?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 )

Include Files

mkl.fi

Description

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

A = (xy) 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

DOUBLE COMPLEX 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

DOUBLE COMPLEX 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 = (xy).