DGELQT(3)

💅 DGELQT(3) — Library Functions Manual ✨

okay bestie, welcome to the DGELQT(3) page from the Library Functions Manual. It’s giving blocked LQ factorization energy, and honestly? We’re obsessed. 💖

🌸 NAME 🌸

The NAME section is literally this path, no cap:

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

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

       subroutine DGELQT (m, n, mb, a, lda, t, ldt, work, info)
           DGELQT

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🦋 Function/Subroutine Documentation 🦋

   subroutine DGELQT (integer m, integer n, integer mb, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( ldt, *
       ) t, integer ldt, double precision, dimension( * ) work, integer info)
       DGELQT

🎀 Purpose 🎀

okay so DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q. That’s the whole assignment, 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 138 of file dgelqt.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the vibe check, bestie 🫶 this cutie was brought to you by LAPACK Version 3.12.0, from /home/abui...RC/dgelqt.f(3) 💖✨