DGEQR2(3)

💅 NAME

ok so this is the manual page for dgeqr2.f — like, the actual file lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgeqr2.f and it's part of the Library Functions Manual (LAPACK, bestie, we're in LAPACK territory 🫶).

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines

• subroutine DGEQR2 (m, n, a, lda, tau, work, info) — honestly? she just computes the QR factorization of a general rectangular matrix using an unblocked algorithm. that's the whole vibe. ✨

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👑 Function/Subroutine Documentation 👑

subroutine DGEQR2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm. no cap, that's literally her job description. 💅

🌸 Purpose:

ok so picture this, the tea is:

!>
!> DGEQR2 computes a QR factorization of a real 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.
!>
!>

like she's out here decomposing A into Q times that stacked ( R ) / ( 0 ) situation, and honestly? iconic. 🔥

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🎀 Parameters 🎀

• M — M is INTEGER. it's the number of rows of the matrix A. and the rule is M >= 0. (yes bestie, zero is allowed, we don't discriminate 🫶)
• N — N is INTEGER. the number of columns of the matrix A, with N >= 0. same energy. 💜
• A — A is DOUBLE PRECISION array, dimension (LDA,N).
  • on entry: it's the m by n matrix A. that's her. that's the input.
  • on exit: the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (and R is upper triangular if m >= n); the elements below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details bestie, it's down there 👇).
• LDA — LDA is INTEGER. the leading dimension of the array A, and you need LDA >= max(1,M). not optional, she's strict about this one. 😤
• TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). the scalar factors of the elementary reflectors (again — Further Details, go look 👀).
• WORK — WORK is DOUBLE PRECISION array, dimension (N). that's it. that's the whole description. she's a simple girl. 🍓
• INFO — INFO is INTEGER:
  • = 0: successful exit ✨ slay, we love a clean finish.
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀 so like, check your args bestie.

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🌈 Author 🌈

shoutout to the whole squad who made this happen:

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

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🦋 Further Details: 🦋

ok this is the part where it gets a little spicy, pay attention:

!>
!>  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**T
!>
!>  where tau is a real scalar, and v is a real 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).
!>

so yeah, Q is a whole product of elementary reflectors, k = min(m,n) of them, each H(i) is I - tau * v * v**T, the v vector is zeroed out up to i-1, has a 1 sitting at position i, and the rest of v from i+1 to m lives in A(i+1:m,i) on exit — with tau chillin' in TAU(i). iykyk. 💅✨

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Definition at line 129 of file dgeqr2.f.

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⭐ Author (the meta one) ⭐

Generated automatically by Doxygen for LAPACK from the source code. so like, a robot wrote this one, not a girlie. 🙈

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and that's the whole page bestie!! this masterpiece was brought to you by LAPACK, Version 3.12.0, straight out of /home/abui...RC/dgeqr2.f(3) — go forth and factorize responsibly 🎀💖✨