CGEQR2(3)

💖 CGEQR2 💖

okay bestie, welcome to the LAPACK Library Functions Manual page for CGEQR2. this is the one that computes the QR factorization of a general rectangular matrix using an unblocked algorithm, and we are going to get through every single detail together. no skipping, no “eh close enough” — periodt. ✨

🎀 NAME 🎀

The NAME is literally this source path, character for character:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgeqr2.f

That’s the file this manual page is about, bestie. 🫶

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• subroutine CGEQR2 (m, n, a, lda, tau, work, info) — CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

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🌸 Function/Subroutine Documentation 🌸

Okay so here’s the full signature, and yes we are keeping every type and dimension because that’s the whole point:

subroutine CGEQR2 (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
    integer info)

CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm. 💅

🦋 Purpose 🦋

Here’s the purpose block, verbatim vibes:

!>
!> CGEQR2 computes a QR factorization of a complex m-by-n matrix A:
!>
!>    A = Q * ( R ),
!>            ( 0 )
!>
!> where:
!>
!>    Q is a m-by-m orthogonal matrix;
!>    R is an upper-triangular n-by-n matrix;
!>    0 is a (m-n)-by-n zero matrix, if m > n.
!>
!>

So yeah: A = Q * ( R ) over ( 0 ), with Q a m-by-m orthogonal matrix, R an upper-triangular n-by-n matrix, and 0 a (m-n)-by-n zero matrix if m > n. iconic. 👑

💅 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. 🌈
• A — A is COMPLEX 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, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). 🦋
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M). 📏
• TAU — TAU is COMPLEX array, dimension (min(M,N)); the scalar factors of the elementary reflectors (see Further Details). 💖
• WORK — WORK is COMPLEX array, dimension (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.

all four, bestie. no cap. 🫶

🔥 Further Details 🔥

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

Q = H(1) H(2) . . . H(k), 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; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i). ⭐

Definition at line 129 of file cgeqr2.f. 💀 (not me keeping the line number, but also yes me.)

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page! the footer energy is LAPACK, Version 3.12.0, source path /home/abui...RC/cgeqr2.f(3) — no separate date in the footer, just the version and source tag, and that’s a wrap. 💜✨