I want to make a function of x that uses loop for (x-x(i))

For example, if i have an array x = [1 2 4]

I want to get the output, which is a function that looks something like this,

f =@(x) (x-1) + (x-1)*(x-2) + (x-1)*(x-2)*(x-4)

I am currently trying to get it through this code below, but I still haven't found the way to make the output like the above

%%

x = [1 3 5];

a = 2;

b = 3;

for i = 1:3

c = x(i);

fc = @(a,b,c) str2func(sprintf('@(x) %.3f.*x.^2 + %.3f + (x - %.3f)',a,b,c));

a = a + 1;

b = b + 1;

f = fc(a,b,c)

end

and also, what if for example i want to add another array, Y = [ 3 4 6]

and i want the output to look like this:

Y(1) * (x-1) + Y(2) * (x-1)*(x-3) + Y(3) * (x-1)*(x-3)*(x-5)

with the X = [1 3 5]

[Steven Lord]

Do you need it to be displayed that way or do you just need it to perform those computations?

If you had a Y array with a thousand elements, do you really want that large a function handle display?

[Clara Vivian]

actually I want to make a function that has the output of newton and lagrange interpolation polynomials with the degree of k. @Steven Lord

Answer 1

[Voss]

Here's one way:

mono_x = arrayfun(@(x)sprintf('(x-%.3f)',x),x,'UniformOutput',false);
prod_x = arrayfun(@(i)sprintf('%s*',mono_x{1:i}),1:numel(x),'UniformOutput',false);
prod_x = cellfun(@(x)x(1:end-1),prod_x,'UniformOutput',false);
prod_x(end+1,:) = {'+'};
prod_x = strcat(prod_x{:});
prod_x(end) = [];
f = str2func(['@(x)' prod_x]);

[Clara Vivian]

@Benjamin what if for example i want to add another array, Y = [ 3 4 6]

and i want the output to look like this:

Y(1) * (x-1) + Y(2) * (x-1)*(x-3) + Y(3) * (x-1)*(x-3)*(x-5)

with the X = [1 3 5]

Answer 2

[Mathieu NOE]

hello

my 2 cents suggestion :

%%
x = [1 3 5];

a = 2;
b = 3;

%%%% main loop
strc = [];
for i = 1:3
    str = ['(x-' num2str(x(i)) ')'];
    strc = [strc str '.*'];
end

strc2 = ['@(x) ' strc(1:end-2)];
fhandle = str2func(strc2)

%numerical application
fhandle(a)
fhandle(b)
fhandle([a b])

Answer 3

[Steven Lord]

If the display isn't important:

x = [1 2 4];
f1 = @(value) sum(cumprod(value-x))

f1 = function_handle with value:
    @(value)sum(cumprod(value-x))

f2 =@(x) (x-1) + (x-1)*(x-2) + (x-1)*(x-2)*(x-4)

f2 = function_handle with value:
    @(x)(x-1)+(x-1)*(x-2)+(x-1)*(x-2)*(x-4)

To spot check:

[f1(3); f2(3)]

ans = 2×1

2 2

[f1(pi); f2(pi)]

ans = 2×1

2.4878 2.4878