60 lines
2.1 KiB
C++
60 lines
2.1 KiB
C++
// NOTE: 带参数的多变量函数的导数
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// C++ includes
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#include <iostream>
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// autodiff include
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#include <autodiff/forward/dual.hpp>
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using namespace autodiff;
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// A type defining parameters for a function of interest
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struct Params
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{
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dual a;
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dual b;
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dual c;
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};
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// The function that depends on parameters for which derivatives are needed
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dual f(dual x, const Params& params)
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{
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return params.a * sin(x) + params.b * cos(x) + params.c * sin(x)*cos(x);
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}
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int main()
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{
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Params params; // initialize the parameter variables
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params.a = 1.0; // the parameter a of type dual, not double!
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params.b = 2.0; // the parameter b of type dual, not double!
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params.c = 3.0; // the parameter c of type dual, not double!
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dual x = 0.5; // the input variable x
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dual u = f(x, params); // the output variable u
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double dudx = derivative(f, wrt(x), at(x, params)); // evaluate the derivative du/dx
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double duda = derivative(f, wrt(params.a), at(x, params)); // evaluate the derivative du/da
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double dudb = derivative(f, wrt(params.b), at(x, params)); // evaluate the derivative du/db
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double dudc = derivative(f, wrt(params.c), at(x, params)); // evaluate the derivative du/dc
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std::cout << "u = " << u << std::endl; // print the evaluated output u
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std::cout << "du/dx = " << dudx << std::endl; // print the evaluated derivative du/dx
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std::cout << "du/da = " << duda << std::endl; // print the evaluated derivative du/da
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std::cout << "du/db = " << dudb << std::endl; // print the evaluated derivative du/db
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std::cout << "du/dc = " << dudc << std::endl; // print the evaluated derivative du/dc
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}
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/* NOTE:
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This example would also work if real was used instead of dual. Should you
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need higher-order cross derivatives, however, e.g.,:
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double d2udxda = derivative(f, wrt(x, params.a), at(x, params));
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then higher-order dual types are the right choicesince real types are
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optimally designed for higher-order directional derivatives.
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如果需要计算更高阶的交叉倒数（例如d2udxda）时，应该使用更高阶的dual类型，而不是real类型
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*/
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