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ZLARRV(l)) ZLARRV(l)NAMEZLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^TSYNOPSISSUBROUTINE ZLARRV( N, D, L, ISPLIT, M, W, IBLOCK, GERSCH, TOL, Z, LDZ, ISUPPZ, WORK, IWORK, INFO ) INTEGER INFO, LDZ, M, N DOUBLE PRECISION TOL INTEGER IBLOCK( * ), ISPLIT( * ), ISUPPZ( * ), IWORK( * ) DOUBLE PRECISION D( * ), GERSCH( * ), L( * ), W( * ), WORK( * ) COMPLEX*16 Z( LDZ, * )PURPOSEZLARRV computes the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T. The input eigenvalues should have high relative accuracy with respect to the entries of L and D. The desired accuracy of the output can be specified by the input parameter TOL.ARGUMENTSN (input) INTEGER The order of the matrix. N >= 0. D (input/output) DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the diagonal matrix D. On exit, D may be overwritten. L (input/output) DOUBLE PRECISION array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the unit bidiagonal matrix L in ele- ments 1 to N-1 of L. L(N) need not be set. On exit, L is overwritten. ISPLIT (input) INTEGER array, dimension (N) The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ), etc. TOL (input) DOUBLE PRECISION The absolute error tolerance for the eigenvalues/eigenvectors. Errors in the input eigenvalues must be bounded by TOL. The eigenvectors output have residual norms bounded by TOL, and the dot products between different eigenvectors are bounded by TOL. TOL must be at least N*EPS*|T|, where EPS is the machine precision and |T| is the 1-norm of the tridiagonal matrix. M (input) INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. W (input) DOUBLE PRECISION array, dimension (N) The first M elements of W contain the 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 DLARRE is expected here ). Errors in W must be bounded by TOL (see above). IBLOCK (input) INTEGER array, dimension (N) The submatrix indices associated with the corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the first submatrix from the top, =2 if W(i) belongs to the second submatrix, etc. Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M) ) If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix T corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced. Note: the user must ensure that at least max(1,M) col- umns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). ISUPPZ (output) 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 (workspace) DOUBLE PRECISION array, dimension (13*N) IWORK (workspace) INTEGER array, dimension (6*N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value > 0: if INFO = 1, internal error in DLARRB if INFO = 2, internal error in ZSTEIN-iFURTHER DETAILSBased on contributions by Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USA Ken Stanley, Computer Science Division, University of California at Berkeley, USALAPACK version 3.015 June 2000 ZLARRV(l)

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