DGETSQRHRT(3)

🎀 DGETSQRHRT(3) — Library Functions Manual 🎀

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💖 NAME 💖

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

No cap, that whole path is literally the NAME field on this page. Slay.

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

Here’s the short version — same signature, no edits:

subroutine DGETSQRHRT (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork,
    info)
    DGETSQRHRT

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🦋 Function/Subroutine Documentation 🦋

👑 Full signature 👑

subroutine DGETSQRHRT (integer m, integer n, integer mb1, integer nb1,
    integer nb2, double precision, dimension( lda, * ) a, integer lda,
    double precision, dimension( ldt, * ) t, integer ldt, double precision,
    dimension( * ) work, integer lwork, integer info)
    DGETSQRHRT

🌸 Purpose 🌸

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

A = Q * R.

The routine uses internally a NB1-sized column blocked and MB1-sized row blocked TSQR-factorization and perfors the reconstruction of the Householder vectors from the TSQR output. (Yes, the source says “perfors” — I’m not fixing the typo, I’m just reporting it. 💀) The routine 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 DGEQRT (Q is in blocked compact WY-representation). See the documentation of DGEQRT for more details on the format.

🎀 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 DOUBLE PRECISION array, dimension (LDA,N).
  • On entry: an M-by-N matrix A.
  • On exit:
    1. the elements on and above the diagonal of the array contain the N-by-N upper-triangular matrix R corresponding to the Householder QR;
    2. 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 DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — The dimension of the array WORK.

LWORK >= MAX( 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

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🌈 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 177 of file dgetsqrhrt.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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