SRC/dormr3.f(3)

💖 NAME 💖

Okay bestie, this is the Library Functions Manual page for SRC/dormr3.f(3) — that’s the header title. The NAME entry itself is just SRC/dormr3.f, and the main character is dormr3, a Fortran subroutine. 💅

✨ 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).

subroutine dormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work,
    info)

🛠️ 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).

🎯 Purpose 🎯

Okay so 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'.

Tiny heads-up: the Purpose block says TRANS = 'C' in those formulas, while the TRANS parameter entry says 'T' for transpose. I’m keeping both exactly as written — no cap, not my job to edit LAPACK 💀.

💅 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.
• L — L is INTEGER. The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 DTZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
• 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 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.
• 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.

🌟 Contributors: 🌟

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

🔍 Further Details: 🔍

This block is literally empty in the original — no extra details hiding here. 🫶

Definition at line 176 of file dormr3.f.

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

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And that’s the whole page, bestie! Footer vibes: LAPACK — Version 3.12.0 — SRC/dormr3.f(3). There’s no date in the footer, so I’m not inventing one. Stay orthogonal 💅✨