ZGEQRT(3)

✨ NAME ✨

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

Okay bestie, this is zgeqrt.f(3) from the Library Functions Manual — and it’s giving “blocked QR factorization but make it LAPACK.” 💅

---

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

---

🌸 Function/Subroutine Documentation 🌸

subroutine ZGEQRT (integer m, integer n, integer nb, complex*16, dimension(
       lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt,
       complex*16, dimension( * ) work, integer info)

🎀 Purpose 🎀

ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q. Periodt. 💖

🔧 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. N >= 0.
• NB — NB is INTEGER. The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, 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 the array A. LDA >= max(1,M).
• T — T is COMPLEX*16 array, dimension (LDT,MIN(M,N)). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details. 👀
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= NB.
• WORK — WORK is COMPLEX*16 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. 💀 (iconic behavior, honestly)

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 zgeqrt.f.

---

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

---

That’s the whole page, bestie 💖 Footer vibe check: LAPACK Version 3.12.0, with /home/abui...RC/zgeqrt.f(3) doing its little source/date-footer moment. Slay responsibly 🌈✨