ZUNMQL(3)

💅 NAME

okay so bestie, this is <pink>zunmql.f</pink> — that's the source file living at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zunmql.f, and it's a page from the Library Functions Manual (section 3, iykyk). Slay, let's get into it. 🦋

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✨ SYNOPSIS ✨

Functions/Subroutines

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

ZUNMQL — that's the whole vibe, literally. 💖

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🎀 FUNCTION/SUBROUTINE DOCUMENTATION 🎀

subroutine ZUNMQL (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)

ZUNMQL again, because she's the main character and she knows it. 👑

🌸 Purpose

fr fr, here's what she does. ZUNMQL 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(2) H(1)

exactly as returned by ZGEQLF. Not me stanning a factorization routine but here we are. 💀 And listen: Q is of order M if SIDE = 'L', and of order N if SIDE = 'R'. That's the whole ballgame.

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✨ 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,K)

• The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQLF in the last k columns of its array argument A.

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 COMPLEX*16 array, dimension (K)

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

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.

she gets rewritten, bestie — your original C is gone, no cap. 🙈

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.

🫶 okay but here's the iconic bit: 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. It's giving "just asking, not committing." ✨

INFO

INFO is INTEGER

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author

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

🎀 Definition at line 165 of file zunmql.f.

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. The robots did this one, not me. 💅

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okay that's the whole page, mwah 💋 — this was LAPACK, Version 3.12.0, and it's the manual page for /home/abui...RC/zunmql.f(3) in the Library Functions Manual. periodt. 💖✨