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Merge pull request #388 from fabianp/arpack_doc

DOC: clarification on the `which` parameter of ARPACK.
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2 parents d631749 + 2d9a5f0 commit a7c0e1ec470a85893fccb9c835947790808bb828 @jakevdp jakevdp committed Dec 21, 2012
Showing with 13 additions and 9 deletions.
  1. +13 −9 doc/source/tutorial/arpack.rst
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22 doc/source/tutorial/arpack.rst
@@ -40,15 +40,19 @@ The power of ARPACK is that it can compute only a specified subset of
eigenvalue/eigenvector pairs. This is accomplished through the keyword
``which``. The following values of ``which`` are available:
-* ``which = 'LM'`` : Eigenvectors with largest magnitude (``eigs``, ``eigsh``)
-* ``which = 'SM'`` : Eigenvectors with smallest magnitude (``eigs``, ``eigsh``)
-* ``which = 'LR'`` : Eigenvectors with largest real part (``eigs``)
-* ``which = 'SR'`` : Eigenvectors with smallest real part (``eigs``)
-* ``which = 'LI'`` : Eigenvectors with largest imaginary part (``eigs``)
-* ``which = 'SI'`` : Eigenvectors with smallest imaginary part (``eigs``)
-* ``which = 'LA'`` : Eigenvectors with largest amplitude (``eigsh``)
-* ``which = 'SA'`` : Eigenvectors with smallest amplitude (``eigsh``)
-* ``which = 'BE'`` : Eigenvectors from both ends of the spectrum (``eigsh``)
+* ``which = 'LM'`` : Eigenvalues with largest magnitude (``eigs``, ``eigsh``),
+ that is, largest eigenvalues in the euclidean norm of complex numbers.
+* ``which = 'SM'`` : Eigenvalues with smallest magnitude (``eigs``, ``eigsh``),
+ that is, smallest eigenvalues in the euclidean norm of complex numbers.
+* ``which = 'LR'`` : Eigenvalues with largest real part (``eigs``)
+* ``which = 'SR'`` : Eigenvalues with smallest real part (``eigs``)
+* ``which = 'LI'`` : Eigenvalues with largest imaginary part (``eigs``)
+* ``which = 'SI'`` : Eigenvalues with smallest imaginary part (``eigs``)
+* ``which = 'LA'`` : Eigenvalues with largest algebraic value (``eigsh``),
+ that is, largest eigenvalues inclusive of any negative sign.
+* ``which = 'SA'`` : Eigenvalues with smallest algebraic value (``eigsh``),
+ that is, smallest eigenvalues inclusive of any negative sign.
+* ``which = 'BE'`` : Eigenvalues from both ends of the spectrum (``eigsh``)
Note that ARPACK is generally better at finding extremal eigenvalues: that
is, eigenvalues with large magnitudes. In particular, using ``which = 'SM'``

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