gelq(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 gelq(3) — gelq: LQ factor, flexible

ok so bestie. you clicked on gelq(3) and honestly? good choice. this is the LQ factor, flexible situation, and it lives in the Library Functions Manual ✨. buckle up, because there's a whole family of these routines and they're all doing the same gorgeous thing in different precisions 🎀.

✨ SYNOPSIS ✨

Functions

  • subroutine cgelq (m, n, a, lda, t, tsize, work, lwork, info) — CGELQ 💖
  • subroutine dgelq (m, n, a, lda, t, tsize, work, lwork, info) — DGELQ 💜
  • subroutine sgelq (m, n, a, lda, t, tsize, work, lwork, info) — SGELQ 🌸
  • subroutine zgelq (m, n, a, lda, t, tsize, work, lwork, info) — ZGELQ 🦋

🌈 Detailed Description

the page doesn't spill any extra tea up here, bestie — it just sets the stage for the function docs coming in hot below 👑.

💖 Function Documentation

cgelq 💅

subroutine cgelq (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( * ) t, integer tsize, complex,
    dimension( * ) work, integer lwork, integer info)

CGELQ 🌟

✨ Purpose

ok so here's the whole point, no cap:

CGELQ computes an LQ factorization of a complex M-by-N matrix A:
   A = ( L 0 ) *  Q

where:

  • Q is a N-by-N orthogonal matrix;
  • L is a lower-triangular M-by-M matrix;
  • 0 is a M-by-(N-M) zero matrix, if M < N.

🌸 Parameters

  • M

M is INTEGER The number of rows of the matrix A. M >= 0.

  • N

N is INTEGER The number of columns of the matrix A. N >= 0.

  • A

A is COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the M-by-min(M,N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal are used to store part of the data structure to represent Q.

  • LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

  • T

T is COMPLEX array, dimension (MAX(5,TSIZE)) On exit, if INFO = 0, T(1) returns optimal (or either minimal or optimal, if query is assumed) TSIZE. See TSIZE for details. Remaining T contains part of the data structure used to represent Q. If one wants to apply or construct Q, then one needs to keep T (in addition to A) and pass it to further subroutines.

  • TSIZE

TSIZE is INTEGER If TSIZE >= 5, the dimension of the array T. If TSIZE = -1 or -2, then a workspace query is assumed. The routine only calculates the sizes of the T and WORK arrays, returns these values as the first entries of the T and WORK arrays, and no error message related to T or WORK is issued by XERBLA. If TSIZE = -1, the routine calculates optimal size of T for the optimum performance and returns this value in T(1). If TSIZE = -2, the routine calculates minimal size of T and returns this value in T(1).

  • WORK

(workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) contains optimal (or either minimal or optimal, if query was assumed) LWORK. See LWORK for details.

  • LWORK

LWORK is INTEGER The dimension of the array WORK. LWORK >= 1. If LWORK = -1 or -2, then a workspace query is assumed. The routine only calculates the sizes of the T and WORK arrays, returns these values as the first entries of the T and WORK arrays, and no error message related to T or WORK is issued by XERBLA. If LWORK = -1, the routine calculates optimal size of WORK for the optimal performance and returns this value in WORK(1). If LWORK = -2, the routine calculates minimal size of WORK and returns this value in WORK(1).

  • 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.

🔥 Further Details

ok this part is important, so like, read it 👀:

The goal of the interface is to give maximum freedom to the developers for creating any LQ factorization algorithm they wish. The triangular (trapezoidal) L has to be stored in the lower part of A. The lower part of A and the array T can be used to store any relevant information for applying or constructing the Q factor. The WORK array can safely be discarded after exit.
Caution: One should not expect the sizes of T and WORK to be the same from one LAPACK implementation to the other, or even from one execution to the other. A workspace query (for T and WORK) is needed at each execution. However, for a given execution, the size of T and WORK are fixed and will not change from one query to the next.

bestie fr fr: query every single time. do not assume, do not hardcode, do not pass go 💀.

🧚 Further Details particular to this LAPACK implementation

these deets are this LAPACK implementation only, okay? don't go treating them as law:

These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are not likely true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface.

In this version,

          T(2): row block size (MB)
          T(3): column block size (NB)
          T(6:TSIZE): data structure needed for Q, computed by
                           CLASWLQ or CGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, CGELQ will use either CLASWLQ (if the matrix is short-and-wide) or CGELQT to compute the LQ factorization.

Definition at line 172 of file cgelq.f. ⭐

dgelq 💜

subroutine dgelq (integer m, integer n, double precision, dimension( lda, * )
    a, integer lda, double precision, dimension( * ) t, integer tsize,
    double precision, dimension( * ) work, integer lwork, integer info)

DGELQ 🌟

✨ Purpose

DGELQ computes an LQ factorization of a real M-by-N matrix A:
   A = ( L 0 ) *  Q

where:

  • Q is a N-by-N orthogonal matrix;
  • L is a lower-triangular M-by-M matrix;
  • 0 is a M-by-(N-M) zero matrix, if M < N.

🌸 Parameters

  • M

M is INTEGER The number of rows of the matrix A. M >= 0.

  • N

N is INTEGER The number of columns of the matrix A. N >= 0.

  • A

A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the M-by-min(M,N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal are used to store part of the data structure to represent Q.

  • LDA

LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

  • T

T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)) On exit, if INFO = 0, T(1) returns optimal (or either minimal or optimal, if query is assumed) TSIZE. See TSIZE for details. Remaining T contains part of the data structure used to represent Q. If one wants to apply or construct Q, then one needs to keep T (in addition to A) and pass it to further subroutines.

  • TSIZE

TSIZE is INTEGER If TSIZE >= 5, the dimension of the array T. If TSIZE = -1 or -2, then a workspace query is assumed. The routine only calculates the sizes of the T and WORK arrays, returns these values as the first entries of the T and WORK arrays, and no error message related to T or WORK is issued by XERBLA. If TSIZE = -1, the routine calculates optimal size of T for the optimum performance and returns this value in T(1). If TSIZE = -2, the routine calculates minimal size of T and returns this value in T(1).

  • WORK

(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) contains optimal (or either minimal or optimal, if query was assumed) LWORK. See LWORK for details.

  • LWORK

LWORK is INTEGER The dimension of the array WORK. LWORK >= 1. If LWORK = -1 or -2, then a workspace query is assumed. The routine only calculates the sizes of the T and WORK arrays, returns these values as the first entries of the T and WORK arrays, and no error message related to T or WORK is issued by XERBLA. If LWORK = -1, the routine calculates optimal size of WORK for the optimal performance and returns this value in WORK(1). If LWORK = -2, the routine calculates minimal size of WORK and returns this value in WORK(1).

  • 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.

🔥 Further Details

Okay so the goal of this interface is literally to give devs maximum freedom to create any LQ factorization algorithm they want. The triangular (trapezoidal) L has to be stored in the lower part of A. The lower part of A and the array T can be used to store any relevant info for applying or constructing the Q factor. The WORK array can safely be discarded after exit — no cap.

⚠️ Caution: One should not expect the sizes of T and WORK to be the same from one LAPACK implementation to the other, or even from one execution to the other. A workspace query (for T and WORK) is needed at each execution. However, for a given execution, the size of T and WORK are fixed and will not change from one query to the next. 💅

✨ Further Details particular to this LAPACK implementation ✨

These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are not likely true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface.

In this version:

  • T(2): row block size (MB)
  • T(3): column block size (NB)
  • T(6:TSIZE): data structure needed for Q, computed by DLASWLQ or DGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, DGELQ will use either DLASWLQ (if the matrix is short-and-wide) or DGELQT to compute the LQ factorization.

Definition at line 172 of file dgelq.f.

✨ subroutine sgelq ✨

subroutine sgelq (integer m, integer n, real, dimension( lda, * ) a, integer
    lda, real, dimension( * ) t, integer tsize, real, dimension( * ) work,
    integer lwork, integer info)

SGELQ

Purpose:

SGELQ computes an LQ factorization of a real M-by-N matrix A:

A = ( L 0 ) * Q

where:

  • Q is a N-by-N orthogonal matrix;
  • L is a lower-triangular M-by-M matrix;
  • 0 is a M-by-(N-M) zero matrix, if M < N.

Parameters

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. N >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the M-by-min(M,N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal are used to store part of the data structure to represent Q.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • T — T is REAL array, dimension (MAX(5,TSIZE)). On exit, if INFO = 0, T(1) returns optimal (or either minimal or optimal, if query is assumed) TSIZE. See TSIZE for details. Remaining T contains part of the data structure used to represent Q. If one wants to apply or construct Q, then one needs to keep T (in addition to A) and pass it to further subroutines.
  • TSIZE — TSIZE is INTEGER. If TSIZE >= 5, the dimension of the array T. If TSIZE = -1 or -2, then a workspace query is assumed. The routine only calculates the sizes of the T and WORK arrays, returns these values as the first entries of the T and WORK arrays, and no error message related to T or WORK is issued by XERBLA. If TSIZE = -1, the routine calculates optimal size of T for the optimum performance and returns this value in T(1). If TSIZE = -2, the routine calculates minimal size of T and returns this value in T(1).
  • WORK — (workspace) REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) contains optimal (or either minimal or optimal, if query was assumed) LWORK. See LWORK for details.
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1. If LWORK = -1 or -2, then a workspace query is assumed. The routine only calculates the sizes of the T and WORK arrays, returns these values as the first entries of the T and WORK arrays, and no error message related to T or WORK is issued by XERBLA. If LWORK = -1, the routine calculates optimal size of WORK for the optimal performance and returns this value in WORK(1). If LWORK = -2, the routine calculates minimal size of WORK and returns this value in WORK(1).
  • 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.

Further Details

The goal of the interface is to give maximum freedom to the developers for creating any LQ factorization algorithm they wish. The triangular (trapezoidal) L has to be stored in the lower part of A. The lower part of A and the array T can be used to store any relevant information for applying or constructing the Q factor. The WORK array can safely be discarded after exit.

⚠️ Caution: One should not expect the sizes of T and WORK to be the same from one LAPACK implementation to the other, or even from one execution to the other. A workspace query (for T and WORK) is needed at each execution. However, for a given execution, the size of T and WORK are fixed and will not change from one query to the next. 💅

Further Details particular to this LAPACK implementation

These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are not likely true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface.

In this version:

  • T(2): row block size (MB)
  • T(3): column block size (NB)
  • T(6:TSIZE): data structure needed for Q, computed by SLASWLQ or SGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, SGELQ will use either SLASWLQ (if the matrix is short-and-wide) or SGELQT to compute the LQ factorization.

Definition at line 172 of file sgelq.f.

✨ subroutine zgelq ✨

subroutine zgelq (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( * ) t, integer tsize, complex*16,
    dimension( * ) work, integer lwork, integer info)

ZGELQ

Purpose:

ZGELQ computes an LQ factorization of a complex M-by-N matrix A:

A = ( L 0 ) * Q

where:

  • Q is a N-by-N orthogonal matrix;
  • L is a lower-triangular M-by-M matrix;
  • 0 is a M-by-(N-M) zero matrix, if M < N.

Parameters

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the M-by-min(M,N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal are used to store part of the data structure to represent Q.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • T — T is COMPLEX*16 array, dimension (MAX(5,TSIZE)). On exit, if INFO = 0, T(1) returns optimal (or either minimal or optimal, if query is assumed) TSIZE. See TSIZE for details. Remaining T contains part of the data structure used to represent Q. If one wants to apply or construct Q, then one needs to keep T (in addition to A) and pass it to further subroutines.
  • TSIZE — TSIZE is INTEGER. If TSIZE >= 5, the dimension of the array T. If TSIZE = -1 or -2, then a workspace query is assumed. The routine only calculates the sizes of the T and WORK arrays, returns these values as the first entries of the T and WORK arrays, and no error message related to T or WORK is issued by XERBLA. If TSIZE = -1, the routine calculates optimal size of T for the optimum performance and returns this value in T(1). If TSIZE = -2, the routine calculates minimal size of T and returns this value in T(1).
  • WORK — (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) contains optimal (or either minimal or optimal, if query was assumed) LWORK. See LWORK for details.
  • LWORK —
  • LWORK is INTEGER — it's literally the dimension of the array WORK, and LWORK >= 1, no cap.
    • If LWORK = -1 or -2, we're in workspace query mode, bestie. The routine only calculates the sizes of the T and WORK arrays, hands them back as the first entries of the T and WORK arrays, and XERBLA will not come for you with any error message about T or WORK. Peace and quiet, iconic.
    • If LWORK = -1, it computes the optimal size of WORK for optimal performance and returns that value in WORK(1). Go big 💅
    • If LWORK = -2, it computes the minimal size of WORK and returns that value in WORK(1). Budget era 🎀
  • INFO is INTEGER — the vibe report:
    • = 0: successful exit ✨ slay
    • < 0: if INFO = -i, the i-th argument had an illegal value 😭 somebody fumbled

🌸 Author 🌸

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

💖 Further Details 💖

The whole goal of this interface is to give developers maximum freedom to create literally any LQ factorization algorithm they want. Main character energy for the algorithm designers, fr fr.

The triangular (trapezoidal) L has to be stored in the lower part of A. The lower part of A and the array T can be used to store any relevant information for applying or constructing the Q factor. The WORK array can safely be discarded after exit — it said "my work here is done" and left 🫡

Caution: do not expect the sizes of T and WORK to be the same from one LAPACK implementation to the other, or even from one execution to the other. A workspace query (for T and WORK) is needed at each execution. However — for a given execution, the sizes of T and WORK are fixed and will not change from one query to the next. So like, consistent within a run, chaotic across runs. 💀

🦋 Further Details particular to this LAPACK implementation: 🦋

These details are particular for this LAPACK implementation. Users should not take them for granted — no cap. These details may change in the future, and are not likely true for another LAPACK implementation. They're relevant if one wants to try to understand the code. They are not part of the interface. Read them like gossip, not like a contract 🙈

In this version,

T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
                 ZLASWLQ or ZGELQT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, ZGELQ will use either ZLASWLQ (if the matrix is short-and-wide) or ZGELQT to compute the LQ factorization. It's giving "choose your fighter" 🧚

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. (Not a human, just a robot doing its little thing 🤖💜)

And that's the whole page, bestie — LAPACK, Version 3.12.0, gelq(3), officially fully read and understood. Go take a nap, you earned it 🍓💤

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