CGEQLF(3)

💖 CGEQLF(3) 💖

okay so bestie, this is cgeqlf.f(3) from the Library Functions Manual, and she is giving LAPACK — complex matrices, QL factorization, the whole iconic situation. Let's get into it. 💅✨

🌸 NAME

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

That's the file path, periodt. This page is literally about that .f file, no cap. 🎀

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

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

CGEQLF — main character energy, obviously. 👑

🛠️ Function/Subroutine Documentation

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

CGEQLF

🎯 Purpose

CGEQLF computes a QL factorization of a complex M-by-N matrix A:

A = Q * L

Lowkey the whole point. 💖

📋 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:

• if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
• if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L;
• the remaining elements, 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 >= max(1,N). For optimum performance LWORK >= N*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(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 137 of file cgeqlf.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie. Mwah 💋 — LAPACK, Version 3.12.0, from /home/abui...RC/cgeqlf.f(3). Slay. 🌈🫶