SRC/zgelqf.f(3)

🎀 SRC/zgelqf.f 🎀

Hii bestie 💖 welcome to the SRC/zgelqf.f(3) page from the Library Functions Manual — this is the ZGELQF moment, and yes, we’re doing the whole thing, no skips, no vibes-only summary ✨

---

🌸 NAME 🌸

SRC/zgelqf.f

---

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine zgelqf (m, n, a, lda, tau, work, lwork, info) — ZGELQF

---

🫶 Function/Subroutine Documentation 🫶

subroutine zgelqf (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
    work, integer lwork, integer info)

ZGELQF — main character energy, literally 💅

🍓 Purpose 🍓

Bestie, ZGELQF computes an LQ factorization of a complex M-by-N matrix A:

A = ( L 0 ) *  Q

where:

Q is a N-by-N orthogonal matrix;
L is a lower-triangular M-by-M matrix;
0 is a M-by-(N-M) zero matrix, if M < N.

💅 Parameters 💅

• M — M is INTEGER. It’s the number of rows of the matrix A. Condition: M >= 0.
• N — N is INTEGER. It’s the number of columns of the matrix A. Condition: N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, it’s the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
• LDA — LDA is INTEGER. It’s the leading dimension of the array A. Condition: LDA >= max(1,M).
• TAU — TAU is COMPLEX*16 array, dimension (min(M,N)). These are the scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. It’s the dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. 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.

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🔥 Further Details 🔥

The matrix Q is represented as a product of elementary reflectors:

Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).

Each H(i) has the form:

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Definition at line 143 of file zgelqf.f.

---

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

---

That’s the whole page, bestie 🫶 source: SRC/zgelqf.f(3) · version: LAPACK Version 3.12.0 · slay forever 💖✨