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---
:name: dlarrj
:md5sum: 2a08a838ca5660f3b1cf1b9237f3741e
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input
:dims:
- n
- e2:
:type: doublereal
:intent: input
:dims:
- n-1
- ifirst:
:type: integer
:intent: input
- ilast:
:type: integer
:intent: input
- rtol:
:type: doublereal
:intent: input
- offset:
:type: integer
:intent: input
- w:
:type: doublereal
:intent: input/output
:dims:
- n
- werr:
:type: doublereal
:intent: input/output
:dims:
- n
- work:
:type: doublereal
:intent: workspace
:dims:
- 2*n
- iwork:
:type: integer
:intent: workspace
:dims:
- 2*n
- pivmin:
:type: doublereal
:intent: input
- spdiam:
:type: doublereal
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* Given the initial eigenvalue approximations of T, DLARRJ\n\
* does bisection to refine the eigenvalues of T,\n\
* W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial\n\
* guesses for these eigenvalues are input in W, the corresponding estimate\n\
* of the error in these guesses in WERR. During bisection, intervals\n\
* [left, right] are maintained by storing their mid-points and\n\
* semi-widths in the arrays W and WERR respectively.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix.\n\
*\n\
* D (input) DOUBLE PRECISION array, dimension (N)\n\
* The N diagonal elements of T.\n\
*\n\
* E2 (input) DOUBLE PRECISION array, dimension (N-1)\n\
* The Squares of the (N-1) subdiagonal elements of T.\n\
*\n\
* IFIRST (input) INTEGER\n\
* The index of the first eigenvalue to be computed.\n\
*\n\
* ILAST (input) INTEGER\n\
* The index of the last eigenvalue to be computed.\n\
*\n\
* RTOL (input) DOUBLE PRECISION\n\
* Tolerance for the convergence of the bisection intervals.\n\
* An interval [LEFT,RIGHT] has converged if\n\
* RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|).\n\
*\n\
* OFFSET (input) INTEGER\n\
* Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET\n\
* through ILAST-OFFSET elements of these arrays are to be used.\n\
*\n\
* W (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are\n\
* estimates of the eigenvalues of L D L^T indexed IFIRST through\n\
* ILAST.\n\
* On output, these estimates are refined.\n\
*\n\
* WERR (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are\n\
* the errors in the estimates of the corresponding elements in W.\n\
* On output, these errors are refined.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (2*N)\n\
* Workspace.\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (2*N)\n\
* Workspace.\n\
*\n\
* PIVMIN (input) DOUBLE PRECISION\n\
* The minimum pivot in the Sturm sequence for T.\n\
*\n\
* SPDIAM (input) DOUBLE PRECISION\n\
* The spectral diameter of T.\n\
*\n\
* INFO (output) INTEGER\n\
* Error flag.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Beresford Parlett, University of California, Berkeley, USA\n\
* Jim Demmel, University of California, Berkeley, USA\n\
* Inderjit Dhillon, University of Texas, Austin, USA\n\
* Osni Marques, LBNL/NERSC, USA\n\
* Christof Voemel, University of California, Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
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