SRC/sorm2r.f(3)

NAME

okay so this page is SRC/sorm2r.f, straight outta the Library Functions Manual, and it's giving full-on Fortran linear algebra bestie energy. No cap. 💅

SYNOPSIS

Functions/Subroutines

subroutine sorm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work,
     info)

SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).

🔍 Function/Subroutine Documentation 🔍

subroutine sorm2r (character side, character trans, integer m, integer n,
     integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *
     ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * )
     work, integer info)

SORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).

Purpose

Bestie, here's the whole point: SORM2R 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(1) H(2) . . . H(k)

as returned by SGEQRF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'.

Parameters

• SIDE — SIDE is CHARACTER*1, and it says which side Q comes from:
  • = '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. The bounds are If SIDE = 'L', M >= K >= 0; and if SIDE = 'R', N >= K >= 0.
• A — A is REAL 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 SGEQRF in the first k columns 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. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).
• TAU — TAU is REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQRF.
• C — C is 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 — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is REAL 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 157 of file sorm2r.f.

🪄 Author 🪄

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That's the whole page, bestie — LAPACK Version 3.12.0, SRC/sorm2r.f(3). Periodt. 💅✨