gerq2(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 gerq2 — bestie's guide to the RQ factor, level 2 era

okay so real talk, the manual name here is gerq2 — that's the whole squad of routines you're about to meet. she's a level 2 BLAS situation and she's serving.

🌸 NAME 🌸

gerq2 — gerq2: RQ factor, level 2

like, the RQ factorization. but unblocked. level 2. that's the vibe. periodt.

✨ SYNOPSIS ✨

🎀 Functions 🎀

so there's not one but four iconique subroutines under this name, one for each flavor of number you might be living in. here's the whole lineup, no gatekeeping:

  • subroutine cgerq2 (m, n, a, lda, tau, work, info) — CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. the "C" is for complex, iykyk 💜
  • subroutine dgerq2 (m, n, a, lda, tau, work, info) — DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. double precision bestie, she's precise 💅
  • subroutine sgerq2 (m, n, a, lda, tau, work, info) — SGERQ2</sgerq2> wait no — SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. single precision, lowkey the classic 🎀
  • subroutine zgerq2 (m, n, a, lda, tau, work, info) — ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. double complex, ✨main character energy✨ fr fr

so yeah, same function signature, four different precisions. pick your fighter. the arguments are literally identical across all four — m, n, a, lda, tau, work, info — so once you get one you get all four, slay 🫶

🔥 Detailed Description 🔥

this section is literally empty in the original, bestie — nothing but the heading. don't come for me, I'm just the messenger 🙈

okay and that's where part 1 wraps up — but hold on, more is coming, don't go anywhere yet 👑

💖 Function Documentation 💖

Okay bestie, here come the four subroutine entries — same RQ factorization energy, different precision flavors. Let’s get into it. ✨

🌟 cgerq2 🌟

   subroutine cgerq2 (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
       integer info)

CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. 💅

✨ Purpose ✨

CGERQ2 computes an RQ factorization of a complex m by n matrix A:

A = R * Q.

🎀 Parameters 🎀

  • M — INTEGER. The number of rows of the matrix A. M >= 0.
  • N — INTEGER. The number of columns of the matrix A. N >= 0.
  • A — COMPLEX 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 elementary reflectors (see Further Details).
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • TAU — COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
  • WORK — COMPLEX array, dimension (M).
  • INFO — 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 📌

Definition at line 122 of file cgerq2.f.

🌟 dgerq2 🌟

   subroutine dgerq2 (integer m, integer n, double precision, dimension( lda, *
       ) a, integer lda, double precision, dimension( * ) tau, double
       precision, dimension( * ) work, integer info)

DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. 🔥

✨ Purpose ✨

DGERQ2 computes an RQ factorization of a real m by n matrix A:

A = R * Q.

🎀 Parameters 🎀

  • M — INTEGER. The number of rows of the matrix A. M >= 0.
  • N — INTEGER. The number of columns of the matrix A. N >= 0.
  • A — 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 elementary reflectors (see Further Details).
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • TAU — DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
  • WORK — DOUBLE PRECISION array, dimension (M).
  • INFO — 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 📌

Definition at line 122 of file dgerq2.f.

🌟 sgerq2 🌟

   subroutine sgerq2 (integer m, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, real, dimension( * ) work,
       integer info)

SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. 🦋

✨ Purpose ✨

SGERQ2 computes an RQ factorization of a real m by n matrix A:

A = R * Q.

🎀 Parameters 🎀

  • M — INTEGER. The number of rows of the matrix A. M >= 0.
  • N — INTEGER. The number of columns of the matrix A. N >= 0.
  • A — 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 elementary reflectors (see Further Details).
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • TAU — REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
  • WORK — REAL array, dimension (M).
  • INFO — 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 📌

Definition at line 122 of file sgerq2.f.

🌟 zgerq2 🌟

   subroutine zgerq2 (integer m, integer n, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
       work, integer info)

ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. 👑

✨ Purpose ✨

ZGERQ2 computes an RQ factorization of a complex m by n matrix A:

A = R * Q.

🎀 Parameters 🎀

  • M — INTEGER. The number of rows of the matrix A. M >= 0.
  • N — INTEGER. The number of columns of the matrix A. N >= 0.
  • A — 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 elementary reflectors (see Further Details).
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
  • TAU — COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
  • WORK — COMPLEX*16 array, dimension (M).
  • INFO — 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 📌

Definition at line 122 of file zgerq2.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

And that’s the whole gerq2(3) family, bestie — every flag, every array, every formula preserved and slaying. 🫶 Source/version vibes: LAPACK Version 3.12.0, page tag gerq2(3), and yes, that’s the footer moment. Periodt. 💅✨

📦 where this page comes from