here's what I wrote:
public class Math {
public static void main (String[] args){
double degrees = Double.parseDouble(args[0]);
double s = Math.sin(degrees);
double c = Math.cos(degrees);
double x = s*s + c*s;
System.out.println(x);
}
}
I want to enter a number as args[0] that goes into sin() and cos(). then I want to add the 2 variables making it equal 1, because sin² + cos² = 1. What am I doing wrong?
EDIT: i made changes to my code to s*s + c*c, but i'm still getting the same error.
I'm also getting this error:
2 errors found:
File:... [line: 4]
Error: cannot find symbol
symbol: method sin(double)
location: class Math
File:... [line: 5]
Error: cannot find symbol
symbol: method cos(double)
location: class Math
You are not squaring each term so you are calculating and printing sin(x) + cos(x). Replace
double x = s + c;
with
double x = s*s + c*c;
and you should get the right behaviour.
Here's a list of what I see going wrong:
your class is called Math, but you're making a reference to the system's Math by using Math.sin() and Math.cos() -> rename your class to avoid the ambiguity
you define double x = s*s + c*s;, which should of course be double x = s*s + c*c;
you expect Math.cos() and Math.sin() to take their arguments in degrees, while they actually expect radians. It just happens to work because the identity holds for any input, but remember this for your next assignment :)
Related
I am trying to create a composite type in Julia representing points on an elliptic curve.
Point are valid if satisfying y^2 == x^3 + a*x + b OR both x and y are equal to nothing. Note that the later case represents point at infinity.
I have come up with the below code but can't figure out how to account for point at infinity.
Is there a way to handle different exceptions in struct?
Can exception simply return a valid type instead of an error? e.g. if x == nothing && y == nothing then Point(nothing,nothing,a,b)
IntOrNothing = Union{Int,Nothing}
struct Point
x::IntOrNothing
y::IntOrNothing
a::Int
b::Int
Point(x,y,a,b) = x == nothing || y == nothing || y^2 != x^3 + a*x + b ? error("Point is not on curve") : new(x,y,a,b)
end
I would define two inner constructors for Point like this:
IntOrNothing = Union{Int,Nothing}
struct Point
x::IntOrNothing
y::IntOrNothing
a::Int
b::Int
Point(x::Nothing,y::Nothing,a,b) = new(x,y,a,b)
Point(x,y,a,b) = y^2 != x^3 + a*x + b ? error("Point is not on curve") : new(x,y,a,b)
end
as this would be most readable in my opinion.
Note that you will get MethodError if you call Point(nothing,2,1,3) but I guess from your code you do not care about the type of exception thrown as long as it is thrown on invalid data.
Does it solve your problem?
How do I evaluate the function in only one of its variables, that is, I hope to obtain another function after evaluating the function. I have the following piece of code.
deff ('[F] = fun (x, y)', 'F = x ^ 2-3 * y ^ 2 + x * y ^ 3');
fun (4, y)
I hope to get 16-3y ^ 2 + 4y ^ 3
If what you want to do is to write x = f(4,y), and later just do x(2) to get -36, that is called partial application:
Intuitively, partial function application says "if you fix the first arguments of the function, you get a function of the remaining arguments".
This is a very useful feature, and very common Functional Programming Languages, such as Haskell, but even JS and Python now are able to do it. It is also possible to do this in MATLAB and GNU/Octave using anonymous functions (see this answer). In Scilab, however, this feature is not available.
Workround
Nonetheless, Scilab itself uses a workarounds to carry a function with its arguments without fully evaluating. You see this being used in ode(), fsolve(), optim(), and others:
Create a list containing the function and the arguments to partial evaluation: list(f,arg1,arg2,...,argn)
Use another function to evaluate such list and the last argument: evalPartList(list(...),last_arg)
The implementation of evalPartList() can be something like this:
function y = evalPartList(fList,last_arg)
//fList: list in which the first element is a function
//last_arg: last argument to be applied to the function
func = fList(1); //extract function from the list
y = func(fList(2:$),last_arg); //each element of the list, from second
//to last, becomes an argument
endfunction
You can test it on Scilab's console:
--> deff ('[F] = fun (x, y)', 'F = x ^ 2-3 * y ^ 2 + x * y ^ 3');
--> x = list(fun,4)
x =
x(1)
[F]= x(1)(x,y)
x(2)
4.
--> evalPartList(x,2)
ans =
36.
This is a very simple implementation for evalPartList(), and you have to be careful not to exceed or be short on the number of arguments.
In the way you're asking, you can't.
What you're looking is called symbolic (or formal) computational mathematics, because you don't pass actual numerical values to functions.
Scilab is numerical software so it can't do such thing. But there is a toolbox scimax (installation guide) that rely on a the free formal software wxmaxima.
BUT
An ugly, stupid but still sort of working solution is to takes advantages of strings :
function F = fun (x, y) // Here we define a function that may return a constant or string depending on the input
fmt = '%10.3E'
if (type(x)==type('')) & (type(y)==type(0)) // x is string is
ys = msprintf(fmt,y)
F = x+'^2 - 3*'+ys+'^2 + '+x+'*'+ys+'^3'
end
if (type(y)==type('')) & (type(x)==type(0)) // y is string so is F
xs = msprintf(fmt,x)
F = xs+'^2 - 3*'+y+'^2 + '+xs+'*'+y+'^3'
end
if (type(y)==type('')) & (type(x)==type('')) // x&y are strings so is F
F = x+'^2 - 3*'+y+'^2 + '+x+'*'+y+'^3'
end
if (type(y)==type(0)) & (type(x)==type(0)) // x&y are constant so is F
F = x^2 - 3*y^2 + x*y^3
end
endfunction
// Then we can use this 'symbolic' function
deff('F2 = fun2(y)',' F2 = '+fun(4,'y'))
F2=fun2(2) // does compute fun(4,2)
disp(F2)
Given a vector, A=[1,2,10,10,10,1], [m,k]=max(A) returns k=3.
How to get the last index of the maximum element? In this example, I want to get 5.
The most succinct way I can think of is: [m,k]=max(A($:-1:1))
Is there a better way or does scilab provide a parameter to do this? Reversing a large vertex is not a good idea in any way.
Use the find command
You can use the find command to get all indices of the maximum:
indices = find(A==max(A))
last = max(indices)
Implement it yourself
Or if you want a single pass, you can implement it yourself:
//Create a c-function with your wanted behaviour
f1=['void max_array(int in_array[],int* in_num_elements,int *out_max, int *out_index)'
'{'
'int i;'
'*out_max=in_array[0];'
'*out_index=-1;'
'for (i=0; i<*in_num_elements; i++)'
'{'
'if(in_array[i]>=*out_max)'
'{'
'*out_max=in_array[i];'
'*out_index=i;'
'}'
'}'
'}'];
//Place it in a file in the current directory
mputl(f1,'max_array.c')
//Create the shared library (a gateway, a Makefile and a loader are
//generated.
ilib_for_link('max_array','max_array.c',[],"c")
//Load the library
exec loader.sce
//Create wrapper for readability
function [m,k] = last_max(vector)
[m, k] = call('max_array', vector, 1,'i', length(vector),2,'i', 'out',[1,1],3,'i',[1,1],4,'i');
// Because c is zero-indexed add 1
k = k + 1
endfunction
//Your data
A=[1,2,10,10,10,1];
//Call function on your data
[m,k] = last_max(A)
disp("Max value is " + string(m) + " at index " + string(k) )
I want to use instead of matlab integration command, a basic self created one. Do you have any Idea how to fix the error? If I use Matlab quad command, my algorithm works good but when I try to use my self created integral function,not suprisingly for sure, it does not work:(
M-File:
function y = trapapa(low, up, ints, fun)
y = 0;
step = (up - low) / ints;
for j = low : step : up
y = y + feval(fun,j);
end
y = (y - (feval(fun, low) + feval(fun, up))/2) * step;
Mean algorithm:
clear;
x0=linspace(0,4,3);
y=linspace(0,2,3);
for i=1:length(x0)
for j=1:length(y)
x(i,j)=y(j)+x0(i);
alpha=#(rho)((5-2*x(i,j)).*exp(y(j)-rho))./2;
%int(i,j)=quad(alpha,0,y(j))
int(i,j)=trapapa(alpha,0,y(j),10)
end
end
You are not following your function definition in the script. The fun parameter (variable alpha) is supposed to be the last one.
Try int(i,j)=trapapa(0,y(j),10,alpha)
I'm having some problems with my code. Here it is:
lambdaz = 1.2;
n = 24;
mu = 0.00055e9;
lambda = sym('lambda','clear');
W = (((2.*mu)./n.^2)).*((lambda.^n)+(lambdaz.^n)+((lambda.^-n).*(lambdaz.^-n))-3);
dW_dlambda = diff(W, lambda);
W2=(((2.*mu)./n.^2).*(lambda.^n))+(((2.*mu)./n.^2).*(lambdaz.^n))+(((2.*mu)./n.^2).*((lambda.^-n).*(lambdaz.^-n)))-(3.*((2.*mu)./n.^2))
dW2_dlambda=diff(W2,lambda)
x=((((lambda.^2).*(lambdaz))-1).^-1).*(dW_dlambda);
x2=((((lambda.^2).*(lambdaz))-1).^-1).*(dW2_dlambda)
P2 = int(x2,lambda)
P=int(x,lambda);
P=(0:1000:26700)
plot(lambda,P)
When I try to plot lambda against P I get the "conversion to double from sym is not possible" error message. I'm not particularly fantastic at Matlab so any help would be gratefully received!
The plot function only works for numeric inputs. Both lambda and P are symbolic expressions (at least before overwrote P by setting it equal to a vector after the integration) that cannot be directly converted to to floating point. You get the same error if try to something like double(sym('exp(x)')). You have two options. The first is the ezplot function in the Symbolic Toolbox:
...
P = int(x,lambda);
ezplot(P,[-5 5]); % Plot's P from lambda = -5 to lambda = 5
Or you can use the subs function:
...
P = int(x,lambda);
lambda = -5:0.01:5;
plot(lambda,real(subs(P,'lambda',lambda)))
axis([lambda(1) lambda(end) -1e15 1e15])
I used real to suppress a warning for negative values of lambda.