# dlapll.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlapll.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlapll (N, X, INCX, Y, INCY, SSMIN)
DLAPLL measures the linear dependence of two vectors.

## Function/Subroutine Documentation

### subroutine dlapll (integer N, double precision, dimension( * ) X, integer INCX, double precision, dimension( * ) Y, integer INCY, double precision SSMIN)

DLAPLL measures the linear dependence of two vectors.

Purpose:

``` Given two column vectors X and Y, let

A = ( X Y ).

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.
```

Parameters:

N

```          N is INTEGER
The length of the vectors X and Y.
```

X

```          X is DOUBLE PRECISION array,
dimension (1+(N-1)*INCX)
On entry, X contains the N-vector X.
On exit, X is overwritten.
```

INCX

```          INCX is INTEGER
The increment between successive elements of X. INCX > 0.
```

Y

```          Y is DOUBLE PRECISION array,
dimension (1+(N-1)*INCY)
On entry, Y contains the N-vector Y.
On exit, Y is overwritten.
```

INCY

```          INCY is INTEGER
The increment between successive elements of Y. INCY > 0.
```

SSMIN

```          SSMIN is DOUBLE PRECISION
The smallest singular value of the N-by-2 matrix A = ( X Y ).
```

Author:

Univ. of Tennessee

Univ. of California Berkeley