ztplqt2.f - Online Linux Manual Page

Section : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEztplqt2.f
SYNOPSIS
Functions/Subroutinessubroutine ztplqt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
ZTPLQT2 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​.
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 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: ZTPLQT2 computes a LQ a factorization of a complex "triangular-pentagonal" 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 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 valueAuthor: Univ​. of Tennessee Univ​. of California Berkeley Univ​. of Colorado Denver NAG Ltd​. Date: June 2017 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 179 of file ztplqt2​.f​.
AuthorGenerated automatically by Doxygen for LAPACK from the source code​. 0
Johanes Gumabo
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