LAPACK  3.4.2
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ztpqrt.f File Reference

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine ztpqrt ( integer  M,
integer  N,
integer  L,
integer  NB,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( ldb, * )  B,
integer  LDB,
complex*16, dimension( ldt, * )  T,
integer  LDT,
complex*16, dimension( * )  WORK,
integer  INFO 
)

ZTPQRT

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Purpose:
 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.
Parameters:
[in]M
          M is INTEGER
          The 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]NB
          NB is INTEGER
          The block size to be used in the blocked QR.  N >= NB >= 1.
[in,out]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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in,out]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.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).
[out]T
          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.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.
[out]WORK
          WORK is COMPLEX*16 array, dimension (NB*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:
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 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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