_HQR2(3F)_HQR2(3F)NAME
HQR2, SHQR2 - EISPACK routine. This subroutine finds the eigenvalues
and eigenvectors of a REAL UPPER Hessenberg matrix by the QR method. The
eigenvectors of a REAL GENERAL matrix can also be found if ELMHES and
ELTRAN or ORTHES and ORTRAN have been used to reduce this general
matrix to Hessenberg form and to accumulate the similarity
transformations.
SYNOPSYS
subroutine hqr2(nm, n, low, igh, h, wr, wi, z, ierr)
integer nm, n, low, igh, ierr
double precision h(nm,n), wr(n), wi(n), z(nm,n)
subroutine shqr2(nm, n, low, igh, h, wr, wi, z, ierr)
integer nm, n, low, igh, ierr
real h(nm,n), wr(n), wi(n), z(nm,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.
Z contains the transformation matrix produced by ELTRAN after the
reduction by ELMHES, or by ORTRAN after the reduction by ORTHES, if
performed. If the eigenvectors of the Hessenberg matrix are desired, Z
must contain the identity matrix. On OUTPUT
H has been destroyed.
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.
Z contains the real and imaginary parts of the eigenvectors. If the I-th
eigenvalue is real, the I-th column of Z contains its eigenvector. If
the I-th eigenvalue is complex with positive imaginary part, the I-th and
(I+1)-th columns of Z contain the real and imaginary parts of its
eigenvector. The eigenvectors are unnormalized. If an error exit is
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_HQR2(3F)_HQR2(3F)
made, none of the eigenvectors has been found.
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. Calls CDIV for complex
division. Questions and comments should be directed to B. S. Garbow,
APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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