_HQR(3F)_HQR(3F)NAME
HQR, SHQR - EISPACK routine. This subroutine finds the eigenvalues of
a REAL UPPER Hessenberg matrix by the QR method.
SYNOPSYS
subroutine hqr(nm, n, low, igh, h, wr, wi, ierr)
integer nm, n, low, igh, ierr
double precision h(nm,n), wr(n), wi(n)
subroutine shqr(nm, n, low, igh, h, wr, wi, ierr)
integer nm, n, low, igh, ierr
real h(nm,n), wr(n), wi(n)DESCRIPTION
On INPUT
NM must be set to the row dimension of two-dimensional array parameters
as declared in the calling program dimension statement.
N is the order of the matrix.
LOW and IGH are integers determined by the balancing subroutine BALANC.
If BALANC has not been used, set LOW=1, IGH=N.
H contains the upper Hessenberg matrix. Information about the
transformations used in the reduction to Hessenberg form by ELMHES or
ORTHES, if performed, is stored in the remaining triangle under the
Hessenberg matrix. On OUTPUT
H has been destroyed. Therefore, it must be saved before calling HQR
if subsequent calculation and back transformation of eigenvectors is to
be performed.
WR and WI contain the real and imaginary parts, respectively, of the
eigenvalues. The eigenvalues are unordered except that complex conjugate
pairs of values appear consecutively with the eigenvalue having the
positive imaginary part first. If an error exit is made, the eigenvalues
should be correct for indices IERR+1,...,N.
IERR is set to Zero for normal return, J if the J-th
eigenvalue has not been
determined after a total of 30*N iterations. Questions and comments
should be directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE
NATIONAL LABORATORY
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