Go to the documentation of this file.00001
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00008
00009 #define WANT_MATH
00010
00011 #include "include.h"
00012 #include "newmatap.h"
00013 #include "newmatrm.h"
00014 #include "precisio.h"
00015
00016 #ifdef use_namespace
00017 namespace NEWMAT {
00018 #endif
00019
00020 #ifdef DO_REPORT
00021 #define REPORT { static ExeCounter ExeCount(__LINE__,17); ++ExeCount; }
00022 #else
00023 #define REPORT {}
00024 #endif
00025
00026
00027
00028 static void tred2(const SymmetricMatrix& A, DiagonalMatrix& D,
00029 DiagonalMatrix& E, Matrix& Z)
00030 {
00031 Tracer et("Evalue(tred2)");
00032 REPORT
00033 Real tol =
00034 FloatingPointPrecision::Minimum()/FloatingPointPrecision::Epsilon();
00035 int n = A.Nrows(); Z.resize(n,n); Z.Inject(A);
00036 D.resize(n); E.resize(n);
00037 Real* z = Z.Store(); int i;
00038
00039 for (i=n-1; i > 0; i--)
00040 {
00041 Real f = Z.element(i,i-1); Real g = 0.0;
00042 int k = i-1; Real* zik = z + i*n;
00043 while (k--) g += square(*zik++);
00044 Real h = g + square(f);
00045 if (g <= tol) { REPORT E.element(i) = f; h = 0.0; }
00046 else
00047 {
00048 REPORT
00049 g = sign(-sqrt(h), f); E.element(i) = g; h -= f*g;
00050 Z.element(i,i-1) = f-g; f = 0.0;
00051 Real* zji = z + i; Real* zij = z + i*n; Real* ej = E.Store();
00052 int j;
00053 for (j=0; j<i; j++)
00054 {
00055 *zji = (*zij++)/h; g = 0.0;
00056 Real* zjk = z + j*n; zik = z + i*n;
00057 k = j; while (k--) g += *zjk++ * (*zik++);
00058 k = i-j;
00059 if (k) for(;;)
00060 { g += *zjk * (*zik++); if (!(--k)) break; zjk += n; }
00061 *ej++ = g/h; f += g * (*zji); zji += n;
00062 }
00063 Real hh = f / (h + h); zij = z + i*n; ej = E.Store();
00064 for (j=0; j<i; j++)
00065 {
00066 f = *zij++; g = *ej - hh * f; *ej++ = g;
00067 Real* zjk = z + j*n; Real* zik = z + i*n;
00068 Real* ek = E.Store(); k = j+1;
00069 while (k--) *zjk++ -= ( f*(*ek++) + g*(*zik++) );
00070 }
00071 }
00072 D.element(i) = h;
00073 }
00074
00075 D.element(0) = 0.0; E.element(0) = 0.0;
00076 for (i=0; i<n; i++)
00077 {
00078 if (D.element(i) != 0.0)
00079 {
00080 REPORT
00081 for (int j=0; j<i; j++)
00082 {
00083 Real g = 0.0;
00084 Real* zik = z + i*n; Real* zkj = z + j;
00085 int k = i;
00086 if (k) for (;;)
00087 { g += *zik++ * (*zkj); if (!(--k)) break; zkj += n; }
00088 Real* zki = z + i; zkj = z + j;
00089 k = i;
00090 if (k) for (;;)
00091 { *zkj -= g * (*zki); if (!(--k)) break; zkj += n; zki += n; }
00092 }
00093 }
00094 Real* zij = z + i*n; Real* zji = z + i;
00095 int j = i;
00096 if (j) for (;;)
00097 { *zij++ = 0.0; *zji = 0.0; if (!(--j)) break; zji += n; }
00098 D.element(i) = *zij; *zij = 1.0;
00099 }
00100 }
00101
00102 static void tql2(DiagonalMatrix& D, DiagonalMatrix& E, Matrix& Z)
00103 {
00104 Tracer et("Evalue(tql2)");
00105 REPORT
00106 Real eps = FloatingPointPrecision::Epsilon();
00107 int n = D.Nrows(); Real* z = Z.Store(); int l;
00108 for (l=1; l<n; l++) E.element(l-1) = E.element(l);
00109 Real b = 0.0; Real f = 0.0; E.element(n-1) = 0.0;
00110 for (l=0; l<n; l++)
00111 {
00112 int i,j;
00113 Real& dl = D.element(l); Real& el = E.element(l);
00114 Real h = eps * ( fabs(dl) + fabs(el) );
00115 if (b < h) { REPORT b = h; }
00116 int m;
00117 for (m=l; m<n; m++) if (fabs(E.element(m)) <= b) break;
00118 bool test = false;
00119 for (j=0; j<30; j++)
00120 {
00121 if (m==l) { REPORT test = true; break; }
00122 Real& dl1 = D.element(l+1);
00123 Real g = dl; Real p = (dl1-g) / (2.0*el); Real r = sqrt(p*p + 1.0);
00124 dl = el / (p < 0.0 ? p-r : p+r); Real h = g - dl; f += h;
00125 Real* dlx = &dl1; i = n-l-1; while (i--) *dlx++ -= h;
00126
00127 p = D.element(m); Real c = 1.0; Real s = 0.0;
00128 for (i=m-1; i>=l; i--)
00129 {
00130 Real ei = E.element(i); Real di = D.element(i);
00131 Real& ei1 = E.element(i+1);
00132 g = c * ei; h = c * p;
00133 if ( fabs(p) >= fabs(ei))
00134 {
00135 REPORT
00136 c = ei / p; r = sqrt(c*c + 1.0);
00137 ei1 = s*p*r; s = c/r; c = 1.0/r;
00138 }
00139 else
00140 {
00141 REPORT
00142 c = p / ei; r = sqrt(c*c + 1.0);
00143 ei1 = s * ei * r; s = 1.0/r; c /= r;
00144 }
00145 p = c * di - s*g; D.element(i+1) = h + s * (c*g + s*di);
00146
00147 Real* zki = z + i; Real* zki1 = zki + 1; int k = n;
00148 if (k) for (;;)
00149 {
00150 REPORT
00151 h = *zki1; *zki1 = s*(*zki) + c*h; *zki = c*(*zki) - s*h;
00152 if (!(--k)) break;
00153 zki += n; zki1 += n;
00154 }
00155 }
00156 el = s*p; dl = c*p;
00157 if (fabs(el) <= b) { REPORT; test = true; break; }
00158 }
00159 if (!test) Throw ( ConvergenceException(D) );
00160 dl += f;
00161 }
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00181 }
00182
00183 static void tred3(const SymmetricMatrix& X, DiagonalMatrix& D,
00184 DiagonalMatrix& E, SymmetricMatrix& A)
00185 {
00186 Tracer et("Evalue(tred3)");
00187 REPORT
00188 Real tol =
00189 FloatingPointPrecision::Minimum()/FloatingPointPrecision::Epsilon();
00190 int n = X.Nrows(); A = X; D.resize(n); E.resize(n);
00191 Real* ei = E.Store() + n;
00192 for (int i = n-1; i >= 0; i--)
00193 {
00194 Real h = 0.0; Real f = - FloatingPointPrecision::Maximum();
00195 Real* d = D.Store(); Real* a = A.Store() + (i*(i+1))/2; int k = i;
00196 while (k--) { f = *a++; *d++ = f; h += square(f); }
00197 if (h <= tol) { REPORT *(--ei) = 0.0; h = 0.0; }
00198 else
00199 {
00200 REPORT
00201 Real g = sign(-sqrt(h), f); *(--ei) = g; h -= f*g;
00202 f -= g; *(d-1) = f; *(a-1) = f; f = 0.0;
00203 Real* dj = D.Store(); Real* ej = E.Store(); int j;
00204 for (j = 0; j < i; j++)
00205 {
00206 Real* dk = D.Store(); Real* ak = A.Store()+(j*(j+1))/2;
00207 Real g = 0.0; k = j;
00208 while (k--) g += *ak++ * *dk++;
00209 k = i-j; int l = j;
00210 if (k) for (;;) { g += *ak * *dk++; if (!(--k)) break; ak += ++l; }
00211 g /= h; *ej++ = g; f += g * *dj++;
00212 }
00213 Real hh = f / (2 * h); Real* ak = A.Store();
00214 dj = D.Store(); ej = E.Store();
00215 for (j = 0; j < i; j++)
00216 {
00217 f = *dj++; g = *ej - hh * f; *ej++ = g;
00218 Real* dk = D.Store(); Real* ek = E.Store(); k = j+1;
00219 while (k--) { *ak++ -= (f * *ek++ + g * *dk++); }
00220 }
00221 }
00222 *d = *a; *a = h;
00223 }
00224 }
00225
00226 static void tql1(DiagonalMatrix& D, DiagonalMatrix& E)
00227 {
00228 Tracer et("Evalue(tql1)");
00229 REPORT
00230 Real eps = FloatingPointPrecision::Epsilon();
00231 int n = D.Nrows(); int l;
00232 for (l=1; l<n; l++) E.element(l-1) = E.element(l);
00233 Real b = 0.0; Real f = 0.0; E.element(n-1) = 0.0;
00234 for (l=0; l<n; l++)
00235 {
00236 int i,j;
00237 Real& dl = D.element(l); Real& el = E.element(l);
00238 Real h = eps * ( fabs(dl) + fabs(el) );
00239 if (b < h) b = h;
00240 int m;
00241 for (m=l; m<n; m++) if (fabs(E.element(m)) <= b) break;
00242 bool test = false;
00243 for (j=0; j<30; j++)
00244 {
00245 if (m==l) { REPORT test = true; break; }
00246 Real& dl1 = D.element(l+1);
00247 Real g = dl; Real p = (dl1-g) / (2.0*el); Real r = sqrt(p*p + 1.0);
00248 dl = el / (p < 0.0 ? p-r : p+r); Real h = g - dl; f += h;
00249 Real* dlx = &dl1; i = n-l-1; while (i--) *dlx++ -= h;
00250
00251 p = D.element(m); Real c = 1.0; Real s = 0.0;
00252 for (i=m-1; i>=l; i--)
00253 {
00254 Real ei = E.element(i); Real di = D.element(i);
00255 Real& ei1 = E.element(i+1);
00256 g = c * ei; h = c * p;
00257 if ( fabs(p) >= fabs(ei))
00258 {
00259 REPORT
00260 c = ei / p; r = sqrt(c*c + 1.0);
00261 ei1 = s*p*r; s = c/r; c = 1.0/r;
00262 }
00263 else
00264 {
00265 REPORT
00266 c = p / ei; r = sqrt(c*c + 1.0);
00267 ei1 = s * ei * r; s = 1.0/r; c /= r;
00268 }
00269 p = c * di - s*g; D.element(i+1) = h + s * (c*g + s*di);
00270 }
00271 el = s*p; dl = c*p;
00272 if (fabs(el) <= b) { REPORT test = true; break; }
00273 }
00274 if (!test) Throw ( ConvergenceException(D) );
00275 Real p = dl + f;
00276 test = false;
00277 for (i=l; i>0; i--)
00278 {
00279 if (p < D.element(i-1)) { REPORT D.element(i) = D.element(i-1); }
00280 else { REPORT test = true; break; }
00281 }
00282 if (!test) i=0;
00283 D.element(i) = p;
00284 }
00285 }
00286
00287 void eigenvalues(const SymmetricMatrix& A, DiagonalMatrix& D, Matrix& Z)
00288 { REPORT DiagonalMatrix E; tred2(A, D, E, Z); tql2(D, E, Z); SortSV(D,Z,true); }
00289
00290 void eigenvalues(const SymmetricMatrix& X, DiagonalMatrix& D)
00291 { REPORT DiagonalMatrix E; SymmetricMatrix A; tred3(X,D,E,A); tql1(D,E); }
00292
00293 void eigenvalues(const SymmetricMatrix& X, DiagonalMatrix& D,
00294 SymmetricMatrix& A)
00295 { REPORT DiagonalMatrix E; tred3(X,D,E,A); tql1(D,E); }
00296
00297
00298 #ifdef use_namespace
00299 }
00300 #endif
00301
00303
