ZLAPLL(3) two column vectors X and Y, let A = ( X Y )

## SYNOPSIS

SUBROUTINE ZLAPLL(
N, X, INCX, Y, INCY, SSMIN )

INTEGER INCX, INCY, N

DOUBLE PRECISION SSMIN

COMPLEX*16 X( * ), Y( * )

## PURPOSE

Given two column vectors X and Y, let 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.

## ARGUMENTS

N (input) INTEGER
The length of the vectors X and Y.
X (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
On entry, X contains the N-vector X. On exit, X is overwritten.
INCX (input) INTEGER
The increment between successive elements of X. INCX > 0.
Y (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCY)
On entry, Y contains the N-vector Y. On exit, Y is overwritten.
INCY (input) INTEGER
The increment between successive elements of Y. INCY > 0.
SSMIN (output) DOUBLE PRECISION
The smallest singular value of the N-by-2 matrix A = ( X Y ).