matlab symfun vs匿名函数 [英] matlab symfun vs anonymous function

问题描述

在Matlab中使用symfun和匿名函数有什么区别？哪一个更好，即更快？看起来，我可以同时使用符号和实数。

在这里，他们讨论了内联函数和匿名函数之间的区别，但是不提及symfun。

解决方案

基本的MATLAB功能专为数值计算而设计，即使用浮点数。默认情况下，MATLAB变量和函数是数字的，这就是为什么在你的链接讨论中只有内联和匿名函数进行比较的原因。然而，使用符号数学工具箱可以使用象征性的表达和功能。这对解决数学问题非常有用，如精确求解，积分，使用任意精度算术或求解方程。然而，符号引擎被设计为聪明的，而不是快速的（毕竟，符号引擎迟早会对函数进行评估，但MATLAB设计的是对数值问题有效的）。只要有可能，人们应该更喜欢数值MATLAB函数，特别是那些经常可以扩展到以矢量化方式工作，沿着数组输入提供数组输出。

当面对混合问题（需要符号数学，但是也需要计算结果的昂贵评估），以参数化（符号）方式解决初始问题可能是最实际的 ，然后使用最后一个结果通过将其转换为适当的数字函数。您应该查看 matlabFunction 功能符号数学工具箱，它执行完全这一点，并适用于合理缩放功能（但这里是 b
$ b

请注意，虽然您可以使用公式定义匿名函数，如 f = @（x）3 * x ^ 2-2 ，这实际上会定义一个数字函数，它返回给定数字输入的值，例如 f（3）。如果您想要计算公式，请使用数字函数。符号数学应该保留给那些无法用基本数字特征精确求解的情况，比如计算多元标量场的精确梯度。

What is the difference between using a symfun and an anonymous function in Matlab? Which one is better i.e. faster? It seems like, I can use both for symbolic and real numbers.

Here they discuss the difference between inline and anonymous functions, but don't mention symfun.

解决方案

Basic MATLAB functionality is designed for numerical calculations, i.e. working with floating-point numbers. By default MATLAB variables and functions are numeric, and this is why in your linked discussion only inline and anonymous functions are compared.

However, using the Symbolic Math Toolbox one may use symbolic expressions and functions. This can be very useful for tackling mathematical problems such as exact differentiation, integration, working with arbitrary-precision arithmetic, or solving equations. However, the symbolic engine is designed to be smart, not to be fast (after all, sooner or later the symbolic engine must perform the evaluation of the function, but MATLAB was designed to be efficient with numerical problems). Whenever possible, one should prefer numerical MATLAB functions, especially those can often be extended to work in a vectorized way, along array inputs to provide array output.

When facing a mixed problem (needing symbolic math, but also computation-expensive evaluation of the results), it might be most practical to solve your initial problem in a parametric (symbolic) way once, then to use the very last result by turning it into an appropriate numerical function. You should have a look at the matlabFunction function of the Symbolic Math Toolbox, which performs exactly this and works quite well for reasonably scaled functions (but here's a counterexample).

Note that while you can define an anonymous function using a formula, as in f=@(x) 3*x^2-2, this will actually define a numeric function which returns a value for given numeric inputs such as f(3). If you have the formula in your hand which you want to compute, always use a numerical function. Symbolic math should be reserved for cases which can not be solved exactly by basic numerical features, such as computing the exact gradient of a multivariate scalar field.

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