clear all
clc
syms x;
A=(x^3)/(exp(x)-1);
B=int(A,0,1)
When I run this code then it shows an expression like below
B =
log(1 - exp(1)) + 3*polylog(2, exp(1)) - 6*polylog(3, exp(1)) + 6*polylog(4, exp(1)) - limit(x^3*log(1 - exp(x)) + 6*polylog(4, exp(x)) + 3*x^2*polylog(2, exp(x)) - x^4/4 - 6*x*polylog(3, exp(x)), x == 0, Right) - 1/4
What is the polylog in the expression. But, i need one definite value, Is there any way to solve this issue so that i get a value. please anyone help me......
X = eps:0.01:1;
Y = (X.^3)./(exp(X)-1.0);
Z = trapz(X,Y);
Related
I would like to know if there is another form of coding that could be used (within CPLEX) to have the same results as in the code below:
dvar int+ n[1..2];
dexpr float z = - 3*n[1]^2 - 4*n[2]^2 - 4*n[1]*n[2]
+ 5000*n[1] + 2000*n[2];
maximize z;
subject to {
ct1: - 7*n[1] - 2*n[2] <= -3000;
ct2: - 5 * n[1] - 3 *n[2] <= -2000;
}
within CPLEX you could also use Constraint Programming:
using CP;
dvar int+ n[1..2] in 0..10000;
dexpr float z = - 3*n[1]^2 - 4*n[2]^2 - 4*n[1]*n[2]
+ 5000*n[1] + 2000*n[2];
maximize z;
subject to {
ct1: - 7*n[1] - 2*n[2] <= -3000;
ct2: - 5 * n[1] - 3 *n[2] <= -2000;
}
gives the same result but relies on CPOptimizer
My problem is simple.
I am searching a mathematical function to distribute number over an interval.
For example I have this list :
[2; 4; 9; 14]
And in my case I wish
2 -> 1 = f(2)
14 -> 20 = f(14)
4 -> f(4) = ?
9 -> f(9) = ?
This is just an example I am searching for f(x).
Someone would have any idea ?
Thanks for advance ! :)
If you want a linear function, then:
f(x) = lowerFunc + (x - lowerX) * (upperFunc - lowerFunc) / (upperX - lowerX),
where:
lowerFunc: function value at the lower end
upperFunc: function value at the upper end
lowerX: x parameter at the lower end
upperX: x parameter at the upper end.
For your example:
f(x) = 1 + (x - 2) * (20 - 1) / (14 - 2)
= 1 + (x - 2) * 19/12
f(2) = 1
f(4) = 4.1666
f(9) = 12.08333
f(14) = 20
I'm writing a simple 2D top-down game in Python 3 using tkinter. All the collidable objects are either circles/arcs or lines. I wrote the following method to detect when a circle hits a line:
I am using the formulas y = mx + b and r^2 = (x-h)^2 + (y-k)^2
def CheckHitCToL(self, LX0, LY0, LX1, LY1, CX0, CX1, Tab):
try:
H = self.Creatures[Tab].X
K = self.Creatures[Tab].Y
R = abs((CX0 - CX1) / 2)
M = (LY0 - LY1) / (LX0 - LX1)
B = M * (-LX1) + LY1
QA = (M * M) + 1
QB = (-H - H) + (((B - K) * M) * 2)
QC = (H * H) + ((B - K) * (B - K)) - (R * R)
X = (- QB + sqrt((QB * QB) - (4 * QA * QC))) / (2 * QA)
Y = (M * X) + B
if ((X <= LX0 and X >= LX1) or (X >= LX0 and X <= LX1)) and ((Y <= LY0 and Y >= LY1) or (Y >= LY0 and Y <= LY1)):
return True
else:
return False
except:
return False
My problem is when you have a vertical line, M (Or the slope) is (LY0 - LY1) / 0. (This is because the slope is equal to rise/run, and vertical lines don't have a run, just a rise) Which of course returns an error, caught by try except, which then informs my movement method that no collision has taken place. Of course I can simply move the "try:" down a few lines, but it's still going to throw an error. How can I adapt this program to not throw an error when working with a vertical line?
Well, the most obvious method would involve using if( (LX0 - LX1)==0 ) and doing this case separately. In such cases, you need to check whether distance between LX0 and CX0 is equal to the radius of circle.
You can use another forms of line equation -
implicit A*x + B*y + C = 0
or parametric x = LX0 + t * (LX1 - LX0), y = LY0 + t *(LY1 - LY0)
with appropriate modification of calculations
Given the input:
double x1,y1,x2,y2;
How can I find the general form equation (double a,b,c where ax + by + c = 0) ?
Note: I want to be able to do this computationally. So the equivalent for slope-intercept form would be something like:
double dx, dy;
double m, b;
dx = x2 - x1;
dy = y2 - y1;
m = dy/dx;
b = y1;
Obviously, this is very simple, but I haven't been able to find the solution for the general equation form (which is more useful since it can do vertical lines). I already looked in my linear algebra book and two books on computational geometry (both too advanced to explain this).
If you start from the equation y-y1 = (y2-y1)/(x2-x1) * (x-x1) (which is the equation of the line defined by two points), through some manipulation you can get (y1-y2) * x + (x2-x1) * y + (x1-x2)*y1 + (y2-y1)*x1 = 0, and you can recognize that:
a = y1-y2,
b = x2-x1,
c = (x1-x2)*y1 + (y2-y1)*x1.
Get the tangent by subtracting the two points (x2-x1, y2-y1). Normalize it and rotate by 90 degrees to get the normal vector (a,b). Take the dot product with one of the points to get the constant, c.
If you start from the equation of defining line from 2 points
(x - x1)/(x2 - x1) = (y - y1)/(y2 - y1)
you can end up with the next equation
x(y2 - y1) - y(x2 - x1) - x1*y2 + y1*x2 = 0
so the coefficients will be:
a = y2 - y1
b = -(x2 - x1) = x1 - x2
c = y1*x2 - x1*y2
My implementation of the algorithm in C
inline v3 LineEquationFrom2Points(v2 P1, v2 P2) {
v3 Result;
Result.A = P2.y - P1.y;
Result.B = -(P2.x - P1.x);
Result.C = P1.y * P2.x - P1.x * P2.y;
return(Result);
}
Shortcut steps:
"Problem : (4,5) (3,-7)"
Solve:
m=-12/1 then
12x-y= 48
"NOTE:m is a slope"
COPY THE NUMERATOR, AFFIX "X"
Positive fraction Negative sign on between.
(tip: simmilar sign = add + copy the sign)
1.Change the second set into opposite signs,
2.ADD y1 to y2 (means add or subtract them depending of the sign),
3.ADD x1 to x2 (also means add or subtract them depending of the sign),
4.Then Multiply 12 and 1 to any of the problem set.
After that "BOOM" Tada!, you have your answer
#include <stdio.h>
main()
{
int a,b,c;
char x,y;
a=5;
b=10;
c=15;
x=2;
y=3;
printf("the equation of line is %dx+%dy=%d" ,a,b,c);
}
This is a geometry question.
I have a line between two points A and B and want separate it into k equal parts. I need the coordinates of the points that partition the line between A and B.
Any help is highly appreciated.
Thanks a lot!
You just need a weighted average of A and B.
C(t) = A * (1-t) + B * t
or, in 2-D
Cx = Ax * (1-t) + Bx * t
Cy = Ay * (1-t) + By * t
When t=0, you get A.
When t=1, you get B.
When t=.25, you a point 25% of the way from A to B
etc
So, to divide the line into k equal parts, make a loop and find C, for t=0/k, t=1/k, t=2/k, ... , t=k/k
for(int i=0;i<38;i++)
{
Points[i].x = m_Pos.x * (1 - (i/38.0)) + m_To.x * (i / 38.0);
Points[i].y = m_Pos.y * (1 - (i/38.0)) + m_To.y * (i / 38.0);
if(i == 0 || i == 37 || i == 19) dbg_msg("CLight","(%d)\nPos(%f,%f)\nTo(%f,%f)\nPoint(%f,%f)",i,m_Pos.x,m_Pos.y,m_To.x,m_To.y,Points[i].x,Points[i].y);
}
prints:
[4c7cba40][CLight]: (0)
Pos(3376.000000,1808.000000)
To(3400.851563,1726.714111)
Point(3376.000000,1808.000000)
[4c7cba40][CLight]: (19)
Pos(3376.000000,1808.000000)
To(3400.851563,1726.714111)
Point(3388.425781,1767.357056)
[4c7cba40][CLight]: (37)
Pos(3376.000000,1808.000000)
To(3400.851563,1726.714111)
Point(3400.851563,1726.714111)
which looks fine but then my program doesn't work :D.
but your method works so thanks