ZTPQRT(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 ZTPQRT(3) — ztpqrt.f(3) 💅

okay so bestie, this page is from the Library Functions Manual, and the file it's repping is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztpqrt.f. It's giving LAPACK subroutine energy, and we're gonna walk through every single detail together 🫶.

✨ NAME ✨

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

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZTPQRT (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
    ZTPQRT

🦋 Function/Subroutine Documentation 🦋

subroutine ZTPQRT (integer m, integer n, integer l, integer nb, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
    integer ldb, complex*16, dimension( ldt, * ) t, integer ldt, complex*16,
    dimension( * ) work, integer info)
    ZTPQRT

🎀 Purpose 🎀

ZTPQRT computes a blocked QR factorization of a complex matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q. That's the whole purpose, no cap ✨.

💖 Parameters 💖

M

M is INTEGER — the number of rows of the matrix B. Constraint: M >= 0.

N

N is INTEGER — the number of columns of the matrix B, and the order of the triangular matrix A. Constraint: N >= 0.

L

L is INTEGER — the number of rows of the upper trapezoidal part of B. Constraint: MIN(M,N) >= L >= 0. See Further Details.

NB

NB is INTEGER — the block size to be used in the blocked QR. Constraint: N >= NB >= 1.

A

A is COMPLEX*16 array, dimension (LDA,N). On entry, the upper triangular N-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the upper triangular matrix R.

LDA

LDA is INTEGER — the leading dimension of the array A. Constraint: LDA >= max(1,N).

B

B is COMPLEX*16 array, dimension (LDB,N). On entry, the pentagonal M-by-N matrix B. The first M-L rows are rectangular, and the last L rows are upper trapezoidal. On exit, B contains the pentagonal matrix V. See Further Details.

LDB

LDB is INTEGER — the leading dimension of the array B. Constraint: LDB >= max(1,M).

T

T is COMPLEX*16 array, dimension (LDT,N). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details.

LDT

LDT is INTEGER — the leading dimension of the array T. Constraint: LDT >= NB.

WORK

WORK is COMPLEX*16 array, dimension (NB*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 input matrix C is a (N+M)-by-N matrix:

C = [ A ]
    [ B ]

where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N upper trapezoidal matrix B2:

B = [ B1 ]  <- (M-L)-by-N rectangular
    [ B2 ]  <-     L-by-N upper trapezoidal.

The upper trapezoidal matrix B2 consists of the first L rows of a N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0, B is rectangular M-by-N; if M=L=N, B is upper triangular.

The matrix W stores the elementary reflectors H(i) in the i-th column below the diagonal (of A) in the (N+M)-by-N input matrix C:

C = [ A ]  <- upper triangular N-by-N
    [ B ]  <- M-by-N pentagonal

so that W can be represented as:

W = [ I ]  <- identity, N-by-N
    [ V ]  <- M-by-N, same form as B.

Thus, all of information needed for W is contained on exit in B, which we call V above. Note that V has the same form as B; that is:

V = [ V1 ] <- (M-L)-by-N rectangular
    [ V2 ] <-     L-by-N upper trapezoidal.

The columns of V represent the vectors which define the H(i)'s.

The number of blocks is B = ceiling(N/NB), where each block is of order NB except for the last block, which is of order IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-N matrix T as:

T = [T1 T2 ... TB].

📍 Definition at line 187 of file ztpqrt.f 📍

🤖 Author 🤖

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and that's the whole page, bestie! 💖 Final sign-off: Library Functions Manual, LAPACK Version 3.12.0, source path /home/abui...RC/ztpqrt.f(3) — periodt, go slay your QR factorization 💅✨

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