SRC/sorgtsqr_row.f(3)

📦
version 3.12.1 · 4 versions
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✨ SRC/sorgtsqr_row.f ✨

ok so bestie, this is a page from the LAPACK Library Functions Manual (vibe: heavy math, but make it cute). It's literally all about SRC/sorgtsqr_row.f and the little legend inside it. buckle up 💖

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine sorgtsqr_row (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) — SORGTSQR_ROW

🦋 Function/Subroutine Documentation 🦋

subroutine sorgtsqr_row (integer m, integer n, integer mb, integer nb, real,
    dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer
    ldt, real, dimension( * ) work, integer lwork, integer info)

SORGTSQR_ROW — say it with me 👑

🎀 Purpose 🎀

ok so SORGTSQR_ROW generates an M-by-N real matrix Q_out with orthonormal columns from the output of SLATSQR. 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 SLATSQR in a special format.

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 SLATSQR 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 SLARFB_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 _ROW in the routine name). This sweep is in reverse order of the order in which SLATSQR generates the output blocks. 💅

bestie the "reverse order" thing is not a random flex, it's literally the whole point of the _ROW suffix, iykyk

⭐ 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 SLATSQR 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 SLATSQR 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 REAL 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 SLATSQR that defines the input matrices Q_in(k) (ones on the diagonal are not stored). See SLATSQR 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. slay 💫

  • LDA
LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).
  • T
T is REAL 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 SLATSQR 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) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
  • LWORK
LWORK is INTEGER
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.
ngl the LWORK = -1 trick is the classic "just tell me how much room I need" move — no XERBLA complaints, no drama 🫶
  • 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.

🌈 Contributors 🌈

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

Definition at line 187 of file sorgtsqr_row.f. 📍

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, a robot wrote this bit, not me 😭)

ok that's the whole page, every last flag and formula intact, no cap. This was SRC/sorgtsqr_row.f(3) from LAPACK Version 3.12.0 — mwah, go forth and compute your orthonormal columns, bestie 💖🎀🦋✨

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