SRC/zgetsqrhrt.f(3)

🌸 NAME 🌸

SRC/zgetsqrhrt.f — bestie, this is the LAPACK manual page for the zgetsqrhrt subroutine, straight out of the LAPACK Library Functions Manual. It’s giving blocked QR factorization, and we’re gonna get into it 💅✨

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine zgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info) — the main character: ZGETSQRHRT 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine zgetsqrhrt (...)

subroutine zgetsqrhrt (integer m, integer n, integer mb1, integer nb1,
    integer nb2, complex*16, dimension( lda, * ) a, integer lda, complex*16,
    dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work,
    integer lwork, integer info)

This is ZGETSQRHRT, no cap. The whole routine is literally called ZGETSQRHRT, and it’s here to do a very specific QR factorization slay 💖

🎯 Purpose 🎯

okay so ZGETSQRHRT computes a NB2-sized column blocked QR-factorization of a complex M-by-N matrix A with M >= N,

A = Q * R.

Internally it uses an NB1-sized column blocked and MB1-sized row blocked TSQR-factorization, and it performs the reconstruction of the Householder vectors from the TSQR output. It also converts the R_tsqr factor from the TSQR-factorization output into the R factor that corresponds to the Householder QR-factorization,

A = Q_tsqr * R_tsqr = Q * R.

The output Q and R factors are stored in the same format as in ZGEQRT (Q is in blocked compact WY-representation). See the documentation of ZGEQRT for more details on the format. iconic behavior, honestly 🫶

💜 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.
• MB1 — MB1 is INTEGER. The row block size to be used in the blocked TSQR. MB1 > N.
• NB1 — NB1 is INTEGER. The column block size to be used in the blocked TSQR. N >= NB1 >= 1.
• NB2 — NB2 is INTEGER. The block size to be used in the blocked QR that is output. NB2 >= 1.
• A — A is COMPLEX*16 array, dimension (LDA,N).
  • On entry: an M-by-N matrix A.
  • On exit:
    • a) the elements on and above the diagonal of the array contain the N-by-N upper-triangular matrix R corresponding to the Householder QR;
    • b) the elements below the diagonal represent Q by the columns of blocked V (compact WY-representation).
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• T — T is COMPLEX*16 array, dimension (LDT,N)). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks.
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= NB2.
• 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.
  • If MIN(M,N) = 0, LWORK >= 1, else

LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),

• where

NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
NB1LOCAL = MIN(NB1,N).
LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
LW1 = NB1LOCAL * N,
LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ).

• 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 180 of file zgetsqrhrt.f.

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👑 Author (Doxygen edition) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 — this page is from LAPACK Version 3.12.0, source file SRC/zgetsqrhrt.f. The footer didn’t hand us a date, so we’re not inventing one, bestie 🙈💖 That’s the whole page — periodt 🫶✨