ctplqt2.f - Man Page

subroutine ctplqt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)

Purpose:

CTPLQT2 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 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 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 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.

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 162 of file ctplqt2.f.