LAPACK  3.7.0
LAPACK: Linear Algebra PACKage
subroutine ctplqt ( integer  M,
integer  N,
integer  L,
integer  MB,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( ldt, * )  T,
integer  LDT,
complex, dimension( * )  WORK,
integer  INFO 
)
Purpose:

CTPLQT computes a blocked LQ 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
[in]M
          M is INTEGER
          The number of rows of the matrix B, and the order of the
          triangular matrix A.
          M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix B.
          N >= 0.
[in]L
          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.
[in]MB
          MB is INTEGER
          The block size to be used in the blocked QR.  M >= MB >= 1.
[in,out]A
          A is COMPLEX array, dimension (LDA,N)
          On entry, the lower triangular N-by-N matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the lower triangular matrix L.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in,out]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.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).
[out]T
          T is COMPLEX array, dimension (LDT,N)
          The lower triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See Further Details.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= MB.
[out]WORK
          WORK is COMPLEX array, dimension (MB*M)
[out]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
December 2016
Further Details:

The input matrix C is a M-by-(M+N) matrix

C = [ A ] [ B ]

where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L upper trapezoidal matrix B2: [ B ] = [ B1 ] [ B2 ] [ B1 ] <- M-by-(N-L) rectangular [ B2 ] <- M-by-L upper 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 N-by-N [ B ] <- M-by-N pentagonal

so that W can be represented as [ W ] = [ I ] [ V ] [ 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 ] [ 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 number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-N matrix T as

T = [T1 T2 ... TB].