NAME¶

ZLAPLL - 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 ).