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< h1 id = "eigensolvers" > eigensolvers< a class = "headerlink" href = "#eigensolvers" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > Solvers for eigenvalue / eigenvector problems< / p >
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< div class = "doc-signature highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "nf" > power_iteration< / span > < span class = "p" > (< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "n" > operator< / span > < span class = "p" > :< / span > < span class = "n" > spmatrix< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > guess_vector< / span > < span class = "p" > :< / span > < span class = "n" > NDArray< / span > < span class = "p" > [< / span > < span class = "n" > complex128< / span > < span class = "p" > ]< / span > < span class = "o" > |< / span > < span class = "kc" > None< / span > < span class = "o" > =< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "n" > iterations< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "o" > =< / span > < span class = "mi" > 20< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > tuple< / span > < span class = "p" > [< / span > < span class = "nb" > complex< / span > < span class = "p" > ,< / span > < span class = "n" > NDArray< / span > < span class = "p" > [< / span > < span class = "n" > numpy< / span > < span class = "o" > .< / span > < span class = "n" > complex128< / span > < span class = "p" > ]]< / span >
< / code > < / pre > < / div >
< div class = "doc doc-contents " >
< p > Use power iteration to estimate the dominant eigenvector of a matrix.< / p >
< p > < span class = "doc-section-title" > Parameters:< / span > < / p >
< table >
< thead >
< tr >
< th > Name< / th >
< th > Type< / th >
< th > Description< / th >
< th > Default< / th >
< / tr >
< / thead >
< tbody >
< tr class = "doc-section-item" >
< td >
< code > operator< / code >
< / td >
< td >
< code > < span title = "scipy.sparse.spmatrix" > spmatrix< / span > < / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Matrix to analyze.< / p >
< / div >
< / td >
< td >
< em > required< / em >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > guess_vector< / code >
< / td >
< td >
< code > < span title = "numpy.typing.NDArray" > NDArray< / span > [< span title = "numpy.complex128" > complex128< / span > ] | None< / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Starting point for the eigenvector. Default is a randomly chosen vector.< / p >
< / div >
< / td >
< td >
< code > None< / code >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > iterations< / code >
< / td >
< td >
< code > < span title = "int" > int< / span > < / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Number of iterations to perform. Default 20.< / p >
< / div >
< / td >
< td >
< code > 20< / code >
< / td >
< / tr >
< / tbody >
< / table >
< p > < span class = "doc-section-title" > Returns:< / span > < / p >
< table >
< thead >
< tr >
< th > Type< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr class = "doc-section-item" >
< td >
< code > < span title = "tuple" > tuple< / span > [< span title = "complex" > complex< / span > , < span title = "numpy.typing.NDArray" > NDArray< / span > [< span title = "numpy.complex128" > complex128< / span > ]]< / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > (Largest-magnitude eigenvalue, Corresponding eigenvector estimate)< / p >
< / div >
< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
< div class = "doc doc-object doc-function" >
< h3 id = "meanas.eigensolvers.rayleigh_quotient_iteration" class = "doc doc-heading" >
< code class = "doc-symbol doc-symbol-heading doc-symbol-function" > < / code > < span class = "doc doc-object-name doc-function-name" > rayleigh_quotient_iteration< / span >
< a href = "#meanas.eigensolvers.rayleigh_quotient_iteration" class = "headerlink" title = "Permanent link" > ¶ < / a > < / h3 >
< div class = "doc-signature highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "nf" > rayleigh_quotient_iteration< / span > < span class = "p" > (< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "n" > operator< / span > < span class = "p" > :< / span > < span class = "n" > spmatrix< / span > < span class = "o" > |< / span > < span class = "n" > LinearOperator< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > guess_vector< / span > < span class = "p" > :< / span > < span class = "n" > NDArray< / span > < span class = "p" > [< / span > < span class = "n" > complex128< / span > < span class = "p" > ],< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "n" > iterations< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "o" > =< / span > < span class = "mi" > 40< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "n" > tolerance< / span > < span class = "p" > :< / span > < span class = "nb" > float< / span > < span class = "o" > =< / span > < span class = "mf" > 1e-13< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "n" > solver< / span > < span class = "p" > :< / span > < span class = "n" > Callable< / span > < span class = "p" > [< / span > < span class = "o" > ...< / span > < span class = "p" > ,< / span > < span class = "n" > NDArray< / span > < span class = "p" > [< / span > < span class = "n" > complex128< / span > < span class = "p" > ]]< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "o" > |< / span > < span class = "kc" > None< / span > < span class = "o" > =< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > tuple< / span > < span class = "p" > [< / span > < span class = "nb" > complex< / span > < span class = "p" > ,< / span > < span class = "n" > NDArray< / span > < span class = "p" > [< / span > < span class = "n" > numpy< / span > < span class = "o" > .< / span > < span class = "n" > complex128< / span > < span class = "p" > ]]< / span >
< / code > < / pre > < / div >
< div class = "doc doc-contents " >
< p > Use Rayleigh quotient iteration to refine an eigenvector guess.< / p >
< p > < span class = "doc-section-title" > Parameters:< / span > < / p >
< table >
< thead >
< tr >
< th > Name< / th >
< th > Type< / th >
< th > Description< / th >
< th > Default< / th >
< / tr >
< / thead >
< tbody >
< tr class = "doc-section-item" >
< td >
< code > operator< / code >
< / td >
< td >
< code > < span title = "scipy.sparse.spmatrix" > spmatrix< / span > | < span title = "scipy.sparse.linalg.LinearOperator" > LinearOperator< / span > < / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Matrix to analyze.< / p >
< / div >
< / td >
< td >
< em > required< / em >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > guess_vector< / code >
< / td >
< td >
< code > < span title = "numpy.typing.NDArray" > NDArray< / span > [< span title = "numpy.complex128" > complex128< / span > ]< / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Eigenvector to refine.< / p >
< / div >
< / td >
< td >
< em > required< / em >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > iterations< / code >
< / td >
< td >
< code > < span title = "int" > int< / span > < / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Maximum number of iterations to perform. Default 40.< / p >
< / div >
< / td >
< td >
< code > 40< / code >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > tolerance< / code >
< / td >
< td >
< code > < span title = "float" > float< / span > < / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Stop iteration if < code > (A - I*eigenvalue) @ v < num_vectors * tolerance< / code > ,
Default 1e-13.< / p >
< / div >
< / td >
< td >
< code > 1e-13< / code >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > solver< / code >
< / td >
< td >
< code > < span title = "collections.abc.Callable" > Callable< / span > [..., < span title = "numpy.typing.NDArray" > NDArray< / span > [< span title = "numpy.complex128" > complex128< / span > ]] | None< / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Solver function of the form < code > x = solver(A, b)< / code > .
By default, use scipy.sparse.spsolve for sparse matrices and
scipy.sparse.bicgstab for general LinearOperator instances.< / p >
< / div >
< / td >
< td >
< code > None< / code >
< / td >
< / tr >
< / tbody >
< / table >
< p > < span class = "doc-section-title" > Returns:< / span > < / p >
< table >
< thead >
< tr >
< th > Type< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr class = "doc-section-item" >
< td >
< code > < span title = "tuple" > tuple< / span > [< span title = "complex" > complex< / span > , < span title = "numpy.typing.NDArray" > NDArray< / span > [< span title = "numpy.complex128" > complex128< / span > ]]< / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > (eigenvalues, eigenvectors)< / p >
< / div >
< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
< div class = "doc doc-object doc-function" >
< h3 id = "meanas.eigensolvers.signed_eigensolve" class = "doc doc-heading" >
< code class = "doc-symbol doc-symbol-heading doc-symbol-function" > < / code > < span class = "doc doc-object-name doc-function-name" > signed_eigensolve< / span >
< a href = "#meanas.eigensolvers.signed_eigensolve" class = "headerlink" title = "Permanent link" > ¶ < / a > < / h3 >
< div class = "doc-signature highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "nf" > signed_eigensolve< / span > < span class = "p" > (< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "n" > operator< / span > < span class = "p" > :< / span > < span class = "n" > spmatrix< / span > < span class = "o" > |< / span > < span class = "n" > LinearOperator< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "n" > how_many< / span > < span class = "p" > :< / span > < span class = "nb" > int< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "n" > negative< / span > < span class = "p" > :< / span > < span class = "nb" > bool< / span > < span class = "o" > =< / span > < span class = "kc" > False< / span > < span class = "p" > ,< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > tuple< / span > < span class = "p" > [< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "n" > NDArray< / span > < span class = "p" > [< / span > < span class = "n" > numpy< / span > < span class = "o" > .< / span > < span class = "n" > complex128< / span > < span class = "p" > ],< / span > < span class = "n" > NDArray< / span > < span class = "p" > [< / span > < span class = "n" > numpy< / span > < span class = "o" > .< / span > < span class = "n" > complex128< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "p" > ]< / span >
< / code > < / pre > < / div >
< div class = "doc doc-contents " >
< p > Find the largest-magnitude positive-only (or negative-only) eigenvalues and
eigenvectors of the provided matrix.< / p >
< p > < span class = "doc-section-title" > Parameters:< / span > < / p >
< table >
< thead >
< tr >
< th > Name< / th >
< th > Type< / th >
< th > Description< / th >
< th > Default< / th >
< / tr >
< / thead >
< tbody >
< tr class = "doc-section-item" >
< td >
< code > operator< / code >
< / td >
< td >
< code > < span title = "scipy.sparse.spmatrix" > spmatrix< / span > | < span title = "scipy.sparse.linalg.LinearOperator" > LinearOperator< / span > < / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Matrix to analyze.< / p >
< / div >
< / td >
< td >
< em > required< / em >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > how_many< / code >
< / td >
< td >
< code > < span title = "int" > int< / span > < / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > How many eigenvalues to find.< / p >
< / div >
< / td >
< td >
< em > required< / em >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > negative< / code >
< / td >
< td >
< code > < span title = "bool" > bool< / span > < / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > Whether to find negative-only eigenvalues.
Default False (positive only).< / p >
< / div >
< / td >
< td >
< code > False< / code >
< / td >
< / tr >
< / tbody >
< / table >
< p > < span class = "doc-section-title" > Returns:< / span > < / p >
< table >
< thead >
< tr >
< th > Type< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr class = "doc-section-item" >
< td >
< code > < span title = "numpy.typing.NDArray" > NDArray< / span > [< span title = "numpy.complex128" > complex128< / span > ]< / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > (sorted list of eigenvalues, 2D ndarray of corresponding eigenvectors)< / p >
< / div >
< / td >
< / tr >
< tr class = "doc-section-item" >
< td >
< code > < span title = "numpy.typing.NDArray" > NDArray< / span > [< span title = "numpy.complex128" > complex128< / span > ]< / code >
< / td >
< td >
< div class = "doc-md-description" >
< p > < code > eigenvectors[:, k]< / code > corresponds to the k-th eigenvalue< / p >
< / div >
< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
< / div >
< / div >
< / div >
< / article >
< / div >
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