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Merge branch 'autodiff' of https://github.com/pulver/math into autodiff
This commit is contained in:
John Maddock
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[/ Copyright Matthew Pulver 2018 - 2019.
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// Distributed under the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt or copy at
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// https://www.boost.org/LICENSE_1_0.txt)]
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[section:autodiff Automatic Differentiation]
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[template autodiff_equation[name] '''<inlinemediaobject><imageobject><imagedata fileref="../equations/autodiff/'''[name]'''"></imagedata></imageobject></inlinemediaobject>''']
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[h1:synopsis Synopsis]
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#include <boost/math/differentiation/autodiff.hpp>
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namespace boost { namespace math { namespace differentiation {
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// Type for variables and constants.
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template<typename RealType, size_t Order, size_t... Orders>
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using autodiff_fvar = typename detail::nest_fvar<RealType,Order,Orders...>::type;
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// Function returning a variable of differentiation.
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template<typename RealType, size_t Order, size_t... Orders>
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autodiff_fvar<RealType,Order,Orders...> make_fvar(const RealType& ca);
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// Type of combined autodiff types.
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template<typename RealType, typename... RealTypes>
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using promote = typename detail::promote_args_n<RealType,RealTypes...>::type;
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namespace detail {
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// Single autodiff variable. Independent variables are created by nesting.
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template<typename RealType, size_t Order>
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class fvar
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{
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public:
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// Query return value of function to get the derivatives.
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template<typename... Orders>
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get_type_at<RealType, sizeof...(Orders)-1> derivative(Orders... orders) const;
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// All of the arithmetic and comparison operators are overloaded.
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template<typename RealType2, size_t Order2>
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fvar& operator+=(const fvar<RealType2,Order2>&);
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fvar& operator+=(const root_type&);
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// ...
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};
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// Standard math functions are overloaded and called via argument-dependent lookup (ADL).
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template<typename RealType, size_t Order>
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fvar<RealType,Order> floor(const fvar<RealType,Order>&);
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template<typename RealType, size_t Order>
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fvar<RealType,Order> exp(const fvar<RealType,Order>&);
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// ...
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} // namespace detail
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} } } // namespace boost::math::differentiation
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[h1:description Description]
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Autodiff is a header-only C++ library that facilitates the [@https://en.wikipedia.org/wiki/Automatic_differentiation
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automatic differentiation] (forward mode) of mathematical functions of single and multiple variables.
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This implementation is based upon the [@https://en.wikipedia.org/wiki/Taylor_series Taylor series] expansion of
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an analytic function /f/ at the point ['x[sub 0]]:
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[/ Thanks to http://www.tlhiv.org/ltxpreview/ for LaTeX-to-SVG conversions. ]
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[/ \Large\begin{align*}
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f(x_0+\varepsilon) &= f(x_0) + f'(x_0)\varepsilon + \frac{f''(x_0)}{2!}\varepsilon^2 + \frac{f'''(x_0)}{3!}\varepsilon^3 + \cdots \\
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&= \sum_{n=0}^N\frac{f^{(n)}(x_0)}{n!}\varepsilon^n + O\left(\varepsilon^{N+1}\right).
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\end{align*} ]
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[:[:[autodiff_equation taylor_series.svg]]]
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The essential idea of autodiff is the replacement of numbers with polynomials in the evaluation of /f/. By inputting
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the first-order polynomial ['x[sub 0]+\u03b5], the resulting polynomial in ['\u03b5] contains the function's
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derivatives within the coefficients. Each coefficient is equal to a derivative of its respective order, divided
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by the factorial of the order.
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Assume one is interested in calculating the first /N/ derivatives of /f/ at ['x[sub 0]]. Then without any loss of
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precision to the calculation of the derivatives, all terms ['O(\u03b5[super N+1])] that include powers of ['\u03b5]
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greater than /N/ can be discarded, and under these truncation rules, /f/ provides a polynomial-to-polynomial
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transformation:
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[/ \Large$$f \qquad : \qquad x_0+\varepsilon \qquad \mapsto \qquad
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\sum_{n=0}^Ny_n\varepsilon^n=\sum_{n=0}^N\frac{f^{(n)}(x_0)}{n!}\varepsilon^n.$$ ]
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[:[:[autodiff_equation polynomial_transform.svg]]]
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C++'s ability to overload operators and functions allows for the creation of a class `fvar` ([_f]orward-mode autodiff
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[_var]iable) that represents polynomials in ['\u03b5]. Thus the same algorithm that calculates the numeric value of
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['y[sub 0]=f(x[sub 0])] is also used to calculate the polynomial ['\u03a3[sub n]y[sub n]\u03b5[super n]=f(x[sub
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0]+\u03b5)]. The derivatives are then found from the product of the respective factorial and coefficient:
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[/ \Large$$\frac{d^nf}{dx^n}(x_0)=n!y_n.$$ ]
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[:[:[autodiff_equation derivative_formula.svg]]]
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[h1:examples Examples]
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[h2:example-single-variable Example 1: Single-variable derivatives]
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[h3 Calculate derivatives of ['f(x)=x[super 4]] at /x/=2.]
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In this example, `autodiff_fvar<double,5>` is a data type that can hold a polynomial of up to degree 5, and
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`make_fvar<double,5>(2)` represents the polynomial 2+['\u03b5]. Internally, this is modeled by a `std::array<double,6>`
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whose elements `{2, 1, 0, 0, 0, 0}` correspond to the 6 coefficients of the polynomial upon initialization.
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Its fourth power is a polynomial with coefficients `y = {16, 32, 24, 8, 1, 0}`. The derivatives are obtained
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using the formula ['f[super (n)](2)=n!*y[n]].
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#include <boost/math/differentiation/autodiff.hpp>
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#include <iostream>
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template<typename T>
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T fourth_power(T x)
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{
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x *= x;
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return x *= x;
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}
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int main()
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{
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using namespace boost::math::differentiation;
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constexpr int Order=5; // The highest order derivative to be calculated.
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const autodiff_fvar<double,Order> x = make_fvar<double,Order>(2.0); // Find derivatives at x=2.
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const autodiff_fvar<double,Order> y = fourth_power(x);
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for (int i=0 ; i<=Order ; ++i)
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std::cout << "y.derivative("<<i<<") = " << y.derivative(i) << std::endl;
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return 0;
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}
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/* Output:
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y.derivative(0) = 16
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y.derivative(1) = 32
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y.derivative(2) = 48
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y.derivative(3) = 48
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y.derivative(4) = 24
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y.derivative(5) = 0
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*/
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The above calculates
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[/ \Large\begin{alignat*}{3}
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{\tt y.derivative(0)} &=& f(2) =&& \left.x^4\right|_{x=2} &= 16\\
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{\tt y.derivative(1)} &=& f'(2) =&& \left.4\cdot x^3\right|_{x=2} &= 32\\
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{\tt y.derivative(2)} &=& f''(2) =&& \left.4\cdot 3\cdot x^2\right|_{x=2} &= 48\\
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{\tt y.derivative(3)} &=& f'''(2) =&& \left.4\cdot 3\cdot2\cdot x\right|_{x=2} &= 48\\
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{\tt y.derivative(4)} &=& f^{(4)}(2) =&& 4\cdot 3\cdot2\cdot1 &= 24\\
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{\tt y.derivative(5)} &=& f^{(5)}(2) =&& 0 &
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\end{alignat*} ]
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[:[:[autodiff_equation example1.svg]]]
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[h2:example-multiprecision
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Example 2: Multi-variable mixed partial derivatives with multi-precision data type]
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[/ \Large$\frac{\partial^{12}f}{\partial w^{3}\partial x^{2}\partial y^{4}\partial z^{3}}(11,12,13,14)$]
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[/ \Large$f(w,x,y,z)=\exp\left(w\sin\left(\frac{x\log(y)}{z}\right)+\sqrt{\frac{wz}{xy}}\right)+\frac{w^2}{\tan(z)}$]
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[h3 Calculate [autodiff_equation mixed12.svg] with a precision of about 50 decimal digits,
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where [autodiff_equation example2f.svg].]
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In this example, the data type `autodiff_fvar<cpp_bin_float_50,Nw,Nx,Ny,Nz>` represents a multivariate polynomial in
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4 independent variables, where the highest powers of each are `Nw`, `Nx`, `Ny` and `Nz`. The underlying arithmetic
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data type, aliased as `root_type`, is `boost::multiprecision::cpp_bin_float_50`. The internal data structure is
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`std::array<std::array<std::array<std::array<cpp_bin_float_50,Nz+1>,Ny+1>,Nx+1>,Nw+1>`. The `root_type` is always
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the first template parameter to `autodiff_fvar<...>` followed by the maximum derivative orders that are to be
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calculated for each independent variable.
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When variables are initialized with `make_fvar<...>()`, the position of the last derivative order given in the
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template parameter pack determines which variable is taken to be independent. In other words, it determines which
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of the 4 different polynomial variables ['\u03b5[sub w]], ['\u03b5[sub x]], ['\u03b5[sub y]], or ['\u03b5[sub z]]
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are to be added to the constant term:
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[/ \Large\begin{align*}
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\texttt{make\_fvar<cpp\_bin\_float\_50,Nw>(11)} &= 11+\varepsilon_w \\
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\texttt{make\_fvar<cpp\_bin\_float\_50,0,Nx>(12)} &= 12+\varepsilon_x \\
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\texttt{make\_fvar<cpp\_bin\_float\_50,0,0,Ny>(13)} &= 13+\varepsilon_y \\
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\texttt{make\_fvar<cpp\_bin\_float\_50,0,0,0,Nz>(14)} &= 14+\varepsilon_z
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\end{align*}\]
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[:[:[autodiff_equation example2make_fvar.svg]]]
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Instances of different types are automatically promoted to the smallest multi-variable type that accommodates both
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when they are combined (added, subtracted, multiplied, divided.)
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#include <boost/math/differentiation/autodiff.hpp>
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#include <boost/multiprecision/cpp_bin_float.hpp>
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#include <iostream>
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template<typename T>
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T f(const T& w, const T& x, const T& y, const T& z)
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{
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using namespace std;
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return exp(w*sin(x*log(y)/z) + sqrt(w*z/(x*y))) + w*w/tan(z);
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}
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int main()
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{
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using cpp_bin_float_50 = boost::multiprecision::cpp_bin_float_50;
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using namespace boost::math::differentiation;
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constexpr int Nw=3; // Max order of derivative to calculate for w
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constexpr int Nx=2; // Max order of derivative to calculate for x
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constexpr int Ny=4; // Max order of derivative to calculate for y
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constexpr int Nz=3; // Max order of derivative to calculate for z
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using var = autodiff_fvar<cpp_bin_float_50,Nw,Nx,Ny,Nz>;
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const var w = make_fvar<cpp_bin_float_50,Nw>(11);
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const var x = make_fvar<cpp_bin_float_50,0,Nx>(12);
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const var y = make_fvar<cpp_bin_float_50,0,0,Ny>(13);
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const var z = make_fvar<cpp_bin_float_50,0,0,0,Nz>(14);
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const var v = f(w,x,y,z);
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// Calculated from Mathematica symbolic differentiation. See multiprecision.nb for script.
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const cpp_bin_float_50 answer("1976.319600747797717779881875290418720908121189218755");
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std::cout << std::setprecision(std::numeric_limits<cpp_bin_float_50>::digits10)
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<< "mathematica : " << answer << '\n'
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<< "autodiff : " << v.derivative(Nw,Nx,Ny,Nz) << '\n'
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<< "relative error: " << std::setprecision(3) << (v.derivative(Nw,Nx,Ny,Nz)/answer-1) << std::endl;
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return 0;
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}
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/*
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Output:
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mathematica : 1976.3196007477977177798818752904187209081211892188
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autodiff : 1976.3196007477977177798818752904187209081211892188
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relative error: 2.67e-50
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*/
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[h1 Manual]
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Additional details are in the [@../differentiation/autodiff.pdf autodiff manual].
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[endsect]
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</svg>
|
||||
|
After Width: | Height: | Size: 34 KiB |
@@ -1,13 +1,13 @@
|
||||
[book Math Toolkit
|
||||
[quickbook 1.7]
|
||||
[copyright 2006, 2007, 2008, 2009, 2010, 2012, 2013, 2014, 2017 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker and Xiaogang Zhang]
|
||||
[copyright 2006, 2007, 2008, 2009, 2010, 2012, 2013, 2014, 2017 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker and Xiaogang Zhang]
|
||||
[/purpose ISBN 0-9504833-2-X 978-0-9504833-2-0, Classification 519.2-dc22]
|
||||
[license
|
||||
Distributed under the Boost Software License, Version 1.0.
|
||||
(See accompanying file LICENSE_1_0.txt or copy at
|
||||
[@http://www.boost.org/LICENSE_1_0.txt])
|
||||
]
|
||||
[authors [Agrawal, Nikhar], [Bikineev, Anton], [Bristow, Paul A.], [Holin, Hubert], [Guazzone, Marco], [Kormanyos, Christopher], [Lalande, Bruno], [Maddock, John], [Murphy, Jeremy W.], [Råde, Johan], [Sobotta, Benjamin], [Sewani, Gautam], [Thompson, Nicholas], [van den Berg, Thijs], [Walker, Daryle], [Zhang, Xiaogang]]
|
||||
[authors [Agrawal, Nikhar], [Bikineev, Anton], [Bristow, Paul A.], [Holin, Hubert], [Guazzone, Marco], [Kormanyos, Christopher], [Lalande, Bruno], [Maddock, John], [Murphy, Jeremy W.], [Pulver, Matthew], [Råde, Johan], [Sobotta, Benjamin], [Sewani, Gautam], [Thompson, Nicholas], [van den Berg, Thijs], [Walker, Daryle], [Zhang, Xiaogang]]
|
||||
[/last-revision $Date$]
|
||||
[version 2.9.0]
|
||||
]
|
||||
@@ -669,6 +669,7 @@ and as a CD ISBN 0-9504833-2-X 978-0-9504833-2-0, Classification 519.2-dc22.
|
||||
[include quadrature/double_exponential.qbk]
|
||||
[include quadrature/naive_monte_carlo.qbk]
|
||||
[include differentiation/numerical_differentiation.qbk]
|
||||
[include differentiation/autodiff.qbk]
|
||||
[include differentiation/lanczos_smoothing.qbk]
|
||||
[endmathpart]
|
||||
|
||||
|
||||
@@ -137,6 +137,10 @@ test-suite examples :
|
||||
[ run cubic_b_spline_example.cpp : : : [ requires cxx11_smart_ptr cxx11_hdr_random cxx11_defaulted_functions ] ]
|
||||
[ compile naive_monte_carlo_example.cpp : [ requires cxx11_auto_declarations cxx11_lambdas cxx11_unified_initialization_syntax cxx11_hdr_thread cxx11_hdr_atomic cxx11_decltype cxx11_hdr_future cxx11_hdr_chrono cxx11_hdr_random cxx11_allocator ] ] # requires user input, can't run it, take a long time too!
|
||||
[ run catmull_rom_example.cpp : : : [ requires cxx17_if_constexpr cxx11_auto_declarations cxx17_std_apply ] ] # Actually the C++17 features used is std::size, not if constexpr; looks like there isn't yet a test for it.
|
||||
[ run autodiff_black_scholes.cpp : : : [ requires cxx11_inline_namespaces ] ]
|
||||
[ run autodiff_fourth_power.cpp : : : [ requires cxx11_inline_namespaces ] ]
|
||||
[ run autodiff_mixed_partials.cpp : : : [ requires cxx11_inline_namespaces ] ]
|
||||
[ run autodiff_multiprecision.cpp : : : [ requires cxx11_inline_namespaces ] ]
|
||||
;
|
||||
|
||||
run root_elliptic_finding.cpp /boost/timer : : : release <link>static [ requires cxx11_unified_initialization_syntax cxx11_defaulted_functions ] <target-os>freebsd:<linkflags>"-lrt" <target-os>linux:<linkflags>"-lrt -lpthread" ;
|
||||
|
||||
183
example/autodiff_black_scholes.cpp
Normal file
183
example/autodiff_black_scholes.cpp
Normal file
@@ -0,0 +1,183 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include <boost/math/differentiation/autodiff.hpp>
|
||||
#include <iostream>
|
||||
|
||||
using namespace boost::math::differentiation;
|
||||
|
||||
// Equations and function/variable names are from
|
||||
// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
|
||||
|
||||
// Standard normal probability density function
|
||||
template<typename X>
|
||||
X phi(const X& x)
|
||||
{
|
||||
return boost::math::constants::one_div_root_two_pi<X>()*exp(-0.5*x*x);
|
||||
}
|
||||
|
||||
// Standard normal cumulative distribution function
|
||||
template<typename X>
|
||||
X Phi(const X& x)
|
||||
{
|
||||
return 0.5*erfc(-boost::math::constants::one_div_root_two<X>()*x);
|
||||
}
|
||||
|
||||
enum CP { call, put };
|
||||
|
||||
// Assume zero annual dividend yield (q=0).
|
||||
template<typename Price,typename Sigma,typename Tau,typename Rate>
|
||||
promote<Price,Sigma,Tau,Rate>
|
||||
black_scholes_option_price(CP cp, double K, const Price& S, const Sigma& sigma, const Tau& tau, const Rate& r)
|
||||
{
|
||||
using namespace std;
|
||||
const auto d1 = (log(S/K) + (r+sigma*sigma/2)*tau) / (sigma*sqrt(tau));
|
||||
const auto d2 = (log(S/K) + (r-sigma*sigma/2)*tau) / (sigma*sqrt(tau));
|
||||
if (cp == call)
|
||||
return S*Phi(d1) - exp(-r*tau)*K*Phi(d2);
|
||||
else
|
||||
return exp(-r*tau)*K*Phi(-d2) - S*Phi(-d1);
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
const double K = 100.0; // Strike price.
|
||||
const auto S = make_fvar<double,3>(105); // Stock price.
|
||||
const auto sigma = make_fvar<double,0,3>(5); // Volatility.
|
||||
const auto tau = make_fvar<double,0,0,1>(30.0/365); // Time to expiration in years. (30 days).
|
||||
const auto r = make_fvar<double,0,0,0,1>(1.25/100); // Interest rate.
|
||||
const auto call_price = black_scholes_option_price(call, K, S, sigma, tau, r);
|
||||
const auto put_price = black_scholes_option_price(put, K, S, sigma, tau, r);
|
||||
|
||||
// Compare automatically calculated greeks by autodiff with formulas for greeks.
|
||||
// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
|
||||
const double d1 = static_cast<double>((log(S/K) + (r+sigma*sigma/2)*tau) / (sigma*sqrt(tau)));
|
||||
const double d2 = static_cast<double>((log(S/K) + (r-sigma*sigma/2)*tau) / (sigma*sqrt(tau)));
|
||||
const double formula_call_delta = +Phi(+d1);
|
||||
const double formula_put_delta = -Phi(-d1);
|
||||
const double formula_vega = static_cast<double>(S*phi(d1)*sqrt(tau));
|
||||
const double formula_call_theta = static_cast<double>(-S*phi(d1)*sigma/(2*sqrt(tau))-r*K*exp(-r*tau)*Phi(+d2));
|
||||
const double formula_put_theta = static_cast<double>(-S*phi(d1)*sigma/(2*sqrt(tau))+r*K*exp(-r*tau)*Phi(-d2));
|
||||
const double formula_call_rho = static_cast<double>(+K*tau*exp(-r*tau)*Phi(+d2));
|
||||
const double formula_put_rho = static_cast<double>(-K*tau*exp(-r*tau)*Phi(-d2));
|
||||
const double formula_gamma = static_cast<double>(phi(d1)/(S*sigma*sqrt(tau)));
|
||||
const double formula_vanna = static_cast<double>(-phi(d1)*d2/sigma);
|
||||
const double formula_charm = static_cast<double>(phi(d1)*(d2*sigma*sqrt(tau)-2*r*tau)/(2*tau*sigma*sqrt(tau)));
|
||||
const double formula_vomma = static_cast<double>(S*phi(d1)*sqrt(tau)*d1*d2/sigma);
|
||||
const double formula_veta = static_cast<double>(-S*phi(d1)*sqrt(tau)*(r*d1/(sigma*sqrt(tau))-(1+d1*d2)/(2*tau)));
|
||||
const double formula_speed = static_cast<double>(-phi(d1)*(d1/(sigma*sqrt(tau))+1)/(S*S*sigma*sqrt(tau)));
|
||||
const double formula_zomma = static_cast<double>(phi(d1)*(d1*d2-1)/(S*sigma*sigma*sqrt(tau)));
|
||||
const double formula_color =
|
||||
static_cast<double>(-phi(d1)/(2*S*tau*sigma*sqrt(tau))*(1+(2*r*tau-d2*sigma*sqrt(tau))*d1/(sigma*sqrt(tau))));
|
||||
const double formula_ultima = -formula_vega*static_cast<double>((d1*d2*(1-d1*d2)+d1*d1+d2*d2)/(sigma*sigma));
|
||||
|
||||
std::cout << std::setprecision(std::numeric_limits<double>::digits10)
|
||||
<< "autodiff black-scholes call price = " << call_price.derivative(0,0,0,0) << '\n'
|
||||
<< "autodiff black-scholes put price = " << put_price.derivative(0,0,0,0) << '\n'
|
||||
<< "\n## First-order Greeks\n"
|
||||
<< "autodiff call delta = " << call_price.derivative(1,0,0,0) << '\n'
|
||||
<< " formula call delta = " << formula_call_delta << '\n'
|
||||
<< "autodiff call vega = " << call_price.derivative(0,1,0,0) << '\n'
|
||||
<< " formula call vega = " << formula_vega << '\n'
|
||||
<< "autodiff call theta = " << -call_price.derivative(0,0,1,0) << '\n' // minus sign due to tau = T-time
|
||||
<< " formula call theta = " << formula_call_theta << '\n'
|
||||
<< "autodiff call rho = " << call_price.derivative(0,0,0,1) << '\n'
|
||||
<< " formula call rho = " << formula_call_rho << '\n'
|
||||
<< '\n'
|
||||
<< "autodiff put delta = " << put_price.derivative(1,0,0,0) << '\n'
|
||||
<< " formula put delta = " << formula_put_delta << '\n'
|
||||
<< "autodiff put vega = " << put_price.derivative(0,1,0,0) << '\n'
|
||||
<< " formula put vega = " << formula_vega << '\n'
|
||||
<< "autodiff put theta = " << -put_price.derivative(0,0,1,0) << '\n'
|
||||
<< " formula put theta = " << formula_put_theta << '\n'
|
||||
<< "autodiff put rho = " << put_price.derivative(0,0,0,1) << '\n'
|
||||
<< " formula put rho = " << formula_put_rho << '\n'
|
||||
<< "\n## Second-order Greeks\n"
|
||||
<< "autodiff call gamma = " << call_price.derivative(2,0,0,0) << '\n'
|
||||
<< "autodiff put gamma = " << put_price.derivative(2,0,0,0) << '\n'
|
||||
<< " formula gamma = " << formula_gamma << '\n'
|
||||
<< "autodiff call vanna = " << call_price.derivative(1,1,0,0) << '\n'
|
||||
<< "autodiff put vanna = " << put_price.derivative(1,1,0,0) << '\n'
|
||||
<< " formula vanna = " << formula_vanna << '\n'
|
||||
<< "autodiff call charm = " << -call_price.derivative(1,0,1,0) << '\n'
|
||||
<< "autodiff put charm = " << -put_price.derivative(1,0,1,0) << '\n'
|
||||
<< " formula charm = " << formula_charm << '\n'
|
||||
<< "autodiff call vomma = " << call_price.derivative(0,2,0,0) << '\n'
|
||||
<< "autodiff put vomma = " << put_price.derivative(0,2,0,0) << '\n'
|
||||
<< " formula vomma = " << formula_vomma << '\n'
|
||||
<< "autodiff call veta = " << call_price.derivative(0,1,1,0) << '\n'
|
||||
<< "autodiff put veta = " << put_price.derivative(0,1,1,0) << '\n'
|
||||
<< " formula veta = " << formula_veta << '\n'
|
||||
<< "\n## Third-order Greeks\n"
|
||||
<< "autodiff call speed = " << call_price.derivative(3,0,0,0) << '\n'
|
||||
<< "autodiff put speed = " << put_price.derivative(3,0,0,0) << '\n'
|
||||
<< " formula speed = " << formula_speed << '\n'
|
||||
<< "autodiff call zomma = " << call_price.derivative(2,1,0,0) << '\n'
|
||||
<< "autodiff put zomma = " << put_price.derivative(2,1,0,0) << '\n'
|
||||
<< " formula zomma = " << formula_zomma << '\n'
|
||||
<< "autodiff call color = " << call_price.derivative(2,0,1,0) << '\n'
|
||||
<< "autodiff put color = " << put_price.derivative(2,0,1,0) << '\n'
|
||||
<< " formula color = " << formula_color << '\n'
|
||||
<< "autodiff call ultima = " << call_price.derivative(0,3,0,0) << '\n'
|
||||
<< "autodiff put ultima = " << put_price.derivative(0,3,0,0) << '\n'
|
||||
<< " formula ultima = " << formula_ultima << '\n'
|
||||
;
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
Output:
|
||||
autodiff black-scholes call price = 56.5136030677739
|
||||
autodiff black-scholes put price = 51.4109161009333
|
||||
|
||||
## First-order Greeks
|
||||
autodiff call delta = 0.773818444921273
|
||||
formula call delta = 0.773818444921274
|
||||
autodiff call vega = 9.05493427705736
|
||||
formula call vega = 9.05493427705736
|
||||
autodiff call theta = -275.73013426444
|
||||
formula call theta = -275.73013426444
|
||||
autodiff call rho = 2.03320550539396
|
||||
formula call rho = 2.03320550539396
|
||||
|
||||
autodiff put delta = -0.226181555078726
|
||||
formula put delta = -0.226181555078726
|
||||
autodiff put vega = 9.05493427705736
|
||||
formula put vega = 9.05493427705736
|
||||
autodiff put theta = -274.481417851526
|
||||
formula put theta = -274.481417851526
|
||||
autodiff put rho = -6.17753255212599
|
||||
formula put rho = -6.17753255212599
|
||||
|
||||
## Second-order Greeks
|
||||
autodiff call gamma = 0.00199851912993254
|
||||
autodiff put gamma = 0.00199851912993254
|
||||
formula gamma = 0.00199851912993254
|
||||
autodiff call vanna = 0.0410279463126531
|
||||
autodiff put vanna = 0.0410279463126531
|
||||
formula vanna = 0.0410279463126531
|
||||
autodiff call charm = -1.2505564233679
|
||||
autodiff put charm = -1.2505564233679
|
||||
formula charm = -1.2505564233679
|
||||
autodiff call vomma = -0.928114149313108
|
||||
autodiff put vomma = -0.928114149313108
|
||||
formula vomma = -0.928114149313107
|
||||
autodiff call veta = 26.7947073115641
|
||||
autodiff put veta = 26.7947073115641
|
||||
formula veta = 26.7947073115641
|
||||
|
||||
## Third-order Greeks
|
||||
autodiff call speed = -2.90117322380992e-05
|
||||
autodiff put speed = -2.90117322380992e-05
|
||||
formula speed = -2.90117322380992e-05
|
||||
autodiff call zomma = -0.000604548369901419
|
||||
autodiff put zomma = -0.000604548369901419
|
||||
formula zomma = -0.000604548369901419
|
||||
autodiff call color = -0.0184014426606065
|
||||
autodiff put color = -0.0184014426606065
|
||||
formula color = -0.0184014426606065
|
||||
autodiff call ultima = -0.0922426864775683
|
||||
autodiff put ultima = -0.0922426864775683
|
||||
formula ultima = -0.0922426864775685
|
||||
**/
|
||||
35
example/autodiff_fourth_power.cpp
Normal file
35
example/autodiff_fourth_power.cpp
Normal file
@@ -0,0 +1,35 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include <boost/math/differentiation/autodiff.hpp>
|
||||
#include <iostream>
|
||||
|
||||
template<typename T>
|
||||
T fourth_power(T x)
|
||||
{
|
||||
x *= x;
|
||||
return x *= x;
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
using namespace boost::math::differentiation;
|
||||
|
||||
constexpr int Order=5; // The highest order derivative to be calculated.
|
||||
const autodiff_fvar<double,Order> x = make_fvar<double,Order>(2.0); // Find derivatives at x=2.
|
||||
const autodiff_fvar<double,Order> y = fourth_power(x);
|
||||
for (int i=0 ; i<=Order ; ++i)
|
||||
std::cout << "y.derivative("<<i<<") = " << y.derivative(i) << std::endl;
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
Output:
|
||||
y.derivative(0) = 16
|
||||
y.derivative(1) = 32
|
||||
y.derivative(2) = 48
|
||||
y.derivative(3) = 48
|
||||
y.derivative(4) = 24
|
||||
y.derivative(5) = 0
|
||||
**/
|
||||
54
example/autodiff_mixed_partials.cpp
Normal file
54
example/autodiff_mixed_partials.cpp
Normal file
File diff suppressed because one or more lines are too long
46
example/autodiff_multiprecision.cpp
Normal file
46
example/autodiff_multiprecision.cpp
Normal file
@@ -0,0 +1,46 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include <boost/math/differentiation/autodiff.hpp>
|
||||
#include <boost/multiprecision/cpp_bin_float.hpp>
|
||||
#include <iostream>
|
||||
|
||||
template<typename T>
|
||||
T f(const T& w, const T& x, const T& y, const T& z)
|
||||
{
|
||||
using namespace std;
|
||||
return exp(w*sin(x*log(y)/z) + sqrt(w*z/(x*y))) + w*w/tan(z);
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
using cpp_bin_float_50 = boost::multiprecision::cpp_bin_float_50;
|
||||
using namespace boost::math::differentiation;
|
||||
|
||||
constexpr int Nw=3; // Max order of derivative to calculate for w
|
||||
constexpr int Nx=2; // Max order of derivative to calculate for x
|
||||
constexpr int Ny=4; // Max order of derivative to calculate for y
|
||||
constexpr int Nz=3; // Max order of derivative to calculate for z
|
||||
using var = autodiff_fvar<cpp_bin_float_50,Nw,Nx,Ny,Nz>;
|
||||
const var w = make_fvar<cpp_bin_float_50,Nw>(11);
|
||||
const var x = make_fvar<cpp_bin_float_50,0,Nx>(12);
|
||||
const var y = make_fvar<cpp_bin_float_50,0,0,Ny>(13);
|
||||
const var z = make_fvar<cpp_bin_float_50,0,0,0,Nz>(14);
|
||||
const var v = f(w,x,y,z);
|
||||
// Calculated from Mathematica symbolic differentiation.
|
||||
const cpp_bin_float_50 answer("1976.319600747797717779881875290418720908121189218755");
|
||||
std::cout << std::setprecision(std::numeric_limits<cpp_bin_float_50>::digits10)
|
||||
<< "mathematica : " << answer << '\n'
|
||||
<< "autodiff : " << v.derivative(Nw,Nx,Ny,Nz) << '\n'
|
||||
<< "relative error: " << std::setprecision(3) << (v.derivative(Nw,Nx,Ny,Nz)/answer-1)
|
||||
<< std::endl;
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
Output:
|
||||
mathematica : 1976.3196007477977177798818752904187209081211892188
|
||||
autodiff : 1976.3196007477977177798818752904187209081211892188
|
||||
relative error: 2.67e-50
|
||||
**/
|
||||
1632
include/boost/math/differentiation/autodiff.hpp
Normal file
1632
include/boost/math/differentiation/autodiff.hpp
Normal file
File diff suppressed because it is too large
Load Diff
224
include/boost/math/differentiation/autodiff_cpp11.hpp
Normal file
224
include/boost/math/differentiation/autodiff_cpp11.hpp
Normal file
@@ -0,0 +1,224 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
// Contributors:
|
||||
// * Kedar R. Bhat - C++11 compatibility.
|
||||
|
||||
// Notes:
|
||||
// * Any changes to this file should always be downstream from autodiff.cpp.
|
||||
// C++17 is a higher-level language and is easier to maintain. For example, a number of functions which are
|
||||
// lucidly read in autodiff.cpp are forced to be split into multiple structs/functions in this file for C++11.
|
||||
// * Use of typename RootType and SizeType is a hack to prevent Visual Studio 2015 from compiling functions
|
||||
// that are never called, that would otherwise produce compiler errors.
|
||||
|
||||
#ifndef BOOST_MATH_DIFFERENTIATION_AUTODIFF_HPP
|
||||
# error "Do not #include this file directly. This should only be #included by autodiff.hpp for C++11 compatibility."
|
||||
#endif
|
||||
|
||||
namespace boost { namespace math { namespace differentiation { inline namespace autodiff_v1 {
|
||||
|
||||
namespace detail {
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order>::fvar(const root_type& ca, const bool is_variable)
|
||||
{
|
||||
fvar_cpp11(std::integral_constant<bool,is_fvar<RealType>::value>{}, ca, is_variable);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename RootType>
|
||||
void fvar<RealType,Order>::fvar_cpp11(std::true_type, const RootType& ca, const bool is_variable)
|
||||
{
|
||||
v.front() = RealType(ca, is_variable);
|
||||
if (0 < Order)
|
||||
std::fill(v.begin()+1, v.end(), static_cast<RealType>(0));
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename RootType>
|
||||
void fvar<RealType,Order>::fvar_cpp11(std::false_type, const RootType& ca, const bool is_variable)
|
||||
{
|
||||
v.front() = ca;
|
||||
if (0 < Order)
|
||||
{
|
||||
v[1] = static_cast<root_type>(static_cast<int>(is_variable));
|
||||
if (1 < Order)
|
||||
std::fill(v.begin()+2, v.end(), static_cast<RealType>(0));
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename... Orders>
|
||||
get_type_at<RealType, sizeof...(Orders)>
|
||||
fvar<RealType,Order>::at_cpp11(std::true_type, size_t order, Orders... orders) const
|
||||
{
|
||||
return v.at(order);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename... Orders>
|
||||
get_type_at<RealType, sizeof...(Orders)>
|
||||
fvar<RealType,Order>::at_cpp11(std::false_type, size_t order, Orders... orders) const
|
||||
{
|
||||
return v.at(order).at(orders...);
|
||||
}
|
||||
|
||||
// Can throw "std::out_of_range: array::at: __n (which is 7) >= _Nm (which is 7)"
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename... Orders>
|
||||
get_type_at<RealType,sizeof...(Orders)> fvar<RealType,Order>::at(size_t order, Orders... orders) const
|
||||
{
|
||||
return at_cpp11(std::integral_constant<bool,sizeof...(orders)==0>{}, order, orders...);
|
||||
}
|
||||
|
||||
template<typename T, typename... Ts>
|
||||
constexpr T product(Ts... factors)
|
||||
{
|
||||
return 1;
|
||||
}
|
||||
|
||||
template<typename T, typename... Ts>
|
||||
constexpr T product(T factor, Ts... factors)
|
||||
{
|
||||
return factor * product<T>(factors...);
|
||||
}
|
||||
|
||||
// Can throw "std::out_of_range: array::at: __n (which is 7) >= _Nm (which is 7)"
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename... Orders>
|
||||
get_type_at<fvar<RealType,Order>,sizeof...(Orders)> fvar<RealType,Order>::derivative(Orders... orders) const
|
||||
{
|
||||
static_assert(sizeof...(Orders) <= depth, "Number of parameters to derivative(...) cannot exceed fvar::depth.");
|
||||
return at(orders...) * product(boost::math::factorial<root_type>(orders)...);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename SizeType>
|
||||
fvar<RealType,Order> fvar<RealType,Order>::epsilon_multiply_cpp11(std::true_type,
|
||||
SizeType z0, size_t isum0, const fvar<RealType,Order>& cr, size_t z1, size_t isum1) const
|
||||
{
|
||||
const RealType zero(0);
|
||||
const size_t m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
|
||||
const size_t m1 = order_sum + isum1 < Order + z1 ? Order + z1 - (order_sum + isum1) : 0;
|
||||
const size_t i_max = m0 + m1 < Order ? Order - (m0 + m1) : 0;
|
||||
fvar<RealType,Order> retval = fvar<RealType,Order>();
|
||||
for (size_t i=0, j=Order ; i<=i_max ; ++i, --j)
|
||||
retval.v[j] = epsilon_inner_product(z0, isum0, m0, cr, z1, isum1, m1, j);
|
||||
return retval;
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename SizeType>
|
||||
fvar<RealType,Order> fvar<RealType,Order>::epsilon_multiply_cpp11(std::false_type,
|
||||
SizeType z0, size_t isum0, const fvar<RealType,Order>& cr, size_t z1, size_t isum1) const
|
||||
{
|
||||
const RealType zero(0);
|
||||
const size_t m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
|
||||
const size_t m1 = order_sum + isum1 < Order + z1 ? Order + z1 - (order_sum + isum1) : 0;
|
||||
const size_t i_max = m0 + m1 < Order ? Order - (m0 + m1) : 0;
|
||||
fvar<RealType,Order> retval = fvar<RealType,Order>();
|
||||
for (size_t i=0, j=Order ; i<=i_max ; ++i, --j)
|
||||
retval.v[j] = std::inner_product(v.cbegin()+m0, v.cend()-(i+m1), cr.v.crbegin()+(i+m0), zero);
|
||||
return retval;
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> fvar<RealType,Order>::epsilon_multiply(size_t z0, size_t isum0,
|
||||
const fvar<RealType,Order>& cr, size_t z1, size_t isum1) const
|
||||
{
|
||||
return epsilon_multiply_cpp11(std::integral_constant<bool,is_fvar<RealType>::value>{},
|
||||
z0, isum0, cr, z1, isum1);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename SizeType>
|
||||
fvar<RealType,Order> fvar<RealType,Order>::epsilon_multiply_cpp11(std::true_type,
|
||||
SizeType z0, size_t isum0, const root_type& ca) const
|
||||
{
|
||||
fvar<RealType,Order> retval(*this);
|
||||
const size_t m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
|
||||
for (size_t i=m0 ; i<=Order ; ++i)
|
||||
retval.v[i] = retval.v[i].epsilon_multiply(z0, isum0+i, ca);
|
||||
return retval;
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename SizeType>
|
||||
fvar<RealType,Order> fvar<RealType,Order>::epsilon_multiply_cpp11(std::false_type,
|
||||
SizeType z0, size_t isum0, const root_type& ca) const
|
||||
{
|
||||
fvar<RealType,Order> retval(*this);
|
||||
const size_t m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
|
||||
for (size_t i=m0 ; i<=Order ; ++i)
|
||||
if (retval.v[i] != static_cast<RealType>(0))
|
||||
retval.v[i] *= ca;
|
||||
return retval;
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> fvar<RealType,Order>::epsilon_multiply(size_t z0, size_t isum0,
|
||||
const root_type& ca) const
|
||||
{
|
||||
return epsilon_multiply_cpp11(std::integral_constant<bool,is_fvar<RealType>::value>{}, z0, isum0, ca);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename RootType>
|
||||
fvar<RealType,Order>& fvar<RealType,Order>::multiply_assign_by_root_type_cpp11(std::true_type,
|
||||
bool is_root, const RootType& ca)
|
||||
{
|
||||
auto itr = v.begin();
|
||||
itr->multiply_assign_by_root_type(is_root, ca);
|
||||
for (++itr ; itr!=v.end() ; ++itr)
|
||||
itr->multiply_assign_by_root_type(false, ca);
|
||||
return *this;
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename RootType>
|
||||
fvar<RealType,Order>& fvar<RealType,Order>::multiply_assign_by_root_type_cpp11(std::false_type,
|
||||
bool is_root, const RootType& ca)
|
||||
{
|
||||
auto itr = v.begin();
|
||||
if (is_root || *itr != 0)
|
||||
*itr *= ca; // Skip multiplication of 0 by ca=inf to avoid nan. Exception: root value is always multiplied.
|
||||
for (++itr ; itr!=v.end() ; ++itr)
|
||||
if (*itr != 0)
|
||||
*itr *= ca;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order>& fvar<RealType,Order>::multiply_assign_by_root_type(bool is_root, const root_type& ca)
|
||||
{
|
||||
return multiply_assign_by_root_type_cpp11(std::integral_constant<bool,is_fvar<RealType>::value>{},
|
||||
is_root, ca);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename RootType>
|
||||
fvar<RealType,Order>& fvar<RealType,Order>::set_root_cpp11(std::true_type, const RootType& root)
|
||||
{
|
||||
v.front().set_root(root);
|
||||
return *this;
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
template<typename RootType>
|
||||
fvar<RealType,Order>& fvar<RealType,Order>::set_root_cpp11(std::false_type, const RootType& root)
|
||||
{
|
||||
v.front() = root;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order>& fvar<RealType,Order>::set_root(const root_type& root)
|
||||
{
|
||||
return set_root_cpp11(std::integral_constant<bool,is_fvar<RealType>::value>{}, root);
|
||||
}
|
||||
|
||||
} // namespace detail
|
||||
|
||||
} } } } // namespace boost::math::differentiation::autodiff_v1
|
||||
@@ -1241,6 +1241,10 @@ test-suite quadrature :
|
||||
[ run test_numerical_differentiation.cpp ../../test/build//boost_unit_test_framework : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx11_auto_declarations cxx11_constexpr ] ]
|
||||
[ run compile_test/numerical_differentiation_incl_test.cpp compile_test_main : : : [ requires cxx11_auto_declarations cxx11_constexpr ] ]
|
||||
[ compile compile_test/numerical_differentiation_concept_test.cpp : [ requires cxx11_auto_declarations cxx11_constexpr ] ]
|
||||
[ run test_autodiff_1.cpp ../../test/build//boost_unit_test_framework : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx11_inline_namespaces ] ]
|
||||
[ run test_autodiff_2.cpp ../../test/build//boost_unit_test_framework : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx11_inline_namespaces ] ]
|
||||
[ run test_autodiff_3.cpp ../../test/build//boost_unit_test_framework : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx11_inline_namespaces ] ]
|
||||
[ run test_autodiff_4.cpp ../../test/build//boost_unit_test_framework : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx11_inline_namespaces ] ]
|
||||
;
|
||||
|
||||
build-project ../example ;
|
||||
|
||||
72
test/test_autodiff.hpp
Normal file
72
test/test_autodiff.hpp
Normal file
@@ -0,0 +1,72 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include <boost/fusion/include/algorithm.hpp>
|
||||
#include <boost/fusion/include/vector.hpp>
|
||||
#include <boost/math/differentiation/autodiff.hpp>
|
||||
#include <boost/math/special_functions/factorials.hpp>
|
||||
#include <boost/math/special_functions/fpclassify.hpp> // isnan
|
||||
#include <boost/math/special_functions/round.hpp> // iround
|
||||
#include <boost/math/special_functions/trunc.hpp> // itrunc
|
||||
//#include <boost/multiprecision/cpp_bin_float.hpp>
|
||||
|
||||
#define BOOST_TEST_MODULE test_autodiff
|
||||
#include <boost/test/included/unit_test.hpp>
|
||||
|
||||
#include <sstream>
|
||||
|
||||
//boost::fusion::vector<float,double,long double,boost::multiprecision::cpp_bin_float_50> bin_float_types;
|
||||
boost::fusion::vector<float,double,long double> bin_float_types; // cpp_bin_float_50 is fixed in boost 1.70
|
||||
// cpp_dec_float_50 cannot be used with close_at_tolerance
|
||||
//boost::fusion::vector<boost::multiprecision::cpp_dec_float_50>
|
||||
boost::fusion::vector<> multiprecision_float_types;
|
||||
|
||||
using namespace boost::math::differentiation;
|
||||
|
||||
template<typename W,typename X,typename Y,typename Z>
|
||||
promote<W,X,Y,Z> mixed_partials_f(const W& w, const X& x, const Y& y, const Z& z)
|
||||
{
|
||||
return exp(w*sin(x*log(y)/z) + sqrt(w*z/(x*y))) + w*w/tan(z);
|
||||
}
|
||||
|
||||
// Equations and function/variable names are from
|
||||
// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
|
||||
//
|
||||
// Standard normal probability density function
|
||||
template<typename T>
|
||||
T phi(const T& x)
|
||||
{
|
||||
return boost::math::constants::one_div_root_two_pi<T>()*exp(-0.5*x*x);
|
||||
}
|
||||
|
||||
// Standard normal cumulative distribution function
|
||||
template<typename T>
|
||||
T Phi(const T& x)
|
||||
{
|
||||
return 0.5*erfc(-boost::math::constants::one_div_root_two<T>()*x);
|
||||
}
|
||||
|
||||
enum CP { call, put };
|
||||
|
||||
// Assume zero annual dividend yield (q=0).
|
||||
template<typename Price,typename Sigma,typename Tau,typename Rate>
|
||||
promote<Price,Sigma,Tau,Rate>
|
||||
black_scholes_option_price(CP cp, double K, const Price& S, const Sigma& sigma, const Tau& tau, const Rate& r)
|
||||
{
|
||||
const auto d1 = (log(S/K) + (r+sigma*sigma/2)*tau) / (sigma*sqrt(tau));
|
||||
const auto d2 = (log(S/K) + (r-sigma*sigma/2)*tau) / (sigma*sqrt(tau));
|
||||
static_assert(std::is_same<decltype(S*Phi(d1) - exp(-r*tau)*K*Phi(d2)),
|
||||
decltype(exp(-r*tau)*K*Phi(-d2) - S*Phi(-d1))>::value, "decltype(call) != decltype(put)");
|
||||
if (cp == call)
|
||||
return S*Phi(d1) - exp(-r*tau)*K*Phi(d2);
|
||||
else
|
||||
return exp(-r*tau)*K*Phi(-d2) - S*Phi(-d1);
|
||||
}
|
||||
|
||||
template<typename T>
|
||||
T uncast_return(const T& x)
|
||||
{
|
||||
return x == 0 ? 0 : 1;
|
||||
}
|
||||
917
test/test_autodiff_1.cpp
Normal file
917
test/test_autodiff_1.cpp
Normal file
@@ -0,0 +1,917 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include "test_autodiff.hpp"
|
||||
|
||||
BOOST_AUTO_TEST_SUITE(test_autodiff_1)
|
||||
|
||||
struct constructors_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
// Verify value-initialized instance has all 0 entries.
|
||||
const autodiff_fvar<T,m> empty1 = autodiff_fvar<T,m>();
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
BOOST_REQUIRE(empty1.derivative(i) == 0.0);
|
||||
const auto empty2 = autodiff_fvar<T,m,n>();
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE(empty2.derivative(i,j) == 0.0);
|
||||
// Single variable
|
||||
constexpr float cx = 10.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
if (i==0)
|
||||
BOOST_REQUIRE(x.derivative(i) == cx);
|
||||
else if (i==1)
|
||||
BOOST_REQUIRE(x.derivative(i) == 1.0);
|
||||
else
|
||||
BOOST_REQUIRE(x.derivative(i) == 0.0);
|
||||
const autodiff_fvar<T,n> xn = x;
|
||||
for (int i=0 ; i<=n ; ++i)
|
||||
if (i==0)
|
||||
BOOST_REQUIRE(xn.derivative(i) == cx);
|
||||
else if (i==1)
|
||||
BOOST_REQUIRE(xn.derivative(i) == 1.0);
|
||||
else
|
||||
BOOST_REQUIRE(xn.derivative(i) == 0.0);
|
||||
// Second independent variable
|
||||
constexpr float cy = 100.0;
|
||||
const auto y = make_fvar<T,m,n>(cy);
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(y.derivative(i,j) == cy);
|
||||
else if (i==0 && j==1)
|
||||
BOOST_REQUIRE(y.derivative(i,j) == 1.0);
|
||||
else
|
||||
BOOST_REQUIRE(y.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(constructors)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, constructors_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, constructors_test());
|
||||
}
|
||||
|
||||
struct implicit_constructors_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
const autodiff_fvar<T,m> x = 3;
|
||||
const autodiff_fvar<T,m> one = uncast_return(x);
|
||||
const autodiff_fvar<T,m> two_and_a_half = 2.5;
|
||||
BOOST_REQUIRE(static_cast<T>(x) == 3.0);
|
||||
BOOST_REQUIRE(static_cast<T>(one) == 1.0);
|
||||
BOOST_REQUIRE(static_cast<T>(two_and_a_half) == 2.5);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(implicit_constructors)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, implicit_constructors_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, implicit_constructors_test());
|
||||
}
|
||||
|
||||
struct assignment_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 10.0;
|
||||
constexpr float cy = 10.0;
|
||||
autodiff_fvar<T,m,n> empty; // Uninitialized variable<> may have non-zero values.
|
||||
// Single variable
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
empty = static_cast<decltype(empty)>(x); // Test static_cast of single-variable to double-variable type.
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(empty.derivative(i,j) == cx);
|
||||
else if (i==1 && j==0)
|
||||
BOOST_REQUIRE(empty.derivative(i,j) == 1.0);
|
||||
else
|
||||
BOOST_REQUIRE(empty.derivative(i,j) == 0.0);
|
||||
auto y = make_fvar<T,m,n>(cy);
|
||||
empty = y; // default assignment operator
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(empty.derivative(i,j) == cy);
|
||||
else if (i==0 && j==1)
|
||||
BOOST_REQUIRE(empty.derivative(i,j) == 1.0);
|
||||
else
|
||||
BOOST_REQUIRE(empty.derivative(i,j) == 0.0);
|
||||
empty = cx; // set a constant
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(empty.derivative(i,j) == cx);
|
||||
else
|
||||
BOOST_REQUIRE(empty.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(assignment)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, assignment_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, assignment_test());
|
||||
}
|
||||
|
||||
struct ostream_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
const T cx = 10;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
std::ostringstream ss;
|
||||
ss << "x = " << x;
|
||||
BOOST_REQUIRE(ss.str() == "x = depth(1)(10,1,0,0)");
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(ostream)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, ostream_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, ostream_test());
|
||||
}
|
||||
|
||||
struct addition_assignment_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 10.0;
|
||||
auto sum = autodiff_fvar<T,m,n>(); // zero-initialized
|
||||
// Single variable
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
sum += x;
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == cx);
|
||||
else if (i==1 && j==0)
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == 1.0);
|
||||
else
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == 0.0);
|
||||
// Arithmetic constant
|
||||
constexpr float cy = 11.0;
|
||||
sum = 0;
|
||||
sum += cy;
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == cy);
|
||||
else
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(addition_assignment)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, addition_assignment_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, addition_assignment_test());
|
||||
}
|
||||
|
||||
struct subtraction_assignment_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 10.0;
|
||||
auto sum = autodiff_fvar<T,m,n>(); // zero-initialized
|
||||
// Single variable
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
sum -= x;
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == -cx);
|
||||
else if (i==1 && j==0)
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == -1.0);
|
||||
else
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == 0.0);
|
||||
// Arithmetic constant
|
||||
constexpr float cy = 11.0;
|
||||
sum = 0;
|
||||
sum -= cy;
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == -cy);
|
||||
else
|
||||
BOOST_REQUIRE(sum.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(subtraction_assignment)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, subtraction_assignment_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, subtraction_assignment_test());
|
||||
}
|
||||
|
||||
// Try explicit bracing based on feedback. Doesn't add very much except 26 extra lines.
|
||||
struct multiplication_assignment_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 10.0;
|
||||
auto product = autodiff_fvar<T,m,n>(1); // unit constant
|
||||
// Single variable
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
product *= x;
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
{
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
{
|
||||
if (i==0 && j==0)
|
||||
{
|
||||
BOOST_REQUIRE(product.derivative(i,j) == cx);
|
||||
}
|
||||
else if (i==1 && j==0)
|
||||
{
|
||||
BOOST_REQUIRE(product.derivative(i,j) == 1.0);
|
||||
}
|
||||
else
|
||||
{
|
||||
BOOST_REQUIRE(product.derivative(i,j) == 0.0);
|
||||
}
|
||||
}
|
||||
}
|
||||
// Arithmetic constant
|
||||
constexpr float cy = 11.0;
|
||||
product = 1;
|
||||
product *= cy;
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
{
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
{
|
||||
if (i==0 && j==0)
|
||||
{
|
||||
BOOST_REQUIRE(product.derivative(i,j) == cy);
|
||||
}
|
||||
else
|
||||
{
|
||||
BOOST_REQUIRE(product.derivative(i,j) == 0.0);
|
||||
}
|
||||
}
|
||||
}
|
||||
// 0 * inf = nan
|
||||
x = make_fvar<T,m>(0.0);
|
||||
x *= std::numeric_limits<T>::infinity();
|
||||
//std::cout << "x = " << x << std::endl;
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
{
|
||||
if (i==0)
|
||||
{
|
||||
BOOST_REQUIRE(boost::math::isnan(static_cast<T>(x))); // Correct
|
||||
//BOOST_REQUIRE(x.derivative(i) == 0.0); // Wrong. See multiply_assign_by_root_type().
|
||||
}
|
||||
else if (i==1)
|
||||
{
|
||||
BOOST_REQUIRE(boost::math::isinf(x.derivative(i)));
|
||||
}
|
||||
else
|
||||
{
|
||||
BOOST_REQUIRE(x.derivative(i) == 0.0);
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(multiplication_assignment)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, multiplication_assignment_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, multiplication_assignment_test());
|
||||
}
|
||||
|
||||
struct division_assignment_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 16.0;
|
||||
auto quotient = autodiff_fvar<T,m,n>(1); // unit constant
|
||||
// Single variable
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
quotient /= x;
|
||||
BOOST_REQUIRE(quotient.derivative(0,0) == 1/cx);
|
||||
BOOST_REQUIRE(quotient.derivative(1,0) == -1/std::pow(cx,2));
|
||||
BOOST_REQUIRE(quotient.derivative(2,0) == 2/std::pow(cx,3));
|
||||
BOOST_REQUIRE(quotient.derivative(3,0) == -6/std::pow(cx,4));
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=1 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE(quotient.derivative(i,j) == 0.0);
|
||||
// Arithmetic constant
|
||||
constexpr float cy = 32.0;
|
||||
quotient = 1;
|
||||
quotient /= cy;
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(quotient.derivative(i,j) == 1/cy);
|
||||
else
|
||||
BOOST_REQUIRE(quotient.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(division_assignment)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, division_assignment_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, division_assignment_test());
|
||||
}
|
||||
|
||||
struct unary_signs_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 16.0;
|
||||
autodiff_fvar<T,m,n> lhs;
|
||||
// Single variable
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
lhs = static_cast<decltype(lhs)>(-x);
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(lhs.derivative(i,j) == -cx);
|
||||
else if (i==1 && j==0)
|
||||
BOOST_REQUIRE(lhs.derivative(i,j) == -1.0);
|
||||
else
|
||||
BOOST_REQUIRE(lhs.derivative(i,j) == 0.0);
|
||||
lhs = static_cast<decltype(lhs)>(+x);
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
if (i==0 && j==0)
|
||||
BOOST_REQUIRE(lhs.derivative(i,j) == cx);
|
||||
else if (i==1 && j==0)
|
||||
BOOST_REQUIRE(lhs.derivative(i,j) == 1.0);
|
||||
else
|
||||
BOOST_REQUIRE(lhs.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(unary_signs)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, unary_signs_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, unary_signs_test());
|
||||
}
|
||||
|
||||
// TODO 3 tests for 3 operator+() definitions.
|
||||
|
||||
struct cast_double_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr float ca = 13.0;
|
||||
constexpr int i = 12;
|
||||
constexpr int m = 3;
|
||||
const auto x = make_fvar<T,m>(ca);
|
||||
BOOST_REQUIRE(i < x);
|
||||
BOOST_REQUIRE(i*x == i*ca);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(cast_double)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, cast_double_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, cast_double_test());
|
||||
}
|
||||
|
||||
struct int_double_casting_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr float ca = 3.0;
|
||||
const auto x0 = make_fvar<T,0>(ca);
|
||||
BOOST_REQUIRE(static_cast<T>(x0) == ca);
|
||||
const auto x1 = make_fvar<T,1>(ca);
|
||||
BOOST_REQUIRE(static_cast<T>(x1) == ca);
|
||||
const auto x2 = make_fvar<T,2>(ca);
|
||||
BOOST_REQUIRE(static_cast<T>(x2) == ca);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(int_double_casting)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, int_double_casting_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, int_double_casting_test());
|
||||
}
|
||||
|
||||
struct scalar_addition_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr float ca = 3.0;
|
||||
constexpr float cb = 4.0;
|
||||
const auto sum0 = autodiff_fvar<T,0>(ca) + autodiff_fvar<T,0>(cb);
|
||||
BOOST_REQUIRE(ca+cb == static_cast<T>(sum0));
|
||||
const auto sum1 = autodiff_fvar<T,0>(ca) + cb;
|
||||
BOOST_REQUIRE(ca+cb == static_cast<T>(sum1));
|
||||
const auto sum2 = ca + autodiff_fvar<T,0>(cb);
|
||||
BOOST_REQUIRE(ca+cb == static_cast<T>(sum2));
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(scalar_addition)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, scalar_addition_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, scalar_addition_test());
|
||||
}
|
||||
|
||||
struct power8_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int n = 8;
|
||||
constexpr float ca = 3.0;
|
||||
auto x = make_fvar<T,n>(ca);
|
||||
// Test operator*=()
|
||||
x *= x;
|
||||
x *= x;
|
||||
x *= x;
|
||||
const T power_factorial = boost::math::factorial<T>(n);
|
||||
for (int i=0 ; i<=n ; ++i)
|
||||
BOOST_CHECK(static_cast<T>(x.derivative(i)) == static_cast<T>(power_factorial/boost::math::factorial<T>(n-i)*std::pow(ca,n-i)));
|
||||
x = make_fvar<T,n>(ca);
|
||||
// Test operator*()
|
||||
x = x*x*x*x * x*x*x*x;
|
||||
for (int i=0 ; i<=n ; ++i)
|
||||
BOOST_REQUIRE(x.derivative(i) == power_factorial/boost::math::factorial<T>(n-i)*std::pow(ca,n-i));
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(power8)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, power8_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, power8_test());
|
||||
}
|
||||
|
||||
struct dim1_multiplication_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 2;
|
||||
constexpr int n = 3;
|
||||
constexpr float cy = 4.0;
|
||||
auto y0 = make_fvar<T,m>(cy);
|
||||
auto y = make_fvar<T,n>(cy);
|
||||
y *= y0;
|
||||
BOOST_REQUIRE(y.derivative(0) == cy*cy);
|
||||
BOOST_REQUIRE(y.derivative(1) == 2*cy);
|
||||
BOOST_REQUIRE(y.derivative(2) == 2.0);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||||
y = y * cy;
|
||||
BOOST_REQUIRE(y.derivative(0) == cy*cy*cy);
|
||||
BOOST_REQUIRE(y.derivative(1) == 2*cy*cy);
|
||||
BOOST_REQUIRE(y.derivative(2) == 2.0*cy);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(dim1_multiplication)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, dim1_multiplication_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, dim1_multiplication_test());
|
||||
}
|
||||
|
||||
struct dim1and2_multiplication_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 2;
|
||||
constexpr int n = 3;
|
||||
constexpr float cx = 3.0;
|
||||
constexpr float cy = 4.0;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = make_fvar<T,m,n>(cy);
|
||||
y *= x;
|
||||
BOOST_REQUIRE(y.derivative(0,0) == cx*cy);
|
||||
BOOST_REQUIRE(y.derivative(0,1) == cx);
|
||||
BOOST_REQUIRE(y.derivative(1,0) == cy);
|
||||
BOOST_REQUIRE(y.derivative(1,1) == 1.0);
|
||||
for (int i=1 ; i<m ; ++i)
|
||||
for (int j=1 ; j<n ; ++j)
|
||||
if (i==1 && j==1)
|
||||
BOOST_REQUIRE(y.derivative(i,j) == 1.0);
|
||||
else
|
||||
BOOST_REQUIRE(y.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(dim1and2_multiplication)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, dim1and2_multiplication_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, dim1and2_multiplication_test());
|
||||
}
|
||||
|
||||
struct dim2_addition_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 2;
|
||||
constexpr int n = 3;
|
||||
constexpr float cx = 3.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
BOOST_REQUIRE(x.derivative(0) == cx);
|
||||
BOOST_REQUIRE(x.derivative(1) == 1.0);
|
||||
BOOST_REQUIRE(x.derivative(2) == 0.0);
|
||||
constexpr float cy = 4.0;
|
||||
const auto y = make_fvar<T,m,n>(cy);
|
||||
BOOST_REQUIRE(static_cast<T>(y.derivative(0)) == cy);
|
||||
BOOST_REQUIRE(static_cast<T>(y.derivative(1)) == 0.0); // partial of y w.r.t. x.
|
||||
|
||||
BOOST_REQUIRE(y.derivative(0,0) == cy);
|
||||
BOOST_REQUIRE(y.derivative(0,1) == 1.0);
|
||||
BOOST_REQUIRE(y.derivative(1,0) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(1,1) == 0.0);
|
||||
const auto z = x + y;
|
||||
BOOST_REQUIRE(z.derivative(0,0) == cx + cy);
|
||||
BOOST_REQUIRE(z.derivative(0,1) == 1.0);
|
||||
BOOST_REQUIRE(z.derivative(1,0) == 1.0);
|
||||
BOOST_REQUIRE(z.derivative(1,1) == 0.0);
|
||||
// The following 4 are unnecessarily more expensive than the previous 4.
|
||||
BOOST_REQUIRE(z.derivative(0).derivative(0) == cx + cy);
|
||||
BOOST_REQUIRE(z.derivative(0).derivative(1) == 1.0);
|
||||
BOOST_REQUIRE(z.derivative(1).derivative(0) == 1.0);
|
||||
BOOST_REQUIRE(z.derivative(1).derivative(1) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(dim2_addition)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, dim2_addition_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, dim2_addition_test());
|
||||
}
|
||||
|
||||
struct dim2_multiplication_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 6.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
constexpr float cy = 5.0;
|
||||
const auto y = make_fvar<T,0,n>(cy);
|
||||
const auto z = x*x * y*y*y;
|
||||
BOOST_REQUIRE(z.derivative(0,0) == cx*cx * cy*cy*cy); // x^2 * y^3
|
||||
BOOST_REQUIRE(z.derivative(0,1) == cx*cx * 3*cy*cy); // x^2 * 3y^2
|
||||
BOOST_REQUIRE(z.derivative(0,2) == cx*cx * 6*cy); // x^2 * 6y
|
||||
BOOST_REQUIRE(z.derivative(0,3) == cx*cx * 6); // x^2 * 6
|
||||
BOOST_REQUIRE(z.derivative(0,4) == 0.0); // x^2 * 0
|
||||
BOOST_REQUIRE(z.derivative(1,0) == 2*cx * cy*cy*cy); // 2x * y^3
|
||||
BOOST_REQUIRE(z.derivative(1,1) == 2*cx * 3*cy*cy); // 2x * 3y^2
|
||||
BOOST_REQUIRE(z.derivative(1,2) == 2*cx * 6*cy); // 2x * 6y
|
||||
BOOST_REQUIRE(z.derivative(1,3) == 2*cx * 6); // 2x * 6
|
||||
BOOST_REQUIRE(z.derivative(1,4) == 0.0); // 2x * 0
|
||||
BOOST_REQUIRE(z.derivative(2,0) == 2 * cy*cy*cy); // 2 * y^3
|
||||
BOOST_REQUIRE(z.derivative(2,1) == 2 * 3*cy*cy); // 2 * 3y^2
|
||||
BOOST_REQUIRE(z.derivative(2,2) == 2 * 6*cy); // 2 * 6y
|
||||
BOOST_REQUIRE(z.derivative(2,3) == 2 * 6); // 2 * 6
|
||||
BOOST_REQUIRE(z.derivative(2,4) == 0.0); // 2 * 0
|
||||
BOOST_REQUIRE(z.derivative(3,0) == 0.0); // 0 * y^3
|
||||
BOOST_REQUIRE(z.derivative(3,1) == 0.0); // 0 * 3y^2
|
||||
BOOST_REQUIRE(z.derivative(3,2) == 0.0); // 0 * 6y
|
||||
BOOST_REQUIRE(z.derivative(3,3) == 0.0); // 0 * 6
|
||||
BOOST_REQUIRE(z.derivative(3,4) == 0.0); // 0 * 0
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(dim2_multiplication)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, dim2_multiplication_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, dim2_multiplication_test());
|
||||
}
|
||||
|
||||
struct dim2_multiplication_and_subtraction_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 6.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
constexpr float cy = 5.0;
|
||||
const auto y = make_fvar<T,0,n>(cy);
|
||||
const auto z = x*x - y*y;
|
||||
BOOST_REQUIRE(z.derivative(0,0) == cx*cx - cy*cy);
|
||||
BOOST_REQUIRE(z.derivative(0,1) == -2*cy);
|
||||
BOOST_REQUIRE(z.derivative(0,2) == -2.0);
|
||||
BOOST_REQUIRE(z.derivative(0,3) == 0.0);
|
||||
BOOST_REQUIRE(z.derivative(0,4) == 0.0);
|
||||
BOOST_REQUIRE(z.derivative(1,0) == 2*cx);
|
||||
BOOST_REQUIRE(z.derivative(2,0) == 2.0);
|
||||
for (int i=1 ; i<=m ; ++i)
|
||||
for (int j=1 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE(z.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(dim2_multiplication_and_subtraction)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, dim2_multiplication_and_subtraction_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, dim2_multiplication_and_subtraction_test());
|
||||
}
|
||||
|
||||
struct inverse_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr float cx = 4.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
const auto xinv = x.inverse();
|
||||
BOOST_REQUIRE(xinv.derivative(0) == 1/cx);
|
||||
BOOST_REQUIRE(xinv.derivative(1) == -1/std::pow(cx,2));
|
||||
BOOST_REQUIRE(xinv.derivative(2) == 2/std::pow(cx,3));
|
||||
BOOST_REQUIRE(xinv.derivative(3) == -6/std::pow(cx,4));
|
||||
const auto zero = make_fvar<T,m>(0);
|
||||
const auto inf = zero.inverse();
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
BOOST_REQUIRE(inf.derivative(i) == (i&1?-1:1)*std::numeric_limits<T>::infinity());
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(inverse)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, inverse_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, inverse_test());
|
||||
}
|
||||
|
||||
struct division_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 16.0;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
constexpr float cy = 4.0;
|
||||
auto y = make_fvar<T,1,n>(cy);
|
||||
auto z = x*x / (y*y);
|
||||
BOOST_REQUIRE(z.derivative(0,0) == cx*cx / (cy*cy)); // x^2 * y^-2
|
||||
BOOST_REQUIRE(z.derivative(0,1) == cx*cx * (-2)*std::pow(cy,-3));
|
||||
BOOST_REQUIRE(z.derivative(0,2) == cx*cx * (6)*std::pow(cy,-4));
|
||||
BOOST_REQUIRE(z.derivative(0,3) == cx*cx * (-24)*std::pow(cy,-5));
|
||||
BOOST_REQUIRE(z.derivative(0,4) == cx*cx * (120)*std::pow(cy,-6));
|
||||
BOOST_REQUIRE(z.derivative(1,0) == 2*cx / (cy*cy));
|
||||
BOOST_REQUIRE(z.derivative(1,1) == 2*cx * (-2)*std::pow(cy,-3));
|
||||
BOOST_REQUIRE(z.derivative(1,2) == 2*cx * (6)*std::pow(cy,-4));
|
||||
BOOST_REQUIRE(z.derivative(1,3) == 2*cx * (-24)*std::pow(cy,-5));
|
||||
BOOST_REQUIRE(z.derivative(1,4) == 2*cx * (120)*std::pow(cy,-6));
|
||||
BOOST_REQUIRE(z.derivative(2,0) == 2 / (cy*cy));
|
||||
BOOST_REQUIRE(z.derivative(2,1) == 2 * (-2)*std::pow(cy,-3));
|
||||
BOOST_REQUIRE(z.derivative(2,2) == 2 * (6)*std::pow(cy,-4));
|
||||
BOOST_REQUIRE(z.derivative(2,3) == 2 * (-24)*std::pow(cy,-5));
|
||||
BOOST_REQUIRE(z.derivative(2,4) == 2 * (120)*std::pow(cy,-6));
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE(z.derivative(3,j) == 0.0);
|
||||
|
||||
auto x1 = make_fvar<T,m>(cx);
|
||||
auto z1 = x1/cy;
|
||||
BOOST_REQUIRE(z1.derivative(0) == cx/cy);
|
||||
BOOST_REQUIRE(z1.derivative(1) == 1/cy);
|
||||
BOOST_REQUIRE(z1.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(z1.derivative(3) == 0.0);
|
||||
auto y2 = make_fvar<T,m,n>(cy);
|
||||
auto z2 = cx/y2;
|
||||
BOOST_REQUIRE(z2.derivative(0,0) == cx/cy);
|
||||
BOOST_REQUIRE(z2.derivative(0,1) == -cx/std::pow(cy,2));
|
||||
BOOST_REQUIRE(z2.derivative(0,2) == 2*cx/std::pow(cy,3));
|
||||
BOOST_REQUIRE(z2.derivative(0,3) == -6*cx/std::pow(cy,4));
|
||||
BOOST_REQUIRE(z2.derivative(0,4) == 24*cx/std::pow(cy,5));
|
||||
for (int i=1 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE(z2.derivative(i,j) == 0.0);
|
||||
|
||||
const auto z3 = y / x;
|
||||
BOOST_REQUIRE(z3.derivative(0,0) == cy / cx);
|
||||
BOOST_REQUIRE(z3.derivative(0,1) == 1 / cx);
|
||||
BOOST_REQUIRE(z3.derivative(1,0) == -cy / std::pow(cx,2));
|
||||
BOOST_REQUIRE(z3.derivative(1,1) == -1 / std::pow(cx,2));
|
||||
BOOST_REQUIRE(z3.derivative(2,0) == 2*cy / std::pow(cx,3));
|
||||
BOOST_REQUIRE(z3.derivative(2,1) == 2 / std::pow(cx,3));
|
||||
BOOST_REQUIRE(z3.derivative(3,0) == -6*cy / std::pow(cx,4));
|
||||
BOOST_REQUIRE(z3.derivative(3,1) == -6 / std::pow(cx,4));
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
for (int j=2 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE(z3.derivative(i,j) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(division)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, division_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, division_test());
|
||||
}
|
||||
|
||||
struct equality_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 10.0;
|
||||
constexpr float cy = 10.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
const auto y = make_fvar<T,0,n>(cy);
|
||||
BOOST_REQUIRE((x == y));
|
||||
BOOST_REQUIRE((x == cy));
|
||||
BOOST_REQUIRE((cx == y));
|
||||
BOOST_REQUIRE((cy == x));
|
||||
BOOST_REQUIRE((y == cx));
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(equality)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, equality_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, equality_test());
|
||||
}
|
||||
|
||||
struct inequality_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 10.0;
|
||||
constexpr float cy = 11.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
const auto y = make_fvar<T,0,n>(cy);
|
||||
BOOST_REQUIRE((x != y));
|
||||
BOOST_REQUIRE((x != cy));
|
||||
BOOST_REQUIRE((cx != y));
|
||||
BOOST_REQUIRE((cy != x));
|
||||
BOOST_REQUIRE((y != cx));
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(inequality)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, inequality_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, inequality_test());
|
||||
}
|
||||
|
||||
struct less_than_or_equal_to_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 10.0;
|
||||
constexpr float cy = 11.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
const auto y = make_fvar<T,0,n>(cy);
|
||||
BOOST_REQUIRE((x <= y));
|
||||
BOOST_REQUIRE((x <= y-1));
|
||||
BOOST_REQUIRE((x < y));
|
||||
BOOST_REQUIRE((x <= cy));
|
||||
BOOST_REQUIRE((x <= cy-1));
|
||||
BOOST_REQUIRE((x < cy));
|
||||
BOOST_REQUIRE((cx <= y));
|
||||
BOOST_REQUIRE((cx <= y-1));
|
||||
BOOST_REQUIRE((cx < y));
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(less_than_or_equal_to)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, less_than_or_equal_to_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, less_than_or_equal_to_test());
|
||||
}
|
||||
|
||||
struct greater_than_or_equal_to_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr int n = 4;
|
||||
constexpr float cx = 11.0;
|
||||
constexpr float cy = 10.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
const auto y = make_fvar<T,0,n>(cy);
|
||||
BOOST_REQUIRE((x >= y));
|
||||
BOOST_REQUIRE((x >= y+1));
|
||||
BOOST_REQUIRE((x > y));
|
||||
BOOST_REQUIRE((x >= cy));
|
||||
BOOST_REQUIRE((x >= cy+1));
|
||||
BOOST_REQUIRE((x > cy));
|
||||
BOOST_REQUIRE((cx >= y));
|
||||
BOOST_REQUIRE((cx >= y+1));
|
||||
BOOST_REQUIRE((cx > y));
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(greater_than_or_equal_to)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, greater_than_or_equal_to_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, greater_than_or_equal_to_test());
|
||||
}
|
||||
|
||||
struct abs_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr float cx = 11.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
auto a = abs(x);
|
||||
BOOST_REQUIRE(a.derivative(0) == std::abs(cx));
|
||||
BOOST_REQUIRE(a.derivative(1) == 1.0);
|
||||
BOOST_REQUIRE(a.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(a.derivative(3) == 0.0);
|
||||
a = abs(-x);
|
||||
BOOST_REQUIRE(a.derivative(0) == std::abs(cx));
|
||||
BOOST_REQUIRE(a.derivative(1) == 1.0); // abs(-x) = abs(x)
|
||||
BOOST_REQUIRE(a.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(a.derivative(3) == 0.0);
|
||||
const auto xneg = make_fvar<T,m>(-cx);
|
||||
a = abs(xneg);
|
||||
BOOST_REQUIRE(a.derivative(0) == std::abs(cx));
|
||||
BOOST_REQUIRE(a.derivative(1) == -1.0);
|
||||
BOOST_REQUIRE(a.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(a.derivative(3) == 0.0);
|
||||
const auto zero = make_fvar<T,m>(0);
|
||||
a = abs(zero);
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
BOOST_REQUIRE(a.derivative(i) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(abs_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, abs_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, abs_test_test());
|
||||
}
|
||||
|
||||
struct ceil_and_floor_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
float tests[] { -1.5, 0.0, 1.5 };
|
||||
for (unsigned t=0 ; t<sizeof(tests)/sizeof(*tests) ; ++t)
|
||||
{
|
||||
const auto x = make_fvar<T,m>(tests[t]);
|
||||
auto c = ceil(x);
|
||||
auto f = floor(x);
|
||||
BOOST_REQUIRE(c.derivative(0) == std::ceil(tests[t]));
|
||||
BOOST_REQUIRE(f.derivative(0) == std::floor(tests[t]));
|
||||
for (int i=1 ; i<=m ; ++i)
|
||||
{
|
||||
BOOST_REQUIRE(c.derivative(i) == 0.0);
|
||||
BOOST_REQUIRE(f.derivative(i) == 0.0);
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(ceil_and_floor)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, ceil_and_floor_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, ceil_and_floor_test());
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_SUITE_END()
|
||||
462
test/test_autodiff_2.cpp
Normal file
462
test/test_autodiff_2.cpp
Normal file
@@ -0,0 +1,462 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include "test_autodiff.hpp"
|
||||
|
||||
BOOST_AUTO_TEST_SUITE(test_autodiff_2)
|
||||
|
||||
struct one_over_one_plus_x_squared_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 4;
|
||||
constexpr float cx = 1.0;
|
||||
auto f = make_fvar<T,m>(cx);
|
||||
//f = 1 / ((f *= f) += 1);
|
||||
f = ((f *= f) += 1).inverse();
|
||||
BOOST_REQUIRE(f.derivative(0) == 0.5);
|
||||
BOOST_REQUIRE(f.derivative(1) == -0.5);
|
||||
BOOST_REQUIRE(f.derivative(2) == 0.5);
|
||||
BOOST_REQUIRE(f.derivative(3) == 0.0);
|
||||
BOOST_REQUIRE(f.derivative(4) == -3.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(one_over_one_plus_x_squared)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, one_over_one_plus_x_squared_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, one_over_one_plus_x_squared_test());
|
||||
}
|
||||
|
||||
struct exp_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::exp;
|
||||
constexpr int m = 4;
|
||||
const T cx = 2.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
auto y = exp(x);
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
{
|
||||
//std::cout.precision(100);
|
||||
//std::cout << "y.derivative("<<i<<") = " << y.derivative(i) << ", std::exp(cx) = " << std::exp(cx) << std::endl;
|
||||
BOOST_REQUIRE(y.derivative(i) == exp(cx));
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(exp_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, exp_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, exp_test_test());
|
||||
}
|
||||
|
||||
struct pow_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 201*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::exp;
|
||||
using std::log;
|
||||
using std::pow;
|
||||
constexpr int m = 5;
|
||||
constexpr int n = 4;
|
||||
const T cx = 2.0;
|
||||
const T cy = 3.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
const auto y = make_fvar<T,m,n>(cy);
|
||||
auto z0 = pow(x,cy);
|
||||
BOOST_REQUIRE(z0.derivative(0) == pow(cx,cy));
|
||||
BOOST_REQUIRE(z0.derivative(1) == cy*pow(cx,cy-1));
|
||||
BOOST_REQUIRE(z0.derivative(2) == cy*(cy-1)*pow(cx,cy-2));
|
||||
BOOST_REQUIRE(z0.derivative(3) == cy*(cy-1)*(cy-2)*pow(cx,cy-3));
|
||||
BOOST_REQUIRE(z0.derivative(4) == 0.0);
|
||||
BOOST_REQUIRE(z0.derivative(5) == 0.0);
|
||||
auto z1 = pow(cx,y);
|
||||
BOOST_REQUIRE_CLOSE(z1.derivative(0,0), pow(cx,cy), eps);
|
||||
for (int j=1 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE_CLOSE(z1.derivative(0,j), pow(log(cx),j)*exp(cy*log(cx)), eps);
|
||||
for (int i=1 ; i<=m ; ++i)
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE(z1.derivative(i,j) == 0.0);
|
||||
auto z2 = pow(x,y);
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE_CLOSE(z2.derivative(0,j), pow(cx,cy)*pow(log(cx),j), eps);
|
||||
for (int j=0 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE_CLOSE(z2.derivative(1,j), pow(cx,cy-1)*pow(log(cx),j-1)*(cy*log(cx)+j), eps);
|
||||
BOOST_REQUIRE_CLOSE(z2.derivative(2,0), pow(cx,cy-2)*cy*(cy-1), eps);
|
||||
BOOST_REQUIRE_CLOSE(z2.derivative(2,1), pow(cx,cy-2)*(cy*(cy-1)*log(cx)+2*cy-1), eps);
|
||||
for (int j=2 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE_CLOSE(z2.derivative(2,j), pow(cx,cy-2)*pow(log(cx),j-2)*(j*(2*cy-1)*log(cx)+(j-1)*j+(cy-1)*cy*pow(log(cx),2)), eps);
|
||||
BOOST_REQUIRE_CLOSE(z2.derivative(2,4), pow(cx,cy-2)*pow(log(cx),2)*(4*(2*cy-1)*log(cx)+(4-1)*4+(cy-1)*cy*pow(log(cx),2)), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(pow_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, pow_test_test());
|
||||
}
|
||||
|
||||
struct sqrt_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::sqrt;
|
||||
using std::pow;
|
||||
constexpr int m = 5;
|
||||
constexpr float cx = 4.0;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = sqrt(x);
|
||||
BOOST_REQUIRE(y.derivative(0) == sqrt(cx));
|
||||
BOOST_REQUIRE(y.derivative(1) == 0.5*pow(cx,-0.5));
|
||||
BOOST_REQUIRE(y.derivative(2) == -0.5*0.5*pow(cx,-1.5));
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.5*0.5*1.5*pow(cx,-2.5));
|
||||
BOOST_REQUIRE(y.derivative(4) == -0.5*0.5*1.5*2.5*pow(cx,-3.5));
|
||||
BOOST_REQUIRE(y.derivative(5) == 0.5*0.5*1.5*2.5*3.5*pow(cx,-4.5));
|
||||
x = make_fvar<T,m>(0);
|
||||
y = sqrt(x);
|
||||
//std::cout << "sqrt(0) = " << y << std::endl; // (0,inf,-inf,inf,-inf,inf)
|
||||
BOOST_REQUIRE(y.derivative(0) == 0.0);
|
||||
for (int i=1; i<=m ; ++i)
|
||||
BOOST_REQUIRE(y.derivative(i) == (i&1?1:-1)*std::numeric_limits<T>::infinity());
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(sqrt_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, sqrt_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, sqrt_test_test());
|
||||
}
|
||||
|
||||
struct log_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::log;
|
||||
using std::pow;
|
||||
constexpr int m = 5;
|
||||
const T cx = 2.0;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = log(x);
|
||||
BOOST_REQUIRE(y.derivative(0) == log(cx));
|
||||
BOOST_REQUIRE(y.derivative(1) == 1/cx);
|
||||
BOOST_REQUIRE(y.derivative(2) == -1/pow(cx,2));
|
||||
BOOST_REQUIRE(y.derivative(3) == 2/pow(cx,3));
|
||||
BOOST_REQUIRE(y.derivative(4) == -6/pow(cx,4));
|
||||
BOOST_REQUIRE(y.derivative(5) == 24/pow(cx,5));
|
||||
x = make_fvar<T,m>(0);
|
||||
y = log(x);
|
||||
//std::cout << "log(0) = " << y << std::endl; // log(0) = depth(1)(-inf,inf,-inf,inf,-inf,inf)
|
||||
for (int i=0; i<=m ; ++i)
|
||||
BOOST_REQUIRE(y.derivative(i) == (i&1?1:-1)*std::numeric_limits<T>::infinity());
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(log_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, log_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, log_test_test());
|
||||
}
|
||||
|
||||
struct ylogx_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::log;
|
||||
using std::pow;
|
||||
const T eps = 100*std::numeric_limits<T>::epsilon(); // percent
|
||||
constexpr int m = 5;
|
||||
constexpr int n = 4;
|
||||
const T cx = 2.0;
|
||||
const T cy = 3.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
const auto y = make_fvar<T,m,n>(cy);
|
||||
auto z = y*log(x);
|
||||
BOOST_REQUIRE(z.derivative(0,0) == cy*log(cx));
|
||||
BOOST_REQUIRE(z.derivative(0,1) == log(cx));
|
||||
BOOST_REQUIRE(z.derivative(0,2) == 0.0);
|
||||
BOOST_REQUIRE(z.derivative(0,3) == 0.0);
|
||||
BOOST_REQUIRE(z.derivative(0,4) == 0.0);
|
||||
for (size_t i=1 ; i<=m ; ++i)
|
||||
BOOST_REQUIRE_CLOSE(z.derivative(i,0), pow(-1,i-1)*boost::math::factorial<T>(i-1)*cy/pow(cx,i), eps);
|
||||
for (size_t i=1 ; i<=m ; ++i)
|
||||
BOOST_REQUIRE_CLOSE(z.derivative(i,1), pow(-1,i-1)*boost::math::factorial<T>(i-1)/pow(cx,i), eps);
|
||||
for (size_t i=1 ; i<=m ; ++i)
|
||||
for (size_t j=2 ; j<=n ; ++j)
|
||||
BOOST_REQUIRE(z.derivative(i,j) == 0.0);
|
||||
auto z1 = exp(z);
|
||||
// RHS is confirmed by
|
||||
// https://www.wolframalpha.com/input/?i=D%5Bx%5Ey,%7Bx,2%7D,%7By,4%7D%5D+%2F.+%7Bx-%3E2.0,+y-%3E3.0%7D
|
||||
BOOST_REQUIRE_CLOSE(z1.derivative(2,4),
|
||||
pow(cx,cy-2)*pow(log(cx),2)*(4*(2*cy-1)*log(cx)+(4-1)*4+(cy-1)*cy*pow(log(cx),2)), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(ylogx)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, ylogx_test());
|
||||
}
|
||||
|
||||
struct frexp_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::frexp;
|
||||
using std::exp2;
|
||||
constexpr int m = 3;
|
||||
const T cx = 3.5;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
int exp, testexp;
|
||||
auto y = frexp(x,&exp);
|
||||
BOOST_REQUIRE(y.derivative(0) == frexp(cx,&testexp));
|
||||
BOOST_REQUIRE(exp == testexp);
|
||||
BOOST_REQUIRE(y.derivative(1) == exp2(-exp));
|
||||
BOOST_REQUIRE(y.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(frexp_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, frexp_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, frexp_test_test());
|
||||
}
|
||||
|
||||
struct ldexp_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::ldexp;
|
||||
using std::exp2;
|
||||
constexpr int m = 3;
|
||||
const T cx = 3.5;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
constexpr int exp = 3;
|
||||
auto y = ldexp(x,exp);
|
||||
BOOST_REQUIRE(y.derivative(0) == ldexp(cx,exp));
|
||||
BOOST_REQUIRE(y.derivative(1) == exp2(exp));
|
||||
BOOST_REQUIRE(y.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(ldexp_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, ldexp_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, ldexp_test_test());
|
||||
}
|
||||
|
||||
struct cos_and_sin_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::cos;
|
||||
using std::sin;
|
||||
const T eps = 200*std::numeric_limits<T>::epsilon(); // percent
|
||||
constexpr int m = 5;
|
||||
const T cx = boost::math::constants::third_pi<T>();
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
auto cos5 = cos(x);
|
||||
BOOST_REQUIRE_CLOSE(cos5.derivative(0), cos(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(cos5.derivative(1), -sin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(cos5.derivative(2), -cos(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(cos5.derivative(3), sin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(cos5.derivative(4), cos(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(cos5.derivative(5), -sin(cx), eps);
|
||||
auto sin5 = sin(x);
|
||||
BOOST_REQUIRE_CLOSE(sin5.derivative(0), sin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(sin5.derivative(1), cos(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(sin5.derivative(2), -sin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(sin5.derivative(3), -cos(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(sin5.derivative(4), sin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(sin5.derivative(5), cos(cx), eps);
|
||||
// Test Order = 0 for codecov
|
||||
auto cos0 = cos(make_fvar<T,0>(cx));
|
||||
BOOST_REQUIRE_CLOSE(cos0.derivative(0), cos(cx), eps);
|
||||
auto sin0 = sin(make_fvar<T,0>(cx));
|
||||
BOOST_REQUIRE_CLOSE(sin0.derivative(0), sin(cx), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(cos_and_sin)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, cos_and_sin_test());
|
||||
}
|
||||
|
||||
struct acos_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::acos;
|
||||
using std::pow;
|
||||
using std::sqrt;
|
||||
constexpr int m = 5;
|
||||
const T cx = 0.5;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = acos(x);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(0), acos(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), -1/sqrt(1-cx*cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), -cx/pow(1-cx*cx,1.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), -(2*cx*cx+1)/pow(1-cx*cx,2.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), -3*cx*(2*cx*cx+3)/pow(1-cx*cx,3.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(5), -(24*(cx*cx+3)*cx*cx+9)/pow(1-cx*cx,4.5), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(acos_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, acos_test_test());
|
||||
}
|
||||
|
||||
struct acosh_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::acosh;
|
||||
constexpr int m = 5;
|
||||
const T cx = 2;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = acosh(x);
|
||||
//BOOST_REQUIRE(y.derivative(0) == acosh(cx)); // FAILS! acosh(2) is overloaded for integral types
|
||||
BOOST_REQUIRE(y.derivative(0) == acosh(static_cast<T>(x)));
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), 1/boost::math::constants::root_three<T>(), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), -2/(3*boost::math::constants::root_three<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), 1/boost::math::constants::root_three<T>(), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), -22/(9*boost::math::constants::root_three<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(5), 227/(27*boost::math::constants::root_three<T>()), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(acosh_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, acosh_test_test());
|
||||
}
|
||||
|
||||
struct asin_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::asin;
|
||||
using std::pow;
|
||||
using std::sqrt;
|
||||
constexpr int m = 5;
|
||||
const T cx = 0.5;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = asin(x);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(0), asin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), 1/sqrt(1-cx*cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), cx/pow(1-cx*cx,1.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), (2*cx*cx+1)/pow(1-cx*cx,2.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), 3*cx*(2*cx*cx+3)/pow(1-cx*cx,3.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(5), (24*(cx*cx+3)*cx*cx+9)/pow(1-cx*cx,4.5), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(asin_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, asin_test_test());
|
||||
}
|
||||
|
||||
struct asin_infinity_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 100*std::numeric_limits<T>::epsilon(); // percent
|
||||
constexpr int m = 5;
|
||||
auto x = make_fvar<T,m>(1);
|
||||
auto y = asin(x);
|
||||
//std::cout << "asin(1) = " << y << std::endl; // depth(1)(1.5707963267949,inf,inf,-nan,-nan,-nan)
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(0), boost::math::constants::half_pi<T>(), eps); // MacOS is not exact
|
||||
BOOST_REQUIRE(y.derivative(1) == std::numeric_limits<T>::infinity());
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(asin_infinity)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, asin_infinity_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, asin_infinity_test());
|
||||
}
|
||||
|
||||
struct asin_derivative_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::pow;
|
||||
using std::sqrt;
|
||||
constexpr int m = 4;
|
||||
const T cx = 0.5;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = 1-x*x;
|
||||
BOOST_REQUIRE(y.derivative(0) == 1-cx*cx);
|
||||
BOOST_REQUIRE(y.derivative(1) == -2*cx);
|
||||
BOOST_REQUIRE(y.derivative(2) == -2);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0);
|
||||
BOOST_REQUIRE(y.derivative(4) == 0);
|
||||
y = sqrt(y);
|
||||
BOOST_REQUIRE(y.derivative(0) == sqrt(1-cx*cx));
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), -cx/sqrt(1-cx*cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), -1/pow(1-cx*cx,1.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), -3*cx/pow(1-cx*cx,2.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), -(12*cx*cx+3)/pow(1-cx*cx,3.5), eps);
|
||||
y = y.inverse(); // asin'(x) = 1 / sqrt(1-x*x).
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(0), 1/sqrt(1-cx*cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), cx/pow(1-cx*cx,1.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), (2*cx*cx+1)/pow(1-cx*cx,2.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), 3*cx*(2*cx*cx+3)/pow(1-cx*cx,3.5), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), (24*(cx*cx+3)*cx*cx+9)/pow(1-cx*cx,4.5), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(asin_derivative)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, asin_derivative_test());
|
||||
}
|
||||
|
||||
struct asinh_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::asinh;
|
||||
constexpr int m = 5;
|
||||
const T cx = 1;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = asinh(x);
|
||||
//BOOST_REQUIRE(y.derivative(0) == asinh(cx)); // Fails for gcc-mingw - similar to acosh()?
|
||||
BOOST_REQUIRE(y.derivative(0) == asinh(static_cast<T>(x)));
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), 1/boost::math::constants::root_two<T>(), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), -1/(2*boost::math::constants::root_two<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), 1/(4*boost::math::constants::root_two<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), 3/(8*boost::math::constants::root_two<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(5), -39/(16*boost::math::constants::root_two<T>()), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(asinh_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, asinh_test_test());
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_SUITE_END()
|
||||
254
test/test_autodiff_3.cpp
Normal file
254
test/test_autodiff_3.cpp
Normal file
@@ -0,0 +1,254 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include "test_autodiff.hpp"
|
||||
|
||||
BOOST_AUTO_TEST_SUITE(test_autodiff_3)
|
||||
|
||||
struct atanh_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::atanh;
|
||||
constexpr int m = 5;
|
||||
const T cx = 0.5;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = atanh(x);
|
||||
// BOOST_REQUIRE(y.derivative(0) == atanh(cx)); // fails due to overload
|
||||
BOOST_REQUIRE(y.derivative(0) == atanh(static_cast<T>(x)));
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), static_cast<T>(4)/3, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), static_cast<T>(16)/9, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), static_cast<T>(224)/27, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), static_cast<T>(1280)/27, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(5), static_cast<T>(31232)/81, eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(atanh_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, atanh_test_test());
|
||||
}
|
||||
|
||||
struct atan_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 5;
|
||||
constexpr float cx = 1.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
auto y = atan(x);
|
||||
BOOST_REQUIRE(y.derivative(0) == boost::math::constants::pi<T>()/4);
|
||||
BOOST_REQUIRE(y.derivative(1) == 0.5);
|
||||
BOOST_REQUIRE(y.derivative(2) == -0.5);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.5);
|
||||
BOOST_REQUIRE(y.derivative(4) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(5) == -3.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(atan_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, atan_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, atan_test_test());
|
||||
}
|
||||
|
||||
struct erf_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::erf;
|
||||
using namespace boost;
|
||||
constexpr int m = 5;
|
||||
constexpr float cx = 1.0;
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
auto y = erf(x);
|
||||
BOOST_REQUIRE(y.derivative(0) == erf(static_cast<T>(x)));
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), 2/(math::constants::e<T>()*math::constants::root_pi<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), -4/(math::constants::e<T>()*math::constants::root_pi<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), 4/(math::constants::e<T>()*math::constants::root_pi<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), 8/(math::constants::e<T>()*math::constants::root_pi<T>()), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(5), -40/(math::constants::e<T>()*math::constants::root_pi<T>()), eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(erf_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, erf_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, erf_test_test());
|
||||
}
|
||||
|
||||
struct sinc_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 20000*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::sin;
|
||||
using std::cos;
|
||||
constexpr int m = 5;
|
||||
const T cx = 1;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = sinc(x);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(0), sin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), cos(cx)-sin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), sin(cx)-2*cos(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), 5*cos(cx)-3*sin(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), 13*sin(cx)-20*cos(cx), eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(5), 101*cos(cx)-65*sin(cx), eps);
|
||||
// Test at x = 0
|
||||
auto y2 = sinc(make_fvar<T,10>(0));
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(0), 1, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(1), 0, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(2), -cx/3, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(3), 0, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(4), cx/5, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(5), 0, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(6), -cx/7, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(7), 0, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(8), cx/9, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(9), 0, eps);
|
||||
BOOST_REQUIRE_CLOSE(y2.derivative(10), -cx/11, eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(sinc_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, sinc_test_test());
|
||||
}
|
||||
|
||||
struct sinh_and_cosh_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::sinh;
|
||||
using std::cosh;
|
||||
constexpr int m = 5;
|
||||
const T cx = 1;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto s = sinh(x);
|
||||
auto c = cosh(x);
|
||||
BOOST_REQUIRE_CLOSE(s.derivative(0), sinh(static_cast<T>(x)), eps);
|
||||
BOOST_REQUIRE_CLOSE(c.derivative(0), cosh(static_cast<T>(x)), eps);
|
||||
for (size_t i=0 ; i<=m ; ++i)
|
||||
{
|
||||
BOOST_REQUIRE_CLOSE(s.derivative(i), static_cast<T>(i&1?c:s), eps);
|
||||
BOOST_REQUIRE_CLOSE(c.derivative(i), static_cast<T>(i&1?s:c), eps);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(sinh_and_cosh)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, sinh_and_cosh_test());
|
||||
}
|
||||
|
||||
struct tan_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 800*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::sqrt;
|
||||
constexpr int m = 5;
|
||||
const T cx = boost::math::constants::third_pi<T>();
|
||||
const T root_three = boost::math::constants::root_three<T>();
|
||||
const auto x = make_fvar<T,m>(cx);
|
||||
auto y = tan(x);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(0), root_three, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(1), 4.0, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(2), 8*root_three, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(3), 80.0, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(4), 352*root_three, eps);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(5), 5824.0, eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(tan_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, tan_test_test());
|
||||
}
|
||||
|
||||
struct fmod_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr int m = 3;
|
||||
constexpr float cx = 3.25;
|
||||
const T cy = 0.5;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = fmod(x,autodiff_fvar<T,m>(cy));
|
||||
BOOST_REQUIRE(y.derivative(0) == 0.25);
|
||||
BOOST_REQUIRE(y.derivative(1) == 1.0);
|
||||
BOOST_REQUIRE(y.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(fmod_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, fmod_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, fmod_test_test());
|
||||
}
|
||||
|
||||
struct round_and_trunc_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::round;
|
||||
using std::trunc;
|
||||
constexpr int m = 3;
|
||||
constexpr float cx = 3.25;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = round(x);
|
||||
BOOST_REQUIRE(y.derivative(0) == round(cx));
|
||||
BOOST_REQUIRE(y.derivative(1) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||||
y = trunc(x);
|
||||
BOOST_REQUIRE(y.derivative(0) == trunc(cx));
|
||||
BOOST_REQUIRE(y.derivative(1) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(2) == 0.0);
|
||||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(round_and_trunc)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, round_and_trunc_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, round_and_trunc_test());
|
||||
}
|
||||
|
||||
struct iround_and_itrunc_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using namespace boost::math;
|
||||
constexpr int m = 3;
|
||||
constexpr float cx = 3.25;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
int y = iround(x);
|
||||
BOOST_REQUIRE(y == iround(cx));
|
||||
y = itrunc(x);
|
||||
BOOST_REQUIRE(y == itrunc(cx));
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(iround_and_itrunc)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, iround_and_itrunc_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, iround_and_itrunc_test());
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_SUITE_END()
|
||||
64
test/test_autodiff_4.cpp
Normal file
64
test/test_autodiff_4.cpp
Normal file
@@ -0,0 +1,64 @@
|
||||
// Copyright Matthew Pulver 2018 - 2019.
|
||||
// Distributed under the Boost Software License, Version 1.0.
|
||||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include "test_autodiff.hpp"
|
||||
|
||||
BOOST_AUTO_TEST_SUITE(test_autodiff_4)
|
||||
|
||||
struct lround_llround_truncl_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using std::lround;
|
||||
using std::llround;
|
||||
//using std::truncl; // truncl not supported by boost::multiprecision types.
|
||||
constexpr int m = 3;
|
||||
const T cx = 3.25;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
long yl = lround(x);
|
||||
BOOST_REQUIRE(yl == lround(cx));
|
||||
long long yll = llround(x);
|
||||
BOOST_REQUIRE(yll == llround(cx));
|
||||
//long double yld = truncl(x);
|
||||
//BOOST_REQUIRE(yld == truncl(cx));
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(lround_llround_truncl)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, lround_llround_truncl_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, lround_llround_truncl_test());
|
||||
}
|
||||
|
||||
struct multiprecision_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 4000*std::numeric_limits<T>::epsilon(); // percent
|
||||
constexpr int Nw=3;
|
||||
constexpr int Nx=2;
|
||||
constexpr int Ny=4;
|
||||
constexpr int Nz=3;
|
||||
const auto w = make_fvar<T,Nw>(11);
|
||||
const auto x = make_fvar<T,0,Nx>(12);
|
||||
const auto y = make_fvar<T,0,0,Ny>(13);
|
||||
const auto z = make_fvar<T,0,0,0,Nz>(14);
|
||||
const auto v = mixed_partials_f(w,x,y,z); // auto = autodiff_fvar<T,Nw,Nx,Ny,Nz>
|
||||
// Calculated from Mathematica symbolic differentiation.
|
||||
const T answer = boost::lexical_cast<T>("1976.3196007477977177798818752904187209081211892187"
|
||||
"5499076582535951111845769110560421820940516423255314");
|
||||
BOOST_REQUIRE_CLOSE(v.derivative(Nw,Nx,Ny,Nz), answer, eps); // Doesn't work for cpp_dec_float
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(multiprecision)
|
||||
{
|
||||
//multiprecision_test()(boost::multiprecision::cpp_bin_float_50());
|
||||
boost::fusion::for_each(bin_float_types, multiprecision_test());
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_SUITE_END()
|
||||
Reference in New Issue
Block a user