DGERQF(3)

🎀 DGERQF(3) 🎀

okay bestie, welcome to the Library Functions Manual page for DGERQF(3) 💖. It’s a LAPACK subroutine, and it’s lowkey iconic. We’re keeping every parameter, every equation, every little detail — just with way more group-chat energy. no cap.

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✨ NAME ✨

the name block is literally this file path, and yes it’s a whole journey:

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

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🌸 SYNOPSIS 🌸

Functions/Subroutines

the synopsis is serving subroutine realness:

subroutine DGERQF (m, n, a, lda, tau, work, lwork, info)
           DGERQF

and then it just says DGERQF again, because main character energy 💅.

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💅 Function/Subroutine Documentation 💅

subroutine DGERQF — the full signature

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

the routine name pops up again: DGERQF. iconic behavior.

🎯 Purpose

DGERQF computes an RQ factorization of a real M-by-N matrix A:

A = R * Q.

that’s the whole purpose. slay.

🧸 Parameters

• M — M is INTEGER. it’s the number of rows of the matrix A. M >= 0.
• N — N is INTEGER. it’s the number of columns of the matrix A. N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N).
  • On entry, it’s the M-by-N matrix A.
  • On exit:
    • 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, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
• LDA — LDA is INTEGER. it’s the leading dimension of the array A. 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. it’s the dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

📜 Author

the author credits are giving institution realness:

• 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

Definition at line 138 of file dgerqf.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, your Unix bestie 💖 — footer source/version check: LAPACK Version 3.12.0, and the footer path was /home/abui...RC/dgerqf.f(3) 🫶