/[escript]/trunk/escript/src/LocalOps.h
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Annotation of /trunk/escript/src/LocalOps.h

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Revision 583 - (hide annotations)
Wed Mar 8 08:15:34 2006 UTC (13 years, 7 months ago) by gross
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File size: 13882 byte(s)
_eigenvalues_and_eigenvector method added of data object. the algorithm has been tested on floats in python but not on data objects.
1 gross 576 // $Id$
2     /*
3     ******************************************************************************
4     * *
5     * COPYRIGHT ACcESS 2004 - All Rights Reserved *
6     * *
7     * This software is the property of ACcESS. No part of this code *
8     * may be copied in any form or by any means without the expressed written *
9     * consent of ACcESS. Copying, use or modification of this software *
10     * by any unauthorised person is illegal unless that person has a software *
11     * license agreement with ACcESS. *
12     * *
13     ******************************************************************************
14     */
15    
16     #if !defined escript_LocalOps_H
17     #define escript_LocalOps_H
18 gross 580 #include <math.h>
19 gross 576 namespace escript {
20    
21    
22     /**
23     \brief
24     solves a 1x1 eigenvalue A*V=ev*V problem
25    
26     \param A00 Input - A_00
27     \param ev0 Output - eigenvalue
28     */
29     inline
30     void eigenvalues1(const double A00,double* ev0) {
31    
32 gross 580 *ev0=A00;
33 gross 576
34     }
35     /**
36     \brief
37     solves a 2x2 eigenvalue A*V=ev*V problem for symmetric A
38    
39     \param A00 Input - A_00
40     \param A01 Input - A_01
41     \param A11 Input - A_11
42     \param ev0 Output - smallest eigenvalue
43     \param ev1 Output - largest eigenvalue
44     */
45     inline
46 gross 583 void eigenvalues2(const double A00,const double A01,const double A11,
47 gross 576 double* ev0, double* ev1) {
48 gross 580 const register double trA=(A00+A11)/2.;
49     const register double A_00=A00-trA;
50     const register double A_11=A11-trA;
51     const register double s=sqrt(A01*A01-A_00*A_11);
52     *ev0=trA-s;
53     *ev1=trA+s;
54 gross 576 }
55     /**
56     \brief
57     solves a 3x3 eigenvalue A*V=ev*V problem for symmetric A
58    
59     \param A00 Input - A_00
60     \param A01 Input - A_01
61     \param A02 Input - A_02
62     \param A11 Input - A_11
63     \param A12 Input - A_12
64     \param A22 Input - A_22
65     \param ev0 Output - smallest eigenvalue
66     \param ev1 Output - eigenvalue
67     \param ev2 Output - largest eigenvalue
68     */
69     inline
70     void eigenvalues3(const double A00, const double A01, const double A02,
71     const double A11, const double A12,
72     const double A22,
73     double* ev0, double* ev1,double* ev2) {
74    
75 gross 580 const register double trA=(A00+A11+A22)/3.;
76     const register double A_00=A00-trA;
77     const register double A_11=A11-trA;
78     const register double A_22=A22-trA;
79     const register double A01_2=A01*A01;
80     const register double A02_2=A02*A02;
81     const register double A12_2=A12*A12;
82     const register double p=A02_2+A12_2+A01_2+(A_00*A_00+A_11*A_11+A_22*A_22)/2.;
83     const register double q=(A02_2*A_11+A12_2*A_00+A01_2*A_22)-(A_00*A_11*A_22+2*A01*A12*A02);
84     const register double sq_p=sqrt(p/3.);
85     register double z=-q/(2*pow(sq_p,3));
86     if (z<-1.) {
87     z=-1.;
88     } else if (z>1.) {
89     z=1.;
90     }
91     const register double alpha_3=acos(z)/3.;
92     *ev2=trA+2.*sq_p*cos(alpha_3);
93     *ev1=trA-2.*sq_p*cos(alpha_3+M_PI/3.);
94     *ev0=trA-2.*sq_p*cos(alpha_3-M_PI/3.);
95 gross 576 }
96 gross 583 /**
97     \brief
98     solves a 1x1 eigenvalue A*V=ev*V problem for symmetric A
99    
100     \param A00 Input - A_00
101     \param ev0 Output - eigenvalue
102     \param V00 Output - eigenvector
103     \param tol Input - tolerance to identify to eigenvalues
104     */
105     inline
106     void eigenvalues_and_eigenvectors1(const double A00,double* ev0,double* V00,const double tol)
107     {
108     eigenvalues1(A00,ev0);
109     *V00=1.;
110     return;
111     }
112     /**
113     \brief
114     returns a non-zero vector in the kernel of [[A00,A01],[A01,A11]] assuming that the kernel dimension is at least 1.
115    
116     \param A00 Input - matrix component
117     \param A10 Input - matrix component
118     \param A01 Input - matrix component
119     \param A11 Input - matrix component
120     \param V0 Output - vector component
121     \param V1 Output - vector component
122     */
123     inline
124     void vectorInKernel2(const double A00,const double A10,const double A01,const double A11,
125     double* V0, double*V1)
126     {
127     register double absA00=fabs(A00);
128     register double absA01=fabs(A01);
129     register double absA10=fabs(A10);
130     register double absA11=fabs(A11);
131     register double m=absA11>absA01 ? absA11 : absA01;
132     if (absA00>m || absA10>m) {
133     *V0=-A10;
134     *V1=A00;
135     } else {
136     if (m<=0) {
137     *V0=1.;
138     *V1=0.;
139     } else {
140     *V0=A11;
141     *V1=-A01;
142     }
143     }
144     }
145     /**
146     \brief
147     returns a non-zero vector in the kernel of [[A00,A01,A02],[A10,A11,A12],[A20,A21,A22]]
148     assuming that the kernel dimension is at least 1 and A00 is non zero.
149    
150     \param A00 Input - matrix component
151     \param A10 Input - matrix component
152     \param A20 Input - matrix component
153     \param A01 Input - matrix component
154     \param A11 Input - matrix component
155     \param A21 Input - matrix component
156     \param A02 Input - matrix component
157     \param A12 Input - matrix component
158     \param A22 Input - matrix component
159     \param V0 Output - vector component
160     \param V1 Output - vector component
161     \param V2 Output - vector component
162     */
163     inline
164     void vectorInKernel3__nonZeroA00(const double A00,const double A10,const double A20,
165     const double A01,const double A11,const double A21,
166     const double A02,const double A12,const double A22,
167     double* V0,double* V1,double* V2)
168     {
169     double TEMP0,TEMP1;
170     register const double I00=1./A00;
171     register const double IA10=I00*A10;
172     register const double IA20=I00*A20;
173     vectorInKernel2(A11-IA10*A01,A21-IA20*A01,A12-IA10*A02,A22-IA20*A02,&TEMP0,&TEMP1);
174     *V0=-(A10*TEMP0+A20*TEMP1);
175     *V1=A00*TEMP0;
176     *V2=A00*TEMP1;
177     }
178    
179     /**
180     \brief
181     solves a 2x2 eigenvalue A*V=ev*V problem for symmetric A. Eigenvectors are
182     ordered by increasing value and eigen vectors are normalizeVector3d such that
183     length is zero and first non-zero component is positive.
184    
185     \param A00 Input - A_00
186     \param A01 Input - A_01
187     \param A11 Input - A_11
188     \param ev0 Output - smallest eigenvalue
189     \param ev1 Output - eigenvalue
190     \param V00 Output - eigenvector componenent coresponding to ev0
191     \param V10 Output - eigenvector componenent coresponding to ev0
192     \param V01 Output - eigenvector componenent coresponding to ev1
193     \param V11 Output - eigenvector componenent coresponding to ev1
194     \param tol Input - tolerance to identify to eigenvalues
195     */
196     inline
197     void eigenvalues_and_eigenvectors2(const double A00,const double A01,const double A11,
198     double* ev0, double* ev1,
199     double* V00, double* V10, double* V01, double* V11,
200     const double tol)
201     {
202     double TEMP0,TEMP1;
203     eigenvalues2(A00,A01,A11,ev0,ev1);
204     const register double absev0=fabs(*ev0);
205     const register double absev1=fabs(*ev1);
206     register double max_ev=absev0>absev1 ? absev0 : absev1;
207     if (fabs((*ev0)-(*ev1))<tol*max_ev) {
208     *V00=1.;
209     *V10=0.;
210     *V01=0.;
211     *V11=1.;
212     } else {
213     vectorInKernel2(A00-(*ev0),A01,A01,A11-(*ev0),&TEMP0,&TEMP1);
214     const register double scale=1./sqrt(TEMP0*TEMP0+TEMP1*TEMP1);
215     if (TEMP0<0.) {
216     *V00=-TEMP0*scale;
217     *V10=-TEMP1*scale;
218     if (TEMP1<0.) {
219     *V01= *V10;
220     *V11=-(*V00);
221     } else {
222     *V01=-(*V10);
223     *V11= (*V00);
224     }
225     } else if (TEMP0>0.) {
226     *V00=TEMP0*scale;
227     *V10=TEMP1*scale;
228     if (TEMP1<0.) {
229     *V01=-(*V10);
230     *V11= (*V00);
231     } else {
232     *V01= (*V10);
233     *V11=-(*V00);
234     }
235     } else {
236     *V00=0.;
237     *V10=1;
238     *V11=0.;
239     *V01=1.;
240     }
241     }
242     }
243     /**
244     \brief
245     nomalizes a 3-d vector such that length is one and first non-zero component is positive.
246    
247     \param V0 - vector componenent
248     \param V1 - vector componenent
249     \param V2 - vector componenent
250     */
251     inline
252     void normalizeVector3(double* V0,double* V1,double* V2)
253     {
254     register double s;
255     if (*V0>0) {
256     s=1./sqrt((*V0)*(*V0)+(*V1)*(*V1)+(*V2)*(*V2));
257     *V0*=s;
258     *V1*=s;
259     *V2*=s;
260     } else if (*V0<0) {
261     s=-1./sqrt((*V0)*(*V0)+(*V1)*(*V1)+(*V2)*(*V2));
262     *V0*=s;
263     *V1*=s;
264     *V2*=s;
265     } else {
266     if (*V1>0) {
267     s=1./sqrt((*V1)*(*V1)+(*V2)*(*V2));
268     *V1*=s;
269     *V2*=s;
270     } else if (*V1<0) {
271     s=-1./sqrt((*V1)*(*V1)+(*V2)*(*V2));
272     *V1*=s;
273     *V2*=s;
274     } else {
275     *V2=1.;
276     }
277     }
278     }
279     /**
280     \brief
281     solves a 2x2 eigenvalue A*V=ev*V problem for symmetric A. Eigenvectors are
282     ordered by increasing value and eigen vectors are normalizeVector3d such that
283     length is zero and first non-zero component is positive.
284    
285     \param A00 Input - A_00
286     \param A01 Input - A_01
287     \param A11 Input - A_11
288     \param ev0 Output - smallest eigenvalue
289     \param ev1 Output - eigenvalue
290     \param V00 Output - eigenvector componenent coresponding to ev0
291     \param V10 Output - eigenvector componenent coresponding to ev0
292     \param V01 Output - eigenvector componenent coresponding to ev1
293     \param V11 Output - eigenvector componenent coresponding to ev1
294     \param tol Input - tolerance to identify to eigenvalues
295     */
296     inline
297     void eigenvalues_and_eigenvectors3(const double A00, const double A01, const double A02,
298     const double A11, const double A12, const double A22,
299     double* ev0, double* ev1, double* ev2,
300     double* V00, double* V10, double* V20,
301     double* V01, double* V11, double* V21,
302     double* V02, double* V12, double* V22,
303     const double tol)
304     {
305     register const double absA01=fabs(A01);
306     register const double absA02=fabs(A02);
307     register const double m=absA01>absA02 ? absA01 : absA02;
308     if (m<=0) {
309     double TEMP_V00,TEMP_V10,TEMP_V01,TEMP_V11,TEMP_EV0,TEMP_EV1;
310     eigenvalues_and_eigenvectors2(A11,A12,A22,
311     &TEMP_EV0,&TEMP_EV1,
312     &TEMP_V00,&TEMP_V10,&TEMP_V01,&TEMP_V11,tol);
313     if (A00<=TEMP_EV0) {
314     *V00=1.;
315     *V10=0.;
316     *V20=0.;
317     *V01=0.;
318     *V11=TEMP_V00;
319     *V21=TEMP_V10;
320     *V02=0.;
321     *V12=TEMP_V01;
322     *V22=TEMP_V11;
323     *ev0=A00;
324     *ev1=TEMP_EV0;
325     *ev2=TEMP_EV1;
326     } else if (A00>TEMP_EV1) {
327     *V00=TEMP_V00;
328     *V10=TEMP_V10;
329     *V20=0.;
330     *V01=TEMP_V01;
331     *V11=TEMP_V11;
332     *V21=0.;
333     *V02=0.;
334     *V12=0.;
335     *V22=1.;
336     *ev0=TEMP_EV0;
337     *ev1=TEMP_EV1;
338     *ev0=A00;
339     } else {
340     *V00=TEMP_V00;
341     *V10=0;
342     *V20=TEMP_V10;
343     *V01=0.;
344     *V11=1.;
345     *V21=0.;
346     *V02=TEMP_V01;
347     *V12=0.;
348     *V22=TEMP_V11;
349     *ev0=TEMP_EV0;
350     *ev1=A00;
351     *ev2=TEMP_EV1;
352     }
353     } else {
354     eigenvalues3(A00,A01,A02,A11,A12,A22,ev0,ev1,ev2);
355     const register double absev0=fabs(*ev0);
356     const register double absev1=fabs(*ev1);
357     const register double absev2=fabs(*ev2);
358     register double max_ev=absev0>absev1 ? absev0 : absev1;
359     max_ev=max_ev>absev2 ? max_ev : absev2;
360     const register double d_01=fabs((*ev0)-(*ev1));
361     const register double d_12=fabs((*ev1)-(*ev2));
362     const register double max_d=d_01>d_12 ? d_01 : d_12;
363     if (max_d<=tol*max_ev) {
364     *V00=1.;
365     *V10=0;
366     *V20=0;
367     *V01=0;
368     *V11=1.;
369     *V21=0;
370     *V02=0;
371     *V12=0;
372     *V22=1.;
373     } else {
374     const register double S00=A00-(*ev0);
375     const register double absS00=fabs(S00);
376     if (fabs(S00)>m) {
377     vectorInKernel3__nonZeroA00(S00,A01,A02,A01,A11-(*ev0),A12,A02,A12,A22-(*ev0),V00,V10,V20);
378     } else if (absA02<m) {
379     vectorInKernel3__nonZeroA00(A01,A11-(*ev0),A12,S00,A01,A02,A02,A12,A22-(*ev0),V00,V10,V20);
380     } else {
381     vectorInKernel3__nonZeroA00(A02,A12,A22-(*ev0),S00,A01,A02,A01,A11-(*ev0),A12,V00,V10,V20);
382     }
383     normalizeVector3(V00,V10,V20);;
384     const register double T00=A00-(*ev2);
385     const register double absT00=fabs(T00);
386     if (fabs(T00)>m) {
387     vectorInKernel3__nonZeroA00(T00,A01,A02,A01,A11-(*ev2),A12,A02,A12,A22-(*ev2),V02,V12,V22);
388     } else if (absA02<m) {
389     vectorInKernel3__nonZeroA00(A01,A11-(*ev2),A12,T00,A01,A02,A02,A12,A22-(*ev2),V02,V12,V22);
390     } else {
391     vectorInKernel3__nonZeroA00(A02,A12,A22-(*ev2),T00,A01,A02,A01,A11-(*ev2),A12,V02,V12,V22);
392     }
393     const register double dot=(*V02)*(*V00)+(*V12)*(*V10)+(*V22)*(*V20);
394     *V02-=dot*(*V00);
395     *V12-=dot*(*V10);
396     *V22-=dot*(*V20);
397     normalizeVector3(V02,V12,V22);
398     *V01=(*V10)*(*V22)-(*V12)*(*V20);
399     *V11=(*V20)*(*V02)-(*V00)*(*V22);
400     *V21=(*V00)*(*V12)-(*V02)*(*V10);
401     normalizeVector3(V01,V11,V21);
402     }
403     }
404     }
405 gross 576 } // end of namespace
406     #endif

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