gelqt3(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🎀 gelqt3(3) 🎀

okay bestie, welcome to gelqt3(3) from the Library Functions Manual — this is the recursive LQ-factor-with-T situation and it's giving linear algebra main character energy 💅✨

💖 NAME 💖

gelqt3 — gelqt3: LQ factor, with T, recursive

✨ SYNOPSIS ✨

🦋 Functions 🦋

  • recursive subroutine cgelqt3 (m, n, a, lda, t, ldt, info) — CGELQT3
  • recursive subroutine dgelqt3 (m, n, a, lda, t, ldt, info) — DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.
  • recursive subroutine sgelqt3 (m, n, a, lda, t, ldt, info) — SGELQT3
  • recursive subroutine zgelqt3 (m, n, a, lda, t, ldt, info) — ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

🌸 Detailed Description 🌸

bestie, this section is literally empty in the original — no extra tea here, the real goods are all under Function Documentation 💅

🎀 Function Documentation 🎀

🧚 recursive subroutine cgelqt3 🧚

recursive subroutine cgelqt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGELQT3

💜 Purpose

CGELQT3 recursively computes a LQ factorization of a complex M-by-N matrix A, using the compact WY representation of Q. It's based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

🍓 Parameters

  • M — M is INTEGER. It's the number of rows of the matrix A. Heads up: M =< N.
  • N — N is INTEGER. It's the number of columns of the matrix A. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, it's the complex M-by-N matrix A. On exit, the elements on and below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows of V. See below for further details.
  • LDA — LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(1,M).
  • T — T is COMPLEX array, dimension (LDT,N). It's the N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.
  • LDT — LDT is INTEGER. It's the leading dimension of the array T. LDT >= max(1,N).
  • 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 matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is:

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (     1  v3 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by:

               H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 115 of file cgelqt3.f.

🦋 recursive subroutine dgelqt3 🦋

recursive subroutine dgelqt3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)

DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

💜 Purpose

DGELQT3 recursively computes a LQ factorization of a real M-by-N matrix A, using the compact WY representation of Q. It's based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

🍓 Parameters

  • M — M is INTEGER. It's the number of rows of the matrix A. M =< N.
  • N — N is INTEGER. It's the number of columns of the matrix A. N >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, it's the real M-by-N matrix A. On exit, the elements on and below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows of V. See below for further details.
  • LDA — LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(1,M).
  • T — T is DOUBLE PRECISION array, dimension (LDT,N). It's the N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.
  • LDT — LDT is INTEGER. It's the leading dimension of the array T. LDT >= max(1,N).
  • 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 matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is:

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (     1  v3 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by:

               H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 130 of file dgelqt3.f.

🧚 recursive subroutine sgelqt3 🧚

recursive subroutine sgelqt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGELQT3

💜 Purpose

SGELQT3 recursively computes a LQ factorization of a real M-by-N matrix A, using the compact WY representation of Q. It's based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

🍓 Parameters

  • M — M is INTEGER. It's the number of rows of the matrix A. M =< N.
  • N — N is INTEGER. It's the number of columns of the matrix A. N >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry, it's the real M-by-N matrix A. On exit, the elements on and below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows of V. See below for further details.
  • LDA — LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(1,M).
  • T — T is REAL array, dimension (LDT,N). It's the N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.
  • LDT — LDT is INTEGER. It's the leading dimension of the array T. LDT >= max(1,N).
  • 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 matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is:

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (     1  v3 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by:

               H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 115 of file sgelqt3.f.

🦋 recursive subroutine zgelqt3 🦋

recursive subroutine zgelqt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

💜 Purpose

ZGELQT3 recursively computes a LQ factorization of a complex M-by-N matrix A, using the compact WY representation of Q. It's based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

🍓 Parameters

  • M — M is INTEGER. It's the number of rows of the matrix A. M =< N.
  • N — N is INTEGER. It's the number of columns of the matrix A. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, it's the complex M-by-N matrix A. On exit, the elements on and below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows of V. See below for further details.
  • LDA — LDA is INTEGER. It's the leading dimension of the array A. LDA >= max(1,M).
  • T
  • T — okay so this one's a COMPLEX*16 array, dimension (LDT,N) 💖. It's the N-by-N upper triangular factor of the block reflector, bestie. Everything on and above the diagonal? That's the block reflector T living there. Everything below the diagonal? Not used, don't worry about it 🫶. Peep "further details" below for the whole story.
  • LDT — this is an INTEGER, and it's the leading dimension of the array T. The vibe check it has to pass: LDT >= max(1,N) ✨.
  • INFO — INTEGER, the little status report at the end 👑:
    • = 0: successful exit, we ate, no crumbs 💅
    • < 0: if INFO = -i, then the i-th argument had an illegal value 🚨 (not me, not you — the argument, fr fr)

🌸 Author 🌸

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Literally the whole dream team, iconic ✨

🔥 Further Details: 🔥

The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is
         V = (  1  v1 v1 v1 v1 )
             (     1  v2 v2 v2 )
             (     1  v3 v3 v3 )
where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by
         H = I - V * T * V**T
where V**T is the transpose of V.
For details of the algorithm, see Elmroth and Gustavson (cited above).

Like, the 1s on the diagonal of V are so modest they don't even get stored in A — main character energy but make it humble 🙈💜

Definition at line 130 of file zgelqt3.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code. (Yes bestie, a robot wrote this bit — slay, honestly 🤖✨)

And that's a wrap, bestie! This whole gorgeous little page is from LAPACK, Version 3.12.0, and you just read gelqt3(3) 🎀🦋 Go forth and factor those block reflectors, iykyk 💖💅

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