146 lines
4.3 KiB
FortranFixed
146 lines
4.3 KiB
FortranFixed
SUBROUTINE DLARRR( N, D, E, INFO )
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*
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* -- LAPACK auxiliary routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER N, INFO
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION D( * ), E( * )
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* ..
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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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* Perform tests to decide whether the symmetric tridiagonal matrix T
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* warrants expensive computations which guarantee high relative accuracy
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* in the eigenvalues.
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*
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* Arguments
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* =========
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*
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* N (input) INTEGER
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* The order of the matrix. N > 0.
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*
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* D (input) DOUBLE PRECISION 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/output) DOUBLE PRECISION array, dimension (N)
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* On entry, the first (N-1) entries contain the subdiagonal
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* elements of the tridiagonal matrix T; E(N) is set to ZERO.
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*
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* INFO (output) INTEGER
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* INFO = 0(default) : the matrix warrants computations preserving
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* relative accuracy.
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* INFO = 1 : the matrix warrants computations guaranteeing
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* only absolute accuracy.
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*
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* Further Details
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* ===============
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*
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* Based on contributions by
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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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DOUBLE PRECISION ZERO, RELCOND
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PARAMETER ( ZERO = 0.0D0,
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$ RELCOND = 0.999D0 )
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* ..
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* .. Local Scalars ..
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INTEGER I
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LOGICAL YESREL
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DOUBLE PRECISION EPS, SAFMIN, SMLNUM, RMIN, TMP, TMP2,
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$ OFFDIG, OFFDIG2
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH
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EXTERNAL DLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS
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* ..
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* .. Executable Statements ..
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*
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* As a default, do NOT go for relative-accuracy preserving computations.
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INFO = 1
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SAFMIN = DLAMCH( 'Safe minimum' )
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EPS = DLAMCH( 'Precision' )
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SMLNUM = SAFMIN / EPS
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RMIN = SQRT( SMLNUM )
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* Tests for relative accuracy
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*
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* Test for scaled diagonal dominance
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* Scale the diagonal entries to one and check whether the sum of the
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* off-diagonals is less than one
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*
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* The sdd relative error bounds have a 1/(1- 2*x) factor in them,
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* x = max(OFFDIG + OFFDIG2), so when x is close to 1/2, no relative
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* accuracy is promised. In the notation of the code fragment below,
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* 1/(1 - (OFFDIG + OFFDIG2)) is the condition number.
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* We don't think it is worth going into "sdd mode" unless the relative
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* condition number is reasonable, not 1/macheps.
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* The threshold should be compatible with other thresholds used in the
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* code. We set OFFDIG + OFFDIG2 <= .999 =: RELCOND, it corresponds
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* to losing at most 3 decimal digits: 1 / (1 - (OFFDIG + OFFDIG2)) <= 1000
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* instead of the current OFFDIG + OFFDIG2 < 1
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*
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YESREL = .TRUE.
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OFFDIG = ZERO
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TMP = SQRT(ABS(D(1)))
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IF (TMP.LT.RMIN) YESREL = .FALSE.
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IF(.NOT.YESREL) GOTO 11
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DO 10 I = 2, N
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TMP2 = SQRT(ABS(D(I)))
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IF (TMP2.LT.RMIN) YESREL = .FALSE.
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IF(.NOT.YESREL) GOTO 11
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OFFDIG2 = ABS(E(I-1))/(TMP*TMP2)
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IF(OFFDIG+OFFDIG2.GE.RELCOND) YESREL = .FALSE.
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IF(.NOT.YESREL) GOTO 11
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TMP = TMP2
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OFFDIG = OFFDIG2
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10 CONTINUE
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11 CONTINUE
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IF( YESREL ) THEN
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INFO = 0
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RETURN
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ELSE
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ENDIF
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*
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*
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* *** MORE TO BE IMPLEMENTED ***
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*
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*
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* Test if the lower bidiagonal matrix L from T = L D L^T
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* (zero shift facto) is well conditioned
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*
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*
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* Test if the upper bidiagonal matrix U from T = U D U^T
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* (zero shift facto) is well conditioned.
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* In this case, the matrix needs to be flipped and, at the end
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* of the eigenvector computation, the flip needs to be applied
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* to the computed eigenvectors (and the support)
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*
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*
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RETURN
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*
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* END OF DLARRR
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*
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END
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