syevd_2stage#

ssyevd_2stage

Functions

void ssyevd_2stage(
    const char* jobz,
    const char* uplo,
    const INT   n,
          f32*  A,
    const INT   lda,
          f32*  W,
          f32*  work,
    const INT   lwork,
          INT*  iwork,
    const INT   liwork,
          INT*  info
);

void ssyevd_2stage(const char *jobz, const char *uplo, const INT n, f32 *A, const INT lda, f32 *W, f32 *work, const INT lwork, INT *iwork, const INT liwork, INT *info)#

SSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A using the 2stage technique for the reduction to tridiagonal.

If eigenvectors are desired, it uses a divide and conquer algorithm.

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. https://doi.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. https://doi.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. https://doi.org/10.1177/1094342013502097

Parameters

in

jobz

'N': Compute eigenvalues only; 'V': Compute eigenvalues and eigenvectors. Not available in this release.

in

uplo

'U': Upper triangle of A is stored; 'L': Lower triangle of A is stored.

in

n

The order of the matrix A. n>=0.

inout

A

On entry, the symmetric 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.

in

lda

The leading dimension of the array A. lda>=max(1,n).

out

W

Array of dimension (n). If info=0, the eigenvalues in ascending order.

out

work

Array of dimension (lwork). On exit, if info=0, work[0] returns the optimal lwork.

in

lwork

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 + 2*n+1
          = n*kd + n*max(kd+1,FACTOPTNB)
            + max(2*kd*kd, kd*NTHREADS)
            + (kd+1)*n + 2*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 1 + 6*n + 2*n**2. 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.

out

iwork

Integer array, dimension (max(1,liwork)). On exit, if info=0, iwork[0] returns the optimal liwork.

in

liwork

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 and iwork arrays, returns these values as the first entries of the work and iwork arrays.

out

info

info=0: successful exit
info<0: if info=-i, the i-th argument had an illegal value
info>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).

dsyevd_2stage

Functions

void dsyevd_2stage(
    const char* jobz,
    const char* uplo,
    const INT   n,
          f64*  A,
    const INT   lda,
          f64*  W,
          f64*  work,
    const INT   lwork,
          INT*  iwork,
    const INT   liwork,
          INT*  info
);

void dsyevd_2stage(const char *jobz, const char *uplo, const INT n, f64 *A, const INT lda, f64 *W, f64 *work, const INT lwork, INT *iwork, const INT liwork, INT *info)#

DSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A using the 2stage technique for the reduction to tridiagonal.

If eigenvectors are desired, it uses a divide and conquer algorithm.

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. https://doi.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. https://doi.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. https://doi.org/10.1177/1094342013502097

Parameters

in

jobz

'N': Compute eigenvalues only; 'V': Compute eigenvalues and eigenvectors. Not available in this release.

in

uplo

'U': Upper triangle of A is stored; 'L': Lower triangle of A is stored.

in

n

The order of the matrix A. n>=0.

inout

A

On entry, the symmetric 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.

in

lda

The leading dimension of the array A. lda>=max(1,n).

out

W

Array of dimension (n). If info=0, the eigenvalues in ascending order.

out

work

Array of dimension (lwork). On exit, if info=0, work[0] returns the optimal lwork.

in

lwork

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 + 2*n+1
          = n*kd + n*max(kd+1,FACTOPTNB)
            + max(2*kd*kd, kd*NTHREADS)
            + (kd+1)*n + 2*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 1 + 6*n + 2*n**2. 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.

out

iwork

Integer array, dimension (max(1,liwork)). On exit, if info=0, iwork[0] returns the optimal liwork.

in

liwork

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 and iwork arrays, returns these values as the first entries of the work and iwork arrays.

out

info

info=0: successful exit
info<0: if info=-i, the i-th argument had an illegal value
info>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).