29 |
|
* @date 10/11/2004 |
30 |
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* @version 1.0 |
31 |
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*/ |
32 |
< |
#ifndef MATH_SQUAREMATRIX_HPP |
32 |
> |
#ifndef MATH_SQUAREMATRIX_HPP |
33 |
|
#define MATH_SQUAREMATRIX_HPP |
34 |
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|
35 |
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#include "math/RectMatrix.hpp" |
45 |
|
template<typename Real, int Dim> |
46 |
|
class SquareMatrix : public RectMatrix<Real, Dim, Dim> { |
47 |
|
public: |
48 |
+ |
typedef Real ElemType; |
49 |
+ |
typedef Real* ElemPoinerType; |
50 |
|
|
51 |
< |
/** default constructor */ |
52 |
< |
SquareMatrix() { |
53 |
< |
for (unsigned int i = 0; i < Dim; i++) |
54 |
< |
for (unsigned int j = 0; j < Dim; j++) |
55 |
< |
data_[i][j] = 0.0; |
56 |
< |
} |
51 |
> |
/** default constructor */ |
52 |
> |
SquareMatrix() { |
53 |
> |
for (unsigned int i = 0; i < Dim; i++) |
54 |
> |
for (unsigned int j = 0; j < Dim; j++) |
55 |
> |
data_[i][j] = 0.0; |
56 |
> |
} |
57 |
|
|
58 |
< |
/** copy constructor */ |
59 |
< |
SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
60 |
< |
} |
59 |
< |
|
60 |
< |
/** copy assignment operator */ |
61 |
< |
SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { |
62 |
< |
RectMatrix<Real, Dim, Dim>::operator=(m); |
63 |
< |
return *this; |
64 |
< |
} |
65 |
< |
|
66 |
< |
/** Retunrs an identity matrix*/ |
67 |
< |
|
68 |
< |
static SquareMatrix<Real, Dim> identity() { |
69 |
< |
SquareMatrix<Real, Dim> m; |
58 |
> |
/** copy constructor */ |
59 |
> |
SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
60 |
> |
} |
61 |
|
|
62 |
< |
for (unsigned int i = 0; i < Dim; i++) |
63 |
< |
for (unsigned int j = 0; j < Dim; j++) |
64 |
< |
if (i == j) |
65 |
< |
m(i, j) = 1.0; |
66 |
< |
else |
67 |
< |
m(i, j) = 0.0; |
62 |
> |
/** copy assignment operator */ |
63 |
> |
SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { |
64 |
> |
RectMatrix<Real, Dim, Dim>::operator=(m); |
65 |
> |
return *this; |
66 |
> |
} |
67 |
> |
|
68 |
> |
/** Retunrs an identity matrix*/ |
69 |
|
|
70 |
< |
return m; |
71 |
< |
} |
70 |
> |
static SquareMatrix<Real, Dim> identity() { |
71 |
> |
SquareMatrix<Real, Dim> m; |
72 |
> |
|
73 |
> |
for (unsigned int i = 0; i < Dim; i++) |
74 |
> |
for (unsigned int j = 0; j < Dim; j++) |
75 |
> |
if (i == j) |
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> |
m(i, j) = 1.0; |
77 |
> |
else |
78 |
> |
m(i, j) = 0.0; |
79 |
|
|
80 |
< |
/** Retunrs the inversion of this matrix. */ |
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< |
SquareMatrix<Real, Dim> inverse() { |
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< |
SquareMatrix<Real, Dim> result; |
80 |
> |
return m; |
81 |
> |
} |
82 |
|
|
83 |
< |
return result; |
84 |
< |
} |
83 |
> |
/** |
84 |
> |
* Retunrs the inversion of this matrix. |
85 |
> |
* @todo need implementation |
86 |
> |
*/ |
87 |
> |
SquareMatrix<Real, Dim> inverse() { |
88 |
> |
SquareMatrix<Real, Dim> result; |
89 |
|
|
90 |
< |
/** Returns the determinant of this matrix. */ |
91 |
< |
double determinant() const { |
90 |
< |
double det; |
91 |
< |
return det; |
92 |
< |
} |
90 |
> |
return result; |
91 |
> |
} |
92 |
|
|
93 |
< |
/** Returns the trace of this matrix. */ |
94 |
< |
double trace() const { |
95 |
< |
double tmp = 0; |
96 |
< |
|
97 |
< |
for (unsigned int i = 0; i < Dim ; i++) |
98 |
< |
tmp += data_[i][i]; |
93 |
> |
/** |
94 |
> |
* Returns the determinant of this matrix. |
95 |
> |
* @todo need implementation |
96 |
> |
*/ |
97 |
> |
Real determinant() const { |
98 |
> |
Real det; |
99 |
> |
return det; |
100 |
> |
} |
101 |
|
|
102 |
< |
return tmp; |
103 |
< |
} |
102 |
> |
/** Returns the trace of this matrix. */ |
103 |
> |
Real trace() const { |
104 |
> |
Real tmp = 0; |
105 |
> |
|
106 |
> |
for (unsigned int i = 0; i < Dim ; i++) |
107 |
> |
tmp += data_[i][i]; |
108 |
|
|
109 |
< |
/** Tests if this matrix is symmetrix. */ |
110 |
< |
bool isSymmetric() const { |
106 |
< |
for (unsigned int i = 0; i < Dim - 1; i++) |
107 |
< |
for (unsigned int j = i; j < Dim; j++) |
108 |
< |
if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) |
109 |
< |
return false; |
110 |
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|
111 |
< |
return true; |
112 |
< |
} |
109 |
> |
return tmp; |
110 |
> |
} |
111 |
|
|
112 |
< |
/** Tests if this matrix is orthogonal. */ |
113 |
< |
bool isOrthogonal() { |
114 |
< |
SquareMatrix<Real, Dim> tmp; |
112 |
> |
/** Tests if this matrix is symmetrix. */ |
113 |
> |
bool isSymmetric() const { |
114 |
> |
for (unsigned int i = 0; i < Dim - 1; i++) |
115 |
> |
for (unsigned int j = i; j < Dim; j++) |
116 |
> |
if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) |
117 |
> |
return false; |
118 |
> |
|
119 |
> |
return true; |
120 |
> |
} |
121 |
|
|
122 |
< |
tmp = *this * transpose(); |
122 |
> |
/** Tests if this matrix is orthogonal. */ |
123 |
> |
bool isOrthogonal() { |
124 |
> |
SquareMatrix<Real, Dim> tmp; |
125 |
|
|
126 |
< |
return tmp.isDiagonal(); |
121 |
< |
} |
126 |
> |
tmp = *this * transpose(); |
127 |
|
|
128 |
< |
/** Tests if this matrix is diagonal. */ |
129 |
< |
bool isDiagonal() const { |
125 |
< |
for (unsigned int i = 0; i < Dim ; i++) |
126 |
< |
for (unsigned int j = 0; j < Dim; j++) |
127 |
< |
if (i !=j && fabs(data_[i][j]) > oopse::epsilon) |
128 |
< |
return false; |
129 |
< |
|
130 |
< |
return true; |
131 |
< |
} |
128 |
> |
return tmp.isDiagonal(); |
129 |
> |
} |
130 |
|
|
131 |
< |
/** Tests if this matrix is the unit matrix. */ |
132 |
< |
bool isUnitMatrix() const { |
133 |
< |
if (!isDiagonal()) |
134 |
< |
return false; |
135 |
< |
|
136 |
< |
for (unsigned int i = 0; i < Dim ; i++) |
137 |
< |
if (fabs(data_[i][i] - 1) > oopse::epsilon) |
131 |
> |
/** Tests if this matrix is diagonal. */ |
132 |
> |
bool isDiagonal() const { |
133 |
> |
for (unsigned int i = 0; i < Dim ; i++) |
134 |
> |
for (unsigned int j = 0; j < Dim; j++) |
135 |
> |
if (i !=j && fabs(data_[i][j]) > oopse::epsilon) |
136 |
> |
return false; |
137 |
> |
|
138 |
> |
return true; |
139 |
> |
} |
140 |
> |
|
141 |
> |
/** Tests if this matrix is the unit matrix. */ |
142 |
> |
bool isUnitMatrix() const { |
143 |
> |
if (!isDiagonal()) |
144 |
|
return false; |
145 |
|
|
146 |
< |
return true; |
147 |
< |
} |
146 |
> |
for (unsigned int i = 0; i < Dim ; i++) |
147 |
> |
if (fabs(data_[i][i] - 1) > oopse::epsilon) |
148 |
> |
return false; |
149 |
> |
|
150 |
> |
return true; |
151 |
> |
} |
152 |
|
|
153 |
< |
void diagonalize() { |
154 |
< |
jacobi(m, eigenValues, ortMat); |
155 |
< |
} |
148 |
< |
|
149 |
< |
/** |
150 |
< |
* Finds the eigenvalues and eigenvectors of a symmetric matrix |
151 |
< |
* @param eigenvals a reference to a vector3 where the |
152 |
< |
* eigenvalues will be stored. The eigenvalues are ordered so |
153 |
< |
* that eigenvals[0] <= eigenvals[1] <= eigenvals[2]. |
154 |
< |
* @return an orthogonal matrix whose ith column is an |
155 |
< |
* eigenvector for the eigenvalue eigenvals[i] |
156 |
< |
*/ |
157 |
< |
SquareMatrix<Real, Dim> findEigenvectors(Vector<Real, Dim>& eigenValues) { |
158 |
< |
SquareMatrix<Real, Dim> ortMat; |
159 |
< |
|
160 |
< |
if ( !isSymmetric()){ |
161 |
< |
throw(); |
153 |
> |
/** @todo need implementation */ |
154 |
> |
void diagonalize() { |
155 |
> |
//jacobi(m, eigenValues, ortMat); |
156 |
|
} |
163 |
– |
|
164 |
– |
SquareMatrix<Real, Dim> m(*this); |
165 |
– |
jacobi(m, eigenValues, ortMat); |
157 |
|
|
158 |
< |
return ortMat; |
159 |
< |
} |
160 |
< |
/** |
161 |
< |
* Jacobi iteration routines for computing eigenvalues/eigenvectors of |
162 |
< |
* real symmetric matrix |
163 |
< |
* |
164 |
< |
* @return true if success, otherwise return false |
165 |
< |
* @param a source matrix |
166 |
< |
* @param w output eigenvalues |
167 |
< |
* @param v output eigenvectors |
168 |
< |
*/ |
169 |
< |
bool jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, |
170 |
< |
SquareMatrix<Real, Dim>& v); |
158 |
> |
/** |
159 |
> |
* Jacobi iteration routines for computing eigenvalues/eigenvectors of |
160 |
> |
* real symmetric matrix |
161 |
> |
* |
162 |
> |
* @return true if success, otherwise return false |
163 |
> |
* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
164 |
> |
* overwritten |
165 |
> |
* @param w will contain the eigenvalues of the matrix On return of this function |
166 |
> |
* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
167 |
> |
* normalized and mutually orthogonal. |
168 |
> |
*/ |
169 |
> |
|
170 |
> |
static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d, |
171 |
> |
SquareMatrix<Real, Dim>& v); |
172 |
|
};//end SquareMatrix |
173 |
|
|
174 |
|
|
175 |
< |
#define ROT(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);a(k, l)=h+s*(g-h*tau) |
184 |
< |
#define MAX_ROTATIONS 60 |
175 |
> |
/*========================================================================= |
176 |
|
|
177 |
< |
template<typename Real, int Dim> |
178 |
< |
bool SquareMatrix<Real, Dim>::jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, |
188 |
< |
SquareMatrix<Real, Dim>& v) { |
189 |
< |
const int N = Dim; |
190 |
< |
int i, j, k, iq, ip; |
191 |
< |
double tresh, theta, tau, t, sm, s, h, g, c; |
192 |
< |
double tmp; |
193 |
< |
Vector<Real, Dim> b, z; |
177 |
> |
Program: Visualization Toolkit |
178 |
> |
Module: $RCSfile: SquareMatrix.hpp,v $ |
179 |
|
|
180 |
< |
// initialize |
181 |
< |
for (ip=0; ip<N; ip++) { |
182 |
< |
for (iq=0; iq<N; iq++) |
198 |
< |
v(ip, iq) = 0.0; |
199 |
< |
v(ip, ip) = 1.0; |
200 |
< |
} |
201 |
< |
|
202 |
< |
for (ip=0; ip<N; ip++) { |
203 |
< |
b(ip) = w(ip) = a(ip, ip); |
204 |
< |
z(ip) = 0.0; |
205 |
< |
} |
180 |
> |
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen |
181 |
> |
All rights reserved. |
182 |
> |
See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
183 |
|
|
184 |
< |
// begin rotation sequence |
185 |
< |
for (i=0; i<MAX_ROTATIONS; i++) { |
186 |
< |
sm = 0.0; |
210 |
< |
for (ip=0; ip<2; ip++) { |
211 |
< |
for (iq=ip+1; iq<N; iq++) |
212 |
< |
sm += fabs(a(ip, iq)); |
213 |
< |
} |
214 |
< |
|
215 |
< |
if (sm == 0.0) |
216 |
< |
break; |
184 |
> |
This software is distributed WITHOUT ANY WARRANTY; without even |
185 |
> |
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
186 |
> |
PURPOSE. See the above copyright notice for more information. |
187 |
|
|
188 |
< |
if (i < 4) |
219 |
< |
tresh = 0.2*sm/(9); |
220 |
< |
else |
221 |
< |
tresh = 0.0; |
188 |
> |
=========================================================================*/ |
189 |
|
|
190 |
< |
for (ip=0; ip<2; ip++) { |
191 |
< |
for (iq=ip+1; iq<N; iq++) { |
225 |
< |
g = 100.0*fabs(a(ip, iq)); |
226 |
< |
if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip)) |
227 |
< |
&& (fabs(w(iq))+g) == fabs(w(iq))) { |
228 |
< |
a(ip, iq) = 0.0; |
229 |
< |
} else if (fabs(a(ip, iq)) > tresh) { |
230 |
< |
h = w(iq) - w(ip); |
231 |
< |
if ( (fabs(h)+g) == fabs(h)) { |
232 |
< |
t = (a(ip, iq)) / h; |
233 |
< |
} else { |
234 |
< |
theta = 0.5*h / (a(ip, iq)); |
235 |
< |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
190 |
> |
#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\ |
191 |
> |
a(k, l)=h+s*(g-h*tau) |
192 |
|
|
193 |
< |
if (theta < 0.0) |
238 |
< |
t = -t; |
239 |
< |
} |
193 |
> |
#define VTK_MAX_ROTATIONS 20 |
194 |
|
|
195 |
< |
c = 1.0 / sqrt(1+t*t); |
196 |
< |
s = t*c; |
197 |
< |
tau = s/(1.0+c); |
198 |
< |
h = t*a(ip, iq); |
199 |
< |
z(ip) -= h; |
200 |
< |
z(iq) += h; |
201 |
< |
w(ip) -= h; |
202 |
< |
w(iq) += h; |
203 |
< |
a(ip, iq)=0.0; |
204 |
< |
|
205 |
< |
for (j=0;j<ip-1;j++) |
206 |
< |
ROT(a,j,ip,j,iq); |
195 |
> |
// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn |
196 |
> |
// real symmetric matrix. Square nxn matrix a; size of matrix in n; |
197 |
> |
// output eigenvalues in w; and output eigenvectors in v. Resulting |
198 |
> |
// eigenvalues/vectors are sorted in decreasing order; eigenvectors are |
199 |
> |
// normalized. |
200 |
> |
template<typename Real, int Dim> |
201 |
> |
int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, |
202 |
> |
SquareMatrix<Real, Dim>& v) { |
203 |
> |
const int n = Dim; |
204 |
> |
int i, j, k, iq, ip, numPos; |
205 |
> |
Real tresh, theta, tau, t, sm, s, h, g, c, tmp; |
206 |
> |
Real bspace[4], zspace[4]; |
207 |
> |
Real *b = bspace; |
208 |
> |
Real *z = zspace; |
209 |
|
|
210 |
< |
for (j=ip+1;j<iq-1;j++) |
211 |
< |
ROT(a,ip,j,j,iq); |
210 |
> |
// only allocate memory if the matrix is large |
211 |
> |
if (n > 4) { |
212 |
> |
b = new Real[n]; |
213 |
> |
z = new Real[n]; |
214 |
> |
} |
215 |
|
|
216 |
< |
for (j=iq+1; j<N; j++) |
217 |
< |
ROT(a,ip,j,iq,j); |
218 |
< |
for (j=0; j<N; j++) |
219 |
< |
ROT(v,j,ip,j,iq); |
216 |
> |
// initialize |
217 |
> |
for (ip=0; ip<n; ip++) { |
218 |
> |
for (iq=0; iq<n; iq++) { |
219 |
> |
v(ip, iq) = 0.0; |
220 |
> |
} |
221 |
> |
v(ip, ip) = 1.0; |
222 |
> |
} |
223 |
> |
for (ip=0; ip<n; ip++) { |
224 |
> |
b[ip] = w[ip] = a(ip, ip); |
225 |
> |
z[ip] = 0.0; |
226 |
> |
} |
227 |
> |
|
228 |
> |
// begin rotation sequence |
229 |
> |
for (i=0; i<VTK_MAX_ROTATIONS; i++) { |
230 |
> |
sm = 0.0; |
231 |
> |
for (ip=0; ip<n-1; ip++) { |
232 |
> |
for (iq=ip+1; iq<n; iq++) { |
233 |
> |
sm += fabs(a(ip, iq)); |
234 |
|
} |
235 |
|
} |
236 |
< |
}//for (ip=0; ip<2; ip++) |
236 |
> |
if (sm == 0.0) { |
237 |
> |
break; |
238 |
> |
} |
239 |
|
|
240 |
< |
for (ip=0; ip<N; ip++) { |
241 |
< |
b(ip) += z(ip); |
242 |
< |
w(ip) = b(ip); |
243 |
< |
z(ip) = 0.0; |
240 |
> |
if (i < 3) { // first 3 sweeps |
241 |
> |
tresh = 0.2*sm/(n*n); |
242 |
> |
} else { |
243 |
> |
tresh = 0.0; |
244 |
> |
} |
245 |
> |
|
246 |
> |
for (ip=0; ip<n-1; ip++) { |
247 |
> |
for (iq=ip+1; iq<n; iq++) { |
248 |
> |
g = 100.0*fabs(a(ip, iq)); |
249 |
> |
|
250 |
> |
// after 4 sweeps |
251 |
> |
if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
252 |
> |
&& (fabs(w[iq])+g) == fabs(w[iq])) { |
253 |
> |
a(ip, iq) = 0.0; |
254 |
> |
} else if (fabs(a(ip, iq)) > tresh) { |
255 |
> |
h = w[iq] - w[ip]; |
256 |
> |
if ( (fabs(h)+g) == fabs(h)) { |
257 |
> |
t = (a(ip, iq)) / h; |
258 |
> |
} else { |
259 |
> |
theta = 0.5*h / (a(ip, iq)); |
260 |
> |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
261 |
> |
if (theta < 0.0) { |
262 |
> |
t = -t; |
263 |
> |
} |
264 |
> |
} |
265 |
> |
c = 1.0 / sqrt(1+t*t); |
266 |
> |
s = t*c; |
267 |
> |
tau = s/(1.0+c); |
268 |
> |
h = t*a(ip, iq); |
269 |
> |
z[ip] -= h; |
270 |
> |
z[iq] += h; |
271 |
> |
w[ip] -= h; |
272 |
> |
w[iq] += h; |
273 |
> |
a(ip, iq)=0.0; |
274 |
> |
|
275 |
> |
// ip already shifted left by 1 unit |
276 |
> |
for (j = 0;j <= ip-1;j++) { |
277 |
> |
VTK_ROTATE(a,j,ip,j,iq); |
278 |
> |
} |
279 |
> |
// ip and iq already shifted left by 1 unit |
280 |
> |
for (j = ip+1;j <= iq-1;j++) { |
281 |
> |
VTK_ROTATE(a,ip,j,j,iq); |
282 |
> |
} |
283 |
> |
// iq already shifted left by 1 unit |
284 |
> |
for (j=iq+1; j<n; j++) { |
285 |
> |
VTK_ROTATE(a,ip,j,iq,j); |
286 |
> |
} |
287 |
> |
for (j=0; j<n; j++) { |
288 |
> |
VTK_ROTATE(v,j,ip,j,iq); |
289 |
> |
} |
290 |
> |
} |
291 |
> |
} |
292 |
> |
} |
293 |
> |
|
294 |
> |
for (ip=0; ip<n; ip++) { |
295 |
> |
b[ip] += z[ip]; |
296 |
> |
w[ip] = b[ip]; |
297 |
> |
z[ip] = 0.0; |
298 |
> |
} |
299 |
|
} |
270 |
– |
|
271 |
– |
} // end for (i=0; i<MAX_ROTATIONS; i++) |
300 |
|
|
301 |
< |
if ( i >= MAX_ROTATIONS ) |
302 |
< |
return false; |
301 |
> |
//// this is NEVER called |
302 |
> |
if ( i >= VTK_MAX_ROTATIONS ) { |
303 |
> |
std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; |
304 |
> |
return 0; |
305 |
> |
} |
306 |
|
|
307 |
< |
// sort eigenfunctions |
308 |
< |
for (j=0; j<N; j++) { |
309 |
< |
k = j; |
310 |
< |
tmp = w(k); |
311 |
< |
for (i=j; i<N; i++) { |
312 |
< |
if (w(i) >= tmp) { |
313 |
< |
k = i; |
314 |
< |
tmp = w(k); |
307 |
> |
// sort eigenfunctions these changes do not affect accuracy |
308 |
> |
for (j=0; j<n-1; j++) { // boundary incorrect |
309 |
> |
k = j; |
310 |
> |
tmp = w[k]; |
311 |
> |
for (i=j+1; i<n; i++) { // boundary incorrect, shifted already |
312 |
> |
if (w[i] >= tmp) { // why exchage if same? |
313 |
> |
k = i; |
314 |
> |
tmp = w[k]; |
315 |
> |
} |
316 |
|
} |
317 |
+ |
if (k != j) { |
318 |
+ |
w[k] = w[j]; |
319 |
+ |
w[j] = tmp; |
320 |
+ |
for (i=0; i<n; i++) { |
321 |
+ |
tmp = v(i, j); |
322 |
+ |
v(i, j) = v(i, k); |
323 |
+ |
v(i, k) = tmp; |
324 |
+ |
} |
325 |
+ |
} |
326 |
|
} |
327 |
< |
|
328 |
< |
if (k != j) { |
329 |
< |
w(k) = w(j); |
330 |
< |
w(j) = tmp; |
331 |
< |
for (i=0; i<N; i++) { |
332 |
< |
tmp = v(i, j); |
333 |
< |
v(i, j) = v(i, k); |
334 |
< |
v(i, k) = tmp; |
327 |
> |
// insure eigenvector consistency (i.e., Jacobi can compute vectors that |
328 |
> |
// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can |
329 |
> |
// reek havoc in hyperstreamline/other stuff. We will select the most |
330 |
> |
// positive eigenvector. |
331 |
> |
int ceil_half_n = (n >> 1) + (n & 1); |
332 |
> |
for (j=0; j<n; j++) { |
333 |
> |
for (numPos=0, i=0; i<n; i++) { |
334 |
> |
if ( v(i, j) >= 0.0 ) { |
335 |
> |
numPos++; |
336 |
> |
} |
337 |
|
} |
338 |
+ |
// if ( numPos < ceil(double(n)/double(2.0)) ) |
339 |
+ |
if ( numPos < ceil_half_n) { |
340 |
+ |
for (i=0; i<n; i++) { |
341 |
+ |
v(i, j) *= -1.0; |
342 |
+ |
} |
343 |
+ |
} |
344 |
|
} |
296 |
– |
} |
345 |
|
|
346 |
< |
// insure eigenvector consistency (i.e., Jacobi can compute |
347 |
< |
// vectors that are negative of one another (.707,.707,0) and |
348 |
< |
// (-.707,-.707,0). This can reek havoc in |
349 |
< |
// hyperstreamline/other stuff. We will select the most |
350 |
< |
// positive eigenvector. |
303 |
< |
int numPos; |
304 |
< |
for (j=0; j<N; j++) { |
305 |
< |
for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++; |
306 |
< |
if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0; |
346 |
> |
if (n > 4) { |
347 |
> |
delete [] b; |
348 |
> |
delete [] z; |
349 |
> |
} |
350 |
> |
return 1; |
351 |
|
} |
352 |
|
|
309 |
– |
return true; |
310 |
– |
} |
353 |
|
|
312 |
– |
#undef ROT |
313 |
– |
#undef MAX_ROTATIONS |
314 |
– |
|
354 |
|
} |
316 |
– |
|
355 |
|
#endif //MATH_SQUAREMATRIX_HPP |
356 |
+ |
|