You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
166 lines
4.3 KiB
166 lines
4.3 KiB
*> \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
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlapll.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlapll.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlapll.f">
|
|
*> [TXT]</a>
|
|
*> \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.
|
|
*
|
|
*> \ingroup complex16OTHERauxiliary
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
|
|
*
|
|
* -- LAPACK auxiliary routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INCX, INCY, N
|
|
DOUBLE PRECISION SSMIN
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX*16 X( * ), Y( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ZERO
|
|
PARAMETER ( ZERO = 0.0D+0 )
|
|
COMPLEX*16 CONE
|
|
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
DOUBLE PRECISION SSMAX
|
|
COMPLEX*16 A11, A12, A22, C, TAU
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, DCONJG
|
|
* ..
|
|
* .. External Functions ..
|
|
COMPLEX*16 ZDOTC
|
|
EXTERNAL ZDOTC
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DLAS2, ZAXPY, ZLARFG
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.LE.1 ) THEN
|
|
SSMIN = ZERO
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Compute the QR factorization of the N-by-2 matrix ( X Y )
|
|
*
|
|
CALL ZLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
|
|
A11 = X( 1 )
|
|
X( 1 ) = CONE
|
|
*
|
|
C = -DCONJG( TAU )*ZDOTC( N, X, INCX, Y, INCY )
|
|
CALL ZAXPY( N, C, X, INCX, Y, INCY )
|
|
*
|
|
CALL ZLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
|
|
*
|
|
A12 = Y( 1 )
|
|
A22 = Y( 1+INCY )
|
|
*
|
|
* Compute the SVD of 2-by-2 Upper triangular matrix.
|
|
*
|
|
CALL DLAS2( ABS( A11 ), ABS( A12 ), ABS( A22 ), SSMIN, SSMAX )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of ZLAPLL
|
|
*
|
|
END
|
|
|