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---
:name: zlarrv
:md5sum: ae9ce24a0dd6a243053bd6396969a553
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- vl:
:type: doublereal
:intent: input
- vu:
:type: doublereal
:intent: input
- d:
:type: doublereal
:intent: input/output
:dims:
- n
- l:
:type: doublereal
:intent: input/output
:dims:
- n
- pivmin:
:type: doublereal
:intent: input
- isplit:
:type: integer
:intent: input
:dims:
- n
- m:
:type: integer
:intent: input
- dol:
:type: integer
:intent: input
- dou:
:type: integer
:intent: input
- minrgp:
:type: doublereal
:intent: input
- rtol1:
:type: doublereal
:intent: input
- rtol2:
:type: doublereal
:intent: input
- w:
:type: doublereal
:intent: input/output
:dims:
- n
- werr:
:type: doublereal
:intent: input/output
:dims:
- n
- wgap:
:type: doublereal
:intent: input/output
:dims:
- n
- iblock:
:type: integer
:intent: input
:dims:
- n
- indexw:
:type: integer
:intent: input
:dims:
- n
- gers:
:type: doublereal
:intent: input
:dims:
- 2*n
- z:
:type: doublecomplex
:intent: output
:dims:
- ldz
- MAX(1,m)
- ldz:
:type: integer
:intent: input
- isuppz:
:type: integer
:intent: output
:dims:
- 2*MAX(1,m)
- work:
:type: doublereal
:intent: workspace
:dims:
- 12*n
- iwork:
:type: integer
:intent: workspace
:dims:
- 7*n
- info:
:type: integer
:intent: output
:substitutions:
ldz: n
:fortran_help: " SUBROUTINE ZLARRV( N, VL, VU, D, L, PIVMIN, ISPLIT, M, DOL, DOU, MINRGP, RTOL1, RTOL2, W, WERR, WGAP, IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, WORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZLARRV computes the eigenvectors of the tridiagonal matrix\n\
* T = L D L^T given L, D and APPROXIMATIONS to the eigenvalues of L D L^T.\n\
* The input eigenvalues should have been computed by DLARRE.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix. N >= 0.\n\
*\n\
* VL (input) DOUBLE PRECISION\n\
* VU (input) DOUBLE PRECISION\n\
* Lower and upper bounds of the interval that contains the desired\n\
* eigenvalues. VL < VU. Needed to compute gaps on the left or right\n\
* end of the extremal eigenvalues in the desired RANGE.\n\
*\n\
* D (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, the N diagonal elements of the diagonal matrix D.\n\
* On exit, D may be overwritten.\n\
*\n\
* L (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, the (N-1) subdiagonal elements of the unit\n\
* bidiagonal matrix L are in elements 1 to N-1 of L\n\
* (if the matrix is not split.) At the end of each block\n\
* is stored the corresponding shift as given by DLARRE.\n\
* On exit, L is overwritten.\n\
*\n\
* PIVMIN (in) DOUBLE PRECISION\n\
* The minimum pivot allowed in the Sturm sequence.\n\
*\n\
* ISPLIT (input) INTEGER array, dimension (N)\n\
* The splitting points, at which T breaks up into blocks.\n\
* The first block consists of rows/columns 1 to\n\
* ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1\n\
* through ISPLIT( 2 ), etc.\n\
*\n\
* M (input) INTEGER\n\
* The total number of input eigenvalues. 0 <= M <= N.\n\
*\n\
* DOL (input) INTEGER\n\
* DOU (input) INTEGER\n\
* If the user wants to compute only selected eigenvectors from all\n\
* the eigenvalues supplied, he can specify an index range DOL:DOU.\n\
* Or else the setting DOL=1, DOU=M should be applied.\n\
* Note that DOL and DOU refer to the order in which the eigenvalues\n\
* are stored in W.\n\
* If the user wants to compute only selected eigenpairs, then\n\
* the columns DOL-1 to DOU+1 of the eigenvector space Z contain the\n\
* computed eigenvectors. All other columns of Z are set to zero.\n\
*\n\
* MINRGP (input) DOUBLE PRECISION\n\
*\n\
* RTOL1 (input) DOUBLE PRECISION\n\
* RTOL2 (input) DOUBLE PRECISION\n\
* Parameters for bisection.\n\
* An interval [LEFT,RIGHT] has converged if\n\
* RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )\n\
*\n\
* W (input/output) DOUBLE PRECISION array, dimension (N)\n\
* The first M elements of W contain the APPROXIMATE eigenvalues for\n\
* which eigenvectors are to be computed. The eigenvalues\n\
* should be grouped by split-off block and ordered from\n\
* smallest to largest within the block ( The output array\n\
* W from DLARRE is expected here ). Furthermore, they are with\n\
* respect to the shift of the corresponding root representation\n\
* for their block. On exit, W holds the eigenvalues of the\n\
* UNshifted matrix.\n\
*\n\
* WERR (input/output) DOUBLE PRECISION array, dimension (N)\n\
* The first M elements contain the semiwidth of the uncertainty\n\
* interval of the corresponding eigenvalue in W\n\
*\n\
* WGAP (input/output) DOUBLE PRECISION array, dimension (N)\n\
* The separation from the right neighbor eigenvalue in W.\n\
*\n\
* IBLOCK (input) INTEGER array, dimension (N)\n\
* The indices of the blocks (submatrices) associated with the\n\
* corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue\n\
* W(i) belongs to the first block from the top, =2 if W(i)\n\
* belongs to the second block, etc.\n\
*\n\
* INDEXW (input) INTEGER array, dimension (N)\n\
* The indices of the eigenvalues within each block (submatrix);\n\
* for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the\n\
* i-th eigenvalue W(i) is the 10-th eigenvalue in the second block.\n\
*\n\
* GERS (input) DOUBLE PRECISION array, dimension (2*N)\n\
* The N Gerschgorin intervals (the i-th Gerschgorin interval\n\
* is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should\n\
* be computed from the original UNshifted matrix.\n\
*\n\
* Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M) )\n\
* If INFO = 0, the first M columns of Z contain the\n\
* orthonormal eigenvectors of the matrix T\n\
* corresponding to the input eigenvalues, with the i-th\n\
* column of Z holding the eigenvector associated with W(i).\n\
* Note: the user must ensure that at least max(1,M) columns are\n\
* supplied in the array Z.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= 1, and if\n\
* JOBZ = 'V', LDZ >= max(1,N).\n\
*\n\
* ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) )\n\
* The support of the eigenvectors in Z, i.e., the indices\n\
* indicating the nonzero elements in Z. The I-th eigenvector\n\
* is nonzero only in elements ISUPPZ( 2*I-1 ) through\n\
* ISUPPZ( 2*I ).\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (12*N)\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (7*N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
*\n\
* > 0: A problem occurred in ZLARRV.\n\
* < 0: One of the called subroutines signaled an internal problem.\n\
* Needs inspection of the corresponding parameter IINFO\n\
* for further information.\n\
*\n\
* =-1: Problem in DLARRB when refining a child's eigenvalues.\n\
* =-2: Problem in DLARRF when computing the RRR of a child.\n\
* When a child is inside a tight cluster, it can be difficult\n\
* to find an RRR. A partial remedy from the user's point of\n\
* view is to make the parameter MINRGP smaller and recompile.\n\
* However, as the orthogonality of the computed vectors is\n\
* proportional to 1/MINRGP, the user should be aware that\n\
* he might be trading in precision when he decreases MINRGP.\n\
* =-3: Problem in DLARRB when refining a single eigenvalue\n\
* after the Rayleigh correction was rejected.\n\
* = 5: The Rayleigh Quotient Iteration failed to converge to\n\
* full accuracy in MAXITR steps.\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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