SRC/dormrz.f(3)

okay so this is the SRC/dormrz.f page from the Library Functions Manual — group-chat welcome, bestie, because we’re about to get into DORMRZ and its orthogonal-matrix product era 💅✨

🌸 NAME 🌸

SRC/dormrz.f

✨ SYNOPSIS ✨

🧩 Functions/Subroutines 🧩

Here’s the signature, exactly as it appears, no cap:

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

DORMRZ 👑

💅 Function/Subroutine Documentation 💅

Signature again, now with the full types doing their thing:

subroutine dormrz (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
    lwork, integer info)

DORMRZ 💖

🎯 Purpose: 🎯

DORMRZ overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**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 DTZRZF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

🎀 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': No transpose, apply Q; = 'T': Transpose, apply Q**T. ✨
• 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**H*C or C*Q**H 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For good performance, LWORK should generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• 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: 🔍

bestie, the original section is literally just this tiny marker: !> — no extra lore, just that 🫶

📍 Definition at line 185 of file dormrz.f 📍

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

🎀 okay that’s the whole page, bestie — cute sign-off from LAPACK Version 3.12.0, page SRC/dormrz.f(3), and that’s the footer vibe; the original didn’t include a date, so I’m not inventing one 💖✨