# cheevd_2stage.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **cheevd_2stage** (JOBZ, UPLO, **N**, A, **LDA**, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)

**CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices**

## Function/Subroutine Documentation

### subroutine cheevd_2stage (character JOBZ, character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) W, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, integer LRWORK, integer, dimension( * ) IWORK, integer LIWORK, integer INFO)

**CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices**

**Purpose:**

CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A using the 2stage technique for the reduction to tridiagonal. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

**Parameters:***JOBZ*JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. Not available in this release.

*UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is COMPLEX array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*W*W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.

*WORK*WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. If N <= 1, LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be queried. LWORK = MAX(1, dimension) where dimension = max(stage1,stage2) + (KD+1)*N + N+1 = N*KD + N*max(KD+1,FACTOPTNB) + max(2*KD*KD, KD*NTHREADS) + (KD+1)*N + N+1 where KD is the blocking size of the reduction, FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2 If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.

*RWORK*RWORK is REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

*LRWORK*LRWORK is INTEGER The dimension of the array RWORK. If N <= 1, LRWORK must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.

*IWORK*IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

*LIWORK*LIWORK is INTEGER The dimension of the array IWORK. If N <= 1, LIWORK must be at least 1. If JOBZ = 'N' and N > 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**November 2017

**Further Details:**Modified description of INFO. Sven, 16 Feb 05.

**Contributors:**Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

**Further Details:**

All details about the 2stage techniques are available in: Azzam Haidar, Hatem Ltaief, and Jack Dongarra. Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '11), New York, NY, USA, Article 8 , 11 pages. http://doi.acm.org/10.1145/2063384.2063394 A. Haidar, J. Kurzak, P. Luszczek, 2013. An improved parallel singular value algorithm and its implementation for multicore hardware, In Proceedings of 2013 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '13). Denver, Colorado, USA, 2013. Article 90, 12 pages. http://doi.acm.org/10.1145/2503210.2503292 A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. A novel hybrid CPU-GPU generalized eigensolver for electronic structure calculations based on fine-grained memory aware tasks. International Journal of High Performance Computing Applications. Volume 28 Issue 2, Pages 196-209, May 2014. http://hpc.sagepub.com/content/28/2/196

Definition at line 255 of file cheevd_2stage.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cheevd_2stage(3) is an alias of cheevd_2stage.f(3).