SRC/sorml2.f(3)

🌸 SRC/sorml2.f(3) 🌸

okay so this is a Library Functions Manual page, and the title is SRC/sorml2.f(3) — yes bestie, we're deep in the LAPACK Fortran zone and it's lowkey iconic. 💅

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✨ NAME ✨

SRC/sorml2.f — that's the whole name, no cap. 🎀

✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

subroutine sorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    info)

• sorml2 — SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). slay.

🎀 Function/Subroutine Documentation 🎀

subroutine sorml2 (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)

SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).

🎯 Purpose 🎯

okay so here's the vibe: SORML2 overwrites the general real m by n matrix C with — and now the equations, bestie:

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

as returned by SGELQF. 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': 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 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 SGELQF in the first 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 REAL array, dimension (K)
• TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGELQF.

🦋 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 sorml2.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code. ✨

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💖 okay that's the whole page, bestie — LAPACK Version 3.12.0, SRC/sorml2.f(3) — mwah! 💖