SRC/cunmlq.f(3)

💅 SRC/cunmlq.f(3)

okay so this is the Library Functions Manual, and today’s main character is CUNMLQ — a complex unitary reflector queen 💖

🌸 NAME 🌸

SRC/cunmlq.f — yes bestie, that’s the file we’re reading, and we are not skimming it.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine cunmlq — the routine herself, with the whole argument squad listed below.

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

CUNMLQ (yes, the name again, iconic)

💅 Function/Subroutine Documentation 💅

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

CUNMLQ — okay, deep breath, here’s what she does.

🦋 Purpose 🦋

CUNMLQ overwrites the general complex M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H

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 CGELQF. 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**H from the Left;
  • = 'R': apply Q or Q**H from the Right.
• TRANS — TRANS is CHARACTER*1.
  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.
• 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 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 CGELQF in the first k rows of its array argument A.

• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,K).
• TAU — TAU is COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGELQF.
• C — C is COMPLEX 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 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK.
  • If SIDE = 'L', LWORK >= max(1,N);
  • if SIDE = 'R', LWORK >= max(1,M).
  • For good performance, LWORK should generally be larger.

Heads up, bestie: if LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 💅

• 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 166 of file cunmlq.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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Catch you in the source, bestie — this one is LAPACK Version 3.12.0, from SRC/cunmlq.f(3). Mwah 💖🎀✨