.TH "SRC/chbev_2stage.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/chbev_2stage.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBchbev_2stage\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info)" .br .RI "\fB CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine chbev_2stage (character jobz, character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)" .PP \fB CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of !> a complex Hermitian band matrix A using the 2stage technique for !> the reduction to tridiagonal\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBZ\fP .PP .nf !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors\&. !> Not available in this release\&. !> .fi .PP .br \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIKD\fP .PP .nf !> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'\&. KD >= 0\&. !> .fi .PP .br \fIAB\fP .PP .nf !> AB is COMPLEX array, dimension (LDAB, N) !> On entry, the upper or lower triangle of the Hermitian 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\&. !> .fi .PP .br \fILDAB\fP .PP .nf !> LDAB is INTEGER !> The leading dimension of the array AB\&. LDAB >= KD + 1\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is REAL array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is COMPLEX 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\&. !> .fi .PP .br \fILDZ\fP .PP .nf !> LDZ is INTEGER !> The leading dimension of the array Z\&. LDZ >= 1, and if !> JOBZ = 'V', LDZ >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX array, dimension LWORK !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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 !> 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, 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\&. !> .fi .PP .br \fIRWORK\fP .PP .nf !> RWORK is REAL array, dimension (max(1,3*N-2)) !> .fi .PP .br \fIINFO\fP .PP .nf !> 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\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf !> !> 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 !> !> .fi .PP .RE .PP .PP Definition at line \fB209\fP of file \fBchbev_2stage\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.