associated
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eigenvectors from the real matrix output via the following procedure
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(Note: VL stands for the lapack real matrix output containing the left eigenvectors as columns,
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VR stands for the lapack real matrix output containing the right eigenvectors as columns)
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If the j-th and (j+1)-th eigenvalues form a complex conjugate pair,
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then
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u(j) = VL(:,j)+i*VL(:,j+1)
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u(j+1) = VL(:,j)-i*VL(:,j+1)
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and
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u(j) = VR(:,j)+i*VR(:,j+1)
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v(j+1) = VR(:,j)-i*VR(:,j+1).
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*/
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let n = self.vsl.shape().0;
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let mut l = self
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.vsl
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.clone()
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.map(|x| Complex::new(x, T::RealField::zero()));
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let mut r = self
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.vsr
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.clone()
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.map(|x| Complex::new(x, T::RealField::zero()));
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let eigenvalues = &self.raw_eigenvalues();
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let eigenvalues = self.raw_eigenvalues();
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let mut c = 0;
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