SRC/zgelqt.f(3)

💖 SRC/zgelqt.f 💖

okay bestie, this page comes from the Library Functions Manual — it's the SRC/zgelqt.f(3) page, and it's all about the ZGELQT subroutine. It's LAPACK, so grab your iced coffee and let's get into the linear algebra tea. 🧋✨

💖 NAME 💖

SRC/zgelqt.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

🎀 Function/Subroutine Documentation 🎀

Here's the full signature, no cap — every type, dimension, and argument order stays exactly like this:

subroutine zgelqt (integer m, integer n, integer mb, complex*16, dimension(
       lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt,
       complex*16, dimension( * ) work, integer info)
       ZGELQT

🌸 Purpose 🌸

ZGELQT 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, bestie — it's giving "factorization but make it blocked." 💅

🦋 Parameters 🦋

• M — M is INTEGER. The number of rows of the matrix A. M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0.
• MB — MB is INTEGER. The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
• A — A is COMPLEX*16 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. LDA >= max(1,M).
• T — T is COMPLEX*16 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. LDT >= MB.
• WORK — WORK is COMPLEX*16 array, dimension (MB*N).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author 👑

These are the credited authors, not me:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🔥 Further Details 🔥

okay so 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, an 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 zgelqt.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

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💖 sign-off: LAPACK Version 3.12.0, source page SRC/zgelqt.f(3) — and no separate date is printed on this one. That's the footer tea, bestie. 🎀✨