SRC/stpqrt2.f(3)

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version 3.12.1 · 7 versions
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💖 SRC/stpqrt2.f(3) 💖

Welcome to the Library Functions Manual page for SRC/stpqrt2.f, bestie! This is the LAPACK routine STPQRT2, and she is literally here to factor some triangular-pentagonal realness. 💅

🎀 NAME 🎀

SRC/stpqrt2.f

🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

  • subroutine stpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info) — okay so this is the icon herself. The synopsis says STPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. The original spacing is giving chaotic group-chat energy: "triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ. 😭 iykyk

🦋 Function/Subroutine Documentation 🦋

subroutine stpqrt2 (integer m, integer n, integer l, real, dimension( lda, *
) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real,
dimension( ldt, * ) t, integer ldt, integer info)

STPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. Periodt. ✨

🎀 Purpose 🎀

STPQRT2 computes a 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.

💖 Parameters 💖

  • M — M is INTEGER. The total 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 below. 🫶
  • 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 N-by-N upper triangular factor T of the block reflector. See Further Details. 🧚
  • LDT — LDT is INTEGER. The leading dimension of the array T. Constraint: LDT >= max(1,N) 💜
  • INFO — INFO is INTEGER. Exit status, bestie:
    • INFO = 0: successful exit ✅
    • INFO < 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 (M+N)-by-(M+N) block reflector H is then given by

H = I - W * T * W^H

where W^H is the conjugate transpose of W and T is the upper triangular factor of the block reflector. slay. 💫

Definition at line 172 of file stpqrt2.f.

🌟 Author 🌟

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That's the whole page, bestie — LAPACK Version 3.12.0, source SRC/stpqrt2.f(3), signing off with maximum main-character energy. 🫶💅🎀

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