lapll - Man Page

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.

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 99 of file clapll.f.

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 101 of file dlapll.f.

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 101 of file slapll.f.

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 99 of file zlapll.f.