/home/abui...d_2stage.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssytrd_2stage.f

okay bestie so this is a Library Functions Manual page and it's literally the whole source-file page for ssytrd_2stage.f — no cap, that's the name, that whole giant path is the name. iykyk 🫶

✨ SYNOPSIS ✨

🎀 Functions/Subroutines

subroutine SSYTRD_2STAGE (vect, uplo, n, a, lda, d, e, tau, hous2,
    lhous2, work, lwork, info)
        SSYTRD_2STAGE

like, that's her. that's the subroutine. 💖

🌸 Function/Subroutine Documentation 🌸

🦋 subroutine SSYTRD_2STAGE

subroutine SSYTRD_2STAGE (character vect, character uplo, integer n, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) d, real,
    dimension( * ) e, real, dimension( * ) tau, real, dimension( * ) hous2,
    integer lhous2, real, dimension( * ) work, integer lwork, integer info)

SSYTRD_2STAGE 💅

⭐ Purpose:

!> !> SSYTRD_2STAGE reduces a real symmetric matrix A to real symmetric !> tridiagonal form T by a orthogonal similarity transformation: !> Q1**T Q2**T* A * Q2 * Q1 = T. !>

like yes bestie she reduces A to tridiagonal T and the transformation is Q1**T Q2**T* A * Q2 * Q1 = T — iconic behavior tbh 🔥

👑 Parameters

💜 VECT

!> VECT is CHARACTER*1 !> = 'N': No need for the Housholder representation, !> in particular for the second stage (Band to !> tridiagonal) and thus LHOUS2 is of size max(1, 4*N); !> = 'V': the Householder representation is needed to !> either generate Q1 Q2 or to apply Q1 Q2, !> then LHOUS2 is to be queried and computed. !> (NOT AVAILABLE IN THIS RELEASE). !>

so 'N' means no Householder representation needed (yes, the original spells it "Housholder", i'm not fixing her, that's the vibe), specifically not for the second stage (Band to tridiagonal), so LHOUS2 is max(1, 4*N). 'V' means the Householder representation is needed to generate Q1 Q2 or apply Q1 Q2, and then LHOUS2 has to be queried and computed — but heads up, that option is NOT AVAILABLE IN THIS RELEASE 😭 not me getting excited for nothing

🍓 UPLO

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

'U' = upper triangle stored, 'L' = lower triangle stored. pick your fighter ✨

🌈 N

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

the order of A, and N >= 0 bestie, keep it non-negative 💀

🧚 A

!> A is 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, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> On exit, if UPLO = 'U', the band superdiagonal !> of A are overwritten by the corresponding elements of the !> internal band-diagonal matrix AB, and the elements above !> the KD superdiagonal, with the array TAU, represent the orthogonal !> matrix Q1 as a product of elementary reflectors; if UPLO !> = 'L', the diagonal and band subdiagonal of A are over- !> written by the corresponding elements of the internal band-diagonal !> matrix AB, and the elements below the KD subdiagonal, with !> the array TAU, represent the orthogonal matrix Q1 as a product !> of elementary reflectors. See Further Details. !>

okay so on entry it's the symmetric matrix A. if UPLO = 'U', the leading N-by-N upper triangular part of A holds the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced (she doesn't look at it, she doesn't care). if UPLO = 'L', the leading N-by-N lower triangular part of A holds the lower triangular part of A, and the strictly upper triangular part is not referenced.

on exit, if UPLO = 'U', the band superdiagonal of A are overwritten by the corresponding elements of the internal band-diagonal matrix AB, and the elements above the KD superdiagonal, with the array TAU, represent the orthogonal matrix Q1 as a product of elementary reflectors. if UPLO = 'L', the diagonal and band subdiagonal of A are overwritten by the corresponding elements of the internal band-diagonal matrix AB, and the elements below the KD subdiagonal, with the array TAU, represent the orthogonal matrix Q1 as a product of elementary reflectors. see Further Details, bestie, it's all down there 👇

🎀 LDA

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

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

⭐ D

!> D is REAL array, dimension (N) !> The diagonal elements of the tridiagonal matrix T. !>

the diagonal of T. the main character elements, honestly 👑

🦋 E

!> E is REAL array, dimension (N-1) !> The off-diagonal elements of the tridiagonal matrix T. !>

the off-diagonal elements of T, dimension (N-1) fr fr

🔥 TAU

!> TAU is REAL array, dimension (N-KD) !> The scalar factors of the elementary reflectors of !> the first stage (see Further Details). !>

scalar factors of the elementary reflectors of the first stage — see Further Details 📚

🌸 HOUS2

!> HOUS2 is REAL array, dimension (LHOUS2) !> Stores the Householder representation of the stage2 !> band to tridiagonal. !>

she stores the Householder representation of the stage2 band to tridiagonal 💖

🍓 LHOUS2

!> LHOUS2 is INTEGER !> The dimension of the array HOUS2. !> If LWORK = -1, or LHOUS2 = -1, !> then a query is assumed; the routine !> only calculates the optimal size of the HOUS2 array, returns !> this value as the first entry of the HOUS2 array, and no error !> message related to LHOUS2 is issued by XERBLA. !> If VECT='N', LHOUS2 = max(1, 4*n); !> if VECT='V', option not yet available. !>

the dimension of HOUS2. if LWORK = -1, or LHOUS2 = -1, then a query is assumed: the routine only calculates the optimal size of the HOUS2 array, returns this value as the first entry of the HOUS2 array, and no error message related to LHOUS2 is issued by XERBLA. if VECT='N', LHOUS2 = max(1, 4*n); if VECT='V', option not yet available 😔 (again! she's teasing us)

💜 WORK

!> WORK is REAL array, dimension (LWORK) !>

that's it, that's the whole description. WORK is REAL array, dimension (LWORK). she said what she said 💅

🌈 LWORK

!> LWORK is INTEGER !> The dimension of the array WORK. LWORK = MAX(1, dimension) !> If LWORK = -1, or LHOUS2=-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. !> LWORK = MAX(1, dimension) where !> dimension = max(stage1,stage2) + (KD+1)*N !> = N*KD + N*max(KD+1,FACTOPTNB) !> + max(2*KD*KD, KD*NTHREADS) !> + (KD+1)*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. !>

the dimension of WORK, LWORK = MAX(1, dimension). if LWORK = -1, or LHOUS2=-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.

and the math, bestie, get your calculator out 🧮:

LWORK = MAX(1, dimension) where
dimension   = max(stage1,stage2) + (KD+1)*N
            = N*KD + N*max(KD+1,FACTOPTNB)
              + max(2*KD*KD, KD*NTHREADS)
              + (KD+1)*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, noted 📝), and NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1. lowkey a whole formula but she slayed it.

🎀 INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

0 = successful exit, slay ✅. < 0 = if INFO = -i, the i-th argument had an illegal value 🙈 so go check your args, bestie.

🧚 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

(shoutout to all four, we stan 🫶)

💖 Further Details:

!> !> Implemented by Azzam Haidar. !> !> All details are available on technical report, SC11, SC13 papers. !> !> 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 !> !>

implemented by Azzam Haidar, and all details are available on technical report, SC11, SC13 papers. the receipts:

  1. 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
  2. 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
  3. 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

like, she's well-read. she has citations. main character energy 🔥📚

Definition at line 222 of file ssytrd_2stage.f. 🎯

⭐ Author

Generated automatically by Doxygen for LAPACK from the source code.

and that's the whole page bestie!! 💜 the footer says LAPACK, Version 3.12.0, dated /home/abui...d_2stage.f(3) — so yeah, this is LAPACK version 3.12.0, auto-generated by Doxygen, and honestly? she ate. bye cutie, go reduce some symmetric matrices 🦋✨🎀

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