Compute the eigenvalues and eigenvectors of a real symmetric matrix.
Usage
call EigValVecSym (ain, n, eval, evec, ul, k, exitstatus)
Parameters
ain: input, real(dp), dimension (n,n)- The input real symmetric matrix. By default, only the upper portion of the matrix is used.
n: input, integer(int32)- The rank of the matrix
ain. eval: output, real(dp), dimension (k)- The eigenvalues of
ain, sorted from largest to smallest. evec: output, real(dp), 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. ul: input, character, optional, default =U- If
Uthen the upper portion of the matrixainwill be used (default). IfLthen the lower portion of the matrixainwill be used. k: input, optional, integer(int32), default =n- The number of largest eigenvalues and corresponding eigenvectors to be output.
exitstatus: output, optional, integer(int32)- If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.
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.