Functions/Subroutines¶

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

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:

          M is INTEGER


          The total number of rows of the matrix B.


          M >= 0.

          N is INTEGER


          The number of columns of the matrix B, and the order of


          the triangular matrix A.


          N >= 0.

          L is INTEGER


          The number of rows of the lower trapezoidal part of B.


          MIN(M,N) >= L >= 0.  See Further Details.

          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 is INTEGER


          The leading dimension of the array A.  LDA >= max(1,M).

          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 is INTEGER


          The leading dimension of the array B.  LDB >= max(1,M).

          T is COMPLEX array, dimension (LDT,M)


          The N-by-N upper triangular factor T of the block reflector.


          See Further Details.

          LDT is INTEGER


          The leading dimension of the array T.  LDT >= max(1,M)

          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -i, the i-th argument had an illegal value

Author:

Date:

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.