SRC/zgeqr2p.f(3)

💖 SRC/zgeqr2p.f(3) 💖

okay bestie, welcome to the Library Functions Manual page for SRC/zgeqr2p.f — the file is literally the main character here, no notes.

🌸 NAME 🌸

• SRC/zgeqr2p.f — that’s the name, periodt.

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• 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.

🦋 Function/Subroutine Documentation 🦋

Here’s the whole subroutine, character-for-character, because we do not play with signatures:

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 🎀

The tea, straight from the source:

!>
!> 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.
!>
!>

💅 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). 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).
• 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 (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 zgeqr2p.f.

🌈 Author 🌈

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okay that’s the whole page, bestie — footer says LAPACK Version 3.12.0 and source SRC/zgeqr2p.f(3). There’s no date line on this one, so I’m not inventing one. slay, bye. 💅✨