gemlqt(3)

📦

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3.12.1 · debian trixie

💖 gemlqt(3) 💖

okay bestie, welcome to gemlqt(3) — yes, that's the page name, it's a Library Functions Manual situation, and it's literally four subroutines in a trench coat. the whole vibe is: "multiply by Q from gelqt" ✨

✨ NAME ✨

gemlqt — gemlqt: multiply by Q from gelqt 🎀

🦋 SYNOPSIS 🦋

📚 Functions

here's the whole friend group, all four of them take the exact same argument list and only the types change. iconique 💅

subroutine cgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc,
    work, info)

CGEMLQT 🌸

subroutine dgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc,
    work, info)

DGEMLQT 🌸

subroutine sgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc,
    work, info)

SGEMLQT 🌸

subroutine zgemlqt (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc,
    work, info)

ZGEMLQT 🌸

💫 DETAILED DESCRIPTION 💫

okay so this is where the full breakdown lives — every single function gets its own little spotlight down below 👇 and yes, we're going to go through all of them, no skipping, that's the rules 🫶

🔥 FUNCTION DOCUMENTATION 🔥

👑 `cgemlqt` 👑

subroutine cgemlqt (character side, character trans, integer m, integer n,
    integer k, integer mb, complex, dimension( ldv, * ) v, integer ldv,
    complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, *
    ) c, integer ldc, complex, dimension( * ) work, integer info)

CGEMLQT ✨

🎀 Purpose

bestie, CGEMLQT 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(2) . . . H(K) = I - V T V**H

generated using the compact WY representation as returned by CGELQT. 🦋

and where's Q from? Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. periodt 💅

🌸 Parameters

SIDE — is CHARACTER*1
- = 'L': apply Q or Q**H from the Left;
- = 'R': apply Q or Q**H from the Right.
TRANS — is CHARACTER*1
- = 'N': No transpose, apply Q;
- = 'C': Conjugate transpose, apply Q**H.
M — is INTEGER. The number of rows of the matrix C. M >= 0.
N — is INTEGER. The number of columns of the matrix C. N >= 0.
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.
MB — is INTEGER. The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in CGELQT 🙈
V — is COMPLEX array, dimension

(LDV,M) if SIDE = 'L',
(LDV,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 CGELQT in the first K rows of its array argument A.

LDV — is INTEGER. The leading dimension of the array V. LDV >= max(1,K).
T — is COMPLEX array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by CGELQT, stored as a MB-by-K matrix.
LDT — is INTEGER. The leading dimension of the array T. LDT >= MB.
C — is COMPLEX array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, QH C, C QH or C Q. 🔥
LDC — is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
WORK — is COMPLEX array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
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

Definition at line 151 of file cgemlqt.f.

👑 `dgemlqt` 👑

subroutine dgemlqt (character side, character trans, integer m, integer n,
    integer k, integer mb, double precision, dimension( ldv, * ) v, integer
    ldv, double precision, dimension( ldt, * ) t, integer ldt, double
    precision, dimension( ldc, * ) c, integer ldc, double precision,
    dimension( * ) work, integer info)

DGEMLQT ✨

🎀 Purpose

now the real one — DGEMLQT overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q C            C Q
TRANS = 'T':   Q**T C            C Q**T

where Q is a real orthogonal matrix defined as the product of K elementary reflectors:

      Q = H(1) H(2) . . . H(K) = I - V T V**T

generated using the compact WY representation as returned by DGELQT. 🦋

Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. 💅

🌸 Parameters

SIDE — is CHARACTER*1
- = 'L': apply Q or Q**T from the Left;
- = 'R': apply Q or Q**T from the Right.
TRANS — is CHARACTER*1
- = 'N': No transpose, apply Q;
- = 'C': Transpose, apply Q*T. *(yep, 'C' — that's literally what the docs say bestie, iykyk 🙈)
M — is INTEGER. The number of rows of the matrix C. M >= 0.
N — is INTEGER. The number of columns of the matrix C. N >= 0.
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.
MB — is INTEGER. The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in DGELQT.
V — is DOUBLE PRECISION array, dimension

(LDV,M) if SIDE = 'L',
(LDV,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 DGELQT in the first K rows of its array argument A.

LDV — is INTEGER. The leading dimension of the array V. LDV >= max(1,K).
T — is DOUBLE PRECISION array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by DGELQT, stored as a MB-by-K matrix.
LDT — is INTEGER. The leading dimension of the array T. LDT >= MB.
C — is DOUBLE PRECISION array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, QT C, C QT or C Q. 🔥
LDC — is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
WORK — is DOUBLE PRECISION array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
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

Definition at line 166 of file dgemlqt.f.

👑 `sgemlqt` 👑

subroutine sgemlqt (character side, character trans, integer m, integer n,
    integer k, integer mb, real, dimension( ldv, * ) v, integer ldv, real,
    dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer
    ldc, real, dimension( * ) work, integer info)

SGEMLQT ✨

🎀 Purpose

same energy, single precision — SGEMLQT overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q C            C Q
TRANS = 'T':   Q**T C            C Q**T

where Q is a real orthogonal matrix defined as the product of K elementary reflectors:

      Q = H(1) H(2) . . . H(K) = I - V T V**T

generated using the compact WY representation as returned by SGELQT. 🦋

Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. 💅

🌸 Parameters

SIDE — is CHARACTER*1
- = 'L': apply Q or Q**T from the Left;
- = 'R': apply Q or Q**T from the Right.
TRANS — is CHARACTER*1
- = 'N': No transpose, apply Q;
- = 'C': Transpose, apply Q*T. *(again with the 'C', bestie — that's what the page says, no cap 🙈)
M — is INTEGER. The number of rows of the matrix C. M >= 0.
N — is INTEGER. The number of columns of the matrix C. N >= 0.
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.
MB — is INTEGER. The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in SGELQT.
V — is REAL array, dimension

(LDV,M) if SIDE = 'L',
(LDV,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 SGELQT in the first K rows of its array argument A.

LDV — is INTEGER. The leading dimension of the array V. LDV >= max(1,K).

and T is literally the very next thing — part 2 is gonna catch you up on that one, don't go anywhere 🫶💖

back to sgemlqt — here are the rest of its parameters, bestie 💅

T — T is REAL array, dimension (LDT,K) — the upper triangular factors of the block reflectors as returned by SGELQT, stored as a MB-by-K matrix. 💖
LDT — LDT is INTEGER — the leading dimension of the array T. LDT >= MB. ✨
C — C is REAL array, dimension (LDC,N) — on entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**T C, 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. The dimension of WORK is N*MB if SIDE = 'L', or M*MB 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 151 of file sgemlqt.f.

💜 subroutine zgemlqt 💜

subroutine zgemlqt (character side, character trans, integer m, integer n,
    integer k, integer mb, complex*16, dimension( ldv, * ) v, integer ldv,
    complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension(
    ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)
    ZGEMLQT

Purpose

ZGEMLQT 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(2) . . . H(K) = I - V T V**H

generated using the compact WY representation as returned by ZGELQT.

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. 🔑
MB — MB is INTEGER — the block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in ZGELQT. 🦋
V — V is COMPLEX*16 array, dimension (LDV,M) if SIDE = 'L', (LDV,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 ZGELQT in the first K rows of its array argument A. 💜
LDV — LDV is INTEGER — the leading dimension of the array V. LDV >= max(1,K). ✨
T — T is COMPLEX*16 array, dimension (LDT,K) — the upper triangular factors of the block reflectors as returned by ZGELQT, stored as a MB-by-K matrix. 🎀
LDT — LDT is INTEGER — the leading dimension of the array T. LDT >= MB. 🔥
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, Q**H C, 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. The dimension of WORK is N*MB if SIDE = 'L', or M*MB 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 166 of file zgemlqt.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

and that's a wrap on gemlqt(3)! This page is LAPACK Version 3.12.0, gemlqt(3), and it was auto-generated by Doxygen for LAPACK from the source code. Slay bestie, go apply those reflectors 💅✨💖

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

gemlqt(3)

💖 gemlqt(3) 💖

✨ NAME ✨

🦋 SYNOPSIS 🦋

📚 Functions

💫 DETAILED DESCRIPTION 💫

🔥 FUNCTION DOCUMENTATION 🔥

👑 cgemlqt 👑

🎀 Purpose

🌸 Parameters

🫶 Author

⭐ Definition

👑 dgemlqt 👑

🎀 Purpose

🌸 Parameters

🫶 Author

⭐ Definition

👑 sgemlqt 👑

🎀 Purpose

🌸 Parameters

Author

💜 subroutine zgemlqt 💜

Purpose

Parameters

Author

📜 Author 📜

👑 `cgemlqt` 👑

👑 `dgemlqt` 👑

👑 `sgemlqt` 👑