LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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zgeqrf.f File Reference

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subroutine zgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
 ZGEQRF VARIANT: left-looking Level 3 BLAS of the algorithm.

Function/Subroutine Documentation

subroutine zgeqrf ( integer  M,
integer  N,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( * )  WORK,
integer  LWORK,
integer  INFO 

ZGEQRF VARIANT: left-looking Level 3 BLAS of the algorithm.


 ZGEQRF computes a QR factorization of a real M-by-N matrix A:
 A = Q * R.

 This is the left-looking Level 3 BLAS version of the algorithm.
          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.
          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,
          with the array TAU, represent the orthogonal matrix Q as a
          product of min(m,n) elementary reflectors (see Further
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
          TAU is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
          LWORK is INTEGER
          The dimension of the array WORK. The dimension can be divided into three parts.
          1) The part for the triangular factor T. If the very last T is not bigger 
             than any of the rest, then this part is NB x ceiling(K/NB), otherwise, 
             NB x (K-NT), where K = min(M,N) and NT is the dimension of the very last T              
          2) The part for the very last T when T is bigger than any of the rest T. 
             The size of this part is NT x NT, where NT = K - ceiling ((K-NX)/NB) x NB,
             where K = min(M,N), NX is calculated by
                   NX = MAX( 0, ILAENV( 3, 'ZGEQRF', ' ', M, N, -1, -1 ) )
          3) The part for dlarfb is of size max((N-M)*K, (N-M)*NB, K*NB, NB*NB)
          So LWORK = part1 + part2 + part3
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
          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 2011

Further Details

  The matrix Q is represented as a product of elementary reflectors

     Q = H(1) H(2) . . . H(k), where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v'

  where tau is a real scalar, and v is a real vector with
  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
  and tau in TAU(i).

Definition at line 150 of file zgeqrf.f.

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