LAEBZ: contains the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w. It performs a choice of two types of loops: IJOB=1, followed by IJOB=2: It takes as input a list of intervals and returns a list of sufficiently small intervals whose union contains the same eigenvalues as the union of the original intervals. The input intervals are (AB(j,1),AB(j,2)], j=1,...,MINP. The output interval (AB(j,1),AB(j,2)] will contain eigenvalues NAB(j,1)+1,...,NAB(j,2), where 1 <= j <= MOUT. IJOB=3: It performs a binary search in each input interval (AB(j,1),AB(j,2)] for a point w(j) such that N(w(j))=NVAL(j), and uses C(j) as the starting point of the search. If such a w(j) is found, then on output AB(j,1)=AB(j,2)=w. If no such w(j) is found, then on output (AB(j,1),AB(j,2)] will be a small interval containing the point where N(w) jumps through NVAL(j), unless that point lies outside the initial interval. Note that the intervals are in all cases half-open intervals, i.e., of the form (a,b] , which includes b but not a . To avoid underflow, the matrix should be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value. To assure the most accurate computation of small eigenvalues, the matrix should be scaled to be not much smaller than that, either. See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford University, July 21, 1966 Note: the arguments are, in general, not checked for unreasonable values.
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| pure subroutine | dlaebz (ijob, nitmax, n, mmax, minp, nbmin, abstol, reltol, pivmin, d, e, e2, nval, ab, c, mout, nab, work, iwork, info) |
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| | la_dlaebz |
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| | la_qlaebz |
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| pure subroutine | slaebz (ijob, nitmax, n, mmax, minp, nbmin, abstol, reltol, pivmin, d, e, e2, nval, ab, c, mout, nab, work, iwork, info) |
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| | la_slaebz |
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LAEBZ: contains the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w. It performs a choice of two types of loops: IJOB=1, followed by IJOB=2: It takes as input a list of intervals and returns a list of sufficiently small intervals whose union contains the same eigenvalues as the union of the original intervals. The input intervals are (AB(j,1),AB(j,2)], j=1,...,MINP. The output interval (AB(j,1),AB(j,2)] will contain eigenvalues NAB(j,1)+1,...,NAB(j,2), where 1 <= j <= MOUT. IJOB=3: It performs a binary search in each input interval (AB(j,1),AB(j,2)] for a point w(j) such that N(w(j))=NVAL(j), and uses C(j) as the starting point of the search. If such a w(j) is found, then on output AB(j,1)=AB(j,2)=w. If no such w(j) is found, then on output (AB(j,1),AB(j,2)] will be a small interval containing the point where N(w) jumps through NVAL(j), unless that point lies outside the initial interval. Note that the intervals are in all cases half-open intervals, i.e., of the form (a,b] , which includes b but not a . To avoid underflow, the matrix should be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value. To assure the most accurate computation of small eigenvalues, the matrix should be scaled to be not much smaller than that, either. See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford University, July 21, 1966 Note: the arguments are, in general, not checked for unreasonable values.
◆ dlaebz()
| pure subroutine la_lapack::laebz::dlaebz |
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integer(ilp), intent(in) |
ijob, |
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integer(ilp), intent(in) |
nitmax, |
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integer(ilp), intent(in) |
n, |
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integer(ilp), intent(in) |
mmax, |
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integer(ilp), intent(in) |
minp, |
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integer(ilp), intent(in) |
nbmin, |
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real(dp), intent(in) |
abstol, |
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real(dp), intent(in) |
reltol, |
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real(dp), intent(in) |
pivmin, |
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real(dp), dimension(*), intent(in) |
d, |
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real(dp), dimension(*), intent(in) |
e, |
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real(dp), dimension(*), intent(in) |
e2, |
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integer(ilp), dimension(*), intent(inout) |
nval, |
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real(dp), dimension(mmax,*), intent(inout) |
ab, |
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real(dp), dimension(*), intent(inout) |
c, |
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integer(ilp), intent(out) |
mout, |
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integer(ilp), dimension(mmax,*), intent(inout) |
nab, |
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real(dp), dimension(*), intent(out) |
work, |
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integer(ilp), dimension(*), intent(out) |
iwork, |
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integer(ilp), intent(out) |
info |
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) |
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◆ la_dlaebz()
| la_lapack::laebz::la_dlaebz |
◆ la_qlaebz()
| la_lapack::laebz::la_qlaebz |
◆ la_slaebz()
| la_lapack::laebz::la_slaebz |
◆ slaebz()
| pure subroutine la_lapack::laebz::slaebz |
( |
integer(ilp), intent(in) |
ijob, |
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integer(ilp), intent(in) |
nitmax, |
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integer(ilp), intent(in) |
n, |
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integer(ilp), intent(in) |
mmax, |
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integer(ilp), intent(in) |
minp, |
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integer(ilp), intent(in) |
nbmin, |
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real(sp), intent(in) |
abstol, |
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real(sp), intent(in) |
reltol, |
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real(sp), intent(in) |
pivmin, |
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real(sp), dimension(*), intent(in) |
d, |
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real(sp), dimension(*), intent(in) |
e, |
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real(sp), dimension(*), intent(in) |
e2, |
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integer(ilp), dimension(*), intent(inout) |
nval, |
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real(sp), dimension(mmax,*), intent(inout) |
ab, |
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real(sp), dimension(*), intent(inout) |
c, |
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integer(ilp), intent(out) |
mout, |
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integer(ilp), dimension(mmax,*), intent(inout) |
nab, |
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real(sp), dimension(*), intent(out) |
work, |
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integer(ilp), dimension(*), intent(out) |
iwork, |
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integer(ilp), intent(out) |
info |
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) |
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The documentation for this interface was generated from the following file:
1.9.8