SRC/sgemlq.f(3)

🎀 SRC/sgemlq.f 🎀

ok so this is a page straight out of the LAPACK Library Functions Manual and honestly? it's a whole vibe. it's the docs for SGEMLQ, one single subroutine, and we're gonna go through it together like it's a group project and i actually did the reading 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

here's the lineup, one icon and one icon only:

subroutine sgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work,
    lwork, info)

SGEMLQ — that's her, that's the main character 👑

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📖 Function/Subroutine Documentation 📖

the signature, exactly as written, no cap:

subroutine sgemlq (character side, character trans, integer m, integer n,
    integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *
    ) t, integer tsize, real, dimension( ldc, * ) c, integer ldc, real,
    dimension( * ) work, integer lwork, integer info)

SGEMLQ

💖 Purpose

ok so bestie, here's the whole point of this function. SGEMLQ overwrites the general real M-by-N matrix C with:

                   SIDE = 'L'     SIDE = 'R'
  TRANS = 'N':      Q * C          C * Q
  TRANS = 'T':      Q**T * C       C * Q**T

where Q is a real orthogonal matrix defined as the product of blocked elementary reflectors computed by short wide LQ factorization (SGELQ). like, that's it, that's the tea ☕✨

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🌸 Parameters 🌸

every single one, in order, because we do not skip:

• SIDE — it's a CHARACTER*1, and it decides which side Q or Q**T gets applied from:
  • = 'L': apply Q or Q**T from the Left;
  • = 'R': apply Q or Q**T from the Right.
• TRANS — also CHARACTER*1, the transpose vibe check:
  • = 'N': No transpose, apply Q;
  • = 'T': Transpose, apply Q**T.
• M — INTEGER, the number of rows of the matrix A. M >=0.
• N — INTEGER, the number of columns of the matrix C. N >= 0.
• K — INTEGER, the number of elementary reflectors whose product defines the matrix Q.
  • If SIDE = 'L', M >= K >= 0;
  • if SIDE = 'R', N >= K >= 0.
• A — REAL array, dimension
  • (LDA,M) if SIDE = 'L',
  • (LDA,N) if SIDE = 'R'.

Part of the data structure to represent Q as returned by SGELQ.

• LDA — INTEGER, the leading dimension of the array A. LDA >= max(1,K).
• T — REAL array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by SGELQ.
• TSIZE — INTEGER, the dimension of the array T. TSIZE >= 5.
• C — REAL array, dimension (LDC,N).
  • On entry, the M-by-N matrix C.
  • On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
• LDC — INTEGER, the leading dimension of the array C. LDC >= max(1,M).
• WORK — (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
• LWORK — INTEGER, the dimension of the array WORK. LWORK >= 1.

If LWORK = -1, then a workspace query is assumed. The routine only calculates the size of the WORK array, returns this value as WORK(1), and no error message related to WORK is issued by XERBLA. 🫶

• INFO — INTEGER, the receipts:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author 👑

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

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🦋 Further Details 🦋

⚠️ okay listen up, this part is implementation tea, not interface tea. these details are particular for this LAPACK implementation. users should not take them for granted. these details may change in the future, and are not likely true for another LAPACK implementation. these details are relevant if one wants to try to understand the code. they are not part of the interface. 💀

In this version,

         T(2): row block size (MB)
         T(3): column block size (NB)
         T(6:TSIZE): data structure needed for Q, computed by
                          SLASWLQ or SGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, SGELQ will use either SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute the LQ factorization.

This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to multiply matrix Q by another matrix.

Further Details in SLAMSWLQ or SGEMLQT.

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definition at line 171 of file sgemlq.f. 🔍

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🌈 Author (the meta one) 🌈

Generated automatically by Doxygen for LAPACK from the source code. (she's literally auto-generated and still ate ✨)

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🌈💜 sign-off time, bestie 💜🌈

this lil masterpiece is from LAPACK, Version 3.12.0, and yeah, it's page SRC/sgemlq.f(3) — keep her safe, cite her right, and remember: orthogonal matrices are iconic, LWORK = -1 means just tell me the size, and INFO < 0 means somebody fumbled an argument 🙈 periodt 💅🎀