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

💅 dlatsqr.f — the manual page, but make it make sense 🎀

okay so bestie, this is a page from the Library Functions Manual, and the file in question is literally:

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

yes that's a whole path, no I will not be shortening it, it's iconic in its own chaotic way 💀

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✨ SYNOPSIS ✨

Functions/Subroutines, babes:

subroutine DLATSQR (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)

that's it, that's the subroutine. her name is DLATSQR and she's the main character 🌟

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🦋 Function/Subroutine Documentation 🦋

subroutine DLATSQR (integer m, integer n, integer mb, integer nb, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension(ldt, *) t, integer ldt, double precision, dimension( * ) work,
    integer lwork, integer info)

DLATSQR — say it with me. DLATSQR. 🗣️

🌸 Purpose 🌸

DLATSQR computes a blocked Tall-Skinny QR factorization of a real M-by-N matrix A for M >= N:

A = Q * ( R ),
         ( 0 )

where, and listen close bestie:

• Q is a M-by-M orthogonal matrix, stored on exit in an implicit form in the elements below the diagonal of the array A and in the elements of the array T;
• R is an upper-triangular N-by-N matrix, stored on exit in the elements on and above the diagonal of the array A.
• 0 is a (M-N)-by-N zero matrix, and is not stored. she's not invited to the storage party, periodt. 💅

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🎀 Parameters 🎀

• M — M is INTEGER. The number of rows of the matrix A. M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. M >= N >= 0.
• MB — MB is INTEGER. The row block size to be used in the blocked QR. MB > 0.
• NB — NB is INTEGER. The column block size to be used in the blocked QR. N >= NB >= 1.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the N-by-N upper triangular matrix R; the elements below the diagonal represent Q by the columns of blocked V (see Further Details). glow-up on exit, honestly ✨
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• T — T is DOUBLE PRECISION array, dimension (LDT, N * Number_of_row_blocks) where Number_of_row_blocks = CEIL((M-N)/(MB-N)). The blocked upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details below. compact form is such a vibe 🫶
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= NB.
• WORK — (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)). the workspace, the backstage area, the green room 💜
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= NB*N. 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. sneaky little -1 trick, iykyk 😌
• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. (we love a clean 0, we do not love a negative. 🙈)

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

the whole squad really showed up for this one 🫡

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🌈 Further Details: 🌈

Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations, representing Q as a product of other orthogonal matrices

Q = Q(1) * Q(2) * . . . * Q(k)

where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:

Q(1) zeros out the subdiagonal entries of rows 1:MB of A
Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
. . .

Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors stored under the diagonal of rows 1:MB of A, and by upper triangular block reflectors, stored in array T(1:LDT,1:N). For more information see Further Details in GEQRT. 💫

Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N). The last Q(k) may use fewer rows. For more information see Further Details in TPQRT. 🔥

For more details of the overall algorithm, see the description of Sequential TSQR in Section 2.2 of [1].

[1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,” J. Demmel, L. Grigori, M. Hoemmen, J. Langou, SIAM J. Sci. Comput, vol. 34, no. 1, 2012

ngl the citation is giving academic baddie energy and we respect it 📚

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⭐ Also ⭐

Definition at line 167 of file dlatsqr.f.

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💖 cute sign-off 💖

This page was generated automatically by Doxygen for LAPACK from the source code — so like, nobody hand-wrote this for me, it's a whole robot situation 🤖✨

Source, version and date realness: LAPACK, Version 3.12.0, and the file it came from is /home/abui.../dlatsqr.f(3).

go off, blocked TSQR. slay. 💅🎀🦋