SRC/dtpqrt2.f(3)

💅 SRC/dtpqrt2.f(3) — from the Library Functions Manual 💅

okay so this is the page for SRC/dtpqrt2.f, and it’s giving major LAPACK subroutine dtpqrt2 energy. We’re keeping every parameter, every constraint, and every matrix diagram because bestie, the details are the moment. 🫶

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🌸 NAME 🌸

SRC/dtpqrt2.f — that’s the name, no cap. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine dtpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info) — the main-character signature, periodt.

subroutine dtpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)

The synopsis blurb says DTPQRT2 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. Slay. ✨

🦋 Function/Subroutine Documentation 🦋

Here’s the full declaration, character-for-character, because we do not play about exact signatures:

subroutine dtpqrt2 (integer m, integer n, integer l, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( ldb, *
    ) b, integer ldb, double precision, dimension( ldt, * ) t, integer ldt,
    integer info)

The function blurb says: DTPQRT2 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. 💫

🌈 Purpose 🌈

Purpose, straight up: DTPQRT2 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. 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 upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.
• A — A is DOUBLE PRECISION 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. LDA >= max(1,N).
• B — B is DOUBLE PRECISION 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. LDB >= max(1,M).
• T — T is DOUBLE PRECISION 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. LDT >= max(1,N).
• INFO — INFO is INTEGER. Exit-status tea:
  • = 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 (M+N)-by-(M+N) block reflector H is then given by

H = I - W * T * W**T

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

🌟 Definition at line 🌟

Definition at line 172 of file dtpqrt2.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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