00001 00033 #include <itpp/base/integration.h> 00034 #include <itpp/base/vec.h> 00035 #include <itpp/base/specmat.h> 00036 #include <itpp/base/matfunc.h> 00037 #include <itpp/base/help_functions.h> 00038 00039 00040 namespace itpp { 00041 00042 double quadstep(double (*f)(double), const double a, const double b, const double fa, const double fm, const double fb, const double is) 00043 { 00044 double Q, m, h, fml, fmr, i1, i2; 00045 vec x(2), y(2); 00046 00047 m = (a+b)/2; h = (b-a)/4; 00048 x = vec_2(a+h, b-h); 00049 y = vec_function(f, x); 00050 fml = y(0); fmr = y(1); 00051 00052 i1 = h/1.5 * (fa + 4*fm + fb); 00053 i2 = h/3 * (fa + 4*(fml + fmr) + 2*fm + fb); 00054 i1 = (16*i2 - i1)/15; 00055 00056 if( (is + (i1-i2) == is) || (m<=a) || (b<=m) ) { 00057 if( (m <= a) || (b<=m) ) { 00058 it_warning("Interval contains no more machine number. Required tolerance may not be met"); 00059 } 00060 Q = i1; 00061 return Q; 00062 } else { 00063 Q = quadstep(f, a, m, fa, fml, fm, is) + quadstep(f, m, b, fm, fmr, fb, is); 00064 } 00065 return Q; 00066 } 00067 00068 00069 double quad(double (*f)(double), const double a, const double b, const double tol) 00070 { 00071 vec x(3), y(3), yy(5); 00072 double Q, fa, fm, fb, is; 00073 00074 x = vec_3(a, (a+b)/2, b); 00075 y = vec_function(f, x); 00076 fa = y(0); fm = y(1); fb = y(2); 00077 yy = vec_function(f, a + vec(".9501 .2311 .6068 .4860 .8913")*(b-a)); 00078 is = (b-a)/8*(sum(y)+sum(yy)); 00079 00080 if (is == 0.0) 00081 is = b-a; 00082 00083 is = is*tol/std::numeric_limits<double>::epsilon(); 00084 Q = quadstep(f, a, b, fa, fm, fb, is); 00085 00086 return Q; 00087 } 00088 00089 00090 //--------------------- quadl() ---------------------------------------- 00091 00092 double quadlstep(double (*f)(double), const double a, const double b, const double fa, const double fb, const double is) 00093 { 00094 double Q, h, m, alpha, beta, mll, ml, mr, mrr, fmll, fml, fm, fmr, fmrr, i1, i2; 00095 vec x(5), y(5); 00096 00097 h=(b-a)/2; m=(a+b)/2; 00098 alpha=sqrt(2.0/3); beta=1.0/sqrt(5.0); 00099 mll=m-alpha*h; ml=m-beta*h; mr=m+beta*h; mrr=m+alpha*h; 00100 x(0)=mll; x(1) = ml; x(2) = m; x(3) = mr; x(4) = mrr; 00101 00102 y=vec_function(f, x); 00103 00104 fmll=y(0); fml=y(1); fm=y(2); fmr=y(3); fmrr=y(4); 00105 00106 i2 = (h/6)*(fa+fb+5*(fml+fmr)); 00107 i1 = (h/1470)*(77*(fa+fb)+432*(fmll+fmrr)+625*(fml+fmr)+672*fm); 00108 00109 if( (is + (i1-i2) == is) || (mll<=a) || (b<=mrr) ) { 00110 if( (m <= a) || (b<=m) ) { 00111 it_warning("Interval contains no more machine number. Required tolerance may not be met"); 00112 } 00113 Q = i1; 00114 return Q; 00115 } else { 00116 Q=quadlstep(f, a, mll, fa, fmll, is) + quadlstep(f, mll, ml, fmll, fml, is) + quadlstep(f, ml, m, fml, fm, is) + 00117 quadlstep(f, m, mr, fm, fmr, is) + quadlstep(f, mr, mrr, fmr, fmrr, is) + quadlstep(f, mrr, b, fmrr, fb, is); 00118 } 00119 return Q; 00120 } 00121 00122 double quadl(double (*f)(double), const double a, const double b, const double tol) 00123 { 00124 double Q, m, h, alpha, beta, x1, x2, x3, fa, fb, i1, i2, is, s, erri1, erri2, R; 00125 vec x(13), y(13); 00126 double tol2 = tol; 00127 00128 m=(a+b)/2; h=(b-a)/2; 00129 00130 alpha=std::sqrt(2.0/3); beta=1/sqrt(5.0); 00131 00132 x1=.942882415695480; x2=.641853342345781; x3=.236383199662150; 00133 x(0)=a; x(1)=m-x1*h; x(2)=m-alpha*h; x(3)=m-x2*h; 00134 x(4)=m-beta*h; x(5)=m-x3*h; x(6)=m; x(7)=m+x3*h; 00135 x(8)=m+beta*h; x(9)=m+x2*h; x(10)=m+alpha*h; 00136 x(11)=m+x1*h; x(12)=b; 00137 00138 y=vec_function(f, x); 00139 00140 fa=y(0); fb=y(12); 00141 i2=(h/6)*(y(0)+y(12)+5*(y(4)+y(8))); 00142 i1=(h/1470)*(77*(y(0)+y(12))+432*(y(2)+y(10))+ 625*(y(4)+y(8))+672*y(6)); 00143 00144 is=h*(.0158271919734802*(y(0)+y(12))+.0942738402188500*(y(1)+y(11))+.155071987336585*(y(2)+y(10))+ 00145 .188821573960182*(y(3)+y(9))+.199773405226859 *(y(4)+y(8))+.224926465333340*(y(5)+y(7))+.242611071901408*y(6)); 00146 00147 s=sign(is); 00148 if (s == 0.0) 00149 s = 1; 00150 00151 erri1 = std::abs(i1-is); 00152 erri2 = std::abs(i2-is); 00153 00154 R=1; 00155 if (erri2 != 0.0) 00156 R = erri1/erri2; 00157 00158 if (R>0 && R<1) 00159 tol2=tol2/R; 00160 00161 is = s*std::abs(is)*tol2/std::numeric_limits<double>::epsilon(); 00162 if (is == 0.0) 00163 is=b-a; 00164 00165 Q = quadlstep(f, a, b, fa, fb, is); 00166 00167 return Q; 00168 } 00169 00170 00171 } // namespace itpp
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