Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

A newer version of this document is available. Customers should click here to go to the newest version.

Document Table of Contents

?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).