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---
:name: slarrf
:md5sum: 04503ebe32bcc573b80d9d85b4382ab2
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- d:
:type: real
:intent: input
:dims:
- n
- l:
:type: real
:intent: input
:dims:
- n-1
- ld:
:type: real
:intent: input
:dims:
- n-1
- clstrt:
:type: integer
:intent: input
- clend:
:type: integer
:intent: input
- w:
:type: real
:intent: input
:dims:
- clend-clstrt+1
- wgap:
:type: real
:intent: input/output
:dims:
- clend-clstrt+1
- werr:
:type: real
:intent: input
:dims:
- clend-clstrt+1
- spdiam:
:type: real
:intent: input
- clgapl:
:type: real
:intent: input
- clgapr:
:type: real
:intent: input
- pivmin:
:type: real
:intent: input
- sigma:
:type: real
:intent: output
- dplus:
:type: real
:intent: output
:dims:
- n
- lplus:
:type: real
:intent: output
:dims:
- n-1
- work:
:type: real
:intent: workspace
:dims:
- 2*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SLARRF( N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* Given the initial representation L D L^T and its cluster of close\n\
* eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ...\n\
* W( CLEND ), SLARRF finds a new relatively robust representation\n\
* L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the\n\
* eigenvalues of L(+) D(+) L(+)^T is relatively isolated.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix (subblock, if the matrix split).\n\
*\n\
* D (input) REAL array, dimension (N)\n\
* The N diagonal elements of the diagonal matrix D.\n\
*\n\
* L (input) REAL array, dimension (N-1)\n\
* The (N-1) subdiagonal elements of the unit bidiagonal\n\
* matrix L.\n\
*\n\
* LD (input) REAL array, dimension (N-1)\n\
* The (N-1) elements L(i)*D(i).\n\
*\n\
* CLSTRT (input) INTEGER\n\
* The index of the first eigenvalue in the cluster.\n\
*\n\
* CLEND (input) INTEGER\n\
* The index of the last eigenvalue in the cluster.\n\
*\n\
* W (input) REAL array, dimension\n\
* dimension is >= (CLEND-CLSTRT+1)\n\
* The eigenvalue APPROXIMATIONS of L D L^T in ascending order.\n\
* W( CLSTRT ) through W( CLEND ) form the cluster of relatively\n\
* close eigenalues.\n\
*\n\
* WGAP (input/output) REAL array, dimension\n\
* dimension is >= (CLEND-CLSTRT+1)\n\
* The separation from the right neighbor eigenvalue in W.\n\
*\n\
* WERR (input) REAL array, dimension\n\
* dimension is >= (CLEND-CLSTRT+1)\n\
* WERR contain the semiwidth of the uncertainty\n\
* interval of the corresponding eigenvalue APPROXIMATION in W\n\
*\n\
* SPDIAM (input) REAL\n\
* estimate of the spectral diameter obtained from the\n\
* Gerschgorin intervals\n\
*\n\
* CLGAPL (input) REAL\n\
*\n\
* CLGAPR (input) REAL\n\
* absolute gap on each end of the cluster.\n\
* Set by the calling routine to protect against shifts too close\n\
* to eigenvalues outside the cluster.\n\
*\n\
* PIVMIN (input) REAL\n\
* The minimum pivot allowed in the Sturm sequence.\n\
*\n\
* SIGMA (output) REAL \n\
* The shift used to form L(+) D(+) L(+)^T.\n\
*\n\
* DPLUS (output) REAL array, dimension (N)\n\
* The N diagonal elements of the diagonal matrix D(+).\n\
*\n\
* LPLUS (output) REAL array, dimension (N-1)\n\
* The first (N-1) elements of LPLUS contain the subdiagonal\n\
* elements of the unit bidiagonal matrix L(+).\n\
*\n\
* WORK (workspace) REAL array, dimension (2*N)\n\
* Workspace.\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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