hegv_2stage(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

okay bestie, welcome to hegv_2stage(3) from the Library Functions Manual — the page for the {he,sy}gv_2stage crew, aka eig, QR iteration, 2-stage. it's giving “generalized Hermitian/symmetric-definite eigenvalue problems, but make it 2-stage,” and we are seated. 💅

🎀 NAME 🎀

hegv_2stage — {he,sy}gv_2stage: eig, QR iteration, 2-stage

✨ SYNOPSIS ✨

💖 Functions 💖

🌸 `chegv_2stage` 🌸

subroutine chegv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work,
    lwork, rwork, info)

CHEGV_2STAGE

🦋 `dsygv_2stage` 🦋

subroutine dsygv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work,
    lwork, info)

DSYGV_2STAGE

🎀 `ssygv_2stage` 🎀

subroutine ssygv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work,
    lwork, info)

SSYGV_2STAGE

⭐ `zhegv_2stage` ⭐

subroutine zhegv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work,
    lwork, rwork, info)

ZHEGV_2STAGE

🌈 Detailed Description 🌈

(the original leaves this section empty, bestie — the real tea is in the function docs below 👇)

🦋 Function Documentation 🦋

🍓 subroutine `chegv_2stage` 🍓

subroutine chegv_2stage (integer itype, character jobz, character uplo,
    integer n, complex, dimension( lda, * ) a, integer lda, complex,
    dimension( ldb, * ) b, integer ldb, real, dimension( * ) w, complex,
    dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer
    info)

CHEGV_2STAGE

💖 Purpose 💖

okay so CHEGV_2STAGE computes all the eigenvalues, and optionally the eigenvectors, of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. here A and B are assumed to be Hermitian and B is also positive definite. this routine uses the 2stage technique for the reduction to tridiagonal, which showed higher performance on recent architecture and for large sizes N>2000. periodt. 🔥

🎀 Parameters 🎀

ITYPE — ITYPE is INTEGER. it specifies the problem type to be solved:

= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ — JOBZ is CHARACTER*1.

= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.

heads up bestie: 'V' is Not available in this release. 😭

UPLO — UPLO is CHARACTER*1.

= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.

N — N is INTEGER. the order of the matrices A and B. 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 matrix Z of eigenvectors. the eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed.

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

B — B is COMPLEX array, dimension (LDB, N).

On entry, the Hermitian positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H.

LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= 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 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 = max(stage1,stage2) + (KD+1)*N + N
          = N*KD + N*max(KD+1,FACTOPTNB)
            + max(2*KD*KD, KD*NTHREADS)
            + (KD+1)*N + N

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 queried. Not yet available.

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.

RWORK — RWORK is REAL array, dimension (max(1, 3*N-2)).

INFO — INFO is INTEGER.

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: CPOTRF or CHEEV returned an error code:
- <= N: if INFO = i, CHEEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
- > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

👑 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 230 of file chegv_2stage.f.

🍓 subroutine `dsygv_2stage` 🍓

subroutine dsygv_2stage (integer itype, character jobz, character uplo,
    integer n, double precision, dimension( lda, * ) a, integer lda, double
    precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( * ) w, double precision, dimension( * ) work, integer lwork,
    integer info)

DSYGV_2STAGE

💖 Purpose 💖

okay so DSYGV_2STAGE computes all the eigenvalues, and optionally the eigenvectors, of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. here A and B are assumed to be symmetric and B is also positive definite. this routine uses the 2stage technique for the reduction to tridiagonal, which showed higher performance on recent architecture and for large sizes N>2000. no cap. 🔥

🎀 Parameters 🎀

ITYPE — ITYPE is INTEGER. it specifies the problem type to be solved:

= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ — JOBZ is CHARACTER*1.

= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.

heads up bestie: 'V' is Not available in this release. 😭

UPLO — UPLO is CHARACTER*1.

= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.

N — N is INTEGER. the order of the matrices A and B. N >= 0.

`A`

A — DOUBLE PRECISION array, dimension (LDA, N)

ok so on the way in, A is your symmetric matrix, bestie. If UPLO = 'U', the leading N-by-N upper triangular part of A holds the upper triangular part of matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A holds the lower triangular part of matrix A.

On the way out? If JOBZ = 'V' and INFO = 0, A contains the matrix Z of eigenvectors, and they're normalized like this:

if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.

If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. 💀 gone. she's done.

LDA — INTEGER

The leading dimension of the array A. LDA >= max(1,N). that's the whole vibe check, no notes.

B — DOUBLE PRECISION array, dimension (LDB, N)

On entry, B is the symmetric positive definite matrix. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of matrix B.

On exit, if INFO <= N, the part of B that was holding the matrix gets overwritten by the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T. so yeah she does NOT come back the same 🫶

LDB — INTEGER

The leading dimension of the array B. LDB >= max(1,N).

W — DOUBLE PRECISION array, dimension (N)

If INFO = 0, this is where the eigenvalues live, in ascending order. ✨

WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK))

On exit, if INFO = 0, WORK(1) returns the optimal LWORK. she's a lil self-reporting icon.

LWORK — INTEGER

The length of the array WORK. LWORK >= 1 when N <= 1. Otherwise, listen up:

If JOBZ = 'N' and N > 1, LWORK must be queried. no guessing, babe.

LWORK = MAX(1, dimension) where
          dimension = max(stage1,stage2) + (KD+1)*N + 2*N
                    = N*KD + N*max(KD+1,FACTOPTNB)
                      + max(2*KD*KD, KD*NTHREADS)
                      + (KD+1)*N + 2*N

and what even are those, you ask, slay, so:

KD is the blocking size of the reduction
FACTOPTNB is the blocking used by the QR or LQ algorithm, and 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 queried too — not yet available. like, she's coming, but she's not here yet 🙈

If LWORK = -1, a workspace query is assumed: the routine only calculates the optimal size of the WORK array, returns that value as the first entry of the WORK array, and XERBLA issues no error message related to LWORK. literally just a peek, no commitment.

INFO — INTEGER

= 0: successful exit, we ate 💅
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPOTRF or DSYEV returned an error code:
- <= N: if INFO = i, DSYEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
- > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. 😭 nothing. nada.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌈 Further Details

ok so all the details about the 2stage techniques are available in these papers, and yes we're citing them properly because we're respectful like that:

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 224 of file dsygv_2stage.f.

🦋 subroutine ssygv_2stage

subroutine ssygv_2stage (integer itype, character jobz, character uplo,
    integer n, real, dimension( lda, * ) a, integer lda, real, dimension(
    ldb, * ) b, integer ldb, real, dimension( * ) w, real, dimension( * )
    work, integer lwork, integer info)

SSYGV_2STAGE — the single-precision sister, same energy 🎀

🎯 Purpose

SSYGV_2STAGE computes all the eigenvalues, and optionally the eigenvectors, of a real generalized symmetric-definite eigenproblem, of the form:

A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.

Here A and B are assumed to be symmetric and B is also positive definite. This routine uses the 2stage technique for the reduction to tridiagonal, which showed higher performance on recent architecture and for large sizes N>2000. 🔥 like, big matrices, big slay.

✨ Parameters

ITYPE — INTEGER

Specifies the problem type to be solved:

= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ — CHARACTER*1

= 'N': compute eigenvalues only;
= 'V': compute eigenvalues and eigenvectors. Not available in this release. 💀 sorry bestie, that door's locked for now.

UPLO — CHARACTER*1

= 'U': upper triangles of A and B are stored;
= 'L': lower triangles of A and B are stored.

pick your fighter, either way it's a triangle.

N — INTEGER

The order of the matrices A and B. N >= 0.

A — REAL array, dimension (LDA, N)

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 matrix Z of eigenvectors. The eigenvectors are normalized as follows:

if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.

If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. same tragic ending as her double-precision twin 😭

LDA — INTEGER

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

B — REAL array, dimension (LDB, N)

On entry, the symmetric positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T.

LDB — INTEGER

The leading dimension of the array B. LDB >= max(1,N).

W — REAL array, dimension (N)

If INFO = 0, the eigenvalues in ascending order. 🌸 sorted, tidy, gorgeous.

WORK — REAL array, dimension (MAX(1,LWORK))

On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK — INTEGER. This is the length of the WORK array, bestie. LWORK >= 1, when N <= 1; otherwise:

If JOBZ = 'N' and N > 1, LWORK must be queried.

LWORK = MAX(1, dimension) where
dimension = max(stage1,stage2) + (KD+1)*N + 2*N
          = N*KD + N*max(KD+1,FACTOPTNB)
            + max(2*KD*KD, KD*NTHREADS)
            + (KD+1)*N + 2*N

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 queried. Not yet available.

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.

INFO — INTEGER. The receipts 💅:

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPOTRF or SSYEV returned an error code:
- <= N: if INFO = i, SSYEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
- > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

🌸 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 224 of file ssygv_2stage.f.

🧚 `subroutine zhegv_2stage` 🧚

subroutine zhegv_2stage (integer itype, character jobz, character uplo,
    integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w,
    complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer info)

ZHEGV_2STAGE

🎯 Purpose 🎯

ZHEGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian and B is also positive definite.

This routine use the 2stage technique for the reduction to tridiagonal which showed higher performance on recent architecture and for large sizes N>2000.

🧾 Parameters 🧾

ITYPE — INTEGER. Specifies the problem type to be solved:

= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ — CHARACTER*1.

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

UPLO — CHARACTER*1.

= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.

N — INTEGER. The order of the matrices A and B. N >= 0.

A — COMPLEX*16 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 matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I.

If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed.

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

B — COMPLEX*16 array, dimension (LDB, N).

On entry, the Hermitian positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H.

LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).

W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.

WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK — 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 = max(stage1,stage2) + (KD+1)*N + N
          = N*KD + N*max(KD+1,FACTOPTNB)
            + max(2*KD*KD, KD*NTHREADS)
            + (KD+1)*N + N

If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.

RWORK — DOUBLE PRECISION array, dimension (max(1, 3*N-2)).

INFO — INTEGER.

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPOTRF or ZHEEV returned an error code:
- <= N: if INFO = i, ZHEEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
- > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

🌸 Author 🌸

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📚 Further Details: 📚

okay so bestie, all the details about the 2stage techniques are available in these iconic papers — like, the receipts are right here:

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

and the exact lil source line is: Definition at line 230 of file zhegv_2stage.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. no cap, that's the whole author section — Doxygen did the typing, LAPACK brought the source code 🫶✨

mwah 💋 that's the whole page, bestie. source/version: LAPACK, Version 3.12.0; page: hegv_2stage(3). The footer didn't give me a date to hype, so I'm not making one up — periodt 🌈💅

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

hegv_2stage(3)

🎀 NAME 🎀

✨ SYNOPSIS ✨

💖 Functions 💖

🌸 chegv_2stage 🌸

🦋 dsygv_2stage 🦋

🎀 ssygv_2stage 🎀

⭐ zhegv_2stage ⭐

🌈 Detailed Description 🌈

🦋 Function Documentation 🦋

🍓 subroutine chegv_2stage 🍓

💖 Purpose 💖

🎀 Parameters 🎀

👑 Author 👑

🌟 Further Details 🌟

🍓 subroutine dsygv_2stage 🍓

💖 Purpose 💖

🎀 Parameters 🎀

A

👑 Author

🌈 Further Details

🦋 subroutine ssygv_2stage

🎯 Purpose

✨ Parameters

🌸 Author 🌸

📚 Further Details: 📚

🧚 subroutine zhegv_2stage 🧚

🎯 Purpose 🎯

🧾 Parameters 🧾

🌸 Author 🌸

📚 Further Details: 📚

👑 Author 👑

🌸 `chegv_2stage` 🌸

🦋 `dsygv_2stage` 🦋

🎀 `ssygv_2stage` 🎀

⭐ `zhegv_2stage` ⭐

🍓 subroutine `chegv_2stage` 🍓

🍓 subroutine `dsygv_2stage` 🍓

`A`

🧚 `subroutine zhegv_2stage` 🧚