ZGELQ2(3)

NAME

okay so bestie, this whole page is zgelq2.f(3) from the Library Functions Manual — and the NAME section is literally this source path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgelq2.f

SYNOPSIS

Functions/Subroutines

subroutine ZGELQ2 (m, n, a, lda, tau, work, info)

ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. ✨ no cap.

💖 Function/Subroutine Documentation 💖

subroutine ZGELQ2 (integer m, integer n, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
       work, integer info)

yes it's the same subroutine, but now with the full types. ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. 💅

✨ Purpose ✨

so what's the actual vibe? ZGELQ2 computes an LQ factorization of a complex m-by-n matrix A:

   A = ( L 0 ) *  Q

where:

• Q is a n-by-n orthogonal matrix;
• L is a lower-triangular m-by-m matrix;
• 0 is a m-by-(n-m) zero matrix, if m < n.

🌸 Parameters 🌸

• M — M is INTEGER; it's the number of rows of the matrix A. M >= 0.
• N — N is INTEGER; it's 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 below the diagonal of the array contain the m by min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above 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 (M).
• 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(k)**H . . . H(2)**H H(1)**H, 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; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Definition at line 128 of file zgelq2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo 💅 the footer deets are LAPACK / Version 3.12.0 / /home/abui...RC/zgelq2.f(3) — that's the source/version + date-line moment, periodt. 🎀