SRC/stplqt2.f(3)

💅 SRC/stplqt2.f(3) 💅

okay so this page is from the Library Functions Manual, and it is literally all about SRC/stplqt2.f. Bestie, it is giving Fortran LAPACK main-character energy, and we are going to get through every single detail together. no cap. 🫶

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🌸 NAME 🌸

SRC/stplqt2.f — that is the whole name, simple and iconic. ✨

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine stplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
    STPLQT2 computes a LQ factorization of a real or complex triangular-
    pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.

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💖 Function/Subroutine Documentation 💖

subroutine stplqt2 (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)

STPLQT2 computes a LQ 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. 💅

🎀 Purpose 🎀

The purpose, fr fr: STPLQT2 computes a LQ a 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; M >= 0. 👑
• N — N is INTEGER; the number of columns of the matrix B, and the order of the triangular matrix A; N >= 0. ✨
• L — L is INTEGER; the number of rows of the lower trapezoidal part of B; MIN(M,N) >= L >= 0; see Further Details. 🧚
• A — A is REAL array, dimension (LDA,M); on entry, the lower triangular M-by-M matrix A; on exit, the elements on and below the diagonal of the array contain the lower triangular matrix L. 💖
• LDA — LDA is INTEGER; the leading dimension of the array A; LDA >= max(1,M). 🌸
• B — B is REAL array, dimension (LDB,N); on entry, the pentagonal M-by-N matrix B; the first N-L columns are rectangular, and the last L columns are lower trapezoidal; on exit, B contains the pentagonal matrix V; see Further Details. 🦋
• LDB — LDB is INTEGER; the leading dimension of the array B; LDB >= max(1,M). ⭐
• T — T is REAL array, dimension (LDT,M); 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; LDT >= max(1,M). 🎀
• 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 M-by-(M+N) matrix:

     C = [ A ][ B ]

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

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

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

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

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

so that W can be represented as:

     W = [ I ][ V ]
         [ I ]  <- identity, M-by-M
         [ 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:

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

The rows 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 * T * W

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

Definition at line 176 of file stplqt2.f. ⭐

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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signed off with LAPACK Version 3.12.0 — source SRC/stplqt2.f(3). periodt. 💅✨