SGEQR2(3)

💅 SGEQR2(3) — Library Functions Manual 💅

okay bestie, gather round. This is the Library Functions Manual page for SGEQR2, and she is a LAPACK subroutine with main-character energy. We're keeping every single detail, no cap. 🫶

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgeqr2.f

that's the source file, and yes, that's the whole NAME section. iconic behavior. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine SGEQR2 (m, n, a, lda, tau, work, info) — SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

🦋 Function/Subroutine Documentation 🦋

subroutine SGEQR2 (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) tau, real, dimension( * ) work,
    integer info)

SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

💖 Purpose 💖

ok so the whole point: SGEQR2 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.

🎀 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 REAL 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 orthogonal 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 REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).

WORK

WORK is REAL 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.

🔥 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**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).

Definition at line 129 of file sgeqr2.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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cute sign-off: this page is LAPACK Version 3.12.0, with the source/footer vibe of /home/abui...RC/sgeqr2.f(3). Date-wise, the footer didn't list an explicit date, so we're not gonna invent one. periodt. 💖