SRC/dorm2r.f(3)

🎀 SRC/dorm2r.f(3) 🎀

okay bestie, welcome to the Library Functions Manual page for SRC/dorm2r.f(3) 💖. This is the dorm2r subroutine, and she has main character energy in the LAPACK lineup.

💖 NAME 💖

SRC/dorm2r.f — that's the name, periodt. 🫶

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

Here's the signature and one-liner, exactly as the page gives them:

       subroutine dorm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work,
           info)
           DORM2R multiplies a general matrix by the orthogonal matrix from a
           QR factorization determined by sgeqrf (unblocked algorithm).

That's the synopsis vibe: signature plus the line about DORM2R multiplying a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm). No cap. 🌸

🌟 Function/Subroutine Documentation 🌟

Full signature, character for character:

   subroutine dorm2r (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)
       DORM2R multiplies a general matrix by the orthogonal matrix from a QR
       factorization determined by sgeqrf (unblocked algorithm).

🎯 Purpose 🎯

So DORM2R overwrites the general real m by n matrix C with one of these four glow-ups:

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(1) H(2) . . . H(k)

as returned by DGEQRF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'. That's the whole purpose, and yes she ate. 🔥

🧸 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,K). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQRF in the first k columns of its array argument A.
• LDA — LDA is INTEGER; the leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).
• TAU — TAU is DOUBLE PRECISION array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQRF.
• 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 dorm2r.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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footer sign-off: source/version is LAPACK Version 3.12.0, and the page is SRC/dorm2r.f(3). Date: not listed on this page, so no invented date energy — just accurate facts and good vibes, bestie 💅💖