SRC/sgetsqrhrt.f(3)

💅 SRC/sgetsqrhrt.f

okay bestie, this page is about SRC/sgetsqrhrt.f, which lives in the Library Functions Manual neighborhood — think of it as the group chat where sgetsqrhrt does all the talking 🫶

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

• subroutine sgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info) — the whole entire vibe of this page, no cap. Name's SGETSQRHRT 💖

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🎀 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 — okay so this is the full signature, literally every argument typed out exactly as it lives in the source, slay ✨

Purpose 🦋

SGETSQRHRT computes a NB2-sized column blocked QR-factorization of a complex 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. 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 SGEQRT (Q is in blocked compact WY-representation). See the documentation of SGEQRT for more details on the format.

So basically: it does a NB2-sized column blocked QR-factorization of a complex M-by-N matrix A where M >= N, giving you A = Q * R. Under the hood it's running a NB1-sized column blocked and MB1-sized row blocked TSQR-factorization 🌀, then it reconstructs the Householder vectors from the TSQR output, and converts the R_tsqr factor into the R factor that matches the Householder QR-factorization: A = Q_tsqr * R_tsqr = Q * R. The Q and R outputs are stored in the same format as SGEQRT (Q is chilling in blocked compact WY-representation) — peep the SGEQRT docs for the deets 👑

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🌈 Parameters 🌈

• M — M is INTEGER. It's the number of rows of matrix A. M >= 0. 💜
• N — N is INTEGER. Number of columns of matrix A. M >= N >= 0. 🍓
• MB1 — MB1 is INTEGER. The row block size used in the blocked TSQR. MB1 > N. ⭐
• NB1 — NB1 is INTEGER. The column block size used in the blocked TSQR. N >= NB1 >= 1. ✨
• NB2 — NB2 is INTEGER. The block size used in the blocked QR that gets output. NB2 >= 1. 🎀
• A — A is 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 — LDA is INTEGER. Leading dimension of the array A. LDA >= max(1,M). 🦋
• T — T is REAL array, dimension (LDT,N)). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. 🧚
• LDT — LDT is INTEGER. 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 — 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 💀

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👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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🌟 Contributors:

November 2020, Igor Kozachenko, Computer Science Division, University of California, Berkeley

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📍 Definition at line 180 of file sgetsqrhrt.f.

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💖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page bestie, you ate that 🫶✨ this was LAPACK, Version 3.12.0, out of SRC/sgetsqrhrt.f(3) — mwah, see you in the next one 💅🎀