SRC/cgelqt3.f(3)

🌸 SRC/cgelqt3.f 🌸

okay bestie, welcome to the Library Functions Manual page for SRC/cgelqt3.f — this one is giving recursive LQ factorization energy and it's honestly kinda iconic. 💅✨

💖 NAME 💖

SRC/cgelqt3.f

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✨ SYNOPSIS ✨

Functions/Subroutines

recursive subroutine cgelqt3 (m, n, a, lda, t, ldt, info)
    CGELQT3

🦋 Function/Subroutine Documentation 🦋

recursive subroutine cgelqt3 (integer m, integer n, complex, dimension( lda,
    * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer
    info)

CGELQT3 — that's the whole mood, no cap. 💫

🎯 Purpose 🎯

CGELQT3 recursively computes a LQ factorization of a complex 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. The number of rows of the matrix A. Constraint: M =< N. (Yes, exactly like that, bestie. 🫶)
• N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0.
• A — A is COMPLEX 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. Constraint: LDA >= max(1,M).
• T — T is COMPLEX 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. Constraint: 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 cgelqt3.f.

👑 Author (generated) 👑

Generated automatically by Doxygen for LAPACK from the source code. 🤖

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okay that's the whole page, bestie — footer details are LAPACK Version 3.12.0 and SRC/cgelqt3.f(3) (no date listed, so no invented date, periodt 💀). 🫶✨