I have rewitten this as the following,
NN = 2000;
mu = 0;
sigma = 10;
task3a = Table[Random[NormalDistribution[mu,sigma]], {NN}];
ListPlot[task3a, AxesLabel->{" No.obs.", "value of the obs"},
PlotLabel -> " Normal Distribution"];
a= 0.6;
b =-0.45;
task4a = Table [0, {NN}] ;
task4a[[1]] = task3a[[1]];
task4a[[2]] = a*task4a[[1]] +task3a[[2]];
For [i = 3, i <= NN, i++,
task4a[[i]] = a*task4a[[i -1]]
+ b*task4a[[i -2]]
+ task3a[[i]];
]
ListPlot[task4a, AxesLabel -> {"No.obs.", "value of the obs"}, PlotLabel-> "Autoregression process for norm.dist. white noise"];
(**************************************************)
avg = (1/NN) * Sum[task4a[[i]], {1, NN}];
task5a = Table[0, {33}] ;
For [k = 0, k <= 32, k++,
task5a[[k + 1]] = (1/(NN-k)) *
Sum[(task4a[[i]] -avg)*(task4a[[i + k]] - avg), {1, NN-k}] ;
]
ListPlot[task5a, PlotLabel ->"K estimator for AR(2) normal distribution", Joined -> True, PlotRange ->All, AxesLabel -> {"k", "K(k)"}] ;
Error Message
The above code is generating the following error message Sum::itraw,
Looks like, there is some problem with the for loop.
I cannot understand.
As #agentyp mentioned. Problem is sum indexes in two places. After execution of this code program works correctly.
NN = 2000;
mu = 0;
sigma = 10;
task3a = Table[Random[NormalDistribution[mu, sigma]], {NN}];
ListPlot[task3a, AxesLabel -> {" No.obs.", "value of the obs"},
PlotLabel -> " Normal Distribution"];
a = 0.6;
b = -0.45;
task4a = Table[0, {NN}];
task4a[[1]] = task3a[[1]];
task4a[[2]] = a*task4a[[1]] + task3a[[2]];
For[i = 3, i <= NN, i++,
task4a[[i]] = a*task4a[[i - 1]] + b*task4a[[i - 2]] + task3a[[i]];]
ListPlot[task4a, AxesLabel -> {"No.obs.", "value of the obs"},
PlotLabel -> "Autoregression process for norm.dist. white noise"];
(**************************************************)
avg = (1/NN)*
Sum[task4a[[i]], {i, 1, NN}];
task5a = Table[0, {33}];
For[k = 0, k <= 32, k++,
task5a[[k + 1]] = (1/(NN - k))*
Sum[(task4a[[i]] - avg)*(task4a[[i + k]] - avg), {i, 1, NN - k}];]
ListPlot[task5a,
PlotLabel -> "K estimator for AR(2) normal distribution",
Joined -> True, PlotRange -> All, AxesLabel -> {"k", "K(k)"}]
Related
Does anyone know what does /; mean for example:V[n_][i_/;i<=imax,0];=V[n][i,0]=0 in Mathematica?
It's part of a program to draw the eletrical potential function of a rectangular metal trough using the finite-difference methods.
Here's the improved one, but still cannot work.
V[0][i_, j_] := 0;
tol = 0.0025;
imax = 20; jmax = 20;
V[n_][i_, 0] := V[n][i, 0] = 0;
V[n_][i_, jmax] := V[n][i, jmax] = 100*Sin[0.05*Pi*i];
V[n_][0, j_] := V[n][0, j] = 0;
V[n_][imax, j_] := V[n][imax, j] = 0;
V[n_][i_, j_] := V[n][i, j] = (1/4)*(V[n - 1][i + 1, j] +
V[n - 1][i - 1, j] + V[n - 1][i, j + 1] + V[n - 1][i, j - 1]);
For[m = 1, Max[Table[Abs[V[m][i, j] - V[m - 1][i, j]], {i, 1, imax - 1}, {j, 1, jmax - 1}]] >= tol, m++;
If[m > 20, Break[]]];
Print[m];
Show[ListPlot3D[Table[V[m][i, j], {j, 0, 20}, {i, 0, 20}]], BoxRatios -> {1, 1, 0.85}, PlotRange -> {0, 1}, Axes -> True, AxesLabel -> {"x", "y", "V"}]
I've already get the point through the reference of Wolfram. And here is the web
https://reference.wolfram.com/language/ref/Condition.html. Thanks for #agentp help
I am beginner in Mathematica. I write code in mathematica for finding parametric fractal dimension. But it doesn't work. Can someone explain me where I am wrong.
My code is:
delta[0] = 0.001
lambda[0] = 0
div = 0.0009
a = 2
b = 2
terms = 100
fx[0] = NSum[1/n^b, {n, 1, terms}]
fy[0] = 0
For[i = 1, i < 11, i++,
delta[i] = delta[i - 1] + div;
j = 0
While[lambda[j] <= Pi,
j = j + 1;
lambda[j] = lambda[j - 1] + delta[i];
fx[j] = NSum[Cos[n^a*lambda[j]]/n^b, {n, 1, terms}];
fy[j] = NSum[Sin[n^a*lambda[j]]/n^b, {n, 1, terms}];
deltaL[j] = Sqrt[[fx[j] - fx[j - 1]]^2 + [fy[j] - fy[j - 1]]^2];
]
Ldelta[i] = Sum[deltaL[j], {j, 1, 10}];
]
data = Table[{Log[delta[i]], Log[Ldelta[i]]}, {i, 1, 10}]
line = Fit[data, {1, x}, x]
ListPlot[data]
i want to translate my C++ code to wolfram, to improve my calcs.
C++ code
for(int i = 0; i < N - 1; ++i){
matrix[i][i] += L / 3 * uCoef - duCoef / 2 - (double)du2Coef/L;
matrix[i][i+1] += L / 6 * uCoef + duCoef / 2 + (double)du2Coef/L;
matrix[i+1][i] += L / 6 * uCoef - duCoef / 2 + (double)du2Coef/L;
matrix[i+1][i+1] += L / 3 * uCoef + duCoef / 2- (double)du2Coef/L;
}
all this coef are const, N - size of my matrix.
In[1]:= n = 4; uCoef = 2; duCoef = 3; du2Coef = 7; L = 11.;
matrix = Table[0, {n}, {n}];
For[i = 1, i < n, ++i,
matrix[[i, i]] += L/3*uCoef - duCoef/2 - du2Coef/L;
matrix[[i, i+1]] += L/6*uCoef - duCoef/2 - du2Coef/L;
matrix[[i+1, i]] += L/6*uCoef + duCoef/2 + du2Coef/L;
matrix[[i+1, i+1]] += L/3*uCoef - duCoef/2 + du2Coef/L];
matrix
Out[4]= {
{5.19697, 1.5303, 0, 0},
{5.80303, 11.6667, 1.5303, 0},
{0, 5.80303, 11.6667, 1.5303},
{0, 0, 5.80303, 6.4697}}
Each character that has been changed from your original is hinting there is a fundamental difference between C++ and Mathematica
You should use SparseArray for such banded arrays in mathematica:
n = 5; uCoef = 2; duCoef = 3; du2Coef = 7; L = 11.;
matrix = SparseArray[
{{1, 1} -> L/3*uCoef - duCoef/2 - du2Coef/L,
{i_ /; 1 < i < n, i_} -> -duCoef + 2 L uCoef/3 ,
{n, n} -> ( L/3 uCoef - duCoef/2 + du2Coef/L ),
Band[{1, 2}] -> L/6 uCoef - duCoef/2 - du2Coef/L,
Band[{2, 1}] -> L/6 uCoef + duCoef/2 + du2Coef/L}, {n, n}];
MatrixForm#matrix
Even if you insist on the For loop, initialize the matrix as :
matrix = SparseArray[{{_, _} -> 0}, {n, n}];
I am trying to solve an D-equation and do not know y[0], but I know y[x1]=y1.
I want to solve the DSolve only in the relevant xrange x=[x1, infinitny].
How could it work?
Attached the example that does not work
dsolv2 = DSolve[{y'[x] == c*0.5*t12[x, l2]^2 - alpha*y[x], y[twhenrcomesin] == zwhenrcomesin, x >= twhenrcomesin}, y[x], x]
dsolv2 = Flatten[dsolv2]
zsecondphase[x_] = y[x] /. dsolv2[[1]]
I am aware that DSolve does not allow the inequality condition but I put it in to explain you what I am looking for (t12[x,l2] will give me a value only depending on x since l2 is known).
EDIT
t12[j24_, lambda242_] := (cinv1 - cinv2)/(cop2 - cop1 + (h2*lambda242)*E^(p*j24));
cinv1 = 30; cinv2 = 4; cinv3 = 3; h2 = 1.4; h3 = 1.2; alpha = 0.04; z = 50; p = 0.06; cop1 = 0; cop2 = 1; cop3 = 1.3; teta2 = 0.19; teta3 =0.1; co2 = -0.6; z0 = 10;l2 = 0.1;
Your equation is first order and linear, so you can get a very general solution :
generic = DSolve[{y'[x] == f[x] - alpha*y[x], y[x0] == y0}, y[x], x]
Then you can substitute your specific term :
c = 1;
x0 = 1;
y0 = 1;
solution[x_] = generic[[1, 1, 2]] /. {f[x_] -> c*0.5*t12[x, l2]^2}
Plot[solution[x], {x, x0, 100}]
What is wrong with this example?
t12[x_] := Exp[-x .01] Sin[x];
dsolv2 = Chop#DSolve[{y'[x] == c*0.5*t12[x]^2 - alpha*y[x], y[1] == 1}, y[x], x];
Plot[y[x] /. dsolv2[[1]] /. {alpha -> 1, c -> 1}, {x, 1, 100}, PlotRange -> Full]
Edit
Regarding your commentary:
Try using a piecewise function to restrict the domain:
t12[x_] := Piecewise[{{ Exp[-x .01] Sin[x], x >= 1}, {Indeterminate, True}}] ;
dsolv2 = Chop#DSolve[{y'[x] == c*0.5*t12[x]^2 - alpha*y[x], y[1] == 1}, y[x], x];
Plot[y[x] /. dsolv2[[1]] /. {alpha -> 1, c -> 1}, {x, 1, 100}, PlotRange -> Full]
I'm learning about dynamic programming via the 0-1 knapsack problem.
I'm getting some weird Nulls out from the function part1. Like 3Null, 5Null etc. Why is this?
The code is an implementation of:
http://www.youtube.com/watch?v=EH6h7WA7sDw
I use a matrix to store all the values and keeps, dont know how efficient this is since it is a list of lists(indexing O(1)?).
This is my code:
(* 0-1 Knapsack problem
item = {value, weight}
Constraint is maxweight. Objective is to max value.
Input on the form:
Matrix[{value,weight},
{value,weight},
...
]
*)
lookup[x_, y_, m_] := m[[x, y]];
part1[items_, maxweight_] := {
nbrofitems = Dimensions[items][[1]];
keep = values = Table[0, {j, 0, nbrofitems}, {i, 1, maxweight}];
For[j = 2, j <= nbrofitems + 1, j++,
itemweight = items[[j - 1, 2]];
itemvalue = items[[j - 1, 1]];
For[i = 1, i <= maxweight, i++,
{
x = lookup[j - 1, i, values];
diff = i - itemweight;
If[diff > 0, y = lookup[j - 1, diff, values], y = 0];
If[itemweight <= i ,
{If[x < itemvalue + y,
{values[[j, i]] = itemvalue + y; keep[[j, i]] = 1;},
{values[[j, i]] = x; keep[[j, i]] = 0;}]
},
y(*y eller x?*)]
}
]
]
{values, keep}
}
solvek[keep_, items_, maxweight_] :=
{
(*w=remaining weight in knapsack*)
(*i=current item*)
w = maxweight;
knapsack = {};
nbrofitems = Dimensions[items][[1]];
For[i = nbrofitems, i > 0, i--,
If[keep[[i, w]] == 1, {Append[knapsack, i]; w -= items[[i, 2]];
i -= 1;}, i - 1]];
knapsack
}
Clear[keep, v, a, b, c]
maxweight = 5;
nbrofitems = 3;
a = {5, 3};
b = {3, 2};
c = {4, 1};
items = {a, b, c};
MatrixForm[items]
Print["Results:"]
results = part1[items, 5];
keep = results[[1]];
Print["keep:"];
Print[keep];
Print["------"];
results2 = solvek[keep, items, 5];
MatrixForm[results2]
(*MatrixForm[results[[1]]]
MatrixForm[results[[2]]]*)
{{{0,0,0,0,0},{0,0,5 Null,5 Null,5 Null},{0,3 Null,5 Null,5 Null,8 Null},{4 Null,4 Null,7 Null,9 Null,9 Null}},{{0,0,0,0,0},{0,0,Null,Null,Null},{0,Null,0,0,Null},{Null,Null,Null,Null,Null}}}
While your code gives errors here, the Null problem occurs because For[] returns Null. So add a ; at the end of the outermost For statement in part1 (ie, just before {values,keep}.
As I said though, the code snippet gives errors when I run it.
In case my answer isn't clear, here is how the problem occurs:
(
Do[i, {i, 1, 10}]
3
)
(*3 Null*)
while
(
Do[i, {i, 1, 10}];
3
)
(*3*)
The Null error has been reported by acl. There are more errors though.
Your keep matrix actually contains two matrices. You need to call solvek with the second one: solvek[keep[[2]], items, 5]
Various errors in solvek:
i -= 1 and i - 1 are more than superfluous (the latter one is a coding error anyway). The i-- in the beginning of the For is sufficient. As it is now you're decreasing i twice per iteration.
Append must be AppendTo
keep[[i, w]] == 1 must be keep[[i + 1, w]] == 1 as the keep matrix has one more row than there are items.
Not wrong but superfluous: nbrofitems = Dimensions[items][[1]]; nbrofitems is already globally defined
The code of your second part could look like:
solvek[keep_, items_, maxweight_] :=
Module[{w = maxweight, knapsack = {}, nbrofitems = Dimensions[items][[1]]},
For[i = nbrofitems, i > 0, i--,
If[keep[[i + 1, w]] == 1, AppendTo[knapsack, i]; w -= items[[i, 2]]]
];
knapsack
]