/home/abui.../dgeqrt2.f(3)

💅 NAME 💅

okay so the page is titled /home/abui.../dgeqrt2.f(3), and the manual name is Library Functions Manual — folded in right here so we don’t have to copy the header line, periodt. The file in question is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgeqrt2.f, and the main character of this page is DGEQRT2. 💖

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• subroutine DGEQRT2 (m, n, a, lda, t, ldt, info) — DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

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🫶 Function/Subroutine Documentation 🫶

🎀 subroutine DGEQRT2 🎀

Full signature, exactly as printed, no edits:

subroutine DGEQRT2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

The one-liner says: DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. The Purpose block below then gets specific about a real M-by-N matrix A — both are in the original, so both stay, bestie. 💖

🎯 Purpose 🎯

DGEQRT2 computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. That’s the whole purpose. No side quests.

🧸 Parameters 🧸

• M — M is INTEGER; it’s the number of rows of matrix A, and the rule is M >= N.
• N — N is INTEGER; it’s the number of columns of matrix A, and the rule is N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, it’s the real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R, and the elements below the diagonal are the columns of V. See below for further details.
• LDA — LDA is INTEGER; it’s the leading dimension of array A, and LDA >= max(1,M).
• T — T is DOUBLE PRECISION array, dimension (LDT,N). It’s the N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.
• LDT — LDT is INTEGER; it’s the leading dimension of array T, and LDT >= max(1,N).
• INFO — INFO is INTEGER; = 0 means successful exit. < 0 means 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 V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is:

V = (  1       )
    ( v1  1    )
    ( v1 v2  1 )
    ( v1 v2 v3 )
    ( v1 v2 v3 )

where the vi’s represent the vectors which define H(i), which are returned in the matrix A. The 1’s along the diagonal of V are not stored in A. The block reflector H is then given by:

H = I - V * T * V**T

where V**T is the transpose of V.

Definition at line 126 of file dgeqrt2.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie: source/version sign-off is LAPACK Version 3.12.0, page path /home/abui.../dgeqrt2.f(3). There’s no date printed in the original footer, so I’m not inventing one — no cap, periodt. 💅✨