CLARRV (3) Linux Manual Page

clarrv.f –

Synopsis

Functions/Subroutines

subroutine clarrv (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)
CLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT.

Function/Subroutine Documentation

subroutine clarrv (integerN, realVL, realVU, real, dimension( * )D, real, dimension( * )L, realPIVMIN, integer, dimension( * )ISPLIT, integerM, integerDOL, integerDOU, realMINRGP, realRTOL1, realRTOL2, real, dimension( * )W, real, dimension( * )WERR, real, dimension( * )WGAP, integer, dimension( * )IBLOCK, integer, dimension( * )INDEXW, real, dimension( * )GERS, complex, dimension( ldz, * )Z, integerLDZ, integer, dimension( * )ISUPPZ, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

CLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT.

Purpose:

 CLARRV computes the eigenvectors of the tridiagonal matrix

 T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.

 The input eigenvalues should have been computed by SLARRE.

 

Parameters:

N

 N is INTEGER

 The order of the matrix. N >= 0.

VL

 VL is REAL

VU

 VU is REAL

 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.

D

 D is REAL array, dimension (N)

 On entry, the N diagonal elements of the diagonal matrix D.

 On exit, D may be overwritten.

L

 L is REAL 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

 is stored the corresponding shift as given by SLARRE.

 On exit, L is overwritten.

PIVMIN

 PIVMIN is REAL

 The minimum pivot allowed in the Sturm sequence.

ISPLIT

 ISPLIT is INTEGER array, dimension (N)

 The splitting points, at which T breaks up into blocks.

 The first block consists of rows/columns 1 to

 ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1

 through ISPLIT( 2 ), etc.

M

 M is INTEGER

 The total number of input eigenvalues. 0 <= M <= N.

DOL

 DOL is INTEGER

DOU

 DOU is INTEGER

 If the user wants to compute only selected eigenvectors from all

 the eigenvalues supplied, he can specify an index range DOL:DOU.

 Or else the setting DOL=1, DOU=M should be applied.

 Note that DOL and DOU refer to the order in which the eigenvalues

 are stored in W.

 If the user wants to compute only selected eigenpairs, then

 the columns DOL-1 to DOU+1 of the eigenvector space Z contain the

 computed eigenvectors. All other columns of Z are set to zero.

MINRGP

 MINRGP is REAL

RTOL1

 RTOL1 is REAL

RTOL2

 RTOL2 is REAL

 Parameters for bisection.

 An interval [LEFT,RIGHT] has converged if

 RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )

W

 W is REAL array, dimension (N)

 The first M elements of W contain the APPROXIMATE eigenvalues for

 which eigenvectors are to be computed. The eigenvalues

 should be grouped by split-off block and ordered from

 smallest to largest within the block ( The output array

 W from SLARRE is expected here ). Furthermore, they are with

 respect to the shift of the corresponding root representation

 for their block. On exit, W holds the eigenvalues of the

 UNshifted matrix.

WERR

 WERR is REAL array, dimension (N)

 The first M elements contain the semiwidth of the uncertainty

 interval of the corresponding eigenvalue in W

WGAP

 WGAP is REAL array, dimension (N)

 The separation from the right neighbor eigenvalue in W.

IBLOCK

 IBLOCK is INTEGER array, dimension (N)

 The indices of the blocks (submatrices) associated with the

 corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue

 W(i) belongs to the first block from the top, =2 if W(i)

 belongs to the second block, etc.

INDEXW

 INDEXW is INTEGER array, dimension (N)

 The indices of the eigenvalues within each block (submatrix);

 for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the

 i-th eigenvalue W(i) is the 10-th eigenvalue in the second block.

GERS

 GERS is REAL array, dimension (2*N)

 The N Gerschgorin intervals (the i-th Gerschgorin interval

 is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should

 be computed from the original UNshifted matrix.

Z

 Z is array, dimension (LDZ, max(1,M) )

 If INFO = 0, the first M columns of Z contain the

 orthonormal eigenvectors of the matrix T

 corresponding to the input eigenvalues, with the i-th

 column of Z holding the eigenvector associated with W(i).

 Note: the user must ensure that at least max(1,M) columns are

 supplied in the array Z.

LDZ

 LDZ is INTEGER

 The leading dimension of the array Z. LDZ >= 1, and if

 JOBZ = ‘V’, LDZ >= max(1,N).

ISUPPZ

 ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )

 The support of the eigenvectors in Z, i.e., the indices

 indicating the nonzero elements in Z. The I-th eigenvector

 is nonzero only in elements ISUPPZ( 2*I-1 ) through

 ISUPPZ( 2*I ).

WORK

 WORK is REAL array, dimension (12*N)

IWORK

 IWORK is INTEGER array, dimension (7*N)

INFO

 INFO is INTEGER

 = 0: successful exit

 > 0: A problem occured in CLARRV.

 < 0: One of the called subroutines signaled an internal problem.

 Needs inspection of the corresponding parameter IINFO

 for further information.

 =-1: Problem in SLARRB when refining a child’s eigenvalues.

 =-2: Problem in SLARRF when computing the RRR of a child.

 When a child is inside a tight cluster, it can be difficult

 to find an RRR. A partial remedy from the user’s point of

 view is to make the parameter MINRGP smaller and recompile.

 However, as the orthogonality of the computed vectors is

 proportional to 1/MINRGP, the user should be aware that

 he might be trading in precision when he decreases MINRGP.

 =-3: Problem in SLARRB when refining a single eigenvalue

 after the Rayleigh correction was rejected.

 = 5: The Rayleigh Quotient Iteration failed to converge to

 full accuracy in MAXITR steps.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

Beresford Parlett, University of California, Berkeley, USA

 Jim Demmel, University of California, Berkeley, USA 

 Inderjit Dhillon, University of Texas, Austin, USA 

 Osni Marques, LBNL/NERSC, USA 

 Christof Voemel, University of California, Berkeley, USA 

Definition at line 280 of file clarrv.f.

Author

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