geqr2p(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

✨ NAME ✨

okay so this is geqr2p(3) — the whole family of geqr2p routines — and the tagline the page gives it is literally geqr2p: QR factor, diag( R ) ≥ 0, level 2. bestie that's QR factorization with a non-negative diagonal, level 2, no cap 💅

✨ SYNOPSIS ✨

🌸 Functions 🌸

  • subroutine cgeqr2p (m, n, a, lda, tau, work, info) — CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm. 💖
  • subroutine dgeqr2p (m, n, a, lda, tau, work, info) — DGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
  • subroutine sgeqr2p (m, n, a, lda, tau, work, info) — SGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
  • subroutine zgeqr2p (m, n, a, lda, tau, work, info) — ZGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm. 🦋

✨ Detailed Description ✨

so like, four routines, same energy, different precision. each one does the same unblocked QR thing but with non-negative diagonal entries — that's the whole p situation, iykyk 👑

✨ Function Documentation ✨

💜 subroutine cgeqr2p (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info) 💜

CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

🎀 Purpose: 🎀

so CGEQR2P computes a QR factorization of a complex m-by-n matrix A, like this:

   A = Q * ( R ),
           ( 0 )

where, in the page's own words:

  • Q is a m-by-m orthogonal matrix;
  • R is an upper-triangular n-by-n matrix with nonnegative diagonal entries;
  • 0 is a (m-n)-by-n zero matrix, if m > n.

that's it, that's the whole vibe ✨

🌈 Parameters 🌈

  • M — M is INTEGER. The number of rows of the matrix A. M >= 0. lowkey the most important number here, no pressure 🫶
  • 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 above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are real and nonnegative; the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). 💀 like she does a whole transformation on the way out
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). respect the leading dimension bestie 🚨
  • 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 (N).
  • 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**H

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

See Lapack Working Note 203 for details. ⭐

Definition at line 133 of file cgeqr2p.f.

🦋 subroutine dgeqr2p (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info) 🦋

DGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

🎀 Purpose: 🎀

DGEQR2P computes a QR factorization of a real m-by-n matrix A:

   A = Q * ( R ),
           ( 0 )

where:

  • Q is a m-by-m orthogonal matrix;
  • R is an upper-triangular n-by-n matrix with nonnegative diagonal entries;
  • 0 is a (m-n)-by-n zero matrix, if m > n.

same energy, double the precision, we love to see it 💖

🌈 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 above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are nonnegative; the elements below 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 (N).
  • 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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

See Lapack Working Note 203 for details. 🌸

Definition at line 133 of file dgeqr2p.f.

🌟 subroutine sgeqr2p (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info) 🌟

SGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

🎀 Purpose: 🎀

SGEQR2P computes a QR factorization of a real m-by-n matrix A:

   A = Q * ( R ),
           ( 0 )

where:

  • Q is a m-by-m orthogonal matrix;
  • R is an upper-triangular n-by-n matrix with nonnegative diagonal entries;
  • 0 is a (m-n)-by-n zero matrix, if m > n.

single precision but the confidence is at least double, fr fr 🔥

🌈 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 above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n). The diagonal entries of R are nonnegative; the elements below 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 (N).
  • 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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

See Lapack Working Note 203 for details. 🫶

Definition at line 133 of file sgeqr2p.f.

🍓 subroutine zgeqr2p (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info) 🍓

ZGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

🎀 Purpose: 🎀

ZGEQR2P computes a QR factorization of a complex m-by-n matrix A:

   A = Q * ( R ),
           ( 0 )

where:

  • Q is a m-by-m orthogonal matrix;
  • R is an upper-triangular n-by-n matrix with nonnegative diagonal entries;
  • 0 is a (m-n)-by-n zero matrix, if m > n.

double complex, double drama, zero notes 😭

🌈 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)…

(and the rest of A — plus LDA, TAU, WORK, INFO, the Author block, the Further Details and the definition line — rolls on into part 2, bestie, don't go anywhere 💅)

  • A — COMPLEX*16 array, dimension (LDA,N), bestie. On entry it's the m by n matrix A. On exit, the elements on and above the diagonal of the array hold the min(m,n) by n upper trapezoidal matrix R (and R is upper triangular if m >= n, iykyk). The diagonal entries of R are real and nonnegative; the elements below the diagonal, together with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details, it's cute down there 💅).
  • LDA — INTEGER, no cap. The leading dimension of the array A. Constraint: LDA >= max(1,M). That's the vibe check, don't fail it 🙈.
  • TAU — COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors (again: Further Details ✨).
  • WORK — COMPLEX*16 array, dimension (N). That's it, that's the whole job. She's just a workspace 🫶.
  • INFO — INTEGER, and the receipts:
    • = 0: successful exit 🎉 slay
    • < 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.

(like, a whole squad of authors, main character energy all around 🌈)

💜 Further Details:

So here's the lore, and it is literally iconic:

Q = H(1) H(2) . . . H(k), 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; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i). No cap, that's just how she's built 🦋.

See Lapack Working Note 203 for details 👀.

Definition at line 133 of file zgeqr2p.f.

🌸 Author

Generated automatically by Doxygen for LAPACK from the source code. (The robots wrote this one, not me. Respect tho 🤖💖)

Heads up bestie: this page is auto-generated, so the "author" of the page is Doxygen and the authors of the code are the whole university lineup above. Both are serving 💅

Okay that's the whole page, you made it to the end, I'm so proud 🥹🫶 This treasure dropped as LAPACK Version 3.12.0, filed under geqr2p(3) — go forth and factorize, my love ✨🎀⭐

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