julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
721 lines
26 KiB
FortranFixed
721 lines
26 KiB
FortranFixed
SUBROUTINE SLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS,
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$ RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT,
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$ M, W, WERR, WL, WU, IBLOCK, INDEXW,
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$ WORK, IWORK, INFO )
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*
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* -- LAPACK auxiliary routine (version 3.2.1) --
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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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* -- April 2009 --
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*
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* .. Scalar Arguments ..
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CHARACTER ORDER, RANGE
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INTEGER IL, INFO, IU, M, N, NSPLIT
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REAL PIVMIN, RELTOL, VL, VU, WL, WU
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* ..
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* .. Array Arguments ..
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INTEGER IBLOCK( * ), INDEXW( * ),
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$ ISPLIT( * ), IWORK( * )
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REAL D( * ), E( * ), E2( * ),
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$ GERS( * ), W( * ), WERR( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* SLARRD computes the eigenvalues of a symmetric tridiagonal
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* matrix T to suitable accuracy. This is an auxiliary code to be
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* called from SSTEMR.
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* The user may ask for all eigenvalues, all eigenvalues
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* in the half-open interval (VL, VU], or the IL-th through IU-th
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* eigenvalues.
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*
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* To avoid overflow, the matrix must be scaled so that its
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* largest element is no greater than overflow**(1/2) *
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* underflow**(1/4) in absolute value, and for greatest
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* accuracy, it should not be much smaller than that.
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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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* Arguments
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* =========
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*
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* RANGE (input) CHARACTER
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* = 'A': ("All") all eigenvalues will be found.
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* = 'V': ("Value") all eigenvalues in the half-open interval
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* (VL, VU] will be found.
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* = 'I': ("Index") the IL-th through IU-th eigenvalues (of the
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* entire matrix) will be found.
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*
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* ORDER (input) CHARACTER
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* = 'B': ("By Block") the eigenvalues will be grouped by
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* split-off block (see IBLOCK, ISPLIT) and
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* ordered from smallest to largest within
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* the block.
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* = 'E': ("Entire matrix")
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* the eigenvalues for the entire matrix
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* will be ordered from smallest to
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* largest.
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*
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* N (input) INTEGER
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* The order of the tridiagonal matrix T. N >= 0.
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*
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* VL (input) REAL
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* VU (input) REAL
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* If RANGE='V', the lower and upper bounds of the interval to
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* be searched for eigenvalues. Eigenvalues less than or equal
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* to VL, or greater than VU, will not be returned. VL < VU.
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* Not referenced if RANGE = 'A' or 'I'.
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*
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* IL (input) INTEGER
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* IU (input) INTEGER
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* If RANGE='I', the indices (in ascending order) of the
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* smallest and largest eigenvalues to be returned.
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* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
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* Not referenced if RANGE = 'A' or 'V'.
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*
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* GERS (input) REAL array, dimension (2*N)
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* The N Gerschgorin intervals (the i-th Gerschgorin interval
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* is (GERS(2*i-1), GERS(2*i)).
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*
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* RELTOL (input) REAL
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* The minimum relative width of an interval. When an interval
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* is narrower 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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*
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* D (input) REAL array, dimension (N)
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* The n diagonal elements of the tridiagonal matrix T.
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*
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* E (input) REAL array, dimension (N-1)
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* The (n-1) off-diagonal elements of the tridiagonal matrix T.
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*
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* E2 (input) REAL array, dimension (N-1)
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* The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
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*
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* PIVMIN (input) REAL
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* The minimum pivot allowed in the Sturm sequence for T.
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*
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* NSPLIT (input) INTEGER
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* The number of diagonal blocks in the matrix T.
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* 1 <= NSPLIT <= N.
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*
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* ISPLIT (input) INTEGER array, dimension (N)
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* The splitting points, at which T breaks up into submatrices.
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* The first submatrix consists of rows/columns 1 to ISPLIT(1),
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* the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
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* etc., and the NSPLIT-th consists of rows/columns
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* ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
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* (Only the first NSPLIT elements will actually be used, but
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* since the user cannot know a priori what value NSPLIT will
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* have, N words must be reserved for ISPLIT.)
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*
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* M (output) INTEGER
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* The actual number of eigenvalues found. 0 <= M <= N.
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* (See also the description of INFO=2,3.)
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*
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* W (output) REAL array, dimension (N)
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* On exit, the first M elements of W will contain the
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* eigenvalue approximations. SLARRD computes an interval
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* I_j = (a_j, b_j] that includes eigenvalue j. The eigenvalue
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* approximation is given as the interval midpoint
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* W(j)= ( a_j + b_j)/2. The corresponding error is bounded by
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* WERR(j) = abs( a_j - b_j)/2
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*
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* WERR (output) REAL array, dimension (N)
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* The error bound on the corresponding eigenvalue approximation
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* in W.
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*
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* WL (output) REAL
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* WU (output) REAL
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* The interval (WL, WU] contains all the wanted eigenvalues.
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* If RANGE='V', then WL=VL and WU=VU.
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* If RANGE='A', then WL and WU are the global Gerschgorin bounds
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* on the spectrum.
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* If RANGE='I', then WL and WU are computed by SLAEBZ from the
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* index range specified.
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*
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* IBLOCK (output) INTEGER array, dimension (N)
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* At each row/column j where E(j) is zero or small, the
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* matrix T is considered to split into a block diagonal
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* matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which
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* block (from 1 to the number of blocks) the eigenvalue W(i)
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* belongs. (SLARRD may use the remaining N-M elements as
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* workspace.)
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*
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* INDEXW (output) INTEGER array, dimension (N)
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* The indices of the eigenvalues within each block (submatrix);
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* for example, INDEXW(i)= j and IBLOCK(i)=k imply that the
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* i-th eigenvalue W(i) is the j-th eigenvalue in block k.
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*
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* WORK (workspace) REAL array, dimension (4*N)
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*
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* IWORK (workspace) INTEGER array, dimension (3*N)
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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* > 0: some or all of the eigenvalues failed to converge or
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* were not computed:
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* =1 or 3: Bisection failed to converge for some
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* eigenvalues; these eigenvalues are flagged by a
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* negative block number. The effect is that the
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* eigenvalues may not be as accurate as the
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* absolute and relative tolerances. This is
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* generally caused by unexpectedly inaccurate
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* arithmetic.
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* =2 or 3: RANGE='I' only: Not all of the eigenvalues
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* IL:IU were found.
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* Effect: M < IU+1-IL
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* Cause: non-monotonic arithmetic, causing the
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* Sturm sequence to be non-monotonic.
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* Cure: recalculate, using RANGE='A', and pick
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* out eigenvalues IL:IU. In some cases,
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* increasing the PARAMETER "FUDGE" may
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* make things work.
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* = 4: RANGE='I', and the Gershgorin interval
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* initially used was too small. No eigenvalues
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* were computed.
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* Probable cause: your machine has sloppy
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* floating-point arithmetic.
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* Cure: Increase the PARAMETER "FUDGE",
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* recompile, and try again.
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*
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* Internal Parameters
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* ===================
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*
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* FUDGE REAL , default = 2
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* A "fudge factor" to widen the Gershgorin intervals. Ideally,
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* a value of 1 should work, but on machines with sloppy
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* arithmetic, this needs to be larger. The default for
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* publicly released versions should be large enough to handle
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* the worst machine around. Note that this has no effect
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* on accuracy of the solution.
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*
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* Based on contributions by
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* W. Kahan, University of California, Berkeley, USA
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* Beresford Parlett, University of California, Berkeley, USA
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* Jim Demmel, University of California, Berkeley, USA
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* Inderjit Dhillon, University of Texas, Austin, USA
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* Osni Marques, LBNL/NERSC, USA
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* Christof Voemel, University of California, Berkeley, USA
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE, TWO, HALF, FUDGE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0,
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$ TWO = 2.0E0, HALF = ONE/TWO,
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$ FUDGE = TWO )
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INTEGER ALLRNG, VALRNG, INDRNG
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PARAMETER ( ALLRNG = 1, VALRNG = 2, INDRNG = 3 )
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* ..
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* .. Local Scalars ..
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LOGICAL NCNVRG, TOOFEW
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INTEGER I, IB, IBEGIN, IDISCL, IDISCU, IE, IEND, IINFO,
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$ IM, IN, IOFF, IOUT, IRANGE, ITMAX, ITMP1,
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$ ITMP2, IW, IWOFF, J, JBLK, JDISC, JE, JEE, NB,
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$ NWL, NWU
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REAL ATOLI, EPS, GL, GU, RTOLI, TMP1, TMP2,
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$ TNORM, UFLOW, WKILL, WLU, WUL
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* ..
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* .. Local Arrays ..
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INTEGER IDUMMA( 1 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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REAL SLAMCH
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EXTERNAL LSAME, ILAENV, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL SLAEBZ
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, INT, LOG, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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*
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* Decode RANGE
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*
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IF( LSAME( RANGE, 'A' ) ) THEN
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IRANGE = ALLRNG
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ELSE IF( LSAME( RANGE, 'V' ) ) THEN
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IRANGE = VALRNG
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ELSE IF( LSAME( RANGE, 'I' ) ) THEN
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IRANGE = INDRNG
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ELSE
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IRANGE = 0
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END IF
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*
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* Check for Errors
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*
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IF( IRANGE.LE.0 ) THEN
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INFO = -1
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ELSE IF( .NOT.(LSAME(ORDER,'B').OR.LSAME(ORDER,'E')) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( IRANGE.EQ.VALRNG ) THEN
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IF( VL.GE.VU )
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$ INFO = -5
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ELSE IF( IRANGE.EQ.INDRNG .AND.
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$ ( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) ) THEN
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INFO = -6
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ELSE IF( IRANGE.EQ.INDRNG .AND.
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$ ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) ) THEN
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INFO = -7
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END IF
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*
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IF( INFO.NE.0 ) THEN
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RETURN
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END IF
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* Initialize error flags
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INFO = 0
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NCNVRG = .FALSE.
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TOOFEW = .FALSE.
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* Quick return if possible
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M = 0
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IF( N.EQ.0 ) RETURN
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* Simplification:
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IF( IRANGE.EQ.INDRNG .AND. IL.EQ.1 .AND. IU.EQ.N ) IRANGE = 1
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* Get machine constants
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EPS = SLAMCH( 'P' )
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UFLOW = SLAMCH( 'U' )
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* Special Case when N=1
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* Treat case of 1x1 matrix for quick return
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IF( N.EQ.1 ) THEN
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IF( (IRANGE.EQ.ALLRNG).OR.
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$ ((IRANGE.EQ.VALRNG).AND.(D(1).GT.VL).AND.(D(1).LE.VU)).OR.
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$ ((IRANGE.EQ.INDRNG).AND.(IL.EQ.1).AND.(IU.EQ.1)) ) THEN
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M = 1
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W(1) = D(1)
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* The computation error of the eigenvalue is zero
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WERR(1) = ZERO
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IBLOCK( 1 ) = 1
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INDEXW( 1 ) = 1
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ENDIF
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RETURN
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END IF
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* NB is the minimum vector length for vector bisection, or 0
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* if only scalar is to be done.
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NB = ILAENV( 1, 'SSTEBZ', ' ', N, -1, -1, -1 )
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IF( NB.LE.1 ) NB = 0
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* Find global spectral radius
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GL = D(1)
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GU = D(1)
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DO 5 I = 1,N
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GL = MIN( GL, GERS( 2*I - 1))
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GU = MAX( GU, GERS(2*I) )
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5 CONTINUE
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* Compute global Gerschgorin bounds and spectral diameter
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TNORM = MAX( ABS( GL ), ABS( GU ) )
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GL = GL - FUDGE*TNORM*EPS*N - FUDGE*TWO*PIVMIN
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GU = GU + FUDGE*TNORM*EPS*N + FUDGE*TWO*PIVMIN
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* [JAN/28/2009] remove the line below since SPDIAM variable not use
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* SPDIAM = GU - GL
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* Input arguments for SLAEBZ:
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* The relative tolerance. An interval (a,b] lies within
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* "relative tolerance" if b-a < RELTOL*max(|a|,|b|),
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RTOLI = RELTOL
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* Set the absolute tolerance for interval convergence to zero to force
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* interval convergence based on relative size of the interval.
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* This is dangerous because intervals might not converge when RELTOL is
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* small. But at least a very small number should be selected so that for
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* strongly graded matrices, the code can get relatively accurate
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* eigenvalues.
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ATOLI = FUDGE*TWO*UFLOW + FUDGE*TWO*PIVMIN
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IF( IRANGE.EQ.INDRNG ) THEN
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* RANGE='I': Compute an interval containing eigenvalues
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* IL through IU. The initial interval [GL,GU] from the global
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* Gerschgorin bounds GL and GU is refined by SLAEBZ.
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ITMAX = INT( ( LOG( TNORM+PIVMIN )-LOG( PIVMIN ) ) /
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$ LOG( TWO ) ) + 2
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WORK( N+1 ) = GL
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WORK( N+2 ) = GL
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WORK( N+3 ) = GU
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WORK( N+4 ) = GU
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WORK( N+5 ) = GL
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WORK( N+6 ) = GU
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IWORK( 1 ) = -1
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IWORK( 2 ) = -1
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IWORK( 3 ) = N + 1
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IWORK( 4 ) = N + 1
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IWORK( 5 ) = IL - 1
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IWORK( 6 ) = IU
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*
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CALL SLAEBZ( 3, ITMAX, N, 2, 2, NB, ATOLI, RTOLI, PIVMIN,
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$ D, E, E2, IWORK( 5 ), WORK( N+1 ), WORK( N+5 ), IOUT,
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$ IWORK, W, IBLOCK, IINFO )
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IF( IINFO .NE. 0 ) THEN
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INFO = IINFO
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RETURN
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END IF
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* On exit, output intervals may not be ordered by ascending negcount
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IF( IWORK( 6 ).EQ.IU ) THEN
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WL = WORK( N+1 )
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WLU = WORK( N+3 )
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NWL = IWORK( 1 )
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WU = WORK( N+4 )
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WUL = WORK( N+2 )
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NWU = IWORK( 4 )
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ELSE
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WL = WORK( N+2 )
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WLU = WORK( N+4 )
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NWL = IWORK( 2 )
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WU = WORK( N+3 )
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WUL = WORK( N+1 )
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NWU = IWORK( 3 )
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END IF
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* On exit, the interval [WL, WLU] contains a value with negcount NWL,
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* and [WUL, WU] contains a value with negcount NWU.
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IF( NWL.LT.0 .OR. NWL.GE.N .OR. NWU.LT.1 .OR. NWU.GT.N ) THEN
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INFO = 4
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RETURN
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END IF
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ELSEIF( IRANGE.EQ.VALRNG ) THEN
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WL = VL
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WU = VU
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ELSEIF( IRANGE.EQ.ALLRNG ) THEN
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WL = GL
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WU = GU
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ENDIF
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* Find Eigenvalues -- Loop Over blocks and recompute NWL and NWU.
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* NWL accumulates the number of eigenvalues .le. WL,
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* NWU accumulates the number of eigenvalues .le. WU
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M = 0
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IEND = 0
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INFO = 0
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NWL = 0
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NWU = 0
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*
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DO 70 JBLK = 1, NSPLIT
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IOFF = IEND
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IBEGIN = IOFF + 1
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IEND = ISPLIT( JBLK )
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IN = IEND - IOFF
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*
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IF( IN.EQ.1 ) THEN
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* 1x1 block
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IF( WL.GE.D( IBEGIN )-PIVMIN )
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$ NWL = NWL + 1
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IF( WU.GE.D( IBEGIN )-PIVMIN )
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$ NWU = NWU + 1
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IF( IRANGE.EQ.ALLRNG .OR.
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$ ( WL.LT.D( IBEGIN )-PIVMIN
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$ .AND. WU.GE. D( IBEGIN )-PIVMIN ) ) THEN
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M = M + 1
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W( M ) = D( IBEGIN )
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WERR(M) = ZERO
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* The gap for a single block doesn't matter for the later
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* algorithm and is assigned an arbitrary large value
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IBLOCK( M ) = JBLK
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INDEXW( M ) = 1
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END IF
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* Disabled 2x2 case because of a failure on the following matrix
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* RANGE = 'I', IL = IU = 4
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* Original Tridiagonal, d = [
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* -0.150102010615740E+00
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* -0.849897989384260E+00
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* -0.128208148052635E-15
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* 0.128257718286320E-15
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* ];
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* e = [
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* -0.357171383266986E+00
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* -0.180411241501588E-15
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* -0.175152352710251E-15
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* ];
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*
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* ELSE IF( IN.EQ.2 ) THEN
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** 2x2 block
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* DISC = SQRT( (HALF*(D(IBEGIN)-D(IEND)))**2 + E(IBEGIN)**2 )
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* TMP1 = HALF*(D(IBEGIN)+D(IEND))
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* L1 = TMP1 - DISC
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* IF( WL.GE. L1-PIVMIN )
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* $ NWL = NWL + 1
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* IF( WU.GE. L1-PIVMIN )
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* $ NWU = NWU + 1
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* IF( IRANGE.EQ.ALLRNG .OR. ( WL.LT.L1-PIVMIN .AND. WU.GE.
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* $ L1-PIVMIN ) ) THEN
|
|
* M = M + 1
|
|
* W( M ) = L1
|
|
** The uncertainty of eigenvalues of a 2x2 matrix is very small
|
|
* WERR( M ) = EPS * ABS( W( M ) ) * TWO
|
|
* IBLOCK( M ) = JBLK
|
|
* INDEXW( M ) = 1
|
|
* ENDIF
|
|
* L2 = TMP1 + DISC
|
|
* IF( WL.GE. L2-PIVMIN )
|
|
* $ NWL = NWL + 1
|
|
* IF( WU.GE. L2-PIVMIN )
|
|
* $ NWU = NWU + 1
|
|
* IF( IRANGE.EQ.ALLRNG .OR. ( WL.LT.L2-PIVMIN .AND. WU.GE.
|
|
* $ L2-PIVMIN ) ) THEN
|
|
* M = M + 1
|
|
* W( M ) = L2
|
|
** The uncertainty of eigenvalues of a 2x2 matrix is very small
|
|
* WERR( M ) = EPS * ABS( W( M ) ) * TWO
|
|
* IBLOCK( M ) = JBLK
|
|
* INDEXW( M ) = 2
|
|
* ENDIF
|
|
ELSE
|
|
* General Case - block of size IN >= 2
|
|
* Compute local Gerschgorin interval and use it as the initial
|
|
* interval for SLAEBZ
|
|
GU = D( IBEGIN )
|
|
GL = D( IBEGIN )
|
|
TMP1 = ZERO
|
|
|
|
DO 40 J = IBEGIN, IEND
|
|
GL = MIN( GL, GERS( 2*J - 1))
|
|
GU = MAX( GU, GERS(2*J) )
|
|
40 CONTINUE
|
|
* [JAN/28/2009]
|
|
* change SPDIAM by TNORM in lines 2 and 3 thereafter
|
|
* line 1: remove computation of SPDIAM (not useful anymore)
|
|
* SPDIAM = GU - GL
|
|
* GL = GL - FUDGE*SPDIAM*EPS*IN - FUDGE*PIVMIN
|
|
* GU = GU + FUDGE*SPDIAM*EPS*IN + FUDGE*PIVMIN
|
|
GL = GL - FUDGE*TNORM*EPS*IN - FUDGE*PIVMIN
|
|
GU = GU + FUDGE*TNORM*EPS*IN + FUDGE*PIVMIN
|
|
*
|
|
IF( IRANGE.GT.1 ) THEN
|
|
IF( GU.LT.WL ) THEN
|
|
* the local block contains none of the wanted eigenvalues
|
|
NWL = NWL + IN
|
|
NWU = NWU + IN
|
|
GO TO 70
|
|
END IF
|
|
* refine search interval if possible, only range (WL,WU] matters
|
|
GL = MAX( GL, WL )
|
|
GU = MIN( GU, WU )
|
|
IF( GL.GE.GU )
|
|
$ GO TO 70
|
|
END IF
|
|
|
|
* Find negcount of initial interval boundaries GL and GU
|
|
WORK( N+1 ) = GL
|
|
WORK( N+IN+1 ) = GU
|
|
CALL SLAEBZ( 1, 0, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN,
|
|
$ D( IBEGIN ), E( IBEGIN ), E2( IBEGIN ),
|
|
$ IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IM,
|
|
$ IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO )
|
|
IF( IINFO .NE. 0 ) THEN
|
|
INFO = IINFO
|
|
RETURN
|
|
END IF
|
|
*
|
|
NWL = NWL + IWORK( 1 )
|
|
NWU = NWU + IWORK( IN+1 )
|
|
IWOFF = M - IWORK( 1 )
|
|
|
|
* Compute Eigenvalues
|
|
ITMAX = INT( ( LOG( GU-GL+PIVMIN )-LOG( PIVMIN ) ) /
|
|
$ LOG( TWO ) ) + 2
|
|
CALL SLAEBZ( 2, ITMAX, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN,
|
|
$ D( IBEGIN ), E( IBEGIN ), E2( IBEGIN ),
|
|
$ IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IOUT,
|
|
$ IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO )
|
|
IF( IINFO .NE. 0 ) THEN
|
|
INFO = IINFO
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Copy eigenvalues into W and IBLOCK
|
|
* Use -JBLK for block number for unconverged eigenvalues.
|
|
* Loop over the number of output intervals from SLAEBZ
|
|
DO 60 J = 1, IOUT
|
|
* eigenvalue approximation is middle point of interval
|
|
TMP1 = HALF*( WORK( J+N )+WORK( J+IN+N ) )
|
|
* semi length of error interval
|
|
TMP2 = HALF*ABS( WORK( J+N )-WORK( J+IN+N ) )
|
|
IF( J.GT.IOUT-IINFO ) THEN
|
|
* Flag non-convergence.
|
|
NCNVRG = .TRUE.
|
|
IB = -JBLK
|
|
ELSE
|
|
IB = JBLK
|
|
END IF
|
|
DO 50 JE = IWORK( J ) + 1 + IWOFF,
|
|
$ IWORK( J+IN ) + IWOFF
|
|
W( JE ) = TMP1
|
|
WERR( JE ) = TMP2
|
|
INDEXW( JE ) = JE - IWOFF
|
|
IBLOCK( JE ) = IB
|
|
50 CONTINUE
|
|
60 CONTINUE
|
|
*
|
|
M = M + IM
|
|
END IF
|
|
70 CONTINUE
|
|
|
|
* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU
|
|
* If NWL+1 < IL or NWU > IU, discard extra eigenvalues.
|
|
IF( IRANGE.EQ.INDRNG ) THEN
|
|
IDISCL = IL - 1 - NWL
|
|
IDISCU = NWU - IU
|
|
*
|
|
IF( IDISCL.GT.0 ) THEN
|
|
IM = 0
|
|
DO 80 JE = 1, M
|
|
* Remove some of the smallest eigenvalues from the left so that
|
|
* at the end IDISCL =0. Move all eigenvalues up to the left.
|
|
IF( W( JE ).LE.WLU .AND. IDISCL.GT.0 ) THEN
|
|
IDISCL = IDISCL - 1
|
|
ELSE
|
|
IM = IM + 1
|
|
W( IM ) = W( JE )
|
|
WERR( IM ) = WERR( JE )
|
|
INDEXW( IM ) = INDEXW( JE )
|
|
IBLOCK( IM ) = IBLOCK( JE )
|
|
END IF
|
|
80 CONTINUE
|
|
M = IM
|
|
END IF
|
|
IF( IDISCU.GT.0 ) THEN
|
|
* Remove some of the largest eigenvalues from the right so that
|
|
* at the end IDISCU =0. Move all eigenvalues up to the left.
|
|
IM=M+1
|
|
DO 81 JE = M, 1, -1
|
|
IF( W( JE ).GE.WUL .AND. IDISCU.GT.0 ) THEN
|
|
IDISCU = IDISCU - 1
|
|
ELSE
|
|
IM = IM - 1
|
|
W( IM ) = W( JE )
|
|
WERR( IM ) = WERR( JE )
|
|
INDEXW( IM ) = INDEXW( JE )
|
|
IBLOCK( IM ) = IBLOCK( JE )
|
|
END IF
|
|
81 CONTINUE
|
|
JEE = 0
|
|
DO 82 JE = IM, M
|
|
JEE = JEE + 1
|
|
W( JEE ) = W( JE )
|
|
WERR( JEE ) = WERR( JE )
|
|
INDEXW( JEE ) = INDEXW( JE )
|
|
IBLOCK( JEE ) = IBLOCK( JE )
|
|
82 CONTINUE
|
|
M = M-IM+1
|
|
END IF
|
|
|
|
IF( IDISCL.GT.0 .OR. IDISCU.GT.0 ) THEN
|
|
* Code to deal with effects of bad arithmetic. (If N(w) is
|
|
* monotone non-decreasing, this should never happen.)
|
|
* Some low eigenvalues to be discarded are not in (WL,WLU],
|
|
* or high eigenvalues to be discarded are not in (WUL,WU]
|
|
* so just kill off the smallest IDISCL/largest IDISCU
|
|
* eigenvalues, by marking the corresponding IBLOCK = 0
|
|
IF( IDISCL.GT.0 ) THEN
|
|
WKILL = WU
|
|
DO 100 JDISC = 1, IDISCL
|
|
IW = 0
|
|
DO 90 JE = 1, M
|
|
IF( IBLOCK( JE ).NE.0 .AND.
|
|
$ ( W( JE ).LT.WKILL .OR. IW.EQ.0 ) ) THEN
|
|
IW = JE
|
|
WKILL = W( JE )
|
|
END IF
|
|
90 CONTINUE
|
|
IBLOCK( IW ) = 0
|
|
100 CONTINUE
|
|
END IF
|
|
IF( IDISCU.GT.0 ) THEN
|
|
WKILL = WL
|
|
DO 120 JDISC = 1, IDISCU
|
|
IW = 0
|
|
DO 110 JE = 1, M
|
|
IF( IBLOCK( JE ).NE.0 .AND.
|
|
$ ( W( JE ).GE.WKILL .OR. IW.EQ.0 ) ) THEN
|
|
IW = JE
|
|
WKILL = W( JE )
|
|
END IF
|
|
110 CONTINUE
|
|
IBLOCK( IW ) = 0
|
|
120 CONTINUE
|
|
END IF
|
|
* Now erase all eigenvalues with IBLOCK set to zero
|
|
IM = 0
|
|
DO 130 JE = 1, M
|
|
IF( IBLOCK( JE ).NE.0 ) THEN
|
|
IM = IM + 1
|
|
W( IM ) = W( JE )
|
|
WERR( IM ) = WERR( JE )
|
|
INDEXW( IM ) = INDEXW( JE )
|
|
IBLOCK( IM ) = IBLOCK( JE )
|
|
END IF
|
|
130 CONTINUE
|
|
M = IM
|
|
END IF
|
|
IF( IDISCL.LT.0 .OR. IDISCU.LT.0 ) THEN
|
|
TOOFEW = .TRUE.
|
|
END IF
|
|
END IF
|
|
*
|
|
IF(( IRANGE.EQ.ALLRNG .AND. M.NE.N ).OR.
|
|
$ ( IRANGE.EQ.INDRNG .AND. M.NE.IU-IL+1 ) ) THEN
|
|
TOOFEW = .TRUE.
|
|
END IF
|
|
|
|
* If ORDER='B', do nothing the eigenvalues are already sorted by
|
|
* block.
|
|
* If ORDER='E', sort the eigenvalues from smallest to largest
|
|
|
|
IF( LSAME(ORDER,'E') .AND. NSPLIT.GT.1 ) THEN
|
|
DO 150 JE = 1, M - 1
|
|
IE = 0
|
|
TMP1 = W( JE )
|
|
DO 140 J = JE + 1, M
|
|
IF( W( J ).LT.TMP1 ) THEN
|
|
IE = J
|
|
TMP1 = W( J )
|
|
END IF
|
|
140 CONTINUE
|
|
IF( IE.NE.0 ) THEN
|
|
TMP2 = WERR( IE )
|
|
ITMP1 = IBLOCK( IE )
|
|
ITMP2 = INDEXW( IE )
|
|
W( IE ) = W( JE )
|
|
WERR( IE ) = WERR( JE )
|
|
IBLOCK( IE ) = IBLOCK( JE )
|
|
INDEXW( IE ) = INDEXW( JE )
|
|
W( JE ) = TMP1
|
|
WERR( JE ) = TMP2
|
|
IBLOCK( JE ) = ITMP1
|
|
INDEXW( JE ) = ITMP2
|
|
END IF
|
|
150 CONTINUE
|
|
END IF
|
|
*
|
|
INFO = 0
|
|
IF( NCNVRG )
|
|
$ INFO = INFO + 1
|
|
IF( TOOFEW )
|
|
$ INFO = INFO + 2
|
|
RETURN
|
|
*
|
|
* End of SLARRD
|
|
*
|
|
END
|