VARIANTS_qr_LL_dgeqrf.f - Man Page

dgeqrf.f

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine dgeqrf (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer LWORK, integer INFO)

DGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm. Purpose:

 DGEQRF 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.
Parameters:

M

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

N

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

A

          A is DOUBLE PRECISION 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
          Details).

LDA

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

TAU

          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

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, 'DGEQRF', ' ', 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

          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:

December 2016

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 151 of file VARIANTS/qr/LL/dgeqrf.f.

Author

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Tue Nov 14 2017 Version 3.8.0 LAPACK