SGEMQR(3)

🌸 NAME 🌸

Okay bestie, the name on this one is literally the file path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgemqr.f. And the manual name is Library Functions Manual — folded in here near the top like a little name tag. This is SGEMQR(3), and she is ready to spill the QR tea. 🎀

✨ SYNOPSIS ✨

Functions/Subroutines 🦋

• Function: SGEMQR

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

Description: SGEMQR. That's it, that's the icon. 💅

🎀 Function/Subroutine Documentation 🎀

   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)

And the star of the show is SGEMQR. Main character energy fr fr. 👑

Purpose 💖

SGEMQR 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 tall skinny QR factorization (SGEQR).

Parameters 🌈

• SIDE — SIDE is CHARACTER*1, bestie: = 'L': apply Q or Q**T from the Left; and = 'R': apply Q or Q**T from the Right.
• TRANS — TRANS is CHARACTER*1: = 'N': No transpose, apply Q; and = '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 — (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 👑

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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💖 That's the whole page, bestie! Footer source/version check: LAPACK Version 3.12.0 and /home/abui...RC/sgemqr.f(3). No date is shown in that footer, just the version and that path — and the manual name up top was Library Functions Manual. Slay. 🎀✨