SRC/sgemqr.f(3)

Okay bestie, welcome to the SRC/sgemqr.f(3) page from the Library Functions Manual — yes, it’s giving LAPACK, and yes, we’re gonna get through every single detail together. 💅

✨ NAME ✨

SRC/sgemqr.f — that’s the name, and this whole page is about SGEMQR. Periodt. 💖

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine sgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info) — the one and only SGEMQR. She’s iconic.

💖 Function/Subroutine Documentation 💖

Here’s the full signature in all her glory, bestie:

subroutine sgemqr (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)

SGEMQR — periodt. 💅

🌸 Purpose 🌸

Okay so SGEMQR overwrites the general real M-by-N matrix C with this exact table, no edits:

                     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 tall skinny QR factorization (SGEQR). That’s the whole vibe. 🦋

🐚 Parameters 🐚

Every param, every constraint, every little detail — here we go:

SIDE

• SIDE is CHARACTER*1
• = 'L': apply Q or Q**T from the Left;
• = 'R': apply Q or Q**T from the Right.

TRANS

• TRANS is CHARACTER*1
• = 'N': No transpose, apply Q;
• = 'T': Transpose, apply Q**T.

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 C. N >= 0.

K

• K is 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

• A is REAL array, dimension (LDA,K)
• Part of the data structure to represent Q as returned by SGEQR.

LDA

• LDA is INTEGER
• The leading dimension of the array A.
• If SIDE = 'L', LDA >= max(1,M);
• if SIDE = 'R', LDA >= max(1,N).

T

• T is REAL array, dimension (MAX(5,TSIZE)).
• Part of the data structure to represent Q as returned by SGEQR.

TSIZE

• TSIZE is INTEGER
• The dimension of the array T. TSIZE >= 5.

C

• C is 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

• LDC is INTEGER
• The leading dimension of the array C. LDC >= max(1,M).

WORK

• WORK is (workspace) REAL array, dimension (MAX(1,LWORK))

LWORK

• LWORK is INTEGER
• The dimension of the array WORK.
• 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

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

🦋 Author 🦋

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

🌈 Further Details 🌈

Okay, important vibe check: 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
                 SLATSQR or SGEQRT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, SGEQR will use either SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute the QR factorization. This version of SGEMQR will use either SLAMTSQR or SGEMQRT to multiply matrix Q by another matrix. Further Details in SLAMTSQR or SGEMQRT.

⭐ Definition at line 172 of file sgemqr.f. ⭐

Definition at line 172 of file sgemqr.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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And that’s the whole page, bestie! The footer says LAPACK, Version 3.12.0, and SRC/sgemqr.f(3) — it does not give a date, so I’m not gonna invent one. This page was generated automatically by Doxygen for LAPACK from the source code. Mwah 💋✨