SRC/dgeqr2p.f(3)

SRC/dgeqr2p.f(3) · Library Functions Manual — okay bestie, this is the page for the dgeqr2p subroutine, and it's lowkey a whole moment. 💅

💖 NAME 💖

SRC/dgeqr2p.f — that's the name, periodt. The manual it lives in is the Library Functions Manual.

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• 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. Slay.

🦋 Function/Subroutine Documentation 🦋

Okay so here's the full signature, and yes, copy it exactly — no autocorrect, no vibes-based renaming:

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

dgeqr2p does exactly what the synopsis said: DGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm. Iconic.

🎀 Purpose: 🎀

The purpose is literally this, bestie:

!>
!> 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.
!>
!>

🌸 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:

!>
!>  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.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Final footer tea, bestie: this is LAPACK, Version 3.12.0, source SRC/dgeqr2p.f(3) — and there's no separate date listed in that footer, so that's the whole source/version moment. 💖✨🎀