gelqf(3)

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🌸 gelqf(3) — Library Functions Manual 🌸

🏷️ NAME

gelqf — gelqf: LQ factor. That's the whole name section, bestie — short, sweet, and iconic. 💖

✨ SYNOPSIS ✨

Functions

  • subroutine cgelqf (m, n, a, lda, tau, work, lwork, info) — CGELQF
  • subroutine dgelqf (m, n, a, lda, tau, work, lwork, info) — DGELQF
  • subroutine sgelqf (m, n, a, lda, tau, work, lwork, info) — SGELQF
  • subroutine zgelqf (m, n, a, lda, tau, work, lwork, info) — ZGELQF

📚 Detailed Description

Okay so this heading is here, but the original doesn't put any extra prose under it — it's giving "just a heading, bestie." We're moving straight to the function docs. 🫶

🧮 Function Documentation

💖 subroutine cgelqf — CGELQF

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

CGELQF

Purpose:

CGELQF 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. No cap, bestie. ✨
  • 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🌈
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. For optimum performance LWORK >= M*NB, where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🫶
  • 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 143 of file cgelqf.f.

💙 subroutine dgelqf — DGELQF

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

DGELQF

Purpose:

DGELQF 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🌈
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. For optimum performance LWORK >= M*NB, where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🫶
  • 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 143 of file dgelqf.f.

💚 subroutine sgelqf — SGELQF

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

SGELQF

Purpose:

SGELQF 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🌈
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. For optimum performance LWORK >= M*NB, where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🫶
  • 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 143 of file sgelqf.f.

💜 subroutine zgelqf — ZGELQF

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

ZGELQF

Purpose:

ZGELQF 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

okay so picking up right where we left off with the parameters, bestie — no cap, every single one is here: 💅

  • M — M is an INTEGER. It's the number of rows of the matrix A. The vibe check is M >= 0. 💖
  • N — N is an INTEGER. It's the number of columns of the matrix A. Also N >= 0. 🎀
  • A — A is a COMPLEX*16 array, dimension (LDA,N). On entry, it's 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 an INTEGER. It's the leading dimension of the array A. And LDA >= max(1,M). periodt. ✨
  • TAU — TAU is a COMPLEX*16 array, dimension (min(M,N)). It holds the scalar factors of the elementary reflectors (see Further Details). 🌸
  • WORK — WORK is a COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, then WORK(1) returns the optimal LWORK. 👑
  • LWORK — LWORK is an INTEGER. It's the dimension of the array WORK. The rules are: LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. For optimum performance, LWORK >= M*NB, where NB is the optimal blocksize. Important: if LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 😭
  • INFO — INFO is an 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 143 of file zgelqf.f.

🤖 Author (the Doxygen one) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

This iconic page is from LAPACK Version 3.12.0, and the footer says gelqf(3). No date was given, but honestly the vibes are timeless. Bye bestie, go forth and LQ-factorize. 💜✨

📦 where this page comes from