Functions/Subroutines
subroutine	ctpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
	CTPQRT2 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 ctpqrt2	(	integer	M,
		integer	N,
		integer	L,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		complex, dimension( ldt, * )	T,
		integer	LDT,
		integer	INFO
	)

CTPQRT2 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.

Download CTPQRT2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 CTPQRT2 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:

[in]	M	M is INTEGER The total number of rows of the matrix B. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0.
[in]	L	L is INTEGER The number of rows of the upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.
[in,out]	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.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in,out]	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.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).
[out]	T	T is COMPLEX array, dimension (LDT,N) The N-by-N upper triangular factor T of the block reflector. See Further Details.
[in]	LDT	LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N)
[out]	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.

Definition at line 174 of file ctpqrt2.f.

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