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DLARRE(l)) DLARRE(l)DLARRE - the tridiagonal matrix T, DLARRE sets "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (i) the numbers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and (iii) eigenvalues of each L_i D_i L_i^TNAMESUBROUTINE DLARRE( N, D, E, TOL, NSPLIT, ISPLIT, M, W, WOFF, GERSCH, WORK, INFO ) INTEGER INFO, M, N, NSPLIT DOUBLE PRECISION TOL INTEGER ISPLIT( * ) DOUBLE PRECISION D( * ), E( * ), GERSCH( * ), W( * ), WOFF( * ), WORK( * )SYNOPSISGiven the tridiagonal matrix T, DLARRE sets "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (i) the numbers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and (iii) eigenvalues of each L_i D_i L_i^T. The representations and eigenvalues found are then used by DSTEGR to compute the eigenvectors of a symmetric tridiagonal matrix. Currently, the base representations are limited to being positive or negative definite, and the eigenvalues of the definite matrices are found by the dqds algo- rithm (subroutine DLASQ2). As an added benefit, DLARRE also outputs the n Gerschgorin intervals for each L_i D_i L_i^T.PURPOSEN (input) INTEGER The order of the matrix. D (input/output) DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix T. On exit, the n diagonal elements of the diagonal matrices D_i. E (input/output) DOUBLE PRECISION array, dimension (N) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix T; E(N) need not be set. On exit, the subdiagonal elements of the unit bidiagonal matrices L_i. TOL (input) DOUBLE PRECISION The threshold for splitting. If on input |E(i)| < TOL, then the matrix T is split into smaller blocks. NSPLIT (input) INTEGER The number of blocks T splits into. 1 <= NSPLIT <= N. ISPLIT (output) INTEGER array, dimension (2*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., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. M (output) INTEGER The total number of eigenvalues (of all the L_i D_i L_i^T) found. W (output) DOUBLE PRECISION array, dimension (N) The first M elements contain the eigenvalues. The eigenvalues of each of the blocks, L_i D_i L_i^T, are sorted in ascending order. WOFF (output) DOUBLE PRECISION array, dimension (N) The NSPLIT base points sigma_i. GERSCH (output) DOUBLE PRECISION array, dimension (2*N) The n Gerschgorin intervals. WORK (input) DOUBLE PRECISION array, dimension (4*N???) Workspace. INFO (output) INTEGER Output error code from DLASQ2ARGUMENTSBased on contributions by Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USAFURTHER DETAILSLAPACK version 3.015 June 2000 DLARRE(l)

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