CGEQRT(3)

💅 CGEQRT(3) — Library Functions Manual 💅

okay so bestie, welcome to the group chat for CGEQRT(3). The manual name is Library Functions Manual, and we are keeping every single technical crumb while making it cute. Periodt. 💖

---

🌸 NAME 🌸

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

no cap, the NAME section is literally just this file path. It's giving "I have one job" energy. 💅

🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine CGEQRT (m, n, nb, a, lda, t, ldt, work, info)
    CGEQRT

💖 Function/Subroutine Documentation 💖

📞 subroutine CGEQRT 📞

subroutine CGEQRT (integer m, integer n, integer nb, complex, dimension(
    lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt,
    complex, dimension( * ) work, integer info)
    CGEQRT

🌟 Purpose 🌟

CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q. slay. ✨

🧸 Parameters 🧸

• M — M is INTEGER; it's the number of rows of matrix A, and M >= 0.
• N — N is INTEGER; it's the number of columns of matrix A, and N >= 0.
• NB — NB is INTEGER; this is the block size for the blocked QR, with MIN(M,N) >= NB >= 1.
• A — A is COMPLEX array, dimension (LDA,N). On entry, it's the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.
• LDA — LDA is INTEGER; the leading dimension of array A, and LDA >= max(1,M).
• T — T is COMPLEX array, dimension (LDT,MIN(M,N)). It holds the upper triangular block reflectors in compact form, as a sequence of upper triangular blocks. See below for the deets.
• LDT — LDT is INTEGER; the leading dimension of array T, and LDT >= NB.
• WORK — WORK is COMPLEX array, dimension (NB*N).
• 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.

🦋 Further Details 🦋

The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1       )
    ( v1  1    )
    ( v1 v2  1 )
    ( v1 v2 v3 )
    ( v1 v2 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A.

Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, an upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as

T = (T1 T2 ... TB).

Definition at line 140 of file cgeqrt.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

---

💌 Sign-off 💌

Footer tea, since we're not copying the footer line: the source/version is LAPACK and Version 3.12.0, and the date/path field is /home/abui...RC/cgeqrt.f(3). Mwah bestie, go slay that blocked QR. 💖✨🎀