--- rpl/lapack/lapack/dlarrv.f 2011/11/21 22:19:34 1.11
+++ rpl/lapack/lapack/dlarrv.f 2023/08/07 08:38:58 1.24
@@ -1,19 +1,19 @@
-*> \brief \b DLARRV
+*> \brief \b DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT.
*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download DLARRV + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DLARRV + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
@@ -23,7 +23,7 @@
* RTOL1, RTOL2, W, WERR, WGAP,
* IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ,
* WORK, IWORK, INFO )
-*
+*
* .. Scalar Arguments ..
* INTEGER DOL, DOU, INFO, LDZ, M, N
* DOUBLE PRECISION MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU
@@ -35,7 +35,7 @@
* $ WGAP( * ), WORK( * )
* DOUBLE PRECISION Z( LDZ, * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -59,14 +59,23 @@
*> \param[in] VL
*> \verbatim
*> VL is DOUBLE PRECISION
+*> Lower bound of the interval that contains the desired
+*> eigenvalues. VL < VU. Needed to compute gaps on the left or right
+*> end of the extremal eigenvalues in the desired RANGE.
*> \endverbatim
*>
*> \param[in] VU
*> \verbatim
*> VU is DOUBLE PRECISION
-*> Lower and upper bounds of the interval that contains the desired
-*> eigenvalues. VL < VU. Needed to compute gaps on the left or right
-*> end of the extremal eigenvalues in the desired RANGE.
+*> Upper bound of the interval that contains the desired
+*> eigenvalues. VL < VU.
+*> Note: VU is currently not used by this implementation of DLARRV, VU is
+*> passed to DLARRV because it could be used compute gaps on the right end
+*> of the extremal eigenvalues. However, with not much initial accuracy in
+*> LAMBDA and VU, the formula can lead to an overestimation of the right gap
+*> and thus to inadequately early RQI 'convergence'. This is currently
+*> prevented this by forcing a small right gap. And so it turns out that VU
+*> is currently not used by this implementation of DLARRV.
*> \endverbatim
*>
*> \param[in,out] D
@@ -81,7 +90,7 @@
*> L is DOUBLE PRECISION array, dimension (N)
*> On entry, the (N-1) subdiagonal elements of the unit
*> bidiagonal matrix L are in elements 1 to N-1 of L
-*> (if the matrix is not splitted.) At the end of each block
+*> (if the matrix is not split.) At the end of each block
*> is stored the corresponding shift as given by DLARRE.
*> On exit, L is overwritten.
*> \endverbatim
@@ -140,7 +149,7 @@
*> RTOL2 is DOUBLE PRECISION
*> Parameters for bisection.
*> An interval [LEFT,RIGHT] has converged if
-*> RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )
+*> RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )
*> \endverbatim
*>
*> \param[in,out] W
@@ -236,7 +245,7 @@
*> INFO is INTEGER
*> = 0: successful exit
*>
-*> > 0: A problem occured in DLARRV.
+*> > 0: A problem occurred in DLARRV.
*> < 0: One of the called subroutines signaled an internal problem.
*> Needs inspection of the corresponding parameter IINFO
*> for further information.
@@ -258,12 +267,10 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
-*
-*> \date November 2011
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \ingroup doubleOTHERauxiliary
*
@@ -283,10 +290,9 @@
$ IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ,
$ WORK, IWORK, INFO )
*
-* -- LAPACK auxiliary routine (version 3.4.0) --
+* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2011
*
* .. Scalar Arguments ..
INTEGER DOL, DOU, INFO, LDZ, M, N
@@ -340,6 +346,14 @@
* .. Executable Statements ..
* ..
+ INFO = 0
+*
+* Quick return if possible
+*
+ IF( (N.LE.0).OR.(M.LE.0) ) THEN
+ RETURN
+ END IF
+*
* The first N entries of WORK are reserved for the eigenvalues
INDLD = N+1
INDLLD= 2*N+1