[英]Сonvert the coefficients of the Hermite polynomial into a function
I want to make a function from the output of Matlab Hermite function (for example, if we had an output from Hermite function [8 0 -12 0]
it would be 8x^3 - 12x
polynomial) and then integrate this function using the Simpson's 3/8 Rule .我想从 Matlab Hermite 函数的输出中创建一个函数(例如,如果我们有 Hermite 函数
[8 0 -12 0]
的输出,它将是8x^3 - 12x
多项式),然后使用Simpson's集成该函数3/8 规则。
I have already created a function in Matlab that integrate any function using this rule and also I have created function that returns coefficients of Hermite's polynomial (with the recursion relation) in the vector form.我已经在 Matlab 中创建了一个函数,该函数使用此规则集成任何函数,并且我还创建了以向量形式返回 Hermite 多项式(具有递归关系)的系数的函数。
My questions:我的问题:
[8 0 -12 0]
make this output 8x^3 - 12x
.[8 0 -12 0]
将此输出8x^3 - 12x
。 This output I will able to integrate. Code of Hermite polynomial function, where n is the order of the polynomial: Hermite 多项式函数的代码,其中 n 是多项式的阶数:
function h = hermite_rec(n)
if( 0==n ), h = 1;
elseif( 1==n ), h = [2 0];
else
h1 = zeros(1,n+1);
h1(1:n) = 2*hermite_rec(n-1);
h2 = zeros(1,n+1);
h2(3:end) = 2*(n-1)*hermite_rec(n-2);
h = h1 - h2;
end
Code of Simpson function, that integrate function using the Simpson 3/8 Rule.辛普森函数代码,使用辛普森 3/8 规则集成函数。 a is a lower limit of integral, b is a upper limit of integral:
a 为积分下限,b 为积分上限:
n = 3;
h = (b-a)/(3*n); %3h = (b-a)/n
IS2=0;
for i=1:n
IS2 = IS2+(f(a+(3*i-3)*h) + 3*f(a+(3*i-2)*h) + 3*f(a+(3*i-1)*h) + f(a+(3*i)*h))*3*h/8;
end
end
Thank you for any advice!感谢您的任何建议!
To create a polynomial function given its coefficients, you can use polyval
(see also anonynmous functions ):要在给定系数的情况下创建多项式函数,可以使用
polyval
(另请参见匿名函数):
p = [1 2]; % example. This represents the polynomial x+2
f = @(x) polyval(p, x); % anonymous function of x, assigned to function handle f
Now f
is a function that you can integrate numerically.现在
f
是一个可以数值积分的函数。
If you want to include this directly as part of your Hermite
function, just add something like this at the end:如果您想直接将其作为
Hermite
函数的一部分包含在内,只需在末尾添加如下内容:
h = @(x) polyval(p, x);
Then the Hermite
function will return a function (handle) representing the Hermite polynomial.然后
Hermite
函数将返回一个表示 Hermite 多项式的函数(句柄)。
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