650 lines
22 KiB
Fortran
650 lines
22 KiB
Fortran
*> \brief \b SLAEBZ computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than or equal to a given value, and performs other tasks required by the routine sstebz.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SLAEBZ + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaebz.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaebz.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaebz.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL,
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* RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT,
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* NAB, WORK, IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER IJOB, INFO, MINP, MMAX, MOUT, N, NBMIN, NITMAX
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* REAL ABSTOL, PIVMIN, RELTOL
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * ), NAB( MMAX, * ), NVAL( * )
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* REAL AB( MMAX, * ), C( * ), D( * ), E( * ), E2( * ),
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* $ WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SLAEBZ contains the iteration loops which compute and use the
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*> function N(w), which is the count of eigenvalues of a symmetric
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*> tridiagonal matrix T less than or equal to its argument w. It
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*> performs a choice of two types of loops:
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*>
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*> IJOB=1, followed by
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*> IJOB=2: It takes as input a list of intervals and returns a list of
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*> sufficiently small intervals whose union contains the same
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*> eigenvalues as the union of the original intervals.
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*> The input intervals are (AB(j,1),AB(j,2)], j=1,...,MINP.
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*> The output interval (AB(j,1),AB(j,2)] will contain
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*> eigenvalues NAB(j,1)+1,...,NAB(j,2), where 1 <= j <= MOUT.
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*>
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*> IJOB=3: It performs a binary search in each input interval
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*> (AB(j,1),AB(j,2)] for a point w(j) such that
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*> N(w(j))=NVAL(j), and uses C(j) as the starting point of
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*> the search. If such a w(j) is found, then on output
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*> AB(j,1)=AB(j,2)=w. If no such w(j) is found, then on output
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*> (AB(j,1),AB(j,2)] will be a small interval containing the
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*> point where N(w) jumps through NVAL(j), unless that point
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*> lies outside the initial interval.
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*>
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*> Note that the intervals are in all cases half-open intervals,
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*> i.e., of the form (a,b] , which includes b but not a .
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*>
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*> To avoid underflow, the matrix should be scaled so that its largest
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*> element is no greater than overflow**(1/2) * underflow**(1/4)
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*> in absolute value. To assure the most accurate computation
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*> of small eigenvalues, the matrix should be scaled to be
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*> not much smaller than that, either.
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*>
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*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
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*> Matrix", Report CS41, Computer Science Dept., Stanford
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*> University, July 21, 1966
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*>
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*> Note: the arguments are, in general, *not* checked for unreasonable
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*> values.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] IJOB
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*> \verbatim
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*> IJOB is INTEGER
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*> Specifies what is to be done:
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*> = 1: Compute NAB for the initial intervals.
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*> = 2: Perform bisection iteration to find eigenvalues of T.
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*> = 3: Perform bisection iteration to invert N(w), i.e.,
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*> to find a point which has a specified number of
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*> eigenvalues of T to its left.
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*> Other values will cause SLAEBZ to return with INFO=-1.
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*> \endverbatim
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*>
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*> \param[in] NITMAX
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*> \verbatim
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*> NITMAX is INTEGER
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*> The maximum number of "levels" of bisection to be
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*> performed, i.e., an interval of width W will not be made
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*> smaller than 2^(-NITMAX) * W. If not all intervals
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*> have converged after NITMAX iterations, then INFO is set
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*> to the number of non-converged intervals.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The dimension n of the tridiagonal matrix T. It must be at
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*> least 1.
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*> \endverbatim
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*>
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*> \param[in] MMAX
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*> \verbatim
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*> MMAX is INTEGER
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*> The maximum number of intervals. If more than MMAX intervals
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*> are generated, then SLAEBZ will quit with INFO=MMAX+1.
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*> \endverbatim
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*>
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*> \param[in] MINP
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*> \verbatim
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*> MINP is INTEGER
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*> The initial number of intervals. It may not be greater than
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*> MMAX.
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*> \endverbatim
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*>
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*> \param[in] NBMIN
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*> \verbatim
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*> NBMIN is INTEGER
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*> The smallest number of intervals that should be processed
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*> using a vector loop. If zero, then only the scalar loop
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*> will be used.
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*> \endverbatim
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*>
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*> \param[in] ABSTOL
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*> \verbatim
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*> ABSTOL is REAL
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*> The minimum (absolute) width of an interval. When an
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*> interval is narrower than ABSTOL, or than RELTOL times the
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*> larger (in magnitude) endpoint, then it is considered to be
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*> sufficiently small, i.e., converged. This must be at least
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*> zero.
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*> \endverbatim
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*>
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*> \param[in] RELTOL
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*> \verbatim
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*> RELTOL is REAL
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*> The minimum relative width of an interval. When an interval
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*> is narrower than ABSTOL, or than RELTOL times the larger (in
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*> magnitude) endpoint, then it is considered to be
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*> sufficiently small, i.e., converged. Note: this should
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*> always be at least radix*machine epsilon.
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*> \endverbatim
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*>
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*> \param[in] PIVMIN
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*> \verbatim
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*> PIVMIN is REAL
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*> The minimum absolute value of a "pivot" in the Sturm
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*> sequence loop.
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*> This must be at least max |e(j)**2|*safe_min and at
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*> least safe_min, where safe_min is at least
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*> the smallest number that can divide one without overflow.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is REAL array, dimension (N)
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*> The diagonal elements of the tridiagonal matrix T.
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is REAL array, dimension (N)
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*> The offdiagonal elements of the tridiagonal matrix T in
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*> positions 1 through N-1. E(N) is arbitrary.
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*> \endverbatim
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*>
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*> \param[in] E2
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*> \verbatim
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*> E2 is REAL array, dimension (N)
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*> The squares of the offdiagonal elements of the tridiagonal
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*> matrix T. E2(N) is ignored.
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*> \endverbatim
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*>
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*> \param[in,out] NVAL
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*> \verbatim
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*> NVAL is INTEGER array, dimension (MINP)
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*> If IJOB=1 or 2, not referenced.
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*> If IJOB=3, the desired values of N(w). The elements of NVAL
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*> will be reordered to correspond with the intervals in AB.
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*> Thus, NVAL(j) on output will not, in general be the same as
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*> NVAL(j) on input, but it will correspond with the interval
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*> (AB(j,1),AB(j,2)] on output.
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*> \endverbatim
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*>
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*> \param[in,out] AB
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*> \verbatim
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*> AB is REAL array, dimension (MMAX,2)
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*> The endpoints of the intervals. AB(j,1) is a(j), the left
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*> endpoint of the j-th interval, and AB(j,2) is b(j), the
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*> right endpoint of the j-th interval. The input intervals
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*> will, in general, be modified, split, and reordered by the
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*> calculation.
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*> \endverbatim
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*>
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*> \param[in,out] C
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*> \verbatim
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*> C is REAL array, dimension (MMAX)
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*> If IJOB=1, ignored.
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*> If IJOB=2, workspace.
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*> If IJOB=3, then on input C(j) should be initialized to the
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*> first search point in the binary search.
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*> \endverbatim
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*>
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*> \param[out] MOUT
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*> \verbatim
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*> MOUT is INTEGER
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*> If IJOB=1, the number of eigenvalues in the intervals.
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*> If IJOB=2 or 3, the number of intervals output.
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*> If IJOB=3, MOUT will equal MINP.
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*> \endverbatim
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*>
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*> \param[in,out] NAB
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*> \verbatim
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*> NAB is INTEGER array, dimension (MMAX,2)
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*> If IJOB=1, then on output NAB(i,j) will be set to N(AB(i,j)).
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*> If IJOB=2, then on input, NAB(i,j) should be set. It must
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*> satisfy the condition:
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*> N(AB(i,1)) <= NAB(i,1) <= NAB(i,2) <= N(AB(i,2)),
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*> which means that in interval i only eigenvalues
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*> NAB(i,1)+1,...,NAB(i,2) will be considered. Usually,
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*> NAB(i,j)=N(AB(i,j)), from a previous call to SLAEBZ with
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*> IJOB=1.
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*> On output, NAB(i,j) will contain
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*> max(na(k),min(nb(k),N(AB(i,j)))), where k is the index of
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*> the input interval that the output interval
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*> (AB(j,1),AB(j,2)] came from, and na(k) and nb(k) are the
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*> the input values of NAB(k,1) and NAB(k,2).
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*> If IJOB=3, then on output, NAB(i,j) contains N(AB(i,j)),
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*> unless N(w) > NVAL(i) for all search points w , in which
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*> case NAB(i,1) will not be modified, i.e., the output
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*> value will be the same as the input value (modulo
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*> reorderings -- see NVAL and AB), or unless N(w) < NVAL(i)
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*> for all search points w , in which case NAB(i,2) will
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*> not be modified. Normally, NAB should be set to some
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*> distinctive value(s) before SLAEBZ is called.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (MMAX)
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*> Workspace.
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (MMAX)
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*> Workspace.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: All intervals converged.
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*> = 1--MMAX: The last INFO intervals did not converge.
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*> = MMAX+1: More than MMAX intervals were generated.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date September 2012
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*
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*> \ingroup auxOTHERauxiliary
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> This routine is intended to be called only by other LAPACK
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*> routines, thus the interface is less user-friendly. It is intended
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*> for two purposes:
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*>
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*> (a) finding eigenvalues. In this case, SLAEBZ should have one or
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*> more initial intervals set up in AB, and SLAEBZ should be called
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*> with IJOB=1. This sets up NAB, and also counts the eigenvalues.
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*> Intervals with no eigenvalues would usually be thrown out at
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*> this point. Also, if not all the eigenvalues in an interval i
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*> are desired, NAB(i,1) can be increased or NAB(i,2) decreased.
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*> For example, set NAB(i,1)=NAB(i,2)-1 to get the largest
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*> eigenvalue. SLAEBZ is then called with IJOB=2 and MMAX
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*> no smaller than the value of MOUT returned by the call with
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*> IJOB=1. After this (IJOB=2) call, eigenvalues NAB(i,1)+1
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*> through NAB(i,2) are approximately AB(i,1) (or AB(i,2)) to the
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*> tolerance specified by ABSTOL and RELTOL.
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*>
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*> (b) finding an interval (a',b'] containing eigenvalues w(f),...,w(l).
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*> In this case, start with a Gershgorin interval (a,b). Set up
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*> AB to contain 2 search intervals, both initially (a,b). One
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*> NVAL element should contain f-1 and the other should contain l
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*> , while C should contain a and b, resp. NAB(i,1) should be -1
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*> and NAB(i,2) should be N+1, to flag an error if the desired
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*> interval does not lie in (a,b). SLAEBZ is then called with
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*> IJOB=3. On exit, if w(f-1) < w(f), then one of the intervals --
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*> j -- will have AB(j,1)=AB(j,2) and NAB(j,1)=NAB(j,2)=f-1, while
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*> if, to the specified tolerance, w(f-k)=...=w(f+r), k > 0 and r
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*> >= 0, then the interval will have N(AB(j,1))=NAB(j,1)=f-k and
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*> N(AB(j,2))=NAB(j,2)=f+r. The cases w(l) < w(l+1) and
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*> w(l-r)=...=w(l+k) are handled similarly.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE SLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL,
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$ RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT,
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$ NAB, WORK, IWORK, INFO )
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*
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* -- LAPACK auxiliary routine (version 3.4.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* September 2012
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*
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* .. Scalar Arguments ..
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INTEGER IJOB, INFO, MINP, MMAX, MOUT, N, NBMIN, NITMAX
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REAL ABSTOL, PIVMIN, RELTOL
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * ), NAB( MMAX, * ), NVAL( * )
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REAL AB( MMAX, * ), C( * ), D( * ), E( * ), E2( * ),
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$ WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, TWO, HALF
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PARAMETER ( ZERO = 0.0E0, TWO = 2.0E0,
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$ HALF = 1.0E0 / TWO )
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* ..
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* .. Local Scalars ..
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INTEGER ITMP1, ITMP2, J, JI, JIT, JP, KF, KFNEW, KL,
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$ KLNEW
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REAL TMP1, TMP2
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Check for Errors
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*
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INFO = 0
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IF( IJOB.LT.1 .OR. IJOB.GT.3 ) THEN
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INFO = -1
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RETURN
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END IF
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*
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* Initialize NAB
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*
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IF( IJOB.EQ.1 ) THEN
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*
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* Compute the number of eigenvalues in the initial intervals.
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*
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MOUT = 0
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DO 30 JI = 1, MINP
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DO 20 JP = 1, 2
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TMP1 = D( 1 ) - AB( JI, JP )
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IF( ABS( TMP1 ).LT.PIVMIN )
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$ TMP1 = -PIVMIN
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NAB( JI, JP ) = 0
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IF( TMP1.LE.ZERO )
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$ NAB( JI, JP ) = 1
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*
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DO 10 J = 2, N
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TMP1 = D( J ) - E2( J-1 ) / TMP1 - AB( JI, JP )
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IF( ABS( TMP1 ).LT.PIVMIN )
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$ TMP1 = -PIVMIN
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IF( TMP1.LE.ZERO )
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$ NAB( JI, JP ) = NAB( JI, JP ) + 1
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10 CONTINUE
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20 CONTINUE
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MOUT = MOUT + NAB( JI, 2 ) - NAB( JI, 1 )
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30 CONTINUE
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RETURN
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END IF
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*
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* Initialize for loop
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*
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* KF and KL have the following meaning:
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* Intervals 1,...,KF-1 have converged.
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* Intervals KF,...,KL still need to be refined.
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*
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KF = 1
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KL = MINP
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*
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* If IJOB=2, initialize C.
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* If IJOB=3, use the user-supplied starting point.
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*
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IF( IJOB.EQ.2 ) THEN
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DO 40 JI = 1, MINP
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C( JI ) = HALF*( AB( JI, 1 )+AB( JI, 2 ) )
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40 CONTINUE
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END IF
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*
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* Iteration loop
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*
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DO 130 JIT = 1, NITMAX
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*
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* Loop over intervals
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*
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IF( KL-KF+1.GE.NBMIN .AND. NBMIN.GT.0 ) THEN
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*
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* Begin of Parallel Version of the loop
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*
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DO 60 JI = KF, KL
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*
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* Compute N(c), the number of eigenvalues less than c
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*
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WORK( JI ) = D( 1 ) - C( JI )
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IWORK( JI ) = 0
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IF( WORK( JI ).LE.PIVMIN ) THEN
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IWORK( JI ) = 1
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WORK( JI ) = MIN( WORK( JI ), -PIVMIN )
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END IF
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*
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DO 50 J = 2, N
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WORK( JI ) = D( J ) - E2( J-1 ) / WORK( JI ) - C( JI )
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IF( WORK( JI ).LE.PIVMIN ) THEN
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IWORK( JI ) = IWORK( JI ) + 1
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WORK( JI ) = MIN( WORK( JI ), -PIVMIN )
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END IF
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50 CONTINUE
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60 CONTINUE
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*
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IF( IJOB.LE.2 ) THEN
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*
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* IJOB=2: Choose all intervals containing eigenvalues.
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*
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KLNEW = KL
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DO 70 JI = KF, KL
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*
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* Insure that N(w) is monotone
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*
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IWORK( JI ) = MIN( NAB( JI, 2 ),
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$ MAX( NAB( JI, 1 ), IWORK( JI ) ) )
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*
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* Update the Queue -- add intervals if both halves
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* contain eigenvalues.
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*
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IF( IWORK( JI ).EQ.NAB( JI, 2 ) ) THEN
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*
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* No eigenvalue in the upper interval:
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* just use the lower interval.
|
|
*
|
|
AB( JI, 2 ) = C( JI )
|
|
*
|
|
ELSE IF( IWORK( JI ).EQ.NAB( JI, 1 ) ) THEN
|
|
*
|
|
* No eigenvalue in the lower interval:
|
|
* just use the upper interval.
|
|
*
|
|
AB( JI, 1 ) = C( JI )
|
|
ELSE
|
|
KLNEW = KLNEW + 1
|
|
IF( KLNEW.LE.MMAX ) THEN
|
|
*
|
|
* Eigenvalue in both intervals -- add upper to
|
|
* queue.
|
|
*
|
|
AB( KLNEW, 2 ) = AB( JI, 2 )
|
|
NAB( KLNEW, 2 ) = NAB( JI, 2 )
|
|
AB( KLNEW, 1 ) = C( JI )
|
|
NAB( KLNEW, 1 ) = IWORK( JI )
|
|
AB( JI, 2 ) = C( JI )
|
|
NAB( JI, 2 ) = IWORK( JI )
|
|
ELSE
|
|
INFO = MMAX + 1
|
|
END IF
|
|
END IF
|
|
70 CONTINUE
|
|
IF( INFO.NE.0 )
|
|
$ RETURN
|
|
KL = KLNEW
|
|
ELSE
|
|
*
|
|
* IJOB=3: Binary search. Keep only the interval containing
|
|
* w s.t. N(w) = NVAL
|
|
*
|
|
DO 80 JI = KF, KL
|
|
IF( IWORK( JI ).LE.NVAL( JI ) ) THEN
|
|
AB( JI, 1 ) = C( JI )
|
|
NAB( JI, 1 ) = IWORK( JI )
|
|
END IF
|
|
IF( IWORK( JI ).GE.NVAL( JI ) ) THEN
|
|
AB( JI, 2 ) = C( JI )
|
|
NAB( JI, 2 ) = IWORK( JI )
|
|
END IF
|
|
80 CONTINUE
|
|
END IF
|
|
*
|
|
ELSE
|
|
*
|
|
* End of Parallel Version of the loop
|
|
*
|
|
* Begin of Serial Version of the loop
|
|
*
|
|
KLNEW = KL
|
|
DO 100 JI = KF, KL
|
|
*
|
|
* Compute N(w), the number of eigenvalues less than w
|
|
*
|
|
TMP1 = C( JI )
|
|
TMP2 = D( 1 ) - TMP1
|
|
ITMP1 = 0
|
|
IF( TMP2.LE.PIVMIN ) THEN
|
|
ITMP1 = 1
|
|
TMP2 = MIN( TMP2, -PIVMIN )
|
|
END IF
|
|
*
|
|
DO 90 J = 2, N
|
|
TMP2 = D( J ) - E2( J-1 ) / TMP2 - TMP1
|
|
IF( TMP2.LE.PIVMIN ) THEN
|
|
ITMP1 = ITMP1 + 1
|
|
TMP2 = MIN( TMP2, -PIVMIN )
|
|
END IF
|
|
90 CONTINUE
|
|
*
|
|
IF( IJOB.LE.2 ) THEN
|
|
*
|
|
* IJOB=2: Choose all intervals containing eigenvalues.
|
|
*
|
|
* Insure that N(w) is monotone
|
|
*
|
|
ITMP1 = MIN( NAB( JI, 2 ),
|
|
$ MAX( NAB( JI, 1 ), ITMP1 ) )
|
|
*
|
|
* Update the Queue -- add intervals if both halves
|
|
* contain eigenvalues.
|
|
*
|
|
IF( ITMP1.EQ.NAB( JI, 2 ) ) THEN
|
|
*
|
|
* No eigenvalue in the upper interval:
|
|
* just use the lower interval.
|
|
*
|
|
AB( JI, 2 ) = TMP1
|
|
*
|
|
ELSE IF( ITMP1.EQ.NAB( JI, 1 ) ) THEN
|
|
*
|
|
* No eigenvalue in the lower interval:
|
|
* just use the upper interval.
|
|
*
|
|
AB( JI, 1 ) = TMP1
|
|
ELSE IF( KLNEW.LT.MMAX ) THEN
|
|
*
|
|
* Eigenvalue in both intervals -- add upper to queue.
|
|
*
|
|
KLNEW = KLNEW + 1
|
|
AB( KLNEW, 2 ) = AB( JI, 2 )
|
|
NAB( KLNEW, 2 ) = NAB( JI, 2 )
|
|
AB( KLNEW, 1 ) = TMP1
|
|
NAB( KLNEW, 1 ) = ITMP1
|
|
AB( JI, 2 ) = TMP1
|
|
NAB( JI, 2 ) = ITMP1
|
|
ELSE
|
|
INFO = MMAX + 1
|
|
RETURN
|
|
END IF
|
|
ELSE
|
|
*
|
|
* IJOB=3: Binary search. Keep only the interval
|
|
* containing w s.t. N(w) = NVAL
|
|
*
|
|
IF( ITMP1.LE.NVAL( JI ) ) THEN
|
|
AB( JI, 1 ) = TMP1
|
|
NAB( JI, 1 ) = ITMP1
|
|
END IF
|
|
IF( ITMP1.GE.NVAL( JI ) ) THEN
|
|
AB( JI, 2 ) = TMP1
|
|
NAB( JI, 2 ) = ITMP1
|
|
END IF
|
|
END IF
|
|
100 CONTINUE
|
|
KL = KLNEW
|
|
*
|
|
END IF
|
|
*
|
|
* Check for convergence
|
|
*
|
|
KFNEW = KF
|
|
DO 110 JI = KF, KL
|
|
TMP1 = ABS( AB( JI, 2 )-AB( JI, 1 ) )
|
|
TMP2 = MAX( ABS( AB( JI, 2 ) ), ABS( AB( JI, 1 ) ) )
|
|
IF( TMP1.LT.MAX( ABSTOL, PIVMIN, RELTOL*TMP2 ) .OR.
|
|
$ NAB( JI, 1 ).GE.NAB( JI, 2 ) ) THEN
|
|
*
|
|
* Converged -- Swap with position KFNEW,
|
|
* then increment KFNEW
|
|
*
|
|
IF( JI.GT.KFNEW ) THEN
|
|
TMP1 = AB( JI, 1 )
|
|
TMP2 = AB( JI, 2 )
|
|
ITMP1 = NAB( JI, 1 )
|
|
ITMP2 = NAB( JI, 2 )
|
|
AB( JI, 1 ) = AB( KFNEW, 1 )
|
|
AB( JI, 2 ) = AB( KFNEW, 2 )
|
|
NAB( JI, 1 ) = NAB( KFNEW, 1 )
|
|
NAB( JI, 2 ) = NAB( KFNEW, 2 )
|
|
AB( KFNEW, 1 ) = TMP1
|
|
AB( KFNEW, 2 ) = TMP2
|
|
NAB( KFNEW, 1 ) = ITMP1
|
|
NAB( KFNEW, 2 ) = ITMP2
|
|
IF( IJOB.EQ.3 ) THEN
|
|
ITMP1 = NVAL( JI )
|
|
NVAL( JI ) = NVAL( KFNEW )
|
|
NVAL( KFNEW ) = ITMP1
|
|
END IF
|
|
END IF
|
|
KFNEW = KFNEW + 1
|
|
END IF
|
|
110 CONTINUE
|
|
KF = KFNEW
|
|
*
|
|
* Choose Midpoints
|
|
*
|
|
DO 120 JI = KF, KL
|
|
C( JI ) = HALF*( AB( JI, 1 )+AB( JI, 2 ) )
|
|
120 CONTINUE
|
|
*
|
|
* If no more intervals to refine, quit.
|
|
*
|
|
IF( KF.GT.KL )
|
|
$ GO TO 140
|
|
130 CONTINUE
|
|
*
|
|
* Converged
|
|
*
|
|
140 CONTINUE
|
|
INFO = MAX( KL+1-KF, 0 )
|
|
MOUT = KL
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SLAEBZ
|
|
*
|
|
END
|