SRC/zgelqt3.f(3)

💖 NAME 💖

okay so this page is literally SRC/zgelqt3.f(3) from the Library Functions Manual, and it's all about zgelqt3 — a recursive LQ factorization situation with the compact WY representation of Q. no cap, bestie, this is giving linear algebra main character energy. 🦋

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• recursive subroutine zgelqt3 (m, n, a, lda, t, ldt, info) — ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

🫶 Function/Subroutine Documentation 🫶

recursive subroutine zgelqt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

🔥 Purpose 🔥

ZGELQT3 recursively computes a LQ factorization of a complex M-by-N matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

🎀 Parameters 🎀

• M — M is INTEGER. The number of rows of the matrix A. M =< N.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the complex M-by-N matrix A. On exit, the elements on and below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows of V. See below for further details.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• T — T is COMPLEX*16 array, dimension (LDT,N). The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details.
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= max(1,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 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. The block reflector H is then given by

H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 130 of file zgelqt3.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, bestie 💅✨ — this iconic page came from LAPACK Version 3.12.0, SRC/zgelqt3.f(3). periodt. 🫶