_TSTURM(3F)_TSTURM(3F)NAME
TSTURM, STSTURM - EISPACK routine. This subroutine finds those
eigenvalues of a TRIDIAGONAL SYMMETRIC matrix which lie in a specified
interval and their associated eigenvectors, using bisection and inverse
iteration.
SYNOPSYS
subroutine tsturm(nm,n,eps1,d,e,e2,lb,ub,mm,m,w,z,ierr,rv1,rv2,
1 rv3,rv4,rv5,rv6)
integer nm, n, mm, m, ierr
double precision eps1, lb, ub
double precision d(n), e(n), e2(n), w(mm), z(nm, mm)
double precision rv1(n), rv2(n), rv3(n), rv4(n), rv5(n), rv6(n)
subroutine ststurm(nm,n,eps1,d,e,e2,lb,ub,mm,m,w,z,ierr,rv1,rv2,
1 rv3,rv4,rv5,rv6)
integer nm, n, mm, m, ierr
real eps1, lb, ub
real d(n), e(n), e2(n), w(mm), z(nm, mm)
real rv1(n), rv2(n), rv3(n), rv4(n), rv5(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.
EPS1 is an absolute error tolerance for the computed eigenvalues. It
should be chosen commensurate with relative perturbations in the matrix
elements of the order of the relative machine precision. If the input
EPS1 is non-positive, it is reset for each submatrix to a default value,
namely, minus the product of the relative machine precision and the 1-
norm of the submatrix.
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. E2(1) is
arbitrary.
LB and UB define the interval to be searched for eigenvalues. If LB is
not less than UB, no eigenvalues will be found.
MM should be set to an upper bound for the number of eigenvalues in the
interval. WARNING. If more than MM eigenvalues are determined to lie in
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_TSTURM(3F)_TSTURM(3F)
the interval, an error return is made with no values or vectors found.
On Output
EPS1 is unaltered unless it has been reset to its (last) default value.
D and E are unaltered. ELEMENTS of E2, corresponding to elements of E
regarded as negligible, have been replaced by zero causing the matrix to
split into a direct sum of submatrices. E2(1) is also set to zero.
M is the number of eigenvalues determined to lie in (LB,UB).
W contains the M eigenvalues in ascending order if the matrix does not
split. If the matrix splits, the eigenvalues are in ascending order for
each submatrix. If a vector error exit is made, W contains those values
already found.
Z contains the associated set of orthonormal eigenvectors. If an error
exit is made, Z contains those vectors already found.
IERR is set to Zero for normal return, 3*N+1 if M exceeds MM.
4*N+R if the eigenvector corresponding to the R-th
eigenvalue fails to converge in 5 iterations.
RV1 , RV2, RV3, RV4, RV5, and RV6 are temporary storage arrays. The ALGOL
procedure STURMCNT contained in TRISTURM appears in TSTURM in-line.
Questions and comments should be directed to B. S. Garbow, APPLIED
MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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