ZGELQT(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 ZGELQT(3) — Library Functions Manual 💖

okay bestie, welcome to the ZGELQT page from the Library Functions Manual. This is the file-path-flavored one, and the main character is ZGELQT, a blocked LQ factorization subroutine. Let’s get into it 💅

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgelqt.f — yep, that whole path is the NAME here, and the function/star of the show is ZGELQT.

✨ SYNOPSIS ✨

💫 Functions/Subroutines 💫

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

ZGELQT 🫶

💖 Function/Subroutine Documentation 💖

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. slay.

🧮 Parameters 🧮

M

M is INTEGER. It’s the number of rows of the matrix A. M >= 0.

N

N is INTEGER. It’s the number of columns of the matrix A. N >= 0.

MB

MB is INTEGER. It’s 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, it’s 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. the glow-up is real ✨

LDA

LDA is INTEGER. It’s the leading dimension of the array A. LDA >= max(1,M).

T

T is COMPLEX*16 array, dimension (LDT,MIN(M,N)).

These are 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. It’s 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 👑

  • 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, 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 (Doxygen-generated note) 📝

Generated automatically by Doxygen for LAPACK from the source code.

okay that’s the whole page, bestie! 🌈 Cute little footer sign-off: LAPACK, Version 3.12.0, page path /home/abui...RC/zgelqt.f(3) 💖💅

📦 where this page comes from