LAPACK  3.7.1
LAPACK: Linear Algebra PACKage

◆ ctplqt2()

subroutine ctplqt2 ( integer  M,
integer  N,
integer  L,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( ldt, * )  T,
integer  LDT,
integer  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
[in]M
          M is INTEGER
          The total number of rows of the matrix B.
          M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix B, and the order of
          the triangular matrix A.
          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,out]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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[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,M)
          The N-by-N upper triangular factor T of the block reflector.
          See Further Details.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,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
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.