NAME

CLAPLL - two column vectors X and Y, let   A = ( X Y )

SYNOPSIS

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

INTEGER INCX, INCY, N

REAL SSMIN

COMPLEX 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 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 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) REAL
The smallest singular value of the N-by-2 matrix A = ( X Y ).

  —  LAPACK version 2.0  —  08 October 1994