SRC/cgelqf.f(3)

okay bestie, welcome to the SRC/cgelqf.f(3) page from the Library Functions Manual 💖 this one is all about the CGELQF subroutine and it is lowkey iconic ✨

🌸 NAME 🌸

SRC/cgelqf.f — the source page for the CGELQF subroutine, no cap 🫶

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine cgelqf (m, n, a, lda, tau, work, lwork, info)

CGELQF

💅 Function/Subroutine Documentation 💅

subroutine cgelqf (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
       integer lwork, integer info)

CGELQF

🎀 Purpose 🎀

CGELQF computes an LQ factorization of a complex M-by-N matrix A, and the factorization is giving this exact energy:

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. 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 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 array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise. For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
• 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 143 of file cgelqf.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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that’s the whole tea, bestie 🍓: LAPACK Version 3.12.0, source page SRC/cgelqf.f(3), and the footer didn’t print a date so we’re calling it timeless ✨💅