SRC/sormr3.f(3)

💖 SRC/sormr3.f(3) 💖

Welcome to SRC/sormr3.f(3) from the Library Functions Manual, bestie — grab a snack, we're doing LAPACK 💅✨

🌸 NAME 🌸

SRC/sormr3.f

✨ SYNOPSIS ✨

🧁 Functions/Subroutines 🧁

subroutine sormr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work,
    info)
    SORMR3 multiplies a general matrix by the orthogonal matrix from a
    RZ factorization determined by stzrzf (unblocked algorithm).

🦋 Function/Subroutine Documentation 🦋

subroutine sormr3 (character side, character trans, integer m, integer n,
    integer k, integer l, real, dimension( lda, * ) a, integer lda, real,
    dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real,
    dimension( * ) work, integer info)

SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

🎀 Purpose 🎀

Okay so here's the exact vibe of what it does:

!>
!> SORMR3 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 STZRZF. Q is of order m if SIDE = 'L' and of order n
!> if SIDE = 'R'.
!>

🌈 Parameters 🌈

• SIDE — CHARACTER*1. 'L': apply Q or QT from the Left. 'R': apply Q or QT from the Right.
• TRANS — CHARACTER*1. 'N': apply Q (No transpose). 'T': apply Q**T (Transpose).
• M — INTEGER. The number of rows of the matrix C. M >= 0.
• N — INTEGER. The number of columns of the matrix C. N >= 0.
• K — 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 — 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 — REAL 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 STZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,K).
• TAU — REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by STZRZF.
• C — REAL 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 — INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — REAL array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R'.
• INFO — 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 💜

There is literally just this:

!>

Definition at line 176 of file sormr3.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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This iconic page is from LAPACK Version 3.12.0, file SRC/sormr3.f(3) — bye bestie, go slay those reflectors 💅💖✨