SRC/cgelqt.f(3)

okay so this is SRC/cgelqt.f from the LAPACK Library Functions Manual, and it’s literally the CGELQT page — no cap, every flag and every detail is staying. 💅✨

✨ NAME ✨

SRC/cgelqt.f — the home of the cgelqt subroutine, a.k.a. CGELQT, your bestie for blocked LQ factorization. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine cgelqt (m, n, mb, a, lda, t, ldt, work, info) — CGELQT

✨ Function/Subroutine Documentation ✨

subroutine cgelqt (...)

subroutine cgelqt (integer m, integer n, integer mb, complex, dimension(
    lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt,
    complex, dimension( * ) work, integer info)

CGELQT

🎯 Purpose 🎯

Bestie, CGELQT computes a blocked LQ factorization of a complex M-by-N matrix A using the compact WY representation of Q. That’s the whole purpose, and it ate. 💅

🔥 Parameters 🔥

• M — M is INTEGER. The number of rows of the matrix A. Constraint: M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0.
• MB — MB is INTEGER. The block size to be used in the blocked QR. Constraint: MIN(M,N) >= MB >= 1.
• 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 are the rows of V.
• LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,M).
• T — T is COMPLEX array, dimension (LDT,MIN(M,N)). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.
• LDT — LDT is INTEGER. The leading dimension of the array T. Constraint: LDT >= MB.
• WORK — WORK is COMPLEX array, dimension (MB*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 V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1  v1 v1 v1 v1 )
    (     1  v2 v2 v2 )
    (         1 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A.

Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as

T = (T1 T2 ... TB).

Definition at line 123 of file cgelqt.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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With love from the LAPACK crew — Version 3.12.0, page SRC/cgelqt.f(3). Slay. 💖✨🎀