SRC/dorml2.f(3)

🌸 SRC/dorml2.f(3)

okay bestie, welcome to this page from the Library Functions Manual — it's the SRC/dorml2.f one, and it's all about dorml2. No cap, it's an unblocked LAPACK routine and it's lowkey iconic. 💅

✨ NAME ✨

SRC/dorml2.f — that's the file/page name, periodt. 🎀

💅 SYNOPSIS 💅

Functions/Subroutines

subroutine dorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    info)

DORML2 multiplies a general matrix by the orthogonal matrix from the LQ factorization determined by sgelqf (unblocked algorithm). That's the whole vibe. 🦋

🫶 Function/Subroutine Documentation 🫶

subroutine dorml2 (character side, character trans, integer m, integer n,
    integer k, double precision, dimension( lda, * ) a, integer lda, double
    precision, dimension( * ) tau, double precision, dimension( ldc, * ) c,
    integer ldc, double precision, dimension( * ) work, integer info)

DORML2 multiplies a general matrix by the orthogonal matrix from the LQ factorization determined by sgelqf (unblocked algorithm). (Yes, same glow-up as the synopsis — the routine is the main character.) ✨

🎀 Purpose 🎀

The source comments spell it out like this, and we're keeping them exactly:

!>
!> DORML2 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 = 'T', or
!>
!>       C * Q  if SIDE = 'R' and TRANS = 'N', or
!>
!>       C * Q**T if SIDE = 'R' and TRANS = 'T',
!>
!> where Q is a real orthogonal matrix defined as the product of k
!> elementary reflectors
!>
!>       Q = H(k) . . . H(2) H(1)
!>
!> as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n
!> if SIDE = 'R'.
!>

So basically: overwrite real m by n matrix C with one of those four products, where Q is a real orthogonal matrix made from k elementary reflectors. Q has order m when SIDE = 'L', order n when SIDE = 'R'. Slay. 💖

🌈 Parameters 🌈

• SIDE — SIDE is CHARACTER*1.
  • = 'L': apply Q or Q**T from the Left.
  • = 'R': apply Q or Q**T from the Right.
• TRANS — TRANS is CHARACTER*1.
  • = 'N': apply Q (No transpose).
  • = 'T': apply Q**T (Transpose).
• M — M is INTEGER. The number of rows of the matrix C. M >= 0.
• N — N is INTEGER. The number of columns of the matrix C. N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L', (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 DGELQF in the first k rows of its array argument A.
• LDA — LDA is INTEGER. The leading dimension of the array A. 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 DGELQF.
• 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.
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is DOUBLE PRECISION array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R'.
• 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.

Definition at line 156 of file dorml2.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

---

💖 That's the whole page, bestie — brought to you by LAPACK Version 3.12.0 and the SRC/dorml2.f(3) era. Stay orthogonal. 💅