DORMR3(3)

🌸 DORMR3(3) — LAPACK, Library Functions Manual 🌸

okay so bestie, welcome to the dormr3 page 💖 this is LAPACK, Library Functions Manual energy, and we're about to make a Fortran subroutine feel like a main character.

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dormr3.f

yes, that's literally the whole NAME section — it's just the file path, no cap 😭 that's the whole vibe, the path is the name.

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine DORMR3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work,
    info)

DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). slay 💅

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👑 Function/Subroutine Documentation 👑

subroutine DORMR3 (character side, character trans, integer m, integer n,
    integer k, integer l, double precision, dimension( lda, * ) a, integer
    lda, double precision, dimension( * ) tau, double precision, dimension(
    ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer
    info)

DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). again, iconic ✨

🎀 Purpose

!>
!> DORMR3 overwrites the general real m by n matrix C with
!>
!>       Q * C  if SIDE = 'L' and TRANS = 'N', or
!>
!>       Q**T* C  if SIDE = 'L' and TRANS = 'C', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**T if SIDE = 'R' and TRANS = 'C',
!>
!> where Q is a real orthogonal matrix defined as the product of k
!> elementary reflectors
!>
!>       Q = H(1) H(2) . . . H(k)
!>
!> as returned by DTZRZF. Q is of order m if SIDE = 'L' and of order n
!> if SIDE = 'R'.
!>

translation for the girlies 🫶: it overwrites that m-by-n real matrix C, and depending on which side you're applying from and whether you're transposing, you get Q * C, Q**T* C, C * Q, or C * Q**T. And Q? It's a real orthogonal matrix built as the product of k elementary reflectors, Q = H(1) H(2) . . . H(k), exactly like DTZRZF handed them to you. Q is order m when SIDE = 'L' and order n when SIDE = 'R'. periodt 💜

🌈 Parameters

• SIDE — SIDE is CHARACTER*1. Set it to 'L' to apply Q or Q**T from the Left, or 'R' to apply Q or Q**T from the Right. pick your side bestie 💅
• TRANS — TRANS is CHARACTER*1. 'N' means apply Q (No transpose); 'T' means apply Q**T (Transpose). no in-between, choose your fighter.
• M — M is INTEGER. It's the number of rows of the matrix C, and M >= 0. zero rows is valid, we don't judge 🙈
• N — N is INTEGER. Number of columns of the matrix C, and N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', then M >= K >= 0; if SIDE = 'R', then N >= K >= 0. respect the bounds fr fr ⭐
• L — L is INTEGER. The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', then M >= L >= 0; if SIDE = 'R', then N >= L >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L', or (LDA,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DTZRZF in the last k rows of its array argument A. Heads up: A is modified by the routine but restored on exit — it comes back home safe 🏠✨
• LDA — LDA is INTEGER. The leading dimension of the array A, and LDA >= max(1,K).
• TAU — TAU is DOUBLE PRECISION array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DTZRZF.
• C — C is DOUBLE PRECISION array, dimension (LDC,N). On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. she's been through it but she's thriving 💀
• LDC — LDC is INTEGER. The leading dimension of the array C, and LDC >= max(1,M).
• WORK — WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L', or (M) if SIDE = 'R'. do the math before you pass it, iykyk.
• INFO — INFO is INTEGER. = 0: successful exit 🎉 < 0: if INFO = -i, the i-th argument had an illegal value. rude but informative 😭

🧚 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🍓 Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

⭐ Further Details:

!>

that's it. that's the further details. it's giving "nothing further, your honor" 💀 (the block is literally empty, bestie — no secret lore here.)

Definition at line 176 of file dormr3.f.

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💜 Author

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a very diligent robot 🤖✨

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aaand that's the page! the sign-off from the footer, for the record: this is LAPACK, Version 3.12.0, from /home/abui...RC/dormr3.f(3) — mwah, go multiply something 💅🎀