SRC/dgemqr.f(3)

okay bestie, buckle up: this is SRC/dgemqr.f(3) from the Library Functions Manual, and it's giving “LAPACK routine that ships Q around” energy. 💖

✨ NAME ✨

SRC/dgemqr.f — yes, that's the name, no cap. 🦋

✨ SYNOPSIS ✨

Functions/Subroutines

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

🌸 Function/Subroutine Documentation 🌸

🎀 subroutine dgemqr

subroutine dgemqr (character side, character trans, integer m, integer n,
     integer k, double precision, dimension( lda, * ) a, integer lda, double
     precision, dimension( * ) t, integer tsize, double precision, dimension(
     ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer
     lwork, integer info)
     DGEMQR

DGEMQR 👑

💅 Purpose 💅

DGEMQR 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 (DGEQR). ✨

🫶 Parameters 🫶

• SIDE — SIDE is CHARACTER*1; = 'L': apply Q or QT from the Left; = 'R': apply Q or QT 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 DOUBLE PRECISION array, dimension (LDA,K). Part of the data structure to represent Q as returned by DGEQR. 💖
• 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 DOUBLE PRECISION array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by DGEQR. 🎀
• TSIZE — TSIZE is INTEGER; the dimension of the array T. TSIZE >= 5. ⭐
• C — C is DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the minimal LWORK. 🍓
• LWORK — LWORK is 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 — 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
                 DLATSQR or DGEQRT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, DGEQR will use either DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute the QR factorization.

This version of DGEMQR will use either DLAMTSQR or DGEMQRT to multiply matrix Q by another matrix.

Further Details in DLATMSQR or DGEMQRT. ✨

📍 Definition at line 173 of file dgemqr.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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k bye bestie — this page is from LAPACK Version 3.12.0, source SRC/dgemqr.f(3). mwah 💅✨