SRC/zungtsqr_row.f(3)

💖 SRC/zungtsqr_row.f(3) 💖

okay so bestie, welcome to the Library Functions Manual page for SRC/zungtsqr_row.f. this is the whole page, no cap. 💅

✨ NAME ✨

SRC/zungtsqr_row.f — that's literally the page name, bestie.

🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

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

ZUNGTSQR_ROW — iconic.

🎀 Function/Subroutine Documentation 🎀

subroutine zungtsqr_row (integer m, integer n, integer mb, integer nb,
       complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
       ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer lwork,
       integer info)

ZUNGTSQR_ROW — yes queen.

🌼 Purpose:

okay so ZUNGTSQR_ROW generates an M-by-N complex matrix Q_out with orthonormal columns from the output of ZLATSQR. 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 ZLATSQR 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 ZLATSQR 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 ZLARFB_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 ZLATSQR 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 ZLATSQR 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 ZLATSQR 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*16 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 ZLATSQR that defines the input matrices Q_in(k) (ones on the diagonal are not stored). See ZLATSQR 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*16 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 ZLATSQR 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*16 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 zungtsqr_row.f.

🪄 Author 🪄

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