SRC/dgeqrf.f(3)

NAME
SRC/dgeqrf.f

SYNOPSIS

  Functions/Subroutines
subroutine dgeqrf (m, n, a, lda, tau, work, lwork, info)
DGEQRF

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

Purpose:

    !>
    !> DGEQRF computes a QR factorization of a real M-by-N matrix A:
    !>
    !>    A = Q * ( R ),
    !>            ( 0 )
    !>
    !> where:
    !>
    !>    Q is a M-by-M orthogonal matrix;
    !>    R is an upper-triangular N-by-N matrix;
    !>    0 is a (M-N)-by-N zero matrix, if M > N.
    !>
    !>

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.
    !>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise.
    !>          For optimum performance LWORK >= N*NB, where NB is
    !>          the optimal blocksize.
    !>
    !>          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.

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**T
    !>
    !>  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 145 of file dgeqrf.f.

Author

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