ZGETSQRHRT(3)

💖 ZGETSQRHRT(3) 💖

okay bestie, we’re in the Library Functions Manual, and the header path is /home/abui...getsqrhrt.f(3). this page is all about ZGETSQRHRT, no cap. ✨

🎀 NAME 🎀

the name situation is literally just this file path, bestie:

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

🫶 SYNOPSIS 🫶

Functions/Subroutines

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

✨ Function/Subroutine Documentation ✨

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)
    ZGETSQRHRT

💅 Purpose

okay so here’s the vibe: ZGETSQRHRT computes a NB2-sized column blocked QR-factorization of a complex M-by-N matrix A with M >= N,

A = Q * R.

Internally the routine uses a NB1-sized column blocked and MB1-sized row blocked TSQR-factorization, and it perfors the reconstruction of the Householder vectors from the TSQR output. (yes, the original says perfors — iconic typo behavior, we keep 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 ZGEQRT (Q is in blocked compact WY-representation). See the documentation of ZGEQRT for more details on the format.

🌸 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 — 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• T — COMPLEX*16 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) COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER. 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 — 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 zgetsqrhrt.f.

📝 Author

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 that’s the whole page, bestie. this icon came from LAPACK Version 3.12.0, and the footer path is /home/abui...getsqrhrt.f(3) (no date on this footer, just version and path). byeee ✨🦋💖