SRC/cgeqr2p.f(3)

🎀 NAME 🎀

ok so bestie, welcome to the Library Functions Manual entry for SRC/cgeqr2p.f — yes that's the whole name, it's giving "my parents named me after the file path" energy but we move 💅

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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

ok so here's the whole vibe — 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.

no notes, iconic behavior fr fr ✨

🧚 Parameters

• M — M is INTEGER. It's the number of rows of the matrix A. M >= 0. (zero rows? valid, we support you 🫶)
• N — N is INTEGER. It's the number of columns of the matrix A. N >= 0. (same deal, N >= 0 and not a drop more, bestie)
• 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). so yeah she contains multitudes 💀
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). respect the leading dimension or perish 🙈
• 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). that's it, that's the whole parameter, she's just a workspace 💅
• INFO — INFO is INTEGER.
  • = 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.

🔥 Further Details:

ok so 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). lowkey elegant, highkey obsessed 🦋

See Lapack Working Note 203 for details.

Definition at line 133 of file cgeqr2p.f.

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🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. (not me writing my own manpage, a robot did it, and honestly? she ate 🤖💖)

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and that's the whole page bestie!! LAPACK, Version 3.12.0, from SRC/cgeqr2p.f(3) — go forth and factorize responsibly, mwah 🎀💜✨