evalue.cpp
Go to the documentation of this file.00001
00002
00003
00004
00005 #ifndef WANT_MATH
00006 #define WANT_MATH
00007 #endif
00008
00009 #include "include.h"
00010 #include "newmatap.h"
00011 #include "newmatrm.h"
00012 #include "precisio.h"
00013
00014 #ifdef use_namespace
00015 namespace NEWMAT {
00016 #endif
00017
00018 #ifdef DO_REPORT
00019 #define REPORT { static ExeCounter ExeCount(__LINE__,17); ++ExeCount; }
00020 #else
00021 #define REPORT {}
00022 #endif
00023
00024
00025
00026 static void tred2(const SymmetricMatrix& A, DiagonalMatrix& D,
00027 DiagonalMatrix& E, Matrix& Z)
00028 {
00029 Tracer et("Evalue(tred2)");
00030 REPORT
00031 Real tol =
00032 FloatingPointPrecision::Minimum()/FloatingPointPrecision::Epsilon();
00033 int n = A.Nrows(); Z.ReSize(n,n); Z.Inject(A);
00034 D.ReSize(n); E.ReSize(n);
00035 Real* z = Z.Store(); int i;
00036
00037 for (i=n-1; i > 0; i--)
00038 {
00039 Real f = Z.element(i,i-1); Real g = 0.0;
00040 int k = i-1; Real* zik = z + i*n;
00041 while (k--) g += square(*zik++);
00042 Real h = g + square(f);
00043 if (g <= tol) { REPORT E.element(i) = f; h = 0.0; }
00044 else
00045 {
00046 REPORT
00047 g = sign(-sqrt(h), f); E.element(i) = g; h -= f*g;
00048 Z.element(i,i-1) = f-g; f = 0.0;
00049 Real* zji = z + i; Real* zij = z + i*n; Real* ej = E.Store();
00050 int j;
00051 for (j=0; j<i; j++)
00052 {
00053 *zji = (*zij++)/h; g = 0.0;
00054 Real* zjk = z + j*n; zik = z + i*n;
00055 k = j; while (k--) g += *zjk++ * (*zik++);
00056 k = i-j;
00057 if (k) for(;;)
00058 { g += *zjk * (*zik++); if (!(--k)) break; zjk += n; }
00059 *ej++ = g/h; f += g * (*zji); zji += n;
00060 }
00061 Real hh = f / (h + h); zij = z + i*n; ej = E.Store();
00062 for (j=0; j<i; j++)
00063 {
00064 f = *zij++; g = *ej - hh * f; *ej++ = g;
00065 Real* zjk = z + j*n; Real* zik = z + i*n;
00066 Real* ek = E.Store(); k = j+1;
00067 while (k--) *zjk++ -= ( f*(*ek++) + g*(*zik++) );
00068 }
00069 }
00070 D.element(i) = h;
00071 }
00072
00073 D.element(0) = 0.0; E.element(0) = 0.0;
00074 for (i=0; i<n; i++)
00075 {
00076 if (D.element(i) != 0.0)
00077 {
00078 REPORT
00079 for (int j=0; j<i; j++)
00080 {
00081 Real g = 0.0;
00082 Real* zik = z + i*n; Real* zkj = z + j;
00083 int k = i;
00084 if (k) for (;;)
00085 { g += *zik++ * (*zkj); if (!(--k)) break; zkj += n; }
00086 Real* zki = z + i; zkj = z + j;
00087 k = i;
00088 if (k) for (;;)
00089 { *zkj -= g * (*zki); if (!(--k)) break; zkj += n; zki += n; }
00090 }
00091 }
00092 Real* zij = z + i*n; Real* zji = z + i;
00093 int j = i;
00094 if (j) for (;;)
00095 { *zij++ = 0.0; *zji = 0.0; if (!(--j)) break; zji += n; }
00096 D.element(i) = *zij; *zij = 1.0;
00097 }
00098 }
00099
00100 static void tql2(DiagonalMatrix& D, DiagonalMatrix& E, Matrix& Z)
00101 {
00102 Tracer et("Evalue(tql2)");
00103 REPORT
00104 Real eps = FloatingPointPrecision::Epsilon();
00105 int n = D.Nrows(); Real* z = Z.Store(); int l;
00106 for (l=1; l<n; l++) E.element(l-1) = E.element(l);
00107 Real b = 0.0; Real f = 0.0; E.element(n-1) = 0.0;
00108 for (l=0; l<n; l++)
00109 {
00110 int i,j;
00111 Real& dl = D.element(l); Real& el = E.element(l);
00112 Real h = eps * ( fabs(dl) + fabs(el) );
00113 if (b < h) { REPORT b = h; }
00114 int m;
00115 for (m=l; m<n; m++) if (fabs(E.element(m)) <= b) break;
00116 bool test = false;
00117 for (j=0; j<30; j++)
00118 {
00119 if (m==l) { REPORT test = true; break; }
00120 Real& dl1 = D.element(l+1);
00121 Real g = dl; Real p = (dl1-g) / (2.0*el); Real r = sqrt(p*p + 1.0);
00122 dl = el / (p < 0.0 ? p-r : p+r); Real h = g - dl; f += h;
00123 Real* dlx = &dl1; i = n-l-1; while (i--) *dlx++ -= h;
00124
00125 p = D.element(m); Real c = 1.0; Real s = 0.0;
00126 for (i=m-1; i>=l; i--)
00127 {
00128 Real ei = E.element(i); Real di = D.element(i);
00129 Real& ei1 = E.element(i+1);
00130 g = c * ei; h = c * p;
00131 if ( fabs(p) >= fabs(ei))
00132 {
00133 REPORT
00134 c = ei / p; r = sqrt(c*c + 1.0);
00135 ei1 = s*p*r; s = c/r; c = 1.0/r;
00136 }
00137 else
00138 {
00139 REPORT
00140 c = p / ei; r = sqrt(c*c + 1.0);
00141 ei1 = s * ei * r; s = 1.0/r; c /= r;
00142 }
00143 p = c * di - s*g; D.element(i+1) = h + s * (c*g + s*di);
00144
00145 Real* zki = z + i; Real* zki1 = zki + 1; int k = n;
00146 if (k) for (;;)
00147 {
00148 REPORT
00149 h = *zki1; *zki1 = s*(*zki) + c*h; *zki = c*(*zki) - s*h;
00150 if (!(--k)) break;
00151 zki += n; zki1 += n;
00152 }
00153 }
00154 el = s*p; dl = c*p;
00155 if (fabs(el) <= b) { REPORT; test = true; break; }
00156 }
00157 if (!test) Throw ( ConvergenceException(D) );
00158 dl += f;
00159 }
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00177
00178
00179 }
00180
00181 static void tred3(const SymmetricMatrix& X, DiagonalMatrix& D,
00182 DiagonalMatrix& E, SymmetricMatrix& A)
00183 {
00184 Tracer et("Evalue(tred3)");
00185 REPORT
00186 Real tol =
00187 FloatingPointPrecision::Minimum()/FloatingPointPrecision::Epsilon();
00188 int n = X.Nrows(); A = X; D.ReSize(n); E.ReSize(n);
00189 Real* ei = E.Store() + n;
00190 for (int i = n-1; i >= 0; i--)
00191 {
00192 Real h = 0.0; Real f = - FloatingPointPrecision::Maximum();
00193 Real* d = D.Store(); Real* a = A.Store() + (i*(i+1))/2; int k = i;
00194 while (k--) { f = *a++; *d++ = f; h += square(f); }
00195 if (h <= tol) { REPORT *(--ei) = 0.0; h = 0.0; }
00196 else
00197 {
00198 REPORT
00199 Real g = sign(-sqrt(h), f); *(--ei) = g; h -= f*g;
00200 f -= g; *(d-1) = f; *(a-1) = f; f = 0.0;
00201 Real* dj = D.Store(); Real* ej = E.Store(); int j;
00202 for (j = 0; j < i; j++)
00203 {
00204 Real* dk = D.Store(); Real* ak = A.Store()+(j*(j+1))/2;
00205 Real g = 0.0; k = j;
00206 while (k--) g += *ak++ * *dk++;
00207 k = i-j; int l = j;
00208 if (k) for (;;) { g += *ak * *dk++; if (!(--k)) break; ak += ++l; }
00209 g /= h; *ej++ = g; f += g * *dj++;
00210 }
00211 Real hh = f / (2 * h); Real* ak = A.Store();
00212 dj = D.Store(); ej = E.Store();
00213 for (j = 0; j < i; j++)
00214 {
00215 f = *dj++; g = *ej - hh * f; *ej++ = g;
00216 Real* dk = D.Store(); Real* ek = E.Store(); k = j+1;
00217 while (k--) { *ak++ -= (f * *ek++ + g * *dk++); }
00218 }
00219 }
00220 *d = *a; *a = h;
00221 }
00222 }
00223
00224 static void tql1(DiagonalMatrix& D, DiagonalMatrix& E)
00225 {
00226 Tracer et("Evalue(tql1)");
00227 REPORT
00228 Real eps = FloatingPointPrecision::Epsilon();
00229 int n = D.Nrows(); int l;
00230 for (l=1; l<n; l++) E.element(l-1) = E.element(l);
00231 Real b = 0.0; Real f = 0.0; E.element(n-1) = 0.0;
00232 for (l=0; l<n; l++)
00233 {
00234 int i,j;
00235 Real& dl = D.element(l); Real& el = E.element(l);
00236 Real h = eps * ( fabs(dl) + fabs(el) );
00237 if (b < h) b = h;
00238 int m;
00239 for (m=l; m<n; m++) if (fabs(E.element(m)) <= b) break;
00240 bool test = false;
00241 for (j=0; j<30; j++)
00242 {
00243 if (m==l) { REPORT test = true; break; }
00244 Real& dl1 = D.element(l+1);
00245 Real g = dl; Real p = (dl1-g) / (2.0*el); Real r = sqrt(p*p + 1.0);
00246 dl = el / (p < 0.0 ? p-r : p+r); Real h = g - dl; f += h;
00247 Real* dlx = &dl1; i = n-l-1; while (i--) *dlx++ -= h;
00248
00249 p = D.element(m); Real c = 1.0; Real s = 0.0;
00250 for (i=m-1; i>=l; i--)
00251 {
00252 Real ei = E.element(i); Real di = D.element(i);
00253 Real& ei1 = E.element(i+1);
00254 g = c * ei; h = c * p;
00255 if ( fabs(p) >= fabs(ei))
00256 {
00257 REPORT
00258 c = ei / p; r = sqrt(c*c + 1.0);
00259 ei1 = s*p*r; s = c/r; c = 1.0/r;
00260 }
00261 else
00262 {
00263 REPORT
00264 c = p / ei; r = sqrt(c*c + 1.0);
00265 ei1 = s * ei * r; s = 1.0/r; c /= r;
00266 }
00267 p = c * di - s*g; D.element(i+1) = h + s * (c*g + s*di);
00268 }
00269 el = s*p; dl = c*p;
00270 if (fabs(el) <= b) { REPORT test = true; break; }
00271 }
00272 if (!test) Throw ( ConvergenceException(D) );
00273 Real p = dl + f;
00274 test = false;
00275 for (i=l; i>0; i--)
00276 {
00277 if (p < D.element(i-1)) { REPORT D.element(i) = D.element(i-1); }
00278 else { REPORT test = true; break; }
00279 }
00280 if (!test) i=0;
00281 D.element(i) = p;
00282 }
00283 }
00284
00285 void EigenValues(const SymmetricMatrix& A, DiagonalMatrix& D, Matrix& Z)
00286 { REPORT DiagonalMatrix E; tred2(A, D, E, Z); tql2(D, E, Z); SortSV(D,Z,true); }
00287
00288 void EigenValues(const SymmetricMatrix& X, DiagonalMatrix& D)
00289 { REPORT DiagonalMatrix E; SymmetricMatrix A; tred3(X,D,E,A); tql1(D,E); }
00290
00291 void EigenValues(const SymmetricMatrix& X, DiagonalMatrix& D,
00292 SymmetricMatrix& A)
00293 { REPORT DiagonalMatrix E; tred3(X,D,E,A); tql1(D,E); }
00294
00295
00296 #ifdef use_namespace
00297 }
00298 #endif
00299
