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ztpqrt2.f(3) LAPACK ztpqrt2.f(3)

ztpqrt2.f -


subroutine ztpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
 
ZTPQRT2 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.

ZTPQRT2 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:
 ZTPQRT2 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:
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 COMPLEX*16 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*16 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*16 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**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 ztpqrt2.f.

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