SRC/ztplqt2.f(3)

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🌸 NAME 🌸

SRC/ztplqt2.f — yes bestie, that's the file name, periodt.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine ztplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info) — ZTPLQT2 computes an 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.

💖 Function/Subroutine Documentation 💖

subroutine ztplqt2 (integer m, integer n, integer l, complex*16, dimension(
    lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb,
    complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZTPLQT2 computes an 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

ZTPLQT2 computes a LQ a factorization of a complex matrix C — yes, the source literally says “a LQ a factorization,” keeping it iconic 😭 — 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 ztplqt2.f.

📜 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That's the whole page, bestie! This one is from LAPACK Version 3.12.0, and the page is SRC/ztplqt2.f(3). Slay. 💅✨