1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
|
/* lapack/double/dlae2.f -- translated by f2c (version 20090411).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/*< SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) >*/
/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__,
doublereal *rt1, doublereal *rt2)
{
/* System generated locals */
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal ab, df, tb, sm, rt, adf, acmn, acmx;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2006 */
/* .. Scalar Arguments .. */
/*< DOUBLE PRECISION A, B, C, RT1, RT2 >*/
/* .. */
/* Purpose */
/* ======= */
/* DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix */
/* [ A B ] */
/* [ B C ]. */
/* On return, RT1 is the eigenvalue of larger absolute value, and RT2 */
/* is the eigenvalue of smaller absolute value. */
/* Arguments */
/* ========= */
/* A (input) DOUBLE PRECISION */
/* The (1,1) element of the 2-by-2 matrix. */
/* B (input) DOUBLE PRECISION */
/* The (1,2) and (2,1) elements of the 2-by-2 matrix. */
/* C (input) DOUBLE PRECISION */
/* The (2,2) element of the 2-by-2 matrix. */
/* RT1 (output) DOUBLE PRECISION */
/* The eigenvalue of larger absolute value. */
/* RT2 (output) DOUBLE PRECISION */
/* The eigenvalue of smaller absolute value. */
/* Further Details */
/* =============== */
/* RT1 is accurate to a few ulps barring over/underflow. */
/* RT2 may be inaccurate if there is massive cancellation in the */
/* determinant A*C-B*B; higher precision or correctly rounded or */
/* correctly truncated arithmetic would be needed to compute RT2 */
/* accurately in all cases. */
/* Overflow is possible only if RT1 is within a factor of 5 of overflow. */
/* Underflow is harmless if the input data is 0 or exceeds */
/* underflow_threshold / macheps. */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ONE >*/
/*< PARAMETER ( ONE = 1.0D0 ) >*/
/*< DOUBLE PRECISION TWO >*/
/*< PARAMETER ( TWO = 2.0D0 ) >*/
/*< DOUBLE PRECISION ZERO >*/
/*< PARAMETER ( ZERO = 0.0D0 ) >*/
/*< DOUBLE PRECISION HALF >*/
/*< PARAMETER ( HALF = 0.5D0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, SQRT >*/
/* .. */
/* .. Executable Statements .. */
/* Compute the eigenvalues */
/*< SM = A + C >*/
sm = *a + *c__;
/*< DF = A - C >*/
df = *a - *c__;
/*< ADF = ABS( DF ) >*/
adf = abs(df);
/*< TB = B + B >*/
tb = *b + *b;
/*< AB = ABS( TB ) >*/
ab = abs(tb);
/*< IF( ABS( A ).GT.ABS( C ) ) THEN >*/
if (abs(*a) > abs(*c__)) {
/*< ACMX = A >*/
acmx = *a;
/*< ACMN = C >*/
acmn = *c__;
/*< ELSE >*/
} else {
/*< ACMX = C >*/
acmx = *c__;
/*< ACMN = A >*/
acmn = *a;
/*< END IF >*/
}
/*< IF( ADF.GT.AB ) THEN >*/
if (adf > ab) {
/*< RT = ADF*SQRT( ONE+( AB / ADF )**2 ) >*/
/* Computing 2nd power */
d__1 = ab / adf;
rt = adf * sqrt(d__1 * d__1 + 1.);
/*< ELSE IF( ADF.LT.AB ) THEN >*/
} else if (adf < ab) {
/*< RT = AB*SQRT( ONE+( ADF / AB )**2 ) >*/
/* Computing 2nd power */
d__1 = adf / ab;
rt = ab * sqrt(d__1 * d__1 + 1.);
/*< ELSE >*/
} else {
/* Includes case AB=ADF=0 */
/*< RT = AB*SQRT( TWO ) >*/
rt = ab * sqrt(2.);
/*< END IF >*/
}
/*< IF( SM.LT.ZERO ) THEN >*/
if (sm < 0.) {
/*< RT1 = HALF*( SM-RT ) >*/
*rt1 = (sm - rt) * .5;
/* Order of execution important. */
/* To get fully accurate smaller eigenvalue, */
/* next line needs to be executed in higher precision. */
/*< RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B >*/
*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
/*< ELSE IF( SM.GT.ZERO ) THEN >*/
} else if (sm > 0.) {
/*< RT1 = HALF*( SM+RT ) >*/
*rt1 = (sm + rt) * .5;
/* Order of execution important. */
/* To get fully accurate smaller eigenvalue, */
/* next line needs to be executed in higher precision. */
/*< RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B >*/
*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
/*< ELSE >*/
} else {
/* Includes case RT1 = RT2 = 0 */
/*< RT1 = HALF*RT >*/
*rt1 = rt * .5;
/*< RT2 = -HALF*RT >*/
*rt2 = rt * -.5;
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of DLAE2 */
/*< END >*/
} /* dlae2_ */
#ifdef __cplusplus
}
#endif
|
