CUNGTSQR_ROW(3)

💖 CUNGTSQR_ROW(3) 💖

okay so this is the cungtsqr_row.f(3) page from the Library Functions Manual, and bestie we are about to get into the whole CUNGTSQR_ROW situation. It’s giving complex-matrix construction, no cap. 💅✨

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine CUNGTSQR_ROW (m, n, mb, nb, a, lda, t, ldt, work, lwork,
    info)
    CUNGTSQR_ROW

🦋 Function/Subroutine Documentation 🦋

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

okay so the signature is literally right there, and yes it’s a lot of arguments. We stay hydrated. 🫶

💖 Purpose 💖

CUNGTSQR_ROW generates an M-by-N complex matrix Q_out with orthonormal columns from the output of CLATSQR. Those 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 CLATSQR 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 CLATSQR 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 CLARFB_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 CLATSQR 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 CLATSQR 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 CLATSQR 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 COMPLEX 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 CLATSQR that defines the input matrices Q_in(k) (ones on the diagonal are not stored). See CLATSQR 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 COMPLEX 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 CLATSQR 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) COMPLEX 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

👑 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 cungtsqr_row.f.

💀 Author 💀

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xoxo, LAPACK Version 3.12.0 💖 — this page was living at /home/abui...gtsqr_row.f(3) when it was generated 💅