ZGERQF(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 ZGERQF(3) — the RQ factorization glow-up (LAPACK library functions manual, bestie)

okay so real talk, this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgerqf.f in the LAPACK source tree, and it's a Fortran subroutine doc that Doxygen spat out. let's get into it 🎀

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgerqf.f

that's the file, that's the whole name section, she's lowkey just a path bestie 💀

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine ZGERQF (m, n, a, lda, tau, work, lwork, info) — the icon herself. ZGERQF.

🦋 Function/Subroutine Documentation 🦋

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

ZGERQF — say it with me — ZGERQF. main character energy fr fr 💜

🎯 Purpose

!> !> ZGERQF computes an RQ factorization of a complex M-by-N matrix A: !> A = R * Q. !>

so yeah, she computes an RQ factorization of a complex M-by-N matrix A, and it's literally A = R * Q. that's the whole vibe. no cap. ✨

💖 Parameters 💖

M

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

M is INTEGER and it's the number of rows of the matrix A. the rule is M >= 0, respect it 🙏

N

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

N is INTEGER, number of columns of the matrix A, and it's N >= 0. same energy, different axis 💅

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A.
!>          On exit,
!>          if m <= n, the upper triangle of the subarray
!>          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
!>          if m >= n, the elements on and above the (m-n)-th subdiagonal
!>          contain the M-by-N upper trapezoidal matrix R;
!>          the remaining elements, with the array TAU, represent the
!>          unitary matrix Q as a product of min(m,n) elementary
!>          reflectors (see Further Details).
!>

A is a COMPLEX*16 array, dimension (LDA,N). on entry it's the M-by-N matrix A — cute, simple. on exit it gets a whole makeover:

  • if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R
  • if m >= n, the elements on and above the (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix R
  • the remaining elements, together with the array TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors (peep Further Details 👀)

she contains multitudes, honestly 🫶

LDA

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

LDA is INTEGER and it's the leading dimension of the array A. the rule is LDA >= max(1,M) — don't test her 😭

TAU

!>          TAU is COMPLEX*16 array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>

TAU is a COMPLEX*16 array, dimension (min(M,N)), holding the scalar factors of the elementary reflectors (Further Details has the tea 👀)

WORK

!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>

WORK is a COMPLEX*16 array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, then WORK(1) returns the optimal LWORK. she's helpful like that 💖

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.
!>

LWORK is INTEGER, the dimension of the array WORK. the rules:

  • LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise
  • for optimum performance LWORK >= M*NB, where NB is the optimal blocksize

and the spicy bit 🔥 — 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. queen of not yelling at you for asking 💅

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

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.

the whole squad showed up, we love a collab 🫶✨

🧚 Further Details 🧚

!> !> The matrix Q is represented as a product of elementary reflectors !> !> Q = H(1)**H H(2)**H . . . H(k)**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on !> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). !>

okay so here's the lore, bestie 📖 the matrix Q is represented as a product of elementary reflectors:

Q = H(1)**H H(2)**H . . . H(k)**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). literally the blueprint, no notes 💅

📍 Definition at line 138 of file zgerqf.f.

⭐ Author (again, but make it meta) ⭐

Generated automatically by Doxygen for LAPACK from the source code. she was built by a robot and she ate 🤖✨

and that's the page!! 💖 sign-off time: this is LAPACK, Version 3.12.0, and the whole thing lives under /home/abui...RC/zgerqf.f(3) — go forth and factorize your RQ, bestie, you've got this 🦋🌈🎀 periodt.

📦 where this page comes from