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dtpqrt2.f(3)				      LAPACK				     dtpqrt2.f(3)

NAME
       dtpqrt2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dtpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
	   DTPQRT2 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 dtpqrt2 (integerM, integerN, integerL, double precision, dimension( lda, * )A,
       integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision,
       dimension( ldt, * )T, integerLDT, integerINFO)
       DTPQRT2 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:

	    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.

       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 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

       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**T

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

       Definition at line 174 of file dtpqrt2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			     dtpqrt2.f(3)
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