Annotation of rpl/lapack/lapack/dlapll.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLAPLL
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAPLL + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlapll.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlapll.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlapll.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INCX, INCY, N
! 25: * DOUBLE PRECISION SSMIN
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION X( * ), Y( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> Given two column vectors X and Y, let
! 38: *>
! 39: *> A = ( X Y ).
! 40: *>
! 41: *> The subroutine first computes the QR factorization of A = Q*R,
! 42: *> and then computes the SVD of the 2-by-2 upper triangular matrix R.
! 43: *> The smaller singular value of R is returned in SSMIN, which is used
! 44: *> as the measurement of the linear dependency of the vectors X and Y.
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] N
! 51: *> \verbatim
! 52: *> N is INTEGER
! 53: *> The length of the vectors X and Y.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in,out] X
! 57: *> \verbatim
! 58: *> X is DOUBLE PRECISION array,
! 59: *> dimension (1+(N-1)*INCX)
! 60: *> On entry, X contains the N-vector X.
! 61: *> On exit, X is overwritten.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] INCX
! 65: *> \verbatim
! 66: *> INCX is INTEGER
! 67: *> The increment between successive elements of X. INCX > 0.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in,out] Y
! 71: *> \verbatim
! 72: *> Y is DOUBLE PRECISION array,
! 73: *> dimension (1+(N-1)*INCY)
! 74: *> On entry, Y contains the N-vector Y.
! 75: *> On exit, Y is overwritten.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] INCY
! 79: *> \verbatim
! 80: *> INCY is INTEGER
! 81: *> The increment between successive elements of Y. INCY > 0.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[out] SSMIN
! 85: *> \verbatim
! 86: *> SSMIN is DOUBLE PRECISION
! 87: *> The smallest singular value of the N-by-2 matrix A = ( X Y ).
! 88: *> \endverbatim
! 89: *
! 90: * Authors:
! 91: * ========
! 92: *
! 93: *> \author Univ. of Tennessee
! 94: *> \author Univ. of California Berkeley
! 95: *> \author Univ. of Colorado Denver
! 96: *> \author NAG Ltd.
! 97: *
! 98: *> \date November 2011
! 99: *
! 100: *> \ingroup doubleOTHERauxiliary
! 101: *
! 102: * =====================================================================
1.1 bertrand 103: SUBROUTINE DLAPLL( N, X, INCX, Y, INCY, SSMIN )
104: *
1.8 ! bertrand 105: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 106: * -- LAPACK is a software package provided by Univ. of Tennessee, --
107: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 108: * November 2011
1.1 bertrand 109: *
110: * .. Scalar Arguments ..
111: INTEGER INCX, INCY, N
112: DOUBLE PRECISION SSMIN
113: * ..
114: * .. Array Arguments ..
115: DOUBLE PRECISION X( * ), Y( * )
116: * ..
117: *
118: * =====================================================================
119: *
120: * .. Parameters ..
121: DOUBLE PRECISION ZERO, ONE
122: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
123: * ..
124: * .. Local Scalars ..
125: DOUBLE PRECISION A11, A12, A22, C, SSMAX, TAU
126: * ..
127: * .. External Functions ..
128: DOUBLE PRECISION DDOT
129: EXTERNAL DDOT
130: * ..
131: * .. External Subroutines ..
132: EXTERNAL DAXPY, DLARFG, DLAS2
133: * ..
134: * .. Executable Statements ..
135: *
136: * Quick return if possible
137: *
138: IF( N.LE.1 ) THEN
139: SSMIN = ZERO
140: RETURN
141: END IF
142: *
143: * Compute the QR factorization of the N-by-2 matrix ( X Y )
144: *
145: CALL DLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
146: A11 = X( 1 )
147: X( 1 ) = ONE
148: *
149: C = -TAU*DDOT( N, X, INCX, Y, INCY )
150: CALL DAXPY( N, C, X, INCX, Y, INCY )
151: *
152: CALL DLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
153: *
154: A12 = Y( 1 )
155: A22 = Y( 1+INCY )
156: *
157: * Compute the SVD of 2-by-2 Upper triangular matrix.
158: *
159: CALL DLAS2( A11, A12, A22, SSMIN, SSMAX )
160: *
161: RETURN
162: *
163: * End of DLAPLL
164: *
165: END
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