SRC/dgerq2.f(3)

okay so bestie, welcome to the SRC/dgerq2.f page of the Library Functions Manual — it's giving unblocked RQ factorization realness, and we're gonna get through every single detail together 💖

🌸 NAME 🌸

SRC/dgerq2.f — that's the file, bestie. Short, iconic, to the point 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine dgerq2 (m, n, a, lda, tau, work, info) — DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

✨ Function/Subroutine Documentation ✨

Here's the full signature, preserved exactly:

   subroutine dgerq2 (integer m, integer n, double precision, dimension( lda, *
       ) a, integer lda, double precision, dimension( * ) tau, double
       precision, dimension( * ) work, integer info)

DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

💫 Purpose 💫

DGERQ2 computes an RQ factorization of a real m by n matrix A:

A = R * Q.

🌈 Parameters 🌈

• M — M is INTEGER. It's the number of rows of the matrix A, and it has to satisfy M >= 0.
• N — N is INTEGER. It's the number of columns of the matrix A, and it has to satisfy N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, it's the m by n matrix A. On exit, the tea is: 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, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
• LDA — LDA is INTEGER. It's the leading dimension of the array A, and it has to satisfy LDA >= max(1,M).
• TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). These are the scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is DOUBLE PRECISION array, dimension (M).
• 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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 dgerq2.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — LAPACK, Version 3.12.0, SRC/dgerq2.f(3). Go slay your RQ factorization, periodt 💅✨