gemqrt(3)

📦

version 3.12.1 · 9 versions

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3.12.1 · ubuntu stonking
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3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

💅 gemqrt(3) — multiply by Q from geqrt

This is the gemqrt(3) page from the Library Functions Manual, bestie. We're doing the LAPACK thing where you already have a Q from geqrt and now you need to actually multiply by it. Slay. ✨

🌸 NAME 🌸

gemqrt - gemqrt: multiply by Q from geqrt.

✨ SYNOPSIS ✨

🧚 Functions

CGEMQRT:

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

DGEMQRT:

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

SGEMQRT:

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

ZGEMQRT:

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

🫶 Detailed Description 🫶

The actual function docs are below, bestie — this part is just the landing zone. 🦋

👑 Function Documentation 👑

💖 subroutine cgemqrt — CGEMQRT

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

🎯 Purpose

Okay so CGEMQRT 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 orthogonal 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 CGEQRT. 💫

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

💅 Parameters

SIDE — direction check: CHARACTER*1. = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. 💅
TRANS — transpose vibe: CHARACTER*1. = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H. ✨
M — INTEGER. The number of rows of the matrix C. M >= 0. 🌈
N — INTEGER. The number of columns of the matrix C. N >= 0. 🌸
K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. 🎀
NB — INTEGER. The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in CGEQRT. 🔥
V — COMPLEX array, dimension (LDV,K). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRT in the first K columns of its array argument A. 🦋
LDV — INTEGER. The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). 🫶
T — COMPLEX array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by CGEQRT, stored as a NB-by-N matrix. 😭
LDT — INTEGER. The leading dimension of the array T. LDT >= NB. 💜
C — COMPLEX 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 — INTEGER. The leading dimension of the array C. LDC >= max(1,M). 🌸
WORK — COMPLEX array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. 🧚
INFO — 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 cgemqrt.f.

💖 subroutine dgemqrt — DGEMQRT

subroutine dgemqrt (character side, character trans, integer m, integer n,
    integer k, integer nb, 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)

🎯 Purpose

DGEMQRT 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 DGEQRT. 💫

Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. No cap.

💅 Parameters

SIDE — which side are we on: CHARACTER*1. = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. 💅
TRANS — transpose tea: CHARACTER*1. = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**T. ✨
M — INTEGER. The number of rows of the matrix C. M >= 0. 🌈
N — INTEGER. The number of columns of the matrix C. N >= 0. 🌸
K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. 🎀
NB — INTEGER. The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in DGEQRT. 🔥
V — DOUBLE PRECISION array, dimension (LDV,K). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQRT in the first K columns of its array argument A. 🦋
LDV — INTEGER. The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). 🫶
T — DOUBLE PRECISION array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by DGEQRT, stored as a NB-by-N matrix. 😭
LDT — INTEGER. The leading dimension of the array T. LDT >= NB. 💜
C — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array C. LDC >= max(1,M). 🌸
WORK — DOUBLE PRECISION array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. 🧚
INFO — 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 dgemqrt.f.

💖 subroutine sgemqrt — SGEMQRT

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

🎯 Purpose

SGEMQRT 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 SGEQRT. 💫

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

💅 Parameters

SIDE — pick a side: CHARACTER*1. = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. 💅
TRANS — transpose mode: CHARACTER*1. = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T. ✨
M — INTEGER. The number of rows of the matrix C. M >= 0. 🌈
N — INTEGER. The number of columns of the matrix C. N >= 0. 🌸
K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. 🎀
NB — INTEGER. The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in SGEQRT. 🔥
V — REAL array, dimension (LDV,K). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRT in the first K columns of its array argument A. 🦋
LDV — INTEGER. The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). 🫶
T — REAL array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by SGEQRT, stored as a NB-by-N matrix. 😭
LDT
LDT (INTEGER) — the leading dimension of the array T, bestie. Rule of the land: LDT >= NB. ✨
C — REAL array, dimension (LDC,N) 💖
- On entry: the M-by-N matrix C.
- On exit: C gets overwritten by Q C, Q**T C, C Q**T or C Q. Like, it's gone, it's transformed, that's the whole point. 🦋
LDC (INTEGER) — the leading dimension of the array C. Constraint: LDC >= max(1,M). No cap.
WORK — REAL array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. It's giving "scratch space with rules", honestly. 💅
INFO (INTEGER) — the vibe check at the end 😌
- = 0: successful exit, we ate. 🔥
- < 0: if INFO = -i, the i-th argument had an illegal value. Somebody passed something cursed, and this is how you find out. 💀

💜 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 166 of file sgemqrt.f.

🦋 subroutine zgemqrt (character side, character trans, integer m, integer n, integer k, integer nb, complex16, dimension( ldv, ) v, integer ldv, complex16, dimension( ldt, ) t, integer ldt, complex16, dimension( ldc, ) c, integer ldc, complex16, dimension( ) work, integer info)

ZGEMQRT — okay so this is the complex*16 sibling and it is iconic. 👑

✨ Purpose:

!>
!> ZGEMQRT 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 orthogonal 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 ZGEQRT.
!>
!> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
!>

So real talk: Q is a complex orthogonal matrix built as the product of K elementary reflectors, and it was generated with the compact WY representation like ZGEQRT returned it. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. That's literally the whole deal. 🫶

🌸 Parameters

SIDE — CHARACTER1*
- = 'L': apply Q or Q**H from the Left;
- = 'R': apply Q or Q**H from the Right.
TRANS — CHARACTER1*
- = 'N': No transpose, apply Q;
- = 'C': Conjugate transpose, apply Q**H.
M (INTEGER) — the number of rows of the matrix C. Constraint: M >= 0.
N (INTEGER) — the number of columns of the matrix C. Constraint: N >= 0.
K (INTEGER) — the number of elementary reflectors whose product defines the matrix Q. 🎀
- If SIDE = 'L', M >= K >= 0;
- if SIDE = 'R', N >= K >= 0.
NB (INTEGER) — the block size used for the storage of T. Constraint: K >= NB >= 1. ⚠️ Real one here: this must be the same value of NB used to generate T in ZGEQRT. Not a similar value. The same one. Don't fumble this. 💀
V — COMPLEX16 array, dimension (LDV,K)* — the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRT in the first K columns of its array argument A. That's the tea. 🍓
LDV (INTEGER) — the leading dimension of the array V.
- If SIDE = 'L', LDA >= max(1,M);
- if SIDE = 'R', LDA >= max(1,N).
T — COMPLEX16 array, dimension (LDT,K)* — the upper triangular factors of the block reflectors as returned by ZGEQRT, stored as a NB-by-N matrix. 💅
LDT (INTEGER) — the leading dimension of the array T. Constraint: LDT >= NB.
C — COMPLEX16 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 (INTEGER) — the leading dimension of the array C. Constraint: LDC >= max(1,M).
WORK — COMPLEX16 array*. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. Same deal as before, just complex now. ✨
INFO (INTEGER) — the final verdict 😭
- = 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 zgemqrt.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

And that's the whole page, bestie — every flag, every constraint, every vibe. 🧚

Okay so the actual footer energy: this is from LAPACK, Version 3.12.0, and the page is gemqrt(3). Generated automatically by Doxygen, so like, no human wrote it and yet it still ate. Slay. 🎀✨ periodt.

📦 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

gemqrt(3)

💅 gemqrt(3) — multiply by Q from geqrt

🌸 NAME 🌸

✨ SYNOPSIS ✨

🧚 Functions

🫶 Detailed Description 🫶

👑 Function Documentation 👑

💖 subroutine cgemqrt — CGEMQRT

🎯 Purpose

💅 Parameters

🫶 Author

💖 subroutine dgemqrt — DGEMQRT

🎯 Purpose

💅 Parameters

🫶 Author

💖 subroutine sgemqrt — SGEMQRT

🎯 Purpose

💅 Parameters

💜 Author

🦋 subroutine zgemqrt (character side, character trans, integer m, integer n, integer k, integer nb, 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)

✨ Purpose:

🌸 Parameters

💜 Author

👑 Author

🦋 subroutine zgemqrt (character side, character trans, integer m, integer n, integer k, integer nb, complex16, dimension( ldv, ) v, integer ldv, complex16, dimension( ldt, ) t, integer ldt, complex16, dimension( ldc, ) c, integer ldc, complex16, dimension( ) work, integer info)