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DSTEQR2 - i a modified version of LAPACK routine DSTEQR

SUBROUTINE DSTEQR2( COMPZ, N, D, E, Z, LDZ, NR, WORK, INFO ) CHARACTER COMPZ INTEGER INFO, LDZ, N, NR DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )

DSTEQR2 is a modified version of LAPACK routine DSTEQR. DSTEQR2 computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. DSTEQR2 is modified from DSTEQR to allow each ScaLAPACK process running DSTEQR2 to perform updates on a distributed matrix Q. Proper usage of DSTEQR2 can be gleaned from examination of ScaLAPACK’s PDSYEV.

COMPZ (input) CHARACTER*1 = ’N’: Compute eigenvalues only. = ’I’: Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z must be initialized to the identity matrix by PDLASET or DLASET prior to entering this subroutine. N (input) INTEGER The order of the matrix. N >= 0. D (input/output) DOUBLE PRECISION array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order. E (input/output) DOUBLE PRECISION array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. Z (local input/local output) DOUBLE PRECISION array, global dimension (N, N), local dimension (LDZ, NR). On entry, if COMPZ = ’V’, then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if COMPZ = ’V’, Z contains the orthonormal eigenvectors of the original symmetric matrix, and if COMPZ = ’I’, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = ’N’, then Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if eigenvectors are desired, then LDZ >= max(1,N). NR (input) INTEGER NR = MAX(1, NUMROC( N, NB, MYPROW, 0, NPROCS ) ). If COMPZ = ’N’, then NR is not referenced. WORK (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2)) If COMPZ = ’N’, then WORK is not referenced. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if INFO = i, then i elements of E have not converged to zero; on exit, D and E contain the elements of a symmetric tridiagonal matrix which is orthogonally similar to the original matrix.