DTPQRT2 computes a QR factorization of a real "triangular-pentagonal"


 matrix C, which is composed of a triangular block A and pentagonal block B,


 using the compact WY representation for Q.

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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  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**T


  where W^H is the conjugate transpose of W and T is the upper triangular


  factor of the block reflector.