SRC/cgerq2.f(3)

✨ CGERQ2: unblocked RQ factorization, but make it main character ✨

okay bestie, this is the SRC/cgerq2.f(3) page from the Library Functions Manual, and it's literally all about cgerq2. it computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. no cap. 💅

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🦋 NAME 🦋

SRC/cgerq2.f

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

• subroutine cgerq2 (m, n, a, lda, tau, work, info) — CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. ✨

💖 Function/Subroutine Documentation 💖

   subroutine cgerq2 (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
       integer info)

CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. 🫶

🌟 Purpose 🌟

CGERQ2 computes an RQ factorization of a complex m by n matrix A:

A = R * Q.

💅 Parameters 💅

• M — INTEGER. the number of rows of the matrix A. M >= 0. 🔥
• N — INTEGER. the number of columns of the matrix A. N >= 0. 🌈
• A — COMPLEX array, dimension (LDA,N). On entry, the m by n matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). 🫶
• LDA — INTEGER. the leading dimension of the array A. LDA >= max(1,M). 💜
• TAU — COMPLEX array, dimension (min(M,N)). the scalar factors of the elementary reflectors (see Further Details). 🧚
• WORK — COMPLEX array, dimension (M). ⭐
• 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.

🔍 Further Details 🔍

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

Q = H(1)**H H(2)**H . . . H(k)**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). 💖

Definition at line 122 of file cgerq2.f. 📍

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code. 💻

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and that's the tea, bestie! footer vibes: LAPACK Version 3.12.0 from SRC/cgerq2.f(3) — there's no date printed, so no invented date, periodt. mwah 💋