# CentOS 7.0 - man page for dtpqrt2 (centos section 3)

dtpqrt2.f(3) LAPACK dtpqrt2.f(3)dtpqrt2.fNAME-Functions/Subroutines subroutine dtpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO) 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.SYNOPSISFunction/Subroutine Documentation subroutine dtpqrt2 (integerM, integerN, integerL, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldt, * )T, integerLDT, integerINFO) 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: DTPQRT2 computes a QR factorization of a real "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 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 = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 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 174 of file dtpqrt2.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dtpqrt2.f(3)