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
9: *> Download ZLAPLL + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlapll.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlapll.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlapll.f">
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
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