NAME

       ztpqrt2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine ztpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
           ZTPQRT2 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.

Function/Subroutine Documentation

   subroutine ztpqrt2 (integer M, integer N, integer L, complex*16, dimension( lda, * ) A,
       integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldt, *
       ) T, integer LDT, integer INFO)
       ZTPQRT2 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:

            ZTPQRT2 computes a QR 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 upper trapezoidal part of B.
                     MIN(M,N) >= L >= 0.  See Further Details.

           A

                     A is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 = -i, 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**H

             where W**H is the conjugate transpose of W and T is the upper triangular
             factor of the block reflector.

Author

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