SRC/dorgtsqr_row.f(3)

💖 NAME 💖

okay so bestie, you're looking at SRC/dorgtsqr_row.f(3) — that's the page title — from the Library Functions Manual (manual name folded in right here like a little name tag 🫶). It's the whole SRC/dorgtsqr_row.f situation, and we're about to get into it.

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine dorgtsqr_row (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) — the function call, exactly as it appears, no cap. DORGTSQR_ROW is the name on the group chat.

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💅 Function/Subroutine Documentation 💅

🌈 subroutine dorgtsqr_row 🌈

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)
    DORGTSQR_ROW

🌸 Purpose 🌸

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.

It's giving:

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

🍓 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 — 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. 💀
• 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 dorgtsqr_row.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the vibe check, bestie. Footer sign-off tea: LAPACK — Version 3.12.0 — page SRC/dorgtsqr_row.f(3). No separate date was printed, so I'm not inventing one. Periodt. 💅✨