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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: two column vectors X and Y, let A = ( X Y )

```NAME
LAPACK-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 ).

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```