gelq2(3)

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version 3.12.1 · 9 versions
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✨ gelq2 — LQ factor, level 2 ✨

okay so real talk, bestie: this is gelq2 from section 3 of the Library Functions Manual, and it's the whole "LQ factor, level 2" situation — like the level-2 BLAS-flavored glow-up of an LQ factorization 💅 buckle up, because we're getting into the four subroutine flavors of the exact same thing and honestly? iconic.

🌸 NAME 🌸

gelq2 — gelq2: LQ factor, level 2

that's it. that's the name. short, sweet, main character energy 👑

🎀 SYNOPSIS 🎀

💖 Functions 💖

  • subroutine cgelq2 (m, n, a, lda, tau, work, info) — the CGELQ2 one, computing the LQ factorization of a general rectangular matrix using an unblocked algorithm 🦋
  • subroutine dgelq2 (m, n, a, lda, tau, work, info) — the DGELQ2 one, computing the LQ factorization of a general rectangular matrix using an unblocked algorithm 🦋
  • subroutine sgelq2 (m, n, a, lda, tau, work, info) — the SGELQ2 one, computing the LQ factorization of a general rectangular matrix using an unblocked algorithm 🦋
  • subroutine zgelq2 (m, n, a, lda, tau, work, info) — the ZGELQ2 one, computing the LQ factorization of a general rectangular matrix using an unblocked algorithm 🦋

ngl the four of them are literally the same dialogue with different precision casting — c / d / s / z, all four taking the exact same argument list (m, n, a, lda, tau, work, info), all four doing that unblocked LQ factorization thing. periodt 💀

⭐ Detailed Description ⭐

so like… that's the whole description section in this part, bestie 🙈 the details live in the next part, and you already know I'm gonna walk you through every single argument. no skips. no vibes-based guessing. fr fr.

🌈 heads up: more parts are coming, so stay tuned — don't close the tab yet 💜

💻 FUNCTION DOCUMENTATION 💻

Okay so this is where the actual subroutines pop off. Four flavors, same LQ factorization energy, different scalar types. Let's go 💅

🦋 cgelq2

subroutine cgelq2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. Periodt.

🎯 Purpose

CGELQ2 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, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
  • WORK — WORK is COMPLEX array, dimension (M).
  • 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 Q is represented as a product of elementary reflectors

Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Definition at line 128 of file cgelq2.f.

🦋 dgelq2

subroutine dgelq2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. Yup, same vibe, double precision edition.

🎯 Purpose

DGELQ2 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, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
  • WORK — WORK is DOUBLE PRECISION array, dimension (M).
  • 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 Q is represented as a product of elementary reflectors

Q = H(k) . . . H(2) H(1), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**T

where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Definition at line 128 of file dgelq2.f.

🦋 sgelq2

subroutine sgelq2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. Real ones, rise up 🫶

🎯 Purpose

SGELQ2 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, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
  • WORK — WORK is REAL array, dimension (M).
  • 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 Q is represented as a product of elementary reflectors

Q = H(k) . . . H(2) H(1), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**T

where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Definition at line 128 of file sgelq2.f.

🦋 zgelq2

subroutine zgelq2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. Double complex, double iconic 🔥

🎯 Purpose

ZGELQ2 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, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
  • WORK — WORK is COMPLEX*16 array, dimension (M).
  • 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 Q is represented as a product of elementary reflectors

Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Definition at line 128 of file zgelq2.f.

📝 Author

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