NAME

       ctpqrt.f -

SYNOPSIS

   Functions/Subroutines
       subroutine ctpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
           CTPQRT

Function/Subroutine Documentation

   subroutine ctpqrt (integerM, integerN, integerL, integerNB, complex, dimension( lda, * )A,
       integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldt, * )T,
       integerLDT, complex, dimension( * )WORK, integerINFO)
       CTPQRT

       Purpose:

            CTPQRT computes a blocked 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 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.

           NB

                     NB is INTEGER
                     The block size to be used in the blocked QR.  N >= NB >= 1.

           A

                     A is COMPLEX 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 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 array, dimension (LDT,N)
                     The upper triangular block reflectors stored in compact form
                     as a sequence of upper triangular blocks.  See Further Details.

           LDT

                     LDT is INTEGER
                     The leading dimension of the array T.  LDT >= NB.

           WORK

                     WORK is COMPLEX array, dimension (NB*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:
           November 2013

       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 number of blocks is B = ceiling(N/NB), where each
             block is of order NB except for the last block, which is of order
             IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
             reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
             for the last block) T's are stored in the NB-by-N matrix T as

                          T = [T1 T2 ... TB].

       Definition at line 189 of file ctpqrt.f.

Author

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