/home/abui.../cgeqr2p.f(3)

💅 cgeqr2p.f(3) 💅

Okay bestie, this page is from the Library Functions Manual — and the “name” is literally the whole path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgeqr2p.f

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• 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.

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🦋 Function/Subroutine 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 💖

Okay so here's the tea: CGEQR2P 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 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 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.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Okay that's the whole page, bestie 💖 — footer sign-off: LAPACK Version 3.12.0, source /home/abui.../cgeqr2p.f(3). The footer doesn't print a separate date, so I'm not inventing one — periodt.