[NA] Reformatting and updated logic

1 files changed, 37 insertions, 33 deletions

diff --git a/Year 3/Numerical analysis/Project.wl b/Year 3/Numerical analysis/Project.wl
index 9948423..a3ac02a 100644
--- a/Year 3/Numerical analysis/Project.wl
+++ b/Year 3/Numerical analysis/Project.wl
@@ -1,33 +1,33 @@
 (*----------
 * 1 задача
 *----------*)
-ApproxIntegral[M_,a_,b_,f_]:= With[
+ApproxIntegral[M_, a_, b_, f_] := With[
   {
     h=(b-a)/(2M),
-    xk=Function[k,a+k*(b-a)/(2M)]
+    xk=Function[k, a+k*(b-a)/(2M)]
   },
   (h/3)(f[a]+f[b]) +
-  (2h/3)Sum[f[xk[2k]],{k,1,M-1}]+
-  (4h/3)Sum[f[xk[2k-1]],{k,1,M}]
+  (2h/3)Sum[f[xk[2k]], {k, 1, M-1}]+
+  (4h/3)Sum[f[xk[2k-1]], {k, 1, M}]
 ]
 
-Integrand[x_]:=1/((1+2x^2)^5)
-m15:=N[ApproxIntegral[15,-1,1,Integrand],{Infinity,20}]
-m50:=N[ApproxIntegral[50,-1,1,Integrand],{Infinity,20}]
-correct := N[Integrate[Integrand[x],{x,-1,1}],{Infinity,20}]
+Integrand[x_] := 1/((1+2x^2)^5)
+m15 := N[ApproxIntegral[15, -1, 1, Integrand], {Infinity, 20}]
+m50 := N[ApproxIntegral[50, -1, 1, Integrand], {Infinity, 20}]
+correct  := N[Integrate[Integrand[x], {x, -1, 1}], {Infinity, 20}]
 
 Print["1 задача)"]
-Print["При M=15:        ",m15]
-Print["Разлика с точен: ", N[Abs[m15-correct],{Infinity,20}]]
-Print["При M=50:        ",m50]
-Print["Разлика с точен: ", N[Abs[m50-correct],{Infinity,20}]]
+Print["При M=15:        ", m15]
+Print["Разлика с точен: ", N[correct-m15, {Infinity, 20}]]
+Print["При M=50:        ", m50]
+Print["Разлика с точен: ", N[correct-m50, {Infinity, 20}]]
 
 (*----------
 * 2 задача
 *----------*)
 
 (* Намиране Pn *)
-Pncoeff [xs_,f_]:= With[
+Pncoeff [xs_, f_] := With[
   {
     k=Length[xs],
     x0=First[xs],
@@ -39,40 +39,44 @@ Pncoeff [xs_,f_]:= With[
       k==1
     },
     {
-      (Pncoeff[Drop[xs,1],f]-Pncoeff[Drop[xs,-1],f])/(xk-x0),
+      (Pncoeff[Drop[xs, 1], f]-Pncoeff[Drop[xs, -1], f])/(xk-x0),
       x0!=xk
     },
     {
-      D[f,{x,k}][x0]/((k-1)!),
+      (D[f[x], {x, k-1}]/.x->x0)/((k-1)!),
       x0==xk
     }}]
 ]
 
-Pn[f_,xsWithDup_]:=With[
-  { xs = DeleteDuplicates[xsWithDup] },
-  Function[x,Sum[
-    Pncoeff[Take[xs,i],f]*
-    Product[x-xs[[j]],{j,1,i-1}],
-    {i,1,Length[xs]}
+Pn[f_, xsWithDup_] := With[
+  { xs = xsWithDup },
+  Function[x, Sum[
+    FullSimplify[Pncoeff[Take[xs, i], f]*
+    Product[x-xs[[j]], {j, 1, i-1}]],
+    {i, 1, Length[xs]}
   ]]
 ]
 
-f[x_]:=Piecewise[{
-  {Cos[3x],x<=Pi},
-  {x-Pi-1,x>Pi}
+f[x_] := Piecewise[{
+  {Cos[3x], x<=Pi},
+  {x-Pi-1, x>Pi}
 }]
-values:={9Pi/10,10Pi/11,11Pi/10}
-newtonpolyn:=Pn[f,values]
+values := {9Pi/10, 9Pi/10, 9Pi/10, 10Pi/11, 10Pi/11, 11Pi/10}
 
-Collect[FullSimplify[InterpolatingPolynomial[{
-  {9Pi/10,f[9Pi/10]},
-  {10Pi/11,f[10Pi/11]},
-  {11Pi/10,f[11Pi/10]}
-},x]],x]
+
+newtonpolyn := Pn[f, values]
 
 Print["2 задача)"]
-Print["Полином: ",Collect[FullSimplify[newtonpolyn[x]],x]]
+Print["Полином: ", newtonpolyn[x]]
+
+(*
+InterpolatingPolynomial[{
+  {9Pi/10, f[9Pi/10]},
+  {10Pi/11, f[10Pi/11]},
+  {11Pi/10, f[11Pi/10]}
+}, x]
+*)
 
 (* Графика разлика *)
 Print["Графика на разлика:"]
-Plot[Abs[f[z]-newtonpolyn[z]],{z,-2Pi,2Pi}]
+Plot[Abs[f[z]-newtonpolyn[z]], {z, -2Pi, 2Pi}]