SGETSQRHRT(3)

💖 SGETSQRHRT(3) 💖

okay so bestie, we're in the Library Functions Manual and this page is literally all about SGETSQRHRT — a LAPACK subroutine. The file lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgetsqrhrt.f. It's giving very “math girlie who debugged her build at 3am” energy, and honestly? iconic. ✨

📛 NAME 📛

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

🌈 SYNOPSIS 🌈

🧩 Functions/Subroutines

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

SGETSQRHRT — that's the one, bestie. 🫶

🌟 Function/Subroutine Documentation 🌟

subroutine SGETSQRHRT (integer m, integer n, integer mb1, integer nb1,
    integer nb2, real, dimension( lda, * ) a, integer lda, real, dimension(
    ldt, * ) t, integer ldt, real, dimension( * ) work, integer lwork,
    integer info)

SGETSQRHRT

🎯 Purpose:

omg okay so SGETSQRHRT computes a NB2-sized column blocked QR-factorization of a complex M-by-N matrix A with M >= N — that's what the source says, bestie, even though this is an S routine, we don't edit the lore 💀 — and the whole thing is:

A = Q * R.

The routine uses internally a NB1-sized column blocked and MB1-sized row blocked TSQR-factorization, and 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 SGEQRT (Q is in blocked compact WY-representation). See the documentation of SGEQRT for more details on the format. slay. 💅

🧾 Parameters

• M — INTEGER. The number of rows of the matrix A. M >= 0. ✨
• N — INTEGER. The number of columns of the matrix A. M >= N >= 0. ✨
• MB1 — INTEGER. The row block size to be used in the blocked TSQR. MB1 > N. 👑
• NB1 — INTEGER. The column block size to be used in the blocked TSQR. N >= NB1 >= 1. 🎀
• NB2 — INTEGER. The block size to be used in the blocked QR that is output. NB2 >= 1. 🦋
• A — REAL 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,M). 🌸
• T — REAL array, dimension (LDT,N)). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. 🧚
• LDT — INTEGER. The leading dimension of the array T. LDT >= NB2. 💜
• WORK — (workspace) REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🍓
• LWORK — INTEGER. The dimension of the array WORK. It has to satisfy:

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. no cap. 🔥

• INFO — 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 177 of file sgetsqrhrt.f.

🖋️ Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie. Footer vibes: LAPACK Version 3.12.0, file /home/abui...getsqrhrt.f(3) — mwah 💋✨