STPQRT(3)

✨ STPQRT(3) — blocked QR, but make it bestie ✨

okay so this is the Library Functions Manual page for STPQRT(3), and the header path is literally /home/abui...RC/stpqrt.f(3). The full source file path from the NAME section is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stpqrt.f. We’re keeping every flag, every constraint, and every diagram — no cap. 💅

bestie, the diagrams below are exact — do not squish them.

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

🧩 Functions/Subroutines

• subroutine STPQRT (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info) — the whole callable, iconic, and ready to factor.

💖 Function/Subroutine Documentation 💖

🌟 subroutine STPQRT (...)

subroutine STPQRT (integer m, integer n, integer l, integer nb, real,
    dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer
    ldb, real, dimension( ldt, * ) t, integer ldt, real, dimension( * )
    work, integer info)

STPQRT. That’s the name. Slay.

🎯 Purpose

STPQRT computes a blocked QR factorization of a real 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 vibe: triangular A + pentagonal B + compact WY for Q. 💖

🧮 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 REAL 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 REAL 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 REAL 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 REAL 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

okay bestie, here’s the diagram tea. 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

Definition at line 187 of file stpqrt.f.

📚 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie. Footer source/version check: LAPACK / Version 3.12.0, and the footer path is /home/abui...RC/stpqrt.f(3). Mwah, slay, bye 💋💖🎀