_TINVIT(3F)_TINVIT(3F)NAME
TINVIT, STINVIT - EISPACK routine. This subroutine finds those
eigenvectors of a TRIDIAGONAL SYMMETRIC matrix corresponding to specified
eigenvalues, using inverse iteration.
SYNOPSYS
subroutine tinvit(nm,n,d,e,e2,m,w,ind,z,ierr,rv1,rv2,rv3,rv4,rv6)
integer nm, n, m, ierr, ind(m)
double precision d(n), e(n), e2(n), w(m), z(nm,m)
double precision rv1(n), rv2(n), rv3(n), rv4(n), rv6(n)
subroutine stinvit(nm,n,d,e,e2,m,w,ind,z,ierr,rv1,rv2,rv3,rv4,rv6)
integer nm, n, m, ierr, ind(m)
real d(n), e(n), e2(n), w(m), z(nm,m)
real rv1(n), rv2(n), rv3(n), rv4(n), rv6(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.
D contains the diagonal elements of the input matrix.
E contains the subdiagonal elements of the input matrix in its last N-1
positions. E(1) is arbitrary.
E2 contains the squares of the corresponding elements of E, with zeros
corresponding to negligible elements of E. E(I) is considered negligible
if it is not larger than the product of the relative machine precision
and the sum of the magnitudes of D(I) and D(I-1). E2(1) must contain
0.0e0 if the eigenvalues are in ascending order, or 2.0e0 if the
eigenvalues are in descending order. If BISECT, TRIDIB, or IMTQLV has
been used to find the eigenvalues, their output E2 array is exactly what
is expected here.
M is the number of specified eigenvalues.
W CONTAINS the M eigenvalues in ascending or descending order.
IND contains in its first M positions the submatrix indices associated
with the corresponding eigenvalues in W -- 1 for eigenvalues belonging to
the first submatrix from the top, 2 for those belonging to the second
submatrix, etc. On Output
Z contains the associated set of orthonormal eigenvectors. any vector
which fails to converge is set to zero.
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_TINVIT(3F)_TINVIT(3F)
IERR is set to Zero for normal return, -R if the
eigenvector corresponding to the R-th
eigenvalue fails to converge in 5 iterations.
RV1 , RV2, RV3, RV4, and RV6 are temporary storage arrays. Questions and
comments should be directed to B. S. Garbow, APPLIED MATHEMATICS
DIVISION, ARGONNE NATIONAL LABORATORY
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