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.. tab :: Python
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- .. py :method :: Model.eigen(n, solver = " -genBandArpack " )
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-
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+ .. py :method :: Model.eigen(n, solver = " GenBandArpack " )
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+
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Perform an eigenvalue analysis and return a list of eigenvalues.
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:param n: number of eigenvalues required.
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:type n: |integer |
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- :param solver: optional string detailing type of solver: -genBandArpack, -symmBandLapack, -fullGenLapack (default: -genBandArpack ).
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+ :param solver: optional string detailing type of solver: `` GenBandArpack ``, `` SymmBandLapack ``, `` FullGenLapack `` (default: `` GenBandArpack `` ).
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:type solver: |string |
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- :returns: A |list | containing the eigenvalues
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+ :returns: A |list | containing `` n `` eigenvalues
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.. tab :: Tcl
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- .. function :: eigen <$solver> $numEigenvalues
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+ .. function :: eigen <$solver> $n
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.. csv-table ::
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:header: "Argument", "Type", "Description"
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:widths: 10, 10, 40
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- ``numEigenvalues ``, |integer |, number of eigenvalues required.
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+ ``n ``, |integer |, number of eigenvalues required.
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``solver ``, |string |, "optional string detailing type of solver: -genBandArpack, -symmBandLapack, -fullGenLapack (default: -genBandArpack)."
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.. note ::
@@ -41,12 +41,13 @@ Theory
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The *generalized eigenvalue problem * for two symmetric matrices :math: `\boldsymbol {K}` and :math: `M` of size :math: `n \times n` is given by:
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.. math ::
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- \left (\boldsymbol {K} - \lambda M \right ) \Phi = 0
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+
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+ \left ( \boldsymbol {K} - \lambda \boldsymbol {M} \right ) \Phi = 0
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where:
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* :math: `\boldsymbol {K}` is the stiffness matrix
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- * :math: `M ` is the mass matrix
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+ * :math: `\boldsymbol {M} ` is the mass matrix
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* :math: `\lambda ` is the eigenvalue
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* and :math: `\Phi ` is the associated eigenvector
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