SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, $ LIWORK, INFO ) IMPLICIT NONE * * * -- LAPACK computational routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER JOBZ, RANGE INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER ISUPPZ( * ), IWORK( * ) DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) COMPLEX*16 Z( LDZ, * ) * .. * * Purpose * ======= * * ZSTEGR computes selected eigenvalues and, optionally, eigenvectors * of a real symmetric tridiagonal matrix T. Any such unreduced matrix has * a well defined set of pairwise different real eigenvalues, the corresponding * real eigenvectors are pairwise orthogonal. * * The spectrum may be computed either completely or partially by specifying * either an interval (VL,VU] or a range of indices IL:IU for the desired * eigenvalues. * * ZSTEGR is a compatability wrapper around the improved ZSTEMR routine. * See DSTEMR for further details. * * One important change is that the ABSTOL parameter no longer provides any * benefit and hence is no longer used. * * Note : ZSTEGR and ZSTEMR work only on machines which follow * IEEE-754 floating-point standard in their handling of infinities and * NaNs. Normal execution may create these exceptiona values and hence * may abort due to a floating point exception in environments which * do not conform to the IEEE-754 standard. * * Arguments * ========= * * JOBZ (input) CHARACTER*1 * = 'N': Compute eigenvalues only; * = 'V': Compute eigenvalues and eigenvectors. * * RANGE (input) CHARACTER*1 * = 'A': all eigenvalues will be found. * = 'V': all eigenvalues in the half-open interval (VL,VU] * will be found. * = 'I': the IL-th through IU-th eigenvalues will be found. * * N (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 tridiagonal matrix * T. On exit, D is overwritten. * * E (input/output) DOUBLE PRECISION array, dimension (N) * On entry, the (N-1) subdiagonal elements of the tridiagonal * matrix T in elements 1 to N-1 of E. E(N) need not be set on * input, but is used internally as workspace. * On exit, E is overwritten. * * VL (input) DOUBLE PRECISION * VU (input) DOUBLE PRECISION * If RANGE='V', the lower and upper bounds of the interval to * be searched for eigenvalues. VL < VU. * Not referenced if RANGE = 'A' or 'I'. * * IL (input) INTEGER * IU (input) INTEGER * If RANGE='I', the indices (in ascending order) of the * smallest and largest eigenvalues to be returned. * 1 <= IL <= IU <= N, if N > 0. * Not referenced if RANGE = 'A' or 'V'. * * ABSTOL (input) DOUBLE PRECISION * Unused. Was the absolute error tolerance for the * eigenvalues/eigenvectors in previous versions. * * M (output) INTEGER * The total number of eigenvalues found. 0 <= M <= N. * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. * * W (output) DOUBLE PRECISION array, dimension (N) * The first M elements contain the selected eigenvalues in * ascending order. * * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M) ) * If JOBZ = 'V', and if INFO = 0, then 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) columns 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. * Supplying N columns is always safe. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= 1, and if * JOBZ = 'V', then 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 computed eigenvector * is nonzero only in elements ISUPPZ( 2*i-1 ) through * ISUPPZ( 2*i ). This is relevant in the case when the matrix * is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. * * WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) * On exit, if INFO = 0, WORK(1) returns the optimal * (and minimal) LWORK. * * LWORK (input) INTEGER * The dimension of the array WORK. LWORK >= max(1,18*N) * if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the optimal size of the WORK array, returns * this value as the first entry of the WORK array, and no error * message related to LWORK is issued by XERBLA. * * IWORK (workspace/output) INTEGER array, dimension (LIWORK) * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. * * LIWORK (input) INTEGER * The dimension of the array IWORK. LIWORK >= max(1,10*N) * if the eigenvectors are desired, and LIWORK >= max(1,8*N) * if only the eigenvalues are to be computed. * If LIWORK = -1, then a workspace query is assumed; the * routine only calculates the optimal size of the IWORK array, * returns this value as the first entry of the IWORK array, and * no error message related to LIWORK is issued by XERBLA. * * INFO (output) INTEGER * On exit, INFO * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: if INFO = 1X, internal error in DLARRE, * if INFO = 2X, internal error in ZLARRV. * Here, the digit X = ABS( IINFO ) < 10, where IINFO is * the nonzero error code returned by DLARRE or * ZLARRV, respectively. * * Further Details * =============== * * Based on contributions by * Inderjit Dhillon, IBM Almaden, USA * Osni Marques, LBNL/NERSC, USA * Christof Voemel, LBNL/NERSC, USA * * ===================================================================== * * .. Local Scalars .. LOGICAL TRYRAC * .. * .. External Subroutines .. EXTERNAL ZSTEMR * .. * .. Executable Statements .. INFO = 0 TRYRAC = .FALSE. CALL ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, $ M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK, $ IWORK, LIWORK, INFO ) * * End of ZSTEGR * END