New answers tagged parametric-functions
4
Not a one-liner, but straightforward.
z1 = Table[Table[3*k*k, {k, i, i+3}], {i, 1, 256, 8}];
z2 = Table[{1,1,1,1}, {i, 1, 256, 8}];
result = Riffle[z1,z2] // Flatten
3
BlockMap[{#,ConstantArray[1,4]}&,f,4,8]//Flatten
or
BlockMap[{#[[;;4]], Unitize@#[[5;;]]}&,f,8]//Flatten
{3, 12, 27, 48, 1, 1, 1, 1, 243, 300, 363, 432, 1, 1, 1, 1, 867, 972, 1083, 1200, 1, 1, 1, 1, 1875, 2028, 2187, 2352, 1, 1, 1, 1, 3267, 3468, 3675, 3888, 1, 1, 1, 1, 5043, 5292, 5547, 5808, 1, 1, 1, 1, 7203, 7500, 7803, 8112, 1, 1, 1, 1, 9747, ...
5
g[k_Integer] := 3 k^2 /; MemberQ[{1, 2, 3, 4}, Mod[k, 8, 1]];
g[k_Integer] := 1 /; MemberQ[{5, 6, 7, 8}, Mod[k, 8, 1]];
g /@ Range[256]
7
To answer your question directly, a loop could be written like this:
f = Table[3*k*k, {k, 1, 16}];
Do[
f[[4 i + j]] = 1;
,
{i, {1, 3}},
{j, 1, 4}
];
f
{3, 12, 27, 48, 1, 1, 1, 1, 243, 300, 363, 432, 1, 1, 1, 1}
A non-loop alternative is this:
f = Table[3*k*k, {k, 1, 16}];
pos = Flatten@Table[Range[4] + 4 n, {n, {1, 3}}];
f[[pos]] = 1;
f
{3, 12, ...
5
Join @@ MapAt[ConstantArray[1, 4] &, Partition[f, 4], {2 ;; ;; 2}]
{3, 12, 27, 48, 1, 1, 1, 1, 243, 300, 363, 432, 1, 1, 1, 1}
1
You can also use the option NormalsFunction:
ParametricPlot3D[{u, v, Exp[u] Cos[u - v]}, {u, 1, 3}, {v, 1, 5},
Boxed -> False,
ViewPoint -> {0, 0, ∞},
Axes -> False,
Mesh -> None,
ColorFunction -> "TemperatureMap",
NormalsFunction -> ({1, 1, 0} &)]
Use ColorFunction -> (Blend[{White, Orange}, #3] &) (as in ...
2
You could use white ambient light and a custom ColorFunction based on a Blend of White and Darker@Orange.
ParametricPlot3D[{u, v, Exp[u]*Cos[u - v]}, {u, 1, 3}, {v, 1, 5}
, Boxed -> False
, ViewPoint -> {0, 0, Infinity}
, Axes -> False
, ColorFunction -> Function[{x, y, z, u, v}, Blend[{White, Darker@Orange}, z]]
, Mesh -> None
, ...
2
You could follow this example from the documentation and use Glow:
ParametricPlot3D[{u, v, Exp[u]*Cos[u - v]}, {u, 1, 3}, {v, 1, 5},
Boxed -> False, ViewPoint -> {0, 0, Infinity}, Axes -> False,
ColorFunction ->
Function[{x, y, z}, Glow[ColorData["TemperatureMap", z]]],
Mesh -> None, Lighting -> None]
Here is an example ...
1
To plot the volume try ParametricRegion as follows:
First do linear interpolation of your expression
f0 = {(1 - \[CurlyEpsilon])*x1 + \[CurlyEpsilon]*x2, (1 - \[CurlyEpsilon])*y1 + \[CurlyEpsilon]*y2, (1 - \[CurlyEpsilon])*x1*y1 + \[CurlyEpsilon]*x2*y2} /. \[CurlyEpsilon] -> 0
f1 = {(1 - \[CurlyEpsilon])*x1 + \[CurlyEpsilon]*x2, (1 - \[CurlyEpsilon])*y1 + ...
1
We can use NDSolve[] to solve this problem as follows:
system[j_] := {A1'[x] ==
I*\[Kappa]1*Conjugate[A2[x]]*A3[x]*A4[x]*
E^(-I*\[CapitalDelta]kl*x) +
I*A1[x]*(\[Alpha]11*Abs[A1[x]]^2 + \[Alpha]12*
Abs[A2[x]]^2 + \[Alpha]13*Abs[A3[x]]^2 + \[Alpha]14*
Abs[A4[x]]^2),
A2'[x] ==
I*\[Kappa]2*Conjugate[A1[x]]*A3[x]*A4[x]*...
1
After modifying ParametricNDSolve to ParametricNDSolveValue (without argument brackets ...[x])
DEsols = ParametricNDSolveValue[system, {A1 , A2 , A3 , A4 }, {x, 0, 2000}, {j}]
you can access A4
Plot[sols[0][[4]][x], {x, 0, 2000}]
Unfortunately your system seems to be solvable only for j==0
Top 50 recent answers are included
