SRC/ssbevd_2stage.f(3) Library Functions Manual SRC/ssbevd_2stage.f(3) NAME SRC/ssbevd_2stage.f SYNOPSIS Functions/Subroutines subroutine ssbevd_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, iwork, liwork, info) SSBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices Function/Subroutine Documentation subroutine ssbevd_2stage (character jobz, character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info) SSBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices Purpose: !> !> SSBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of !> a real symmetric band matrix A using the 2stage technique for !> the reduction to tridiagonal. If eigenvectors are desired, it uses !> a divide and conquer algorithm. !> !> 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. !> KD !> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KD >= 0. !> AB !> AB is REAL array, dimension (LDAB, N) !> On entry, the upper or lower triangle of the symmetric band !> matrix A, stored in the first KD+1 rows of the array. The !> j-th column of A is stored in the j-th column of the array AB !> as follows: !> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; !> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). !> !> On exit, AB is overwritten by values generated during the !> reduction to tridiagonal form. If UPLO = 'U', the first !> superdiagonal and the diagonal of the tridiagonal matrix T !> are returned in rows KD and KD+1 of AB, and if UPLO = 'L', !> the diagonal and first subdiagonal of T are returned in the !> first two rows of AB. !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD + 1. !> W !> W is REAL array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !> Z !> Z is REAL array, dimension (LDZ, N) !> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal !> eigenvectors of the matrix A, with the i-th column of Z !> holding the eigenvector associated with W(i). !> If JOBZ = 'N', then Z is not referenced. !> LDZ !> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1, and if !> JOBZ = 'V', LDZ >= max(1,N). !> WORK !> WORK is REAL array, dimension LWORK !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> LWORK !> LWORK is INTEGER !> The length of the array WORK. LWORK >= 1, when N <= 1; !> otherwise !> If JOBZ = 'N' and N > 1, LWORK must be queried. !> LWORK = MAX(1, dimension) where !> dimension = (2KD+1)*N + KD*NTHREADS + N !> where KD is the size of the band. !> NTHREADS is the number of threads used when !> openMP compilation is enabled, otherwise =1. !> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal sizes of the WORK and IWORK !> arrays, returns these values as the first entries of the WORK !> and IWORK arrays, and no error message related to LWORK 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 JOBZ = 'N' or N <= 1, LIWORK must be at least 1. !> If JOBZ = 'V' and N > 2, 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 and !> IWORK arrays, returns these values as the first entries of !> the WORK and IWORK arrays, and no error message related to !> LWORK 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, the algorithm failed to converge; i !> off-diagonal elements of an intermediate tridiagonal !> form did not converge to zero. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. 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 226 of file ssbevd_2stage.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 SRC/ssbevd_2stage.f(3)