SRC/zunml2.f(3)

Hiiii bestie! Welcome to the SRC/zunml2.f(3) page from the Library Functions Manual ✨ This one is all about the LAPACK subroutine zunml2, and it’s lowkey iconic 💅

🌸 NAME 🌸

SRC/zunml2.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine zunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work,
    info)

ZUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm). No cap, that’s the whole vibe 🫶

💅 Function/Subroutine Documentation 💅

subroutine zunml2 (character side, character trans, integer m, integer n,
    integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,
    dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc,
    complex*16, dimension( * ) work, integer info)

ZUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm). Same energy as the synopsis, but now with the whole signature flexing 😌

🎀 Purpose 🎀

Okay so here’s the main-character move, bestie: ZUNML2 overwrites the general complex m-by-n matrix C with

      Q * C  if SIDE = 'L' and TRANS = 'N', or

      Q**H* C  if SIDE = 'L' and TRANS = 'C', or

      C * Q  if SIDE = 'R' and TRANS = 'N', or

      C * Q**H if SIDE = 'R' and TRANS = 'C',

where Q is a complex unitary matrix defined as the product of k elementary reflectors

      Q = H(k)**H . . . H(2)**H H(1)**H

as returned by ZGELQF. 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**H from the Left
  • = 'R': apply Q or Q**H from the Right
• TRANS — TRANS is CHARACTER*1
  • = 'N': apply Q (No transpose)
  • = 'C': apply Q**H (Conjugate 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 COMPLEX*16 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 ZGELQF 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 COMPLEX*16 array, dimension (K)
  • TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGELQF.
• C — C is COMPLEX*16 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 COMPLEX*16 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 zunml2.f.

✨ Author ✨

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