如何在双符号和中使用矩阵项? [英] How to use matrix entries in a double symsum?

问题描述

我正在尝试在函数中实现以下双重求和:

I am trying to implement the following double summation in a function:

f(x,y)=\sum_{k=0}^{S}\sum_{l=0}^{S}{a_{kl}x^ky^l}.

这是我的第一次尝试:

function [ a ] = MyFun( S )
a=randi([0 9],S+1);
syms x y k l;
f(x,y)=symsum(symsum(a(k,l)*x^k*y^l,l,1,S+1),k,1,S+1);
f(1,2)
end

实际上，我的代码稍后会在循环中对f进行求值，但这在这里似乎无关紧要.尝试类似MyFun(3)的操作会导致错误:

Actually, my code evaluates f in a loop later on, but that does not seem relevant here. Trying something like MyFun(3) results in an error:

使用sym/subsindex时出错(第766行)无效的索引编制或函数 定义.定义函数时，请确保参数为 符号变量和函数的主体是SYM表达式. 编制索引时，输入必须为数字，逻辑或:".

Error using sym/subsindex (line 766) Invalid indexing or function definition. When defining a function, ensure that the arguments are symbolic variables and the body of the function is a SYM expression. When indexing, the input must be numeric, logical, or ':'.

MyFun中的错误(第4行) f(x，y)=符号(symsum(a(k，l)* x ^(k-1)* y ^(l-1)，l，1，S + 1)，k，1，S + 1 );

Error in MyFun (line 4) f(x,y)=symsum(symsum(a(k,l)*x^(k-1)*y^(l-1),l,1,S+1),k,1,S+1);

如果从内部symsum中删除了a(k,l)*，则一切正常，因此我怀疑索引有问题.不能将符号变量k和l用作索引吗?如果没有，我该如何解决?

Everything works fine if a(k,l)* is removed from the inner symsum, so I suspect that there is something wrong with the indices. Is it not possible to use the symbolical variables k and l as indices? If not, how can I solve this?

推荐答案

使用符号值索引矩阵似乎无效.另外，您可以按如下方式使用逐元素乘法:

Indexing a matrix using a symbolic value does not seem to work. As an alternative you can use elementwise multiplication as follows:

function f = MyFun( S )
    a=randi([0 9],S+1);
    k = repmat((0:S)', 1, S+1);
    l = repmat((0:S), S+1, 1);
    syms x y;
    f(x, y) = sum(sum(a .* x.^k .* y.^l));
end

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