gerqf(3)

📦
version 3.12.1 · 9 versions
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🦋 gerqf(3) — RQ factor, but make it a vibe ✨

okay so this is gerqf, straight out of the Library Functions Manual (section 3, the library-functions girlies 💅). Four subroutines, one job, and honestly? It's giving "let me factor your matrix in a very specific direction" energy. Buckle up bestie, we're going in 💖

🌸 NAME 🌸

gerqf — gerqf: RQ factor

✨ SYNOPSIS ✨

Functions 💫

  • subroutine cgerqf (m, n, a, lda, tau, work, lwork, info) — CGERQF
  • subroutine dgerqf (m, n, a, lda, tau, work, lwork, info) — DGERQF
  • subroutine sgerqf (m, n, a, lda, tau, work, lwork, info) — SGERQF
  • subroutine zgerqf (m, n, a, lda, tau, work, lwork, info) — ZGERQF

🫶 Detailed Description 🫶

this is literally just the landing page for the four function docs below — scroll down, the real content is right there 👇

👑 Function Documentation 👑

cgerqf — the complex one 💜

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

CGERQF 🦋

Purpose ✨

okay so CGERQF computes an RQ factorization of a complex M-by-N matrix A, and it's literally this:

A = R * Q.

Parameters 🎀

  • M — M is INTEGER. It's the number of rows of the matrix A, bestie. Constraint: M >= 0.
  • N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, it's the M-by-N matrix A. On exit, here's the tea: 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; and the remaining elements, with the array TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors (peep Further Details for the receipts).
  • LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,M).
  • TAU — TAU is COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors (again — Further Details, iykyk).
  • 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. Constraints: 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. (yes, XERBLA stays quiet — that's the whole point, no cap)
  • 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(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).

Definition at line 138 of file cgerqf.f.

dgerqf — the double precision one 🌈

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

DGERQF 💙

Purpose ✨

DGERQF computes an RQ factorization of a real M-by-N matrix A:

A = R * Q.

Parameters 🎀

  • M — M is INTEGER. Number of rows of the matrix A. Constraint: M >= 0.
  • N — N is INTEGER. Number of columns of the matrix A. Constraint: N >= 0.
  • A — A is DOUBLE PRECISION 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 orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
  • LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: 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. Constraints: 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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).

Definition at line 138 of file dgerqf.f.

sgerqf — the real single precision one 🍓

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

SGERQF 💚

Purpose ✨

SGERQF computes an RQ factorization of a real M-by-N matrix A:

A = R * Q.

Parameters 🎀

  • M — M is INTEGER. Number of rows of the matrix A. Constraint: M >= 0.
  • N — N is INTEGER. Number of columns of the matrix A. Constraint: N >= 0.
  • A — A is REAL 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 orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
  • LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: 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. Constraints: 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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).

Definition at line 138 of file sgerqf.f.

zgerqf — the complex*16 one 🧚

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 🌟

Purpose ✨

ZGERQF computes an RQ factorization of a complex M-by-N matrix A:

A = R * Q.

Parameters 🎀

  • M — M is INTEGER. Number of rows of the matrix A. Constraint: M >= 0.
  • N — N is INTEGER. Number of columns of the matrix A. Constraint: N >= 0.
  • A

okay bestie the A deets for zgerqf keep going — that's part 2's whole moment, we're not done here yet 💅

okay so the args keep rolling in and this is where A gets its moment 💅

A 🫶

the exact tea:

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).

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 (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(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).
Definition at line 138 of file zgerqf.f.

Author 🤖 — auto-generated credit

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okay that's the whole page, bestie 💜 the footer says source/version LAPACK Version 3.12.0 and the page is gerqf(3) — no date is sitting on that footer line, so I'm not inventing one ✨🎀🫶

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