ungl2(3)

📦
version 3.12.1 · 9 versions
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💅 NAME 💅

Okay bestie, this is the manual page for ungl2(3) — the official name line is ungl2 - {un,or}gl2: generate explicit Q, level 2, step in unglq. Translation: it generates the explicit Q matrix, level 2 style, as one step inside unglq. Iconic. ✨

🌸 SYNOPSIS 🌸

Functions

  • subroutine cungl2 (m, n, k, a, lda, tau, work, info) — CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
  • subroutine dorgl2 (m, n, k, a, lda, tau, work, info) — DORGL2
  • subroutine sorgl2 (m, n, k, a, lda, tau, work, info) — SORGL2
  • subroutine zungl2 (m, n, k, a, lda, tau, work, info) — ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

🦋 Detailed Description 🦋

No big prose intro here, bestie — the page goes straight into the function docs. Pick your precision era and scroll. 🫶

👑 Function Documentation 👑

🧚 cungl2 💜

subroutine cungl2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

The page says: CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

💖 Purpose

CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n:

Q  =  H(k)**H . . . H(2)**H H(1)**H

...as returned by CGELQF.

✨ Parameters

  • M — M is INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix Q. N >= M.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGELQF in the first k rows of its array argument A. On exit, the m by n matrix Q.
  • LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGELQF.
  • WORK — WORK is COMPLEX array, dimension (M).
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument has an illegal value

🎀 Author

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

Definition at line 112 of file cungl2.f.

🧚 dorgl2 💜

subroutine dorgl2 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

The one-liner is literally just DORGL2 — no cap, that’s all it says. 💀

💖 Purpose

DORGL2 generates an m by n real matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n:

Q  =  H(k) . . . H(2) H(1)

...as returned by DGELQF.

✨ Parameters

  • M — M is INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix Q. N >= M.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQF in the first k rows of its array argument A. On exit, the m-by-n matrix Q.
  • LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is DOUBLE PRECISION array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGELQF.
  • WORK — WORK is DOUBLE PRECISION array, dimension (M).
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument has an illegal value

🎀 Author

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

Definition at line 112 of file dorgl2.f.

🧚 sorgl2 💜

subroutine sorgl2 (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

Again, the page’s description is just SORGL2 — short and mysterious. 🙈

💖 Purpose

SORGL2 generates an m by n real matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n:

Q  =  H(k) . . . H(2) H(1)

...as returned by SGELQF.

✨ Parameters

  • M — M is INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix Q. N >= M.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQF in the first k rows of its array argument A. On exit, the m-by-n matrix Q.
  • LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGELQF.
  • WORK — WORK is REAL array, dimension (M).
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument has an illegal value

🎀 Author

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

Definition at line 112 of file sorgl2.f.

🧚 zungl2 💜

subroutine zungl2 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

The description says: ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

💖 Purpose

ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n:

Q  =  H(k)**H . . . H(2)**H H(1)**H

...as returned by ZGELQF.

✨ Parameters

  • M — M is INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — N is INTEGER. The number of columns of the matrix Q. N >= M.
  • K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGELQF in the first k rows of its array argument A. On exit, the m by n matrix Q.
  • LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is COMPLEX*16 array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGELQF.
  • WORK — WORK is COMPLEX*16 array, dimension (M).
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument has an illegal value

🎀 Author

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

Definition at line 112 of file zungl2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 💖

That’s the whole page, bestie — every flag, type, constraint, and author credit accounted for. Periodt. 💅

LAPACK · Version 3.12.0 · ungl2(3) — mwah, go generate that Q 💜✨

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