ZUNMRQ(3)

📦 version 3.12.0, in opensuse-leap 16.0

ZUNMRQ(3) 💅

okay so bestie, this is the <purple>Library Functions Manual</purple> page for ZUNMRQ(3), and yes we are in LAPACK territory. It’s giving unitary matrix, it’s giving elementary reflectors, and honestly? iconic.

🌸 NAME 🌸

The NAME section is literally just this source path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zunmrq.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

🦋 Function/Subroutine Documentation 🦋

The full signature is exactly this, bestie:

   subroutine ZUNMRQ (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 lwork, integer info)
       ZUNMRQ

💖 Purpose 💖

ZUNMRQ 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(1)**H H(2)**H . . . H(k)**H

as returned by ZGERQF. 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*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 ZGERQF in the last 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*16 array, dimension (K)

TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGERQF.

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 (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.

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 165 of file zunmrq.f.

💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

And that’s the whole page, bestie: LAPACK Version 3.12.0, page /home/abui...RC/zunmrq.f(3). Slay responsibly. 💅✨

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