--- rpl/lapack/lapack/zlapll.f 2010/04/21 13:45:34 1.2 +++ rpl/lapack/lapack/zlapll.f 2012/12/14 14:22:51 1.12 @@ -1,9 +1,109 @@ +*> \brief \b ZLAPLL measures the linear dependence of two vectors. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLAPLL + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN ) +* +* .. Scalar Arguments .. +* INTEGER INCX, INCY, N +* DOUBLE PRECISION SSMIN +* .. +* .. Array Arguments .. +* COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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. +* +*> \date September 2012 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- LAPACK auxiliary routine (version 3.4.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* September 2012 * * .. Scalar Arguments .. INTEGER INCX, INCY, N @@ -13,41 +113,6 @@ COMPLEX*16 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) 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 ). -* * ===================================================================== * * .. Parameters ..