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ztpqrt.f(3) LAPACK ztpqrt.f(3)

ztpqrt.f -

subroutine ztpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)

 ZTPQRT computes a blocked 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.
          M is INTEGER
          The number of rows of the matrix B.  
          M >= 0.
          N is INTEGER
          The number of columns of the matrix B, and the order of the
          triangular matrix A.
          N >= 0.
          L is INTEGER
          The number of rows of the upper trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.
          NB is INTEGER
          The block size to be used in the blocked QR.  N >= NB >= 1.
          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 is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
          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 is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).
          T is COMPLEX*16 array, dimension (LDT,N)
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See Further Details.
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.
          WORK is COMPLEX*16 array, dimension (NB*N)
          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.
November 2013
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 number of blocks is B = ceiling(N/NB), where each block is of order NB except for the last block, which is of order IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-N matrix T as
T = [T1 T2 ... TB].
Definition at line 189 of file ztpqrt.f.

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