166 lines
4.3 KiB
Fortran
166 lines
4.3 KiB
Fortran
*> \brief \b DLAPLL measures the linear dependence of two vectors.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DLAPLL + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlapll.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlapll.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlapll.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
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*
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* .. Scalar Arguments ..
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* INTEGER INCX, INCY, N
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* DOUBLE PRECISION SSMIN
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION X( * ), Y( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> Given two column vectors X and Y, let
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*>
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*> A = ( X Y ).
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*>
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*> The subroutine first computes the QR factorization of A = Q*R,
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*> and then computes the SVD of the 2-by-2 upper triangular matrix R.
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*> The smaller singular value of R is returned in SSMIN, which is used
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*> as the measurement of the linear dependency of the vectors X and Y.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The length of the vectors X and Y.
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*> \endverbatim
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*>
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*> \param[in,out] X
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*> \verbatim
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*> X is DOUBLE PRECISION array,
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*> dimension (1+(N-1)*INCX)
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*> On entry, X contains the N-vector X.
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*> On exit, X is overwritten.
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*> \endverbatim
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*>
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*> \param[in] INCX
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*> \verbatim
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*> INCX is INTEGER
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*> The increment between successive elements of X. INCX > 0.
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*> \endverbatim
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*>
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*> \param[in,out] Y
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*> \verbatim
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*> Y is DOUBLE PRECISION array,
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*> dimension (1+(N-1)*INCY)
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*> On entry, Y contains the N-vector Y.
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*> On exit, Y is overwritten.
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*> \endverbatim
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*>
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*> \param[in] INCY
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*> \verbatim
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*> INCY is INTEGER
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*> The increment between successive elements of Y. INCY > 0.
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*> \endverbatim
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*>
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*> \param[out] SSMIN
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*> \verbatim
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*> SSMIN is DOUBLE PRECISION
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*> The smallest singular value of the N-by-2 matrix A = ( X Y ).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date September 2012
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*
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*> \ingroup doubleOTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
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*
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* -- LAPACK auxiliary routine (version 3.4.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* September 2012
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*
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* .. Scalar Arguments ..
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INTEGER INCX, INCY, N
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DOUBLE PRECISION SSMIN
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION X( * ), Y( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION A11, A12, A22, C, SSMAX, TAU
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DDOT
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EXTERNAL DDOT
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* ..
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* .. External Subroutines ..
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EXTERNAL DAXPY, DLARFG, DLAS2
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( N.LE.1 ) THEN
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SSMIN = ZERO
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RETURN
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END IF
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*
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* Compute the QR factorization of the N-by-2 matrix ( X Y )
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*
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CALL DLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
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A11 = X( 1 )
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X( 1 ) = ONE
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*
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C = -TAU*DDOT( N, X, INCX, Y, INCY )
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CALL DAXPY( N, C, X, INCX, Y, INCY )
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*
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CALL DLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
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*
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A12 = Y( 1 )
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A22 = Y( 1+INCY )
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*
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* Compute the SVD of 2-by-2 Upper triangular matrix.
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*
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CALL DLAS2( A11, A12, A22, SSMIN, SSMAX )
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*
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RETURN
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*
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* End of DLAPLL
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*
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END
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