stpqrt2.f(3)							      LAPACK							      stpqrt2.f(3)

NAME

       stpqrt2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine stpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
	   STPQRT2

Function/Subroutine Documentation
   subroutine stpqrt2 (integerM, integerN, integerL, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real,
       dimension( ldt, * )T, integerLDT, integerINFO)
       STPQRT2

       Purpose:

	    STPQRT2 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 REAL 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 REAL 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 REAL 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:
	   April 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.

       Definition at line 174 of file stpqrt2.f.

Author
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Version 3.4.1							  Sun May 26 2013						      stpqrt2.f(3)