SRC/sorm2l.f(3)

🌸 NAME 🌸

SRC/sorm2l.f — okay bestie, this is the SRC/sorm2l.f(3) page from the Library Functions Manual, and the file itself is SRC/sorm2l.f. 💖

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine sorm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work,
           info)

SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

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🦋 Function/Subroutine Documentation 🦋

subroutine sorm2l (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)

SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

💖 Purpose 💖

Okay so here's the vibe: SORM2L 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(k) . . . H(2) H(1)

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

🌸 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,K)
  • The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQLF in the last 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 SGEQLF.
• 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

bestie heads-up: A is modified by the routine but restored on exit — so it does get touched, but it comes back. 💅

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 157 of file sorm2l.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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