SRC/sgelqt3.f(3)

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🎀 NAME

SRC/sgelqt3.f

✨ SYNOPSIS

🫶 Functions/Subroutines

• recursive subroutine sgelqt3 (m, n, a, lda, t, ldt, info) — SGELQT3

💅 Function/Subroutine Documentation

recursive subroutine sgelqt3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)

SGELQT3

🌸 Purpose

SGELQT3 recursively computes a LQ factorization of a real M-by-N matrix A, using the compact WY representation of Q. It's based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000. ✨

🎀 Parameters

• M — M is INTEGER. It's the number of rows of the matrix A. M =< N. 💅
• N — N is INTEGER. It's the number of columns of the matrix A. N >= 0.
• A — A is REAL array, dimension (LDA,N). On entry, it's the real 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. It's the leading dimension of the array A. LDA >= max(1,M).
• T — T is REAL array, dimension (LDT,N). It's 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. It's 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 115 of file sgelqt3.f.

⭐ Author

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