version 1.2, 2010/04/21 13:45:17
|
version 1.18, 2023/08/07 08:38:55
|
Line 1
|
Line 1
|
|
*> \brief \b DLAPLL measures the linear dependence of two vectors. |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download DLAPLL + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlapll.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlapll.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlapll.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN ) |
|
* |
|
* .. Scalar Arguments .. |
|
* INTEGER INCX, INCY, N |
|
* DOUBLE PRECISION SSMIN |
|
* .. |
|
* .. Array Arguments .. |
|
* DOUBLE PRECISION X( * ), Y( * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> 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. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The length of the vectors X and Y. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] X |
|
*> \verbatim |
|
*> X is DOUBLE PRECISION array, |
|
*> dimension (1+(N-1)*INCX) |
|
*> On entry, X contains the N-vector X. |
|
*> On exit, X is overwritten. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] INCX |
|
*> \verbatim |
|
*> INCX is INTEGER |
|
*> The increment between successive elements of X. INCX > 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] Y |
|
*> \verbatim |
|
*> Y is DOUBLE PRECISION array, |
|
*> dimension (1+(N-1)*INCY) |
|
*> On entry, Y contains the N-vector Y. |
|
*> On exit, Y is overwritten. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] INCY |
|
*> \verbatim |
|
*> INCY is INTEGER |
|
*> The increment between successive elements of Y. INCY > 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] SSMIN |
|
*> \verbatim |
|
*> SSMIN is DOUBLE PRECISION |
|
*> The smallest singular value of the N-by-2 matrix A = ( X Y ). |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \ingroup doubleOTHERauxiliary |
|
* |
|
* ===================================================================== |
SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN ) |
SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INCX, INCY, N |
INTEGER INCX, INCY, N |
Line 13
|
Line 112
|
DOUBLE PRECISION X( * ), Y( * ) |
DOUBLE PRECISION X( * ), Y( * ) |
* .. |
* .. |
* |
* |
* 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. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* N (input) INTEGER |
|
* The length of the vectors X and Y. |
|
* |
|
* X (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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 ). |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |