# lapll - Man Page

lapll: linear dependence of 2 vectors

## Synopsis

### Functions

subroutine clapll (n, x, incx, y, incy, ssmin)
CLAPLL measures the linear dependence of two vectors.
subroutine dlapll (n, x, incx, y, incy, ssmin)
DLAPLL measures the linear dependence of two vectors.
subroutine slapll (n, x, incx, y, incy, ssmin)
SLAPLL measures the linear dependence of two vectors.
subroutine zlapll (n, x, incx, y, incy, ssmin)
ZLAPLL measures the linear dependence of two vectors.

## Function Documentation

### subroutine clapll (integer n, complex, dimension( * ) x, integer incx, complex, dimension( * ) y, integer incy, real ssmin)

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 99 of file clapll.f.

### 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

NAG Ltd.

Definition at line 101 of file dlapll.f.

### subroutine slapll (integer n, real, dimension( * ) x, integer incx, real, dimension( * ) y, integer incy, real ssmin)

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 101 of file slapll.f.

### subroutine zlapll (integer n, complex*16, dimension( * ) x, integer incx, complex*16, dimension( * ) y, integer incy, double precision ssmin)

ZLAPLL 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 COMPLEX*16 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 COMPLEX*16 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