1*> \brief \b ZLAPLL measures the linear dependence of two vectors.
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
22*
23*       .. Scalar Arguments ..
24*       INTEGER            INCX, INCY, N
25*       DOUBLE PRECISION   SSMIN
26*       ..
27*       .. Array Arguments ..
28*       COMPLEX*16         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 COMPLEX*16 array, dimension (1+(N-1)*INCX)
59*>          On entry, X contains the N-vector X.
60*>          On exit, X is overwritten.
61*> \endverbatim
62*>
63*> \param[in] INCX
64*> \verbatim
65*>          INCX is INTEGER
66*>          The increment between successive elements of X. INCX > 0.
67*> \endverbatim
68*>
69*> \param[in,out] Y
70*> \verbatim
71*>          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
72*>          On entry, Y contains the N-vector Y.
73*>          On exit, Y is overwritten.
74*> \endverbatim
75*>
76*> \param[in] INCY
77*> \verbatim
78*>          INCY is INTEGER
79*>          The increment between successive elements of Y. INCY > 0.
80*> \endverbatim
81*>
82*> \param[out] SSMIN
83*> \verbatim
84*>          SSMIN is DOUBLE PRECISION
85*>          The smallest singular value of the N-by-2 matrix A = ( X Y ).
86*> \endverbatim
87*
88*  Authors:
89*  ========
90*
91*> \author Univ. of Tennessee
92*> \author Univ. of California Berkeley
93*> \author Univ. of Colorado Denver
94*> \author NAG Ltd.
95*
96*> \ingroup complex16OTHERauxiliary
97*
98*  =====================================================================
99      SUBROUTINE ZLAPLL( N, X, INCX, Y, INCY, SSMIN )
100*
101*  -- LAPACK auxiliary routine --
102*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
103*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
104*
105*     .. Scalar Arguments ..
106      INTEGER            INCX, INCY, N
107      DOUBLE PRECISION   SSMIN
108*     ..
109*     .. Array Arguments ..
110      COMPLEX*16         X( * ), Y( * )
111*     ..
112*
113*  =====================================================================
114*
115*     .. Parameters ..
116      DOUBLE PRECISION   ZERO
117      PARAMETER          ( ZERO = 0.0D+0 )
118      COMPLEX*16         CONE
119      PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
120*     ..
121*     .. Local Scalars ..
122      DOUBLE PRECISION   SSMAX
123      COMPLEX*16         A11, A12, A22, C, TAU
124*     ..
125*     .. Intrinsic Functions ..
126      INTRINSIC          ABS, DCONJG
127*     ..
128*     .. External Functions ..
129      COMPLEX*16         ZDOTC
130      EXTERNAL           ZDOTC
131*     ..
132*     .. External Subroutines ..
133      EXTERNAL           DLAS2, ZAXPY, ZLARFG
134*     ..
135*     .. Executable Statements ..
136*
137*     Quick return if possible
138*
139      IF( N.LE.1 ) THEN
140         SSMIN = ZERO
141         RETURN
142      END IF
143*
144*     Compute the QR factorization of the N-by-2 matrix ( X Y )
145*
146      CALL ZLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU )
147      A11 = X( 1 )
148      X( 1 ) = CONE
149*
150      C = -DCONJG( TAU )*ZDOTC( N, X, INCX, Y, INCY )
151      CALL ZAXPY( N, C, X, INCX, Y, INCY )
152*
153      CALL ZLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU )
154*
155      A12 = Y( 1 )
156      A22 = Y( 1+INCY )
157*
158*     Compute the SVD of 2-by-2 Upper triangular matrix.
159*
160      CALL DLAS2( ABS( A11 ), ABS( A12 ), ABS( A22 ), SSMIN, SSMAX )
161*
162      RETURN
163*
164*     End of ZLAPLL
165*
166      END
167