SRC/sgeqr2.f(3)

🎀 SRC/sgeqr2.f(3) 🎀

okay so this is the Library Functions Manual page for SRC/sgeqr2.f, and it's literally all about the sgeqr2 subroutine. LAPACK bestie, unblocked QR energy, we are so here for it. 💅✨

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🌈 NAME 🌈

SRC/sgeqr2.f — that's the name on the cover, bestie. 🫶

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine sgeqr2 (m, n, a, lda, tau, work, info)

• sgeqr2 — SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

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💖 Function/Subroutine Documentation 💖

🦋 subroutine sgeqr2 🦋

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: 🎀

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.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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and that's a wrap, bestie 🫶 — the footer's source/version/date stamp is LAPACK, Version 3.12.0, SRC/sgeqr2.f(3) (no extra date line printed, that's the whole footer vibe). 💅✨