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EigValVecSym
Compute the eigenvalues and eigenvectors of a real symmetric matrix.
Usage
eval
, evec
= pyshtools.EigValVecSym (ain
, [n
, ul
, k
])
Returns
eval
: float, dimension (k
)- The eigenvalues of
ain
, sorted from largest to smallest. evec
: float, dimension (n
,k
)- The eigenvectors of
ain
, sorted from largest to smallest eigenvalues. The sign of the first element of each eigenvector is chosen to be positive.
Parameters
ain
: float, dimension (nin
,nin
)- The input real symmetric matrix. By default, only the upper portion of the matrix is used.
n
: optional, integer, default =nin
- The rank of the matrix
ain
. ul
: optional, character, default =U
- If
U
then the upper portion of the matrixain
will be used (default). IfL
then the lower portion of the matrixain
will be used. k
: optional, optional, integer, default =nin
- The number of largest eigenvalues and corresponding eigenvectors to be output.
Description
EigValVecSym
will calculate the eigenvalues and eigenvectors of a real symmetric matrix. By default, only the upper portion of the matrix is used, but this can be changed by the optional argument ul
. The eigenvalues and eigenvectors are sorted from largest to smallest eigenvalues. If the optional parameter k
is specified, then only the k
largest eigenvalues and their corresponding eigenvectors will be output.
The matrix ain
is first factorized into a tridiagonal matrix using the LAPACK routine DSYTRD
, and then the eigenvalues are calculated by calls to DSTEGR
and DORMTR
.
See also
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