# ?lapll

Measures the linear dependence of two vectors.

## Syntax

call slapll( n, x, incx, Y, incy, ssmin )

call dlapll( n, x, incx, Y, incy, ssmin )

call clapll( n, x, incx, Y, incy, ssmin )

call zlapll( n, x, incx, Y, incy, ssmin )

## Description

Given two column vectors x and y of length n, let

`A = (x y)` be the n-by-2 matrix.

The routine ?lapll first computes the QR factorization of A as `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.

## Input Parameters

n

  INTEGER. The length of the vectors x and y.

x

  REAL for slapll

  DOUBLE PRECISION for dlapll

  COMPLEX for clapll

  COMPLEX*16 for zlapll

  Array, DIMENSION `(1+(n-1)incx)`.

  On entry, x contains the n-vector x.

y

  REAL for slapll

  DOUBLE PRECISION for dlapll

  COMPLEX for clapll

  COMPLEX*16 for zlapll

  Array, DIMENSION (1+(n-1)incy).

  On entry, y contains the n-vector y.

incx

  INTEGER. The increment between successive elements of x; `incx > 0`.

incy

  INTEGER. The increment between successive elements of y; `incy > 0`.

## Output Parameters

x

  On exit, x is overwritten.

y

  On exit, y is overwritten.

ssmin

  REAL for slapll/clapll

  DOUBLE PRECISION for dlapll/zlapll

  The smallest singular value of the n-by-2 matrix A = (x y).

Parent topic: Auxiliary Routines