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
|
/* $Header: /var/lib/cvs/dynare_cpp/sylv/cc/TriangularSylvester.h,v 1.1.1.1 2004/06/04 13:01:03 kamenik Exp $ */
/* Tag $Name: $ */
#ifndef TRIANGULAR_SYLVESTER_H
#define TRIANGULAR_SYLVESTER_H
#include "SylvesterSolver.h"
#include "KronVector.h"
#include "QuasiTriangular.h"
#include "QuasiTriangularZero.h"
#include "SimilarityDecomp.h"
class TriangularSylvester : public SylvesterSolver
{
const QuasiTriangular *const matrixKK;
const QuasiTriangular *const matrixFF;
public:
TriangularSylvester(const QuasiTriangular &k, const QuasiTriangular &f);
TriangularSylvester(const SchurDecompZero &kdecomp, const SchurDecomp &fdecomp);
TriangularSylvester(const SchurDecompZero &kdecomp, const SimilarityDecomp &fdecomp);
virtual
~TriangularSylvester();
void print() const;
void solve(SylvParams &pars, KronVector &d) const;
void solvi(double r, KronVector &d, double &eig_min) const;
void solvii(double alpha, double beta1, double beta2,
KronVector &d1, KronVector &d2,
double &eig_min) const;
void solviip(double alpha, double betas,
KronVector &d, double &eig_min) const;
/* evaluates:
|x1| |d1| |alpha -beta1| |d1|
| | = | |+| |\otimes F'...\otimes K | |
|x2| |d2| |beta2 alpha| |d2|
*/
void linEval(double alpha, double beta1, double beta2,
KronVector &x1, KronVector &x2,
const ConstKronVector &d1, const ConstKronVector &d2) const;
void
linEval(double alpha, double beta1, double beta2,
KronVector &x1, KronVector &x2,
const KronVector &d1, const KronVector &d2) const
{
linEval(alpha, beta1, beta2, x1, x2,
ConstKronVector(d1), ConstKronVector(d2));
}
/* evaluates:
|x1| |d1| |gamma -delta1| |d1|
| | = | | + 2alpha*| |\otimes F'...\otimes K | | +
|x2| |d2| |delta2 gamma| |d2|
|gamma -delta1|^2 |d1|
+ (alpha^2+betas)*| |\otimes F'2...\otimes K2 | |
|delta2 gamma| |d2|
*/
void quaEval(double alpha, double betas,
double gamma, double delta1, double delta2,
KronVector &x1, KronVector &x2,
const ConstKronVector &d1, const ConstKronVector &d2) const;
void
quaEval(double alpha, double betas,
double gamma, double delta1, double delta2,
KronVector &x1, KronVector &x2,
const KronVector &d1, const KronVector &d2) const
{
quaEval(alpha, betas, gamma, delta1, delta2, x1, x2,
ConstKronVector(d1), ConstKronVector(d2));
}
private:
/* returns square of size of minimal eigenvalue of the system solved,
now obsolete */
double getEigSep(int depth) const;
/* recursivelly calculates kronecker product of complex vectors (used in getEigSep) */
static void multEigVector(KronVector &eig, const Vector &feig, const Vector &keig);
/* auxiliary typedefs */
typedef QuasiTriangular::const_diag_iter const_diag_iter;
typedef QuasiTriangular::const_row_iter const_row_iter;
/* called from solvi */
void solviRealAndEliminate(double r, const_diag_iter di,
KronVector &d, double &eig_min) const;
void solviComplexAndEliminate(double r, const_diag_iter di,
KronVector &d, double &eig_min) const;
/* called from solviip */
void solviipRealAndEliminate(double alpha, double betas,
const_diag_iter di, const_diag_iter dsi,
KronVector &d, double &eig_min) const;
void solviipComplexAndEliminate(double alpha, double betas,
const_diag_iter di, const_diag_iter dsi,
KronVector &d, double &eig_min) const;
/* eliminations */
void solviEliminateReal(const_diag_iter di, KronVector &d,
const KronVector &y, double divisor) const;
void solviEliminateComplex(const_diag_iter di, KronVector &d,
const KronVector &y1, const KronVector &y2,
double divisor) const;
void solviipEliminateReal(const_diag_iter di, const_diag_iter dsi,
KronVector &d,
const KronVector &y1, const KronVector &y2,
double divisor, double divisor2) const;
void solviipEliminateComplex(const_diag_iter di, const_diag_iter dsi,
KronVector &d,
const KronVector &y1, const KronVector &y11,
const KronVector &y2, const KronVector &y22,
double divisor) const;
/* Lemma 2 */
void solviipComplex(double alpha, double betas, double gamma,
double delta1, double delta2,
KronVector &d1, KronVector &d2,
double &eig_min) const;
/* norms for what we consider zero on diagonal of F */
static double diag_zero;
static double diag_zero_sq; // square of diag_zero
};
#endif /* TRIANGULAR_SYLVESTER_H */
// Local Variables:
// mode:C++
// End:
|
