DORGTSQR_ROW(3)

🦋 NAME 🦋

okay so bestie, this is the manual page for DORGTSQR_ROW — it lives in the LAPACK Library Functions Manual (yup, that's the manual name, we're folding it in right here at the top ✨), and the file it documents is literally:

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

like that's the whole path, don't @ me 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DORGTSQR_ROW (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) — the one and only, the main character 👑

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🎀 Function/Subroutine Documentation 🎀

subroutine DORGTSQR_ROW (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)

💜 Purpose 💜

okay so here's the tea, straight from the source (all of this is quoted comment text, no cap):

DORGTSQR_ROW generates an M-by-N real matrix Q_out with orthonormal columns from the output of DLATSQR. These N orthonormal columns are the first N columns of a product of complex unitary matrices Q(k)_in of order M, which are returned by DLATSQR in a special format.

and the whole vibe is:

Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

The input matrices Q(k)_in are stored in row and column blocks in A. See the documentation of DLATSQR for more details on the format of Q(k)_in, where each Q(k)_in is represented by block Householder transformations. This routine calls an auxiliary routine DLARFB_GETT, where the computation is performed on each individual block. The algorithm first sweeps NB-sized column blocks from the right to left starting in the bottom row block and continues to the top row block (hence the _ROW in the routine name 🫶). This sweep is in reverse order of the order in which DLATSQR generates the output blocks.

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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 used by DLATSQR to return arrays A and T. MB > N. (Note that if MB > M, then M is used instead of MB as the row block size).

• NB

NB is INTEGER The column block size used by DLATSQR to return arrays A and T. NB >= 1. (Note that if NB > N, then N is used instead of NB as the column block size).

• A

A is DOUBLE PRECISION array, dimension (LDA,N) On entry: The elements on and above the diagonal are not used as input. The elements below the diagonal represent the unit lower-trapezoidal blocked matrix V computed by DLATSQR that defines the input matrices Q_in(k) (ones on the diagonal are not stored). See DLATSQR for more details. On exit: The array A contains an M-by-N orthonormal matrix Q_out, i.e the columns of A are orthogonal unit vectors.

• LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

• T

T is DOUBLE PRECISION array, dimension (LDT, N * NIRB) where NIRB = Number_of_input_row_blocks = MAX( 1, CEIL((M-N)/(MB-N)) ) Let NICB = Number_of_input_col_blocks = CEIL(N/NB) The upper-triangular block reflectors used to define the input matrices Q_in(k), k=(1:NIRB*NICB). The block reflectors are stored in compact form in NIRB block reflector sequences. Each of the NIRB block reflector sequences is stored in a larger NB-by-N column block of T and consists of NICB smaller NB-by-NB upper-triangular column blocks. See DLATSQR for more details on the format of T.

• LDT

LDT is INTEGER The leading dimension of the array T. LDT >= max(1,min(NB,N)).

• WORK

(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

• LWORK

The dimension of the array WORK. LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)), where NBLOCAL=MIN(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.

• INFO

INFO is INTEGER = 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.

🧚 Contributors 🧚

November 2020, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 186 of file dorgtsqr_row.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, the robot wrote this bit 🤖💖)

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and that's the whole page — slay, you read it all! 💅

signing off with the source/version/date deets: LAPACK, Version 3.12.0, from /home/abui...gtsqr_row.f(3) — periodt 🎀✨