zgeqrt.f - Man Page




subroutine zgeqrt (m, n, nb, a, lda, t, ldt, work, info)

Function/Subroutine Documentation

subroutine zgeqrt (integer m, integer n, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)



 ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
 using the compact WY representation of Q.


          M is INTEGER
          The number of rows of the matrix A.  M >= 0.


          N is INTEGER
          The number of columns of the matrix A.  N >= 0.


          NB is INTEGER
          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.


          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R (R is
          upper triangular if M >= N); the elements below the diagonal
          are the columns of V.


          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).


          T is COMPLEX*16 array, dimension (LDT,MIN(M,N))
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See below
          for 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

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Further Details:

  The matrix V stores the elementary reflectors H(i) in the i-th column
  below the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1       )
                   ( v1  1    )
                   ( v1 v2  1 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.

  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
  block is of order NB except for the last block, which is of order
  IB = K - (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-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 140 of file zgeqrt.f.


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Referenced By

The man page zgeqrt(3) is an alias of zgeqrt.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK