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## zlapll()

subroutine zlapll | ( | integer | n,
|  | complex*16, dimension( * ) | x,
|  | integer | incx,
|  | complex*16, dimension( * ) | y,
|  | integer | incy,
|  | double precision | ssmin )

ZLAPLL measures the linear dependence of two vectors.

Download ZLAPLL + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> Given two column vectors X and Y, let
      !>
      !>                      A = ( X Y ).
      !>
      !> The subroutine first computes the QR factorization of A = Q*R,
      !> and then computes the SVD of the 2-by-2 upper triangular matrix R.
      !> The smaller singular value of R is returned in SSMIN, which is used
      !> as the measurement of the linear dependency of the vectors X and Y.
      !>

Parameters

  [in]

  N

      !>          N is INTEGER
      !>          The length of the vectors X and Y.
      !>

  [in,out]

  X

      !>          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
      !>          On entry, X contains the N-vector X.
      !>          On exit, X is overwritten.
      !>

  [in]

  INCX

      !>          INCX is INTEGER
      !>          The increment between successive elements of X. INCX > 0.
      !>

  [in,out]

  Y

      !>          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
      !>          On entry, Y contains the N-vector Y.
      !>          On exit, Y is overwritten.
      !>

  [in]

  INCY

      !>          INCY is INTEGER
      !>          The increment between successive elements of Y. INCY > 0.
      !>

  [out]

  SSMIN

      !>          SSMIN is DOUBLE PRECISION
      !>          The smallest singular value of the N-by-2 matrix A = ( X Y ).
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.