SRC/dtplqt2.f(3)

SRC/dtplqt2.f(3) — Library Functions Manual ✨

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🌸 NAME 🌸

SRC/dtplqt2.f — that's the whole name section, short and iconic 🎀

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine dtplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
    DTPLQT2 computes a LQ factorization of a real or complex triangular-
    pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.

💅 Function/Subroutine Documentation 💅

subroutine dtplqt2 (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)

DTPLQT2 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. slay, that's the whole vibe 🔥

🎯 Purpose 🎯

!>
!> DTPLQT2 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 — the total row count of matrix B, bestie. M >= 0, no cap.

!>          M is INTEGER
!>          The total number of rows of the matrix B.
!>          M >= 0.
!>

• N — the number of columns of B, and it's also the order of the triangular matrix A. N >= 0.

!>          N is INTEGER
!>          The number of columns of the matrix B, and the order of
!>          the triangular matrix A.
!>          N >= 0.
!>

• L — how many rows of the lower trapezoidal part of B we're dealing with. The constraint is MIN(M,N) >= L >= 0. See Further Details 👀

!>          L is INTEGER
!>          The number of rows of the lower trapezoidal part of B.
!>          MIN(M,N) >= L >= 0.  See Further Details.
!>

• A — a DOUBLE PRECISION array, dimension (LDA,M). On entry it's the lower triangular M-by-M matrix A. On exit, the elements on and below the diagonal contain the lower triangular matrix L. literally the glow-up happens in place.

!>          A is DOUBLE PRECISION 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 — leading dimension of A, and LDA >= max(1,M).

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

• B — DOUBLE PRECISION array, dimension (LDB,N). On entry it's 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 💖

!>          B is DOUBLE PRECISION 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 — leading dimension of B, and LDB >= max(1,M).

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,M).
!>

• T — DOUBLE PRECISION array, dimension (LDT,M). It's the N-by-N upper triangular factor T of the block reflector. See Further Details ✨

!>          T is DOUBLE PRECISION array, dimension (LDT,M)
!>          The N-by-N upper triangular factor T of the block reflector.
!>          See Further Details.
!>

• LDT — leading dimension of T, with LDT >= max(1,M).

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= max(1,M)
!>

• INFO — the status girlie. = 0 means successful exit. < 0 means if INFO = -i, the i-th argument had an illegal value. periodt.

!>          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 📍

Definition at line 176 of file dtplqt2.f.

🧚 Author 🧚

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