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Doc: Add sections Migrating Code, and Function Writing Guidelines. Additional math function overloads: acosh, asinh, atanh, cosh, erf, lambert_w0, sinc, sinh, tanh. Attempt to fix appveyor errors.
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Matt Pulver
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@@ -67,6 +67,7 @@ automatic differentiation] (forward mode) of mathematical functions of single an
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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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@@ -78,20 +79,21 @@ the first-order polynomial ['x[sub 0]+\u03b5], the resulting polynomial in ['\u0
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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 the first /N/ derivatives of /f/ at ['x[sub 0]]. Then without any loss of precision
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to the calculation of the derivatives, all terms ['O(\u03b5[super N+1])] that include powers of ['\u03b5] greater
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than /N/ can be discarded, and under these truncation rules, /f/ provides a polynomial-to-polynomial transformation:
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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` that represents
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polynomials in ['\u03b5]. Thus the same algorithm that calculates the numeric value of ['y[sub 0]=f(x[sub 0])]
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is also used to calculate the polynomial ['\u03a3[sub n]y[sub n]\u03b5[super n]=f(x[sub 0]+\u03b5)].
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The derivatives are then found from the product of the respective factorial and coefficient:
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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$$f^{(n)}(x_0)=n!y_n.$$ ]
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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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@@ -101,11 +103,11 @@ The derivatives are then found from the product of the respective factorial and
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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,
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and `make_fvar<double,5>(2.0)` represents the polynomial 2+['\u03b5]. Internally, this is modeled by a
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`std::array<double,6>` whose elements `{2, 1, 0, 0, 0, 0}` correspond to the 6 coefficients of the polynomial upon
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initialization. Its fourth power is a polynomial with coefficients `y = {16, 32, 24, 8, 1, 0}`. The derivatives
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are obtained using the formula ['f[super (n)](2)=n!*y[n]].
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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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@@ -154,15 +156,15 @@ Example 2: Multi-variable mixed partial derivatives with multi-precision data ty
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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 100 decimal digits,
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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_dec_float_100,Nw,Nx,Ny,Nz>` represents a multivariate polynomial
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in 4 independent variables, where the highest powers of each are `Nw`, `Nx`, `Ny` and `Nz`. The underlying
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arithmetic data type, aliased as `root_type`, is `boost::multiprecision::cpp_dec_float_100`. The internal data
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type is `std::array<std::array<std::array<std::array<cpp_dec_float_100,Nz+1>,Ny+1>,Nx+1>,Nw+1>`. The `root_type`
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is always the first template parameter to `autodiff_fvar<...>` followed by the maximum derivative orders that are
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to be calculated for each independent variable.
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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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@@ -170,10 +172,10 @@ of the 4 different polynomial variables ['\u03b5[sub w]], ['\u03b5[sub x]], ['\u
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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\_dec\_float\_100,Nw>(11)} &= 11+\varepsilon_w \\
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\texttt{make\_fvar<cpp\_dec\_float\_100,0,Nx>(12)} &= 12+\varepsilon_x \\
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\texttt{make\_fvar<cpp\_dec\_float\_100,0,0,Ny>(13)} &= 13+\varepsilon_y \\
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\texttt{make\_fvar<cpp\_dec\_float\_100,0,0,0,Nz>(14)} &= 14+\varepsilon_z
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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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@@ -181,7 +183,7 @@ Instances of different types are automatically promoted to the smallest multi-va
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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_dec_float.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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@@ -193,22 +195,22 @@ when they are combined (added, subtracted, multiplied, divided.)
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int main()
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{
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using cpp_dec_float_100 = boost::multiprecision::cpp_dec_float_100;
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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_dec_float_100,Nw,Nx,Ny,Nz>;
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const var w = make_fvar<cpp_dec_float_100,Nw>(11);
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const var x = make_fvar<cpp_dec_float_100,0,Nx>(12);
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const var y = make_fvar<cpp_dec_float_100,0,0,Ny>(13);
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const var z = make_fvar<cpp_dec_float_100,0,0,0,Nz>(14);
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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_dec_float_100 answer("1976.31960074779771777988187529041872090812118921875499076582535951111845769110560421820940516423255314");
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std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10)
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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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@@ -216,12 +218,12 @@ when they are combined (added, subtracted, multiplied, divided.)
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}
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/*
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Output:
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mathematica : 1976.319600747797717779881875290418720908121189218754990765825359511118457691105604218209405164232553
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autodiff : 1976.319600747797717779881875290418720908121189218754990765825359511118457691105604218209405164232566
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relative error: 6.47e-99
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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 Documentation]
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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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1062
doc/differentiation/autodiff.tex
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1062
doc/differentiation/autodiff.tex
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File diff suppressed because it is too large
Load Diff
@@ -1,90 +1,94 @@
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<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="96pt" height="31pt" viewBox="0 0 96 31" version="1.1">
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|
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|
||||
|
Before Width: | Height: | Size: 58 KiB After Width: | Height: | Size: 60 KiB |
@@ -15,14 +15,14 @@ using namespace boost::math::differentiation;
|
||||
template<typename X>
|
||||
X phi(const X& x)
|
||||
{
|
||||
return boost::math::constants::one_div_root_two_pi<double>()*exp(-0.5*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<double>()*x);
|
||||
return 0.5*erfc(-boost::math::constants::one_div_root_two<X>()*x);
|
||||
}
|
||||
|
||||
enum CP { call, put };
|
||||
|
||||
@@ -4,7 +4,7 @@
|
||||
// https://www.boost.org/LICENSE_1_0.txt)
|
||||
|
||||
#include <boost/math/differentiation/autodiff.hpp>
|
||||
#include <boost/multiprecision/cpp_dec_float.hpp>
|
||||
#include <boost/multiprecision/cpp_bin_float.hpp>
|
||||
#include <iostream>
|
||||
|
||||
template<typename T>
|
||||
@@ -16,30 +16,31 @@ T f(const T& w, const T& x, const T& y, const T& z)
|
||||
|
||||
int main()
|
||||
{
|
||||
using cpp_dec_float_100 = boost::multiprecision::cpp_dec_float_100;
|
||||
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_dec_float_100,Nw,Nx,Ny,Nz>;
|
||||
const var w = make_fvar<cpp_dec_float_100,Nw>(11);
|
||||
const var x = make_fvar<cpp_dec_float_100,0,Nx>(12);
|
||||
const var y = make_fvar<cpp_dec_float_100,0,0,Ny>(13);
|
||||
const var z = make_fvar<cpp_dec_float_100,0,0,0,Nz>(14);
|
||||
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. See multiprecision.nb for script.
|
||||
const cpp_dec_float_100 answer("1976.31960074779771777988187529041872090812118921875499076582535951111845769110560421820940516423255314");
|
||||
std::cout << std::setprecision(std::numeric_limits<cpp_dec_float_100>::digits10)
|
||||
// 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;
|
||||
<< "relative error: " << std::setprecision(3) << (v.derivative(Nw,Nx,Ny,Nz)/answer-1)
|
||||
<< std::endl;
|
||||
return 0;
|
||||
}
|
||||
/*
|
||||
Output:
|
||||
mathematica : 1976.319600747797717779881875290418720908121189218754990765825359511118457691105604218209405164232553
|
||||
autodiff : 1976.319600747797717779881875290418720908121189218754990765825359511118457691105604218209405164232566
|
||||
relative error: 6.47e-99
|
||||
mathematica : 1976.3196007477977177798818752904187209081211892188
|
||||
autodiff : 1976.3196007477977177798818752904187209081211892188
|
||||
relative error: 2.67e-50
|
||||
**/
|
||||
|
||||
@@ -8,7 +8,7 @@
|
||||
|
||||
#include <boost/config.hpp>
|
||||
#include <boost/math/constants/constants.hpp>
|
||||
#include <boost/math/special_functions/factorials.hpp>
|
||||
#include <boost/math/special_functions.hpp>
|
||||
#include <boost/math/tools/promotion.hpp>
|
||||
|
||||
#include <algorithm>
|
||||
@@ -424,9 +424,10 @@ fvar<RealType,Order> tan(const fvar<RealType,Order>&);
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> atan(const fvar<RealType,Order>&);
|
||||
|
||||
// fmod(cr1) | RealType
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> fmod(const fvar<RealType,Order>&, const typename fvar<RealType,Order>::root_type&);
|
||||
// fmod(cr1,cr2) | RealType
|
||||
template<typename RealType1, size_t Order1, typename RealType2, size_t Order2>
|
||||
promote<fvar<RealType1,Order1>,fvar<RealType2,Order2>>
|
||||
fmod(const fvar<RealType1,Order1>&, const fvar<RealType2,Order2>&);
|
||||
|
||||
// round(cr1) | RealType
|
||||
template<typename RealType, size_t Order>
|
||||
@@ -448,9 +449,36 @@ int itrunc(const fvar<RealType,Order>&);
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> acos(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> acosh(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> asinh(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> atanh(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> cosh(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> erf(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> erfc(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> lambert_w0(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> sinc(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> sinh(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> tanh(const fvar<RealType,Order>&);
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
long lround(const fvar<RealType,Order>&);
|
||||
|
||||
@@ -928,8 +956,7 @@ template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> fvar<RealType,Order>::apply_with_horner(const std::function<root_type(size_t)>& f) const
|
||||
{
|
||||
const fvar<RealType,Order> epsilon = fvar<RealType,Order>(*this).set_root(0);
|
||||
auto accumulator = fvar<RealType,Order>( // Cast needed for types where operator/() does not return root_type.
|
||||
static_cast<root_type>(f(order_sum) / boost::math::factorial<root_type>(order_sum)));
|
||||
fvar<RealType,Order> accumulator(static_cast<root_type>(f(order_sum)/boost::math::factorial<root_type>(order_sum)));
|
||||
for (size_t i=order_sum ; i-- ;)
|
||||
(accumulator *= epsilon) += f(i) / boost::math::factorial<root_type>(i);
|
||||
return accumulator;
|
||||
@@ -942,7 +969,7 @@ fvar<RealType,Order>
|
||||
fvar<RealType,Order>::apply_with_horner_factorials(const std::function<root_type(size_t)>& f) const
|
||||
{
|
||||
const fvar<RealType,Order> epsilon = fvar<RealType,Order>(*this).set_root(0);
|
||||
auto accumulator = fvar<RealType,Order>(f(order_sum));
|
||||
fvar<RealType,Order> accumulator(f(order_sum));
|
||||
for (size_t i=order_sum ; i-- ;)
|
||||
(accumulator *= epsilon) += f(i);
|
||||
return accumulator;
|
||||
@@ -1036,9 +1063,9 @@ fvar<RealType,Order> fvar<RealType,Order>::inverse() const
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> fvar<RealType,Order>::inverse_apply() const
|
||||
{
|
||||
root_type derivatives[order_sum+1]; // derivatives of 1/x
|
||||
root_type derivatives[order_sum+1]; // LCOV_EXCL_LINE This causes a false negative on lcov coverage test.
|
||||
const root_type x0 = static_cast<root_type>(*this);
|
||||
derivatives[0] = 1 / x0;
|
||||
*derivatives = 1 / x0;
|
||||
for (size_t i=1 ; i<=order_sum ; ++i)
|
||||
derivatives[i] = -derivatives[i-1] * i / x0;
|
||||
return apply([&derivatives](size_t j) { return derivatives[j]; });
|
||||
@@ -1131,7 +1158,7 @@ fvar<RealType,Order> pow(const fvar<RealType,Order>& x,const typename fvar<RealT
|
||||
using std::pow;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
constexpr size_t order = fvar<RealType,Order>::order_sum;
|
||||
std::array<root_type,order+1> derivatives; // array of derivatives
|
||||
root_type derivatives[order+1];
|
||||
const root_type x0 = static_cast<root_type>(x);
|
||||
size_t i = 0;
|
||||
root_type coef = 1;
|
||||
@@ -1163,21 +1190,21 @@ fvar<RealType,Order> sqrt(const fvar<RealType,Order>& cr)
|
||||
using std::sqrt;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
constexpr size_t order = fvar<RealType,Order>::order_sum;
|
||||
std::array<root_type,order+1> derivatives;
|
||||
root_type derivatives[order+1];
|
||||
const root_type x = static_cast<root_type>(cr);
|
||||
derivatives.front() = sqrt(x);
|
||||
*derivatives = sqrt(x);
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (order == 0)
|
||||
return fvar<RealType,Order>(derivatives.front());
|
||||
return fvar<RealType,Order>(*derivatives);
|
||||
else
|
||||
{
|
||||
root_type numerator = 0.5;
|
||||
root_type powers = 1;
|
||||
derivatives[1] = numerator / derivatives.front();
|
||||
derivatives[1] = numerator / *derivatives;
|
||||
for (size_t i=2 ; i<=order ; ++i)
|
||||
{
|
||||
numerator *= -0.5 * ((i<<1)-3);
|
||||
powers *= x;
|
||||
derivatives[i] = numerator / (powers * derivatives.front());
|
||||
derivatives[i] = numerator / (powers * *derivatives);
|
||||
}
|
||||
return cr.apply([&derivatives](size_t i) { return derivatives[i]; });
|
||||
}
|
||||
@@ -1203,18 +1230,16 @@ fvar<RealType,Order> log(const fvar<RealType,Order>& cr)
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> frexp(const fvar<RealType,Order>& cr, int* exp)
|
||||
{
|
||||
using std::exp2;
|
||||
using std::frexp;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
frexp(static_cast<root_type>(cr), exp);
|
||||
return cr * exp2(-*exp);
|
||||
return cr * std::exp2(-*exp);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> ldexp(const fvar<RealType,Order>& cr, int exp)
|
||||
{
|
||||
using std::exp2;
|
||||
return cr * exp2(exp);
|
||||
return cr * std::exp2(exp);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
@@ -1292,13 +1317,14 @@ fvar<RealType,Order> atan(const fvar<RealType,Order>& cr)
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order>
|
||||
fmod(const fvar<RealType,Order>& cr, const typename fvar<RealType,Order>::root_type& ca)
|
||||
template<typename RealType1, size_t Order1, typename RealType2, size_t Order2>
|
||||
promote<fvar<RealType1,Order1>,fvar<RealType2,Order2>>
|
||||
fmod(const fvar<RealType1,Order1>& cr1, const fvar<RealType2,Order2>& cr2)
|
||||
{
|
||||
using std::fmod;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
return fvar<RealType,Order>(cr).set_root(0) += fmod(static_cast<root_type>(cr), ca);
|
||||
using std::trunc;
|
||||
const auto numer = static_cast<typename fvar<RealType1,Order1>::root_type>(cr1);
|
||||
const auto denom = static_cast<typename fvar<RealType2,Order2>::root_type>(cr2);
|
||||
return cr1 - cr2 * trunc(numer/denom);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
@@ -1351,8 +1377,92 @@ fvar<RealType,Order> acos(const fvar<RealType,Order>& cr)
|
||||
return fvar<RealType,Order>(d0);
|
||||
else
|
||||
{
|
||||
auto d1 = make_fvar<root_type,order-1>(static_cast<root_type>(cr));
|
||||
d1 = -sqrt(1-(d1*=d1)).inverse(); // acos'(x) = -1 / sqrt(1-x*x).
|
||||
auto x = make_fvar<root_type,order-1>(static_cast<root_type>(cr));
|
||||
const auto d1 = -sqrt(1-(x*=x)).inverse(); // acos'(x) = -1 / sqrt(1-x*x).
|
||||
return cr.apply_with_horner_factorials([&d0,&d1](size_t i) { return i ? d1.at(i-1)/i : d0; });
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> acosh(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
using std::acosh;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
constexpr size_t order = fvar<RealType,Order>::order_sum;
|
||||
const root_type d0 = acosh(static_cast<root_type>(cr));
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (order == 0)
|
||||
return fvar<RealType,Order>(d0);
|
||||
else
|
||||
{
|
||||
auto x = make_fvar<root_type,order-1>(static_cast<root_type>(cr));
|
||||
const auto d1 = sqrt((x*=x)-1).inverse(); // acosh'(x) = 1 / sqrt(x*x-1).
|
||||
return cr.apply_with_horner_factorials([&d0,&d1](size_t i) { return i ? d1.at(i-1)/i : d0; });
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> asinh(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
using std::asinh;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
constexpr size_t order = fvar<RealType,Order>::order_sum;
|
||||
const root_type d0 = asinh(static_cast<root_type>(cr));
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (order == 0)
|
||||
return fvar<RealType,Order>(d0);
|
||||
else
|
||||
{
|
||||
auto x = make_fvar<root_type,order-1>(static_cast<root_type>(cr));
|
||||
const auto d1 = sqrt((x*=x)+1).inverse(); // asinh'(x) = 1 / sqrt(x*x+1).
|
||||
return cr.apply_with_horner_factorials([&d0,&d1](size_t i) { return i ? d1.at(i-1)/i : d0; });
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> atanh(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
using std::atanh;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
constexpr size_t order = fvar<RealType,Order>::order_sum;
|
||||
const root_type d0 = atanh(static_cast<root_type>(cr));
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (order == 0)
|
||||
return fvar<RealType,Order>(d0);
|
||||
else
|
||||
{
|
||||
auto x = make_fvar<root_type,order-1>(static_cast<root_type>(cr));
|
||||
const auto d1 = (1-(x*=x)).inverse(); // atanh'(x) = 1 / (1-x*x)
|
||||
return cr.apply_with_horner_factorials([&d0,&d1](size_t i) { return i ? d1.at(i-1)/i : d0; });
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> cosh(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
using std::cosh;
|
||||
using std::sinh;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
const root_type d0 = cosh(static_cast<root_type>(cr));
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (fvar<RealType,Order>::order_sum == 0)
|
||||
return fvar<RealType,Order>(d0);
|
||||
else
|
||||
{
|
||||
const root_type derivatives[2] { d0, sinh(static_cast<root_type>(cr)) };
|
||||
return cr.apply_with_horner([&derivatives](size_t i) { return derivatives[i&1]; });
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> erf(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
using std::erf;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
constexpr size_t order = fvar<RealType,Order>::order_sum;
|
||||
const root_type d0 = erf(static_cast<root_type>(cr));
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (order == 0)
|
||||
return fvar<RealType,Order>(d0);
|
||||
else
|
||||
{
|
||||
auto x = make_fvar<root_type,order-1>(static_cast<root_type>(cr));
|
||||
const auto d1 = 2*boost::math::constants::one_div_root_pi<root_type>()*exp(-(x*=x)); // 2/sqrt(pi)*exp(-x*x)
|
||||
return cr.apply_with_horner_factorials([&d0,&d1](size_t i) { return i ? d1.at(i-1)/i : d0; });
|
||||
}
|
||||
}
|
||||
@@ -1368,12 +1478,91 @@ fvar<RealType,Order> erfc(const fvar<RealType,Order>& cr)
|
||||
return fvar<RealType,Order>(d0);
|
||||
else
|
||||
{
|
||||
auto d1 = make_fvar<root_type,order-1>(static_cast<root_type>(cr));
|
||||
d1 = -2*boost::math::constants::one_div_root_pi<root_type>()*exp(-(d1*=d1)); // erfc'(x)=-2/sqrt(pi)*exp(-x*x)
|
||||
auto x = make_fvar<root_type,order-1>(static_cast<root_type>(cr));
|
||||
const auto d1 = -2*boost::math::constants::one_div_root_pi<root_type>()*exp(-(x*=x)); // erfc'(x)=-erf'(x)
|
||||
return cr.apply_with_horner_factorials([&d0,&d1](size_t i) { return i ? d1.at(i-1)/i : d0; });
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> lambert_w0(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
using boost::math::lambert_w0;
|
||||
using std::exp;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
constexpr size_t order = fvar<RealType,Order>::order_sum;
|
||||
root_type derivatives[order+1];
|
||||
*derivatives = lambert_w0(static_cast<root_type>(cr));
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (order == 0)
|
||||
return fvar<RealType,Order>(*derivatives);
|
||||
else
|
||||
{
|
||||
const root_type expw = exp(*derivatives);
|
||||
derivatives[1] = 1 / (static_cast<root_type>(cr) + expw);
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (order == 1)
|
||||
return cr.apply([&derivatives](size_t i) { return derivatives[i]; });
|
||||
else
|
||||
{
|
||||
root_type d1powers = derivatives[1] * derivatives[1];
|
||||
const root_type x = derivatives[1] * expw;
|
||||
derivatives[2] = d1powers * (-1 - x);
|
||||
std::array<root_type,order> coef { -1, -1 }; // as in derivatives[2].
|
||||
for (size_t n=3 ; n<=order ; ++n)
|
||||
{
|
||||
coef[n-1] = coef[n-2] * -static_cast<root_type>(2*n-3);
|
||||
for (size_t j=n-2 ; j!=0 ; --j)
|
||||
(coef[j] *= -static_cast<root_type>(n-1)) -= (n+j-2) * coef[j-1];
|
||||
coef[0] *= -static_cast<root_type>(n-1);
|
||||
d1powers *= derivatives[1];
|
||||
derivatives[n] = d1powers * std::accumulate(coef.crend()-(n-1), coef.crend(), coef[n-1],
|
||||
[&x](const root_type& a, const root_type& b) { return a*x + b; });
|
||||
}
|
||||
return cr.apply([&derivatives](size_t i) { return derivatives[i]; });
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> sinc(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
if (cr != 0)
|
||||
return sin(cr) / cr;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
constexpr size_t order = fvar<RealType,Order>::order_sum;
|
||||
root_type taylor[order+1] { 1 }; // sinc(0) = 1
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (order == 0)
|
||||
return fvar<RealType,Order>(*taylor);
|
||||
else
|
||||
{
|
||||
for (size_t n=2 ; n<=order ; n+=2)
|
||||
taylor[n] = (1-static_cast<int>(n&2)) / boost::math::factorial<root_type>(n+1);
|
||||
return cr.apply_with_factorials([&taylor](size_t i) { return taylor[i]; });
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> sinh(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
using std::sinh;
|
||||
using std::cosh;
|
||||
using root_type = typename fvar<RealType,Order>::root_type;
|
||||
const root_type d0 = sinh(static_cast<root_type>(cr));
|
||||
if BOOST_AUTODIFF_IF_CONSTEXPR (fvar<RealType,Order>::order_sum == 0)
|
||||
return fvar<RealType,Order>(d0);
|
||||
else
|
||||
{
|
||||
const root_type derivatives[2] { d0, cosh(static_cast<root_type>(cr)) };
|
||||
return cr.apply_with_horner([&derivatives](size_t i) { return derivatives[i&1]; });
|
||||
}
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
fvar<RealType,Order> tanh(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
const fvar<RealType,Order> exp2cr = exp(cr*2);
|
||||
return (exp2cr - 1) /= (exp2cr + 1);
|
||||
}
|
||||
|
||||
template<typename RealType, size_t Order>
|
||||
long lround(const fvar<RealType,Order>& cr)
|
||||
{
|
||||
|
||||
@@ -1238,7 +1238,7 @@ test-suite misc :
|
||||
[ 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 __temporary_test.cpp test_instances//test_instances : : : <test-info>always_show_run_output <pch>off ]
|
||||
[ run test_autodiff.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx11_lambdas ] ]
|
||||
[ run test_autodiff.cpp ../../test/build//boost_unit_test_framework : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx11_inline_namespaces ] ]
|
||||
;
|
||||
|
||||
build-project ../example ;
|
||||
|
||||
@@ -3,24 +3,22 @@
|
||||
// (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/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>
|
||||
#include <boost/multiprecision/cpp_dec_float.hpp>
|
||||
|
||||
#define BOOST_TEST_MODULE test_autodiff
|
||||
#include <boost/test/included/unit_test.hpp>
|
||||
|
||||
#include <iostream>
|
||||
#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; // Add cpp_bin_float_50 for boost 1.70
|
||||
//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;
|
||||
@@ -70,10 +68,7 @@ promote<Price,Sigma,Tau,Rate>
|
||||
template<typename T>
|
||||
T uncast_return(const T& x)
|
||||
{
|
||||
if (x == 0)
|
||||
return 0;
|
||||
else
|
||||
return 1;
|
||||
return x == 0 ? 0 : 1;
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_SUITE(test_autodiff)
|
||||
@@ -199,6 +194,26 @@ BOOST_AUTO_TEST_CASE(assignment)
|
||||
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>
|
||||
@@ -606,7 +621,6 @@ struct dim2_addition_test
|
||||
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; // ambiguous operator when root_type=cpp_bin_float_50
|
||||
const auto z = x + y;
|
||||
BOOST_REQUIRE(z.derivative(0,0) == cx + cy);
|
||||
BOOST_REQUIRE(z.derivative(0,1) == 1.0);
|
||||
@@ -711,6 +725,10 @@ struct inverse_test
|
||||
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());
|
||||
}
|
||||
};
|
||||
|
||||
@@ -970,8 +988,8 @@ struct one_over_one_plus_x_squared_test
|
||||
constexpr int m = 4;
|
||||
constexpr float cx = 1.0;
|
||||
auto f = make_fvar<T,m>(cx);
|
||||
//f = ((f *= f) += 1).inverse(); // Microsoft Visual C++ version 14.0: fatal error C1001: An internal error has occurred in the compiler. on call to order_sum() in inverse_apply().
|
||||
f = 1 / ((f *= f) += 1);
|
||||
//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);
|
||||
@@ -1277,6 +1295,32 @@ 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>
|
||||
@@ -1362,30 +1406,55 @@ BOOST_AUTO_TEST_CASE(asin_derivative)
|
||||
boost::fusion::for_each(bin_float_types, asin_derivative_test());
|
||||
}
|
||||
|
||||
struct tan_test_test
|
||||
struct asinh_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 800*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::sqrt;
|
||||
const T eps = 300*std::numeric_limits<T>::epsilon(); // percent
|
||||
using std::asinh;
|
||||
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);
|
||||
const T cx = 1;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = asinh(x);
|
||||
BOOST_REQUIRE(y.derivative(0) == asinh(cx));
|
||||
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(tan_test)
|
||||
BOOST_AUTO_TEST_CASE(asinh_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, tan_test_test());
|
||||
boost::fusion::for_each(bin_float_types, asinh_test_test());
|
||||
}
|
||||
|
||||
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
|
||||
@@ -1412,6 +1481,125 @@ BOOST_AUTO_TEST_CASE(atan_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;
|
||||
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(s.derivative(0) == sinh(static_cast<T>(x)));
|
||||
BOOST_REQUIRE(c.derivative(0) == cosh(static_cast<T>(x)));
|
||||
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>
|
||||
@@ -1421,7 +1609,7 @@ struct fmod_test_test
|
||||
constexpr float cx = 3.25;
|
||||
const T cy = 0.5;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = fmod(x,cy);
|
||||
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);
|
||||
@@ -1486,6 +1674,49 @@ BOOST_AUTO_TEST_CASE(iround_and_itrunc)
|
||||
boost::fusion::for_each(multiprecision_float_types, iround_and_itrunc_test());
|
||||
}
|
||||
|
||||
struct lambert_w0_test_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
const T eps = 1000*std::numeric_limits<T>::epsilon(); // percent
|
||||
constexpr int m = 10;
|
||||
const T cx = 3;
|
||||
// Mathematica: N[Table[D[ProductLog[x], {x, n}], {n, 0, 10}] /. x -> 3, 52]
|
||||
const char* const answers[m+1] {
|
||||
"1.049908894964039959988697070552897904589466943706341",
|
||||
"0.1707244807388472968312949774415522047470762509741737",
|
||||
"-0.04336545501146252734105411312976167858858970875797718",
|
||||
"0.02321456264324789334313200360870492961288748451791104",
|
||||
"-0.01909049778427783072663170526188353869136655225133878",
|
||||
"0.02122935002563637629500975949987796094687564718834156",
|
||||
"-0.02979093848448877259041971538394953658978044986784643",
|
||||
"0.05051290266216717699803334605370337985567016837482099",
|
||||
"-0.1004503154972645060971099914384090562800544486549660",
|
||||
"0.2292464437392250211967939182075930820454464472006425",
|
||||
"-0.5905839053125614593682763387470654123192290838719517"};
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
auto y = lambert_w0(x);
|
||||
for (int i=0 ; i<=m ; ++i)
|
||||
{
|
||||
const T answer = boost::lexical_cast<T>(answers[i]);
|
||||
BOOST_REQUIRE_CLOSE(y.derivative(i), answer, eps);
|
||||
}
|
||||
//const T cx0 = -1 / boost::math::constants::e<T>();
|
||||
//auto edge = lambert_w0(make_fvar<T,m>(cx0));
|
||||
//std::cout << "edge = " << edge << std::endl;
|
||||
//edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
|
||||
//edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
|
||||
//edge = depth(1)(-1,3.68935e+19,-9.23687e+57,4.62519e+96,-2.89497e+135,2.02945e+174,-1.52431e+213,1.19943e+252,-9.75959e+290,8.14489e+329,-6.93329e+368)
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(lambert_w0_test)
|
||||
{
|
||||
boost::fusion::for_each(bin_float_types, lambert_w0_test_test());
|
||||
boost::fusion::for_each(multiprecision_float_types, lambert_w0_test_test());
|
||||
}
|
||||
|
||||
struct lround_llround_truncl_test
|
||||
{
|
||||
template<typename T>
|
||||
@@ -1493,9 +1724,9 @@ struct lround_llround_truncl_test
|
||||
{
|
||||
using std::lround;
|
||||
using std::llround;
|
||||
//using std::truncl; // truncl not supported by cpp_dec_float<>.
|
||||
//using std::truncl; // truncl not supported by boost::multiprecision types.
|
||||
constexpr int m = 3;
|
||||
constexpr float cx = 3.25;
|
||||
const T cx = 3.25;
|
||||
auto x = make_fvar<T,m>(cx);
|
||||
long yl = lround(x);
|
||||
BOOST_REQUIRE(yl == lround(cx));
|
||||
@@ -1551,29 +1782,30 @@ struct multiprecision_test
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
constexpr double tolerance = 100e-98; // percent
|
||||
using cpp_dec_float_100 = boost::multiprecision::cpp_dec_float_100;
|
||||
// Calculated from Mathematica symbolic differentiation. See example/multiprecision.nb for script.
|
||||
const cpp_dec_float_100 answer("1976.31960074779771777988187529041872090812118921875499076582535951111845769110560421820940516423255314");
|
||||
const T eps = 600*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<cpp_dec_float_100,Nw>(11);
|
||||
const auto x = make_fvar<cpp_dec_float_100,0,Nx>(12);
|
||||
const auto y = make_fvar<cpp_dec_float_100,0,0,Ny>(13);
|
||||
const auto z = make_fvar<cpp_dec_float_100,0,0,0,Nz>(14);
|
||||
const auto v = mixed_partials_f(w,x,y,z); // auto = autodiff_fvar<cpp_dec_float_100,Nw,Nx,Ny,Nz>
|
||||
// BOOST_REQUIRE_CLOSE(v.derivative(Nw,Nx,Ny,Nz), answer, tolerance); Doesn't compile on travis-ci trusty.
|
||||
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
|
||||
using std::fabs;
|
||||
const cpp_dec_float_100 relative_error = fabs(v.derivative(Nw,Nx,Ny,Nz)/answer-1);
|
||||
BOOST_REQUIRE(100*relative_error.convert_to<T>() < tolerance);
|
||||
const double relative_error = static_cast<double>(fabs(v.derivative(Nw,Nx,Ny,Nz)/answer-1));
|
||||
BOOST_REQUIRE(100*relative_error < eps);
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(multiprecision)
|
||||
{
|
||||
multiprecision_test()(boost::multiprecision::cpp_dec_float_100());
|
||||
//multiprecision_test()(boost::multiprecision::cpp_bin_float_50());
|
||||
boost::fusion::for_each(bin_float_types, mixed_partials_test());
|
||||
}
|
||||
|
||||
struct black_scholes_test
|
||||
@@ -1656,4 +1888,78 @@ BOOST_AUTO_TEST_CASE(black_scholes)
|
||||
boost::fusion::for_each(bin_float_types, black_scholes_test());
|
||||
}
|
||||
|
||||
/*
|
||||
// Compilation tests for boost special functions.
|
||||
struct boost_special_functions_test
|
||||
{
|
||||
template<typename T>
|
||||
void operator()(const T&) const
|
||||
{
|
||||
using namespace boost;
|
||||
constexpr int m = 3;
|
||||
BOOST_REQUIRE(math::acosh(make_fvar<T,m>(1.5)) == math::acosh(static_cast<T>(1.5)));
|
||||
// Policy parameter prevents proper ADL for autodiff_fvar objects. E.g. iround(v,pol) instead of iround(v).
|
||||
// In cyl_bessel_j_imp() call is made to iround(v, pol) with v of type autodiff_fvar. It it were just iround(v)
|
||||
// then autodiff's iround would properly be called via ADL.
|
||||
//BOOST_REQUIRE(math::airy_ai(make_fvar<T,m>(1)) == math::airy_ai(static_cast<T>(1)));
|
||||
//BOOST_REQUIRE(math::airy_bi(make_fvar<T,m>(1)) == math::airy_bi(static_cast<T>(1)));
|
||||
//BOOST_REQUIRE(math::airy_ai_prime(make_fvar<T,m>(1)) == math::airy_ai_prime(static_cast<T>(1)));
|
||||
//BOOST_REQUIRE(math::airy_bi_prime(make_fvar<T,m>(1)) == math::airy_bi_prime(static_cast<T>(1)));
|
||||
BOOST_REQUIRE(math::asinh(make_fvar<T,m>(0.5)) == math::asinh(static_cast<T>(0.5)));
|
||||
BOOST_REQUIRE(math::atanh(make_fvar<T,m>(0.5)) == math::atanh(static_cast<T>(0.5)));
|
||||
// Policy parameter prevents ADL.
|
||||
//BOOST_REQUIRE(math::cyl_bessel_j(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_j(0,static_cast<T>(0.5)));
|
||||
//BOOST_REQUIRE(math::cyl_neumann(0,make_fvar<T,m>(0.5)) == math::cyl_neumann(0,static_cast<T>(0.5)));
|
||||
//BOOST_REQUIRE(math::cyl_bessel_j_zero(make_fvar<T,m>(0.5),0) == math::cyl_bessel_j_zero(static_cast<T>(0.5),0));
|
||||
//BOOST_REQUIRE(math::cyl_neumann_zero(make_fvar<T,m>(0.5),0) == math::cyl_neumann_zero(static_cast<T>(0.5),0));
|
||||
// Required sinh() (added) but then has policy parameter ADL issue.
|
||||
//BOOST_REQUIRE(math::cyl_bessel_i(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_i(0,static_cast<T>(0.5)));
|
||||
BOOST_REQUIRE(math::cyl_bessel_k(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_k(0,static_cast<T>(0.5)));
|
||||
// Policy parameter prevents ADL.
|
||||
//BOOST_REQUIRE(math::sph_bessel(0,make_fvar<T,m>(0.5)) == math::sph_bessel(0,static_cast<T>(0.5)));
|
||||
// Required fmod() but then has policy parameter ADL issue.
|
||||
//BOOST_REQUIRE(math::sph_neumann(0,make_fvar<T,m>(0.5)) == math::sph_neumann(0,static_cast<T>(0.5)));
|
||||
// Policy parameter prevents ADL.
|
||||
//BOOST_REQUIRE(math::cyl_bessel_j_prime(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_j_prime(0,static_cast<T>(0.5)));
|
||||
//BOOST_REQUIRE(math::cyl_neumann_prime(0,make_fvar<T,m>(0.5)) == math::cyl_neumann_prime(0,static_cast<T>(0.5)));
|
||||
//BOOST_REQUIRE(math::cyl_bessel_i_prime(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_i_prime(0,static_cast<T>(0.5)));
|
||||
BOOST_REQUIRE(math::cyl_bessel_k_prime(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_k_prime(0,static_cast<T>(0.5)));
|
||||
// Policy parameter prevents ADL.
|
||||
//BOOST_REQUIRE(math::sph_bessel_prime(0,make_fvar<T,m>(0.5)) == math::sph_bessel_prime(0,static_cast<T>(0.5)));
|
||||
//BOOST_REQUIRE(math::sph_neumann_prime(0,make_fvar<T,m>(0.5)) == math::sph_neumann_prime(0,static_cast<T>(0.5)));
|
||||
// Per docs: "the functions can only be instantiated on types float, double and long double."
|
||||
//BOOST_REQUIRE(math::cyl_hankel_1(0,make_fvar<T,m>(0.5)).real() == math::cyl_hankel_1(0,static_cast<T>(0.5)).real());
|
||||
//BOOST_REQUIRE(math::cyl_hankel_2(0,make_fvar<T,m>(0.5)).real() == math::cyl_hankel_2(0,static_cast<T>(0.5)).real());
|
||||
//BOOST_REQUIRE(math::sph_hankel_1(0,make_fvar<T,m>(0.5)).real() == math::sph_hankel_1(0,static_cast<T>(0.5)).real());
|
||||
//BOOST_REQUIRE(math::sph_hankel_2(0,make_fvar<T,m>(0.5)).real() == math::sph_hankel_2(0,static_cast<T>(0.5)).real());
|
||||
// Compiles, but compares 0.74868571757768376251 == 0.74868571757768354047 which is false.
|
||||
// BOOST_REQUIRE(static_cast<T>(math::beta(make_fvar<T,m>(1.1),make_fvar<T,m>(1.2))) == static_cast<T>(math::beta(static_cast<T>(1.1),static_cast<T>(1.2))));
|
||||
// Skipped other beta functions.
|
||||
std::cout.precision(20);
|
||||
// Compiles, but compares 0.7937005259840996807 == 0.79370052598409979172 which is false.
|
||||
//BOOST_REQUIRE(math::cbrt(make_fvar<T,m>(0.5)) == math::cbrt(static_cast<T>(0.5)));
|
||||
//Skipping other Basic Functions
|
||||
BOOST_REQUIRE(math::chebyshev_next(make_fvar<T,m>(0.5),make_fvar<T,m>(0.5),make_fvar<T,m>(0.5)) ==
|
||||
math::chebyshev_next(static_cast<T>(0.5),static_cast<T>(0.5),static_cast<T>(0.5)));
|
||||
// Requires acosh() (added)
|
||||
BOOST_REQUIRE(math::chebyshev_t(0,make_fvar<T,m>(0.5)) == math::chebyshev_t(0,static_cast<T>(0.5)));
|
||||
BOOST_REQUIRE(math::chebyshev_u(0,make_fvar<T,m>(0.5)) == math::chebyshev_u(0,static_cast<T>(0.5)));
|
||||
BOOST_REQUIRE(math::chebyshev_t_prime(0,make_fvar<T,m>(0.5)) == math::chebyshev_t_prime(0,static_cast<T>(0.5)));
|
||||
{
|
||||
std::array<double,4> c{14.2, -13.7, 82.3, 96};
|
||||
// /usr/include/boost/math/special_functions/chebyshev.hpp:164:40: error: cannot convert ‘boost::math::differentiation::autodiff_v1::detail::fvar<double, 3>’ to ‘double’ in return
|
||||
//BOOST_REQUIRE(math::chebyshev_clenshaw_recurrence(c.data(),c.size(),make_fvar<T,m>(0.5)) == math::chebyshev_clenshaw_recurrence(c.data(),c.size(),static_cast<T>(0.5)));
|
||||
}
|
||||
// TODO Continue alphabetically through <boost/math/special_functions.hpp>
|
||||
}
|
||||
};
|
||||
|
||||
BOOST_AUTO_TEST_CASE(boost_special_functions)
|
||||
{
|
||||
boost_special_functions_test()(static_cast<double>(0));
|
||||
//boost::fusion::for_each(bin_float_types, boost_special_functions_test());
|
||||
//boost::fusion::for_each(multiprecision_float_types, boost_special_functions_test());
|
||||
}
|
||||
*/
|
||||
|
||||
BOOST_AUTO_TEST_SUITE_END()
|
||||
|
||||
Reference in New Issue
Block a user