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test.cpp
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test.cpp
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#include "had.h"
#include <cassert>
#include <cmath>
using namespace std;
using namespace had;
DECLARE_ADGRAPH();
#define NearEqualAssert(a, b) \
assert(std::fabs((a) - (b)) < 1e-8)
void TestAdd() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal x2 = AReal(Real(3.0));
AReal y = x0 + x0 + x1 + x2;
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx2 = GetAdjoint(x2);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx0x2 = GetAdjoint(x0, x2);
Real dydx1x1 = GetAdjoint(x1, x1);
Real dydx1x2 = GetAdjoint(x1, x2);
Real dydx2x2 = GetAdjoint(x2, x2);
NearEqualAssert(dydx0, Real(2.0));
NearEqualAssert(dydx1, Real(1.0));
NearEqualAssert(dydx2, Real(1.0));
NearEqualAssert(dydx0x0, Real(0.0));
NearEqualAssert(dydx0x1, Real(0.0));
NearEqualAssert(dydx0x2, Real(0.0));
NearEqualAssert(dydx1x1, Real(0.0));
NearEqualAssert(dydx1x2, Real(0.0));
NearEqualAssert(dydx2x2, Real(0.0));
}
void TestMinus() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal x2 = AReal(Real(3.0));
AReal y = - x0 - x0 - x1 - x2;
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx2 = GetAdjoint(x2);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx0x2 = GetAdjoint(x0, x2);
Real dydx1x1 = GetAdjoint(x1, x1);
Real dydx1x2 = GetAdjoint(x1, x2);
Real dydx2x2 = GetAdjoint(x2, x2);
NearEqualAssert(dydx0, Real(-2.0));
NearEqualAssert(dydx1, Real(-1.0));
NearEqualAssert(dydx2, Real(-1.0));
NearEqualAssert(dydx0x0, Real(0.0));
NearEqualAssert(dydx0x1, Real(0.0));
NearEqualAssert(dydx0x2, Real(0.0));
NearEqualAssert(dydx1x1, Real(0.0));
NearEqualAssert(dydx1x2, Real(0.0));
NearEqualAssert(dydx2x2, Real(0.0));
}
void TestMultiply() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal x2 = AReal(Real(3.0));
AReal y = x0 * x0 * x1 * x1 * x2;
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx2 = GetAdjoint(x2);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx0x2 = GetAdjoint(x0, x2);
Real dydx1x1 = GetAdjoint(x1, x1);
Real dydx1x2 = GetAdjoint(x1, x2);
Real dydx2x2 = GetAdjoint(x2, x2);
NearEqualAssert(dydx0, Real(2.0) * x0.val * x1.val * x1.val * x2.val);
NearEqualAssert(dydx1, Real(2.0) * x0.val * x0.val * x1.val * x2.val);
NearEqualAssert(dydx2, x0.val * x0.val * x1.val * x1.val);
NearEqualAssert(dydx0x0, Real(2.0) * x1.val * x1.val * x2.val);
NearEqualAssert(dydx0x1, Real(4.0) * x0.val * x1.val * x2.val);
NearEqualAssert(dydx0x2, Real(2.0) * x0.val * x1.val * x1.val);
NearEqualAssert(dydx1x1, Real(2.0) * x0.val * x0.val * x2.val);
NearEqualAssert(dydx1x2, Real(2.0) * x0.val * x0.val * x1.val);
NearEqualAssert(dydx2x2, Real(0.0));
}
void TestDivision() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal x2 = AReal(Real(3.0));
AReal y = (x0 * x0) / (x1 * x2);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx2 = GetAdjoint(x2);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx0x2 = GetAdjoint(x0, x2);
Real dydx1x1 = GetAdjoint(x1, x1);
Real dydx1x2 = GetAdjoint(x1, x2);
Real dydx2x2 = GetAdjoint(x2, x2);
NearEqualAssert(dydx0, Real(2.0) * x0.val / (x1.val * x2.val));
NearEqualAssert(dydx1, - (x0.val * x0.val) / (x1.val * x1.val * x2.val));
NearEqualAssert(dydx2, - (x0.val * x0.val) / (x1.val * x2.val * x2.val));
NearEqualAssert(dydx0x0, Real(2.0) / (x1.val * x2.val));
NearEqualAssert(dydx0x1, - Real(2.0) * x0.val / (x1.val * x1.val * x2.val));
NearEqualAssert(dydx0x2, - Real(2.0) * x0.val / (x1.val * x2.val * x2.val));
NearEqualAssert(dydx1x1, (Real(2.0) * x0.val * x0.val) / (x1.val * x1.val * x1.val * x2.val));
NearEqualAssert(dydx1x2, x0.val * x0.val / (x1.val * x1.val * x2.val * x2.val));
NearEqualAssert(dydx2x2, (Real(2.0) * x0.val * x0.val) / (x1.val * x2.val * x2.val * x2.val));
}
void TestSqrt() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal x2 = AReal(Real(3.0));
AReal y = sqrt(x0 * x1 + x2);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx2 = GetAdjoint(x2);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx0x2 = GetAdjoint(x0, x2);
Real dydx1x1 = GetAdjoint(x1, x1);
Real dydx1x2 = GetAdjoint(x1, x2);
Real dydx2x2 = GetAdjoint(x2, x2);
NearEqualAssert(dydx0, x1.val / (Real(2.0) * sqrt(x0.val * x1.val + x2.val)));
NearEqualAssert(dydx1, x0.val / (Real(2.0) * sqrt(x0.val * x1.val + x2.val)));
NearEqualAssert(dydx2, Real(1.0) / (Real(2.0) * sqrt(x0.val * x1.val + x2.val)));
NearEqualAssert(dydx0x0, - (x1.val * x1.val) / (Real(4.0) * pow(x0.val * x1.val + x2.val, Real(3.0/2.0))));
NearEqualAssert(dydx0x1, (x0.val * x1.val + Real(2.0) * x2.val) / (Real(4.0) * pow(x0.val * x1.val + x2.val, Real(3.0/2.0))));
NearEqualAssert(dydx0x2, - (x1.val) / (Real(4.0) * pow(x0.val * x1.val + x2.val, Real(3.0/2.0))));
NearEqualAssert(dydx1x1, - (x0.val * x0.val) / (Real(4.0) * pow(x0.val * x1.val + x2.val, Real(3.0/2.0))));
NearEqualAssert(dydx1x2, - (x0.val) / (Real(4.0) * pow(x0.val * x1.val + x2.val, Real(3.0/2.0))));
NearEqualAssert(dydx2x2, - Real(1.0) / (Real(4.0) * pow(x0.val * x1.val + x2.val, Real(3.0/2.0))));
}
void TestPow() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal y = pow(x0 + x1, Real(5.3));
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx1x1 = GetAdjoint(x1, x1);
NearEqualAssert(dydx0, Real(5.3) * pow(x0.val + x1.val, Real(4.3)));
NearEqualAssert(dydx1, Real(5.3) * pow(x0.val + x1.val, Real(4.3)));
NearEqualAssert(dydx0x0, Real(22.79) * pow(x0.val + x1.val, Real(3.3)));
NearEqualAssert(dydx0x1, Real(22.79) * pow(x0.val + x1.val, Real(3.3)));
NearEqualAssert(dydx1x1, Real(22.79) * pow(x0.val + x1.val, Real(3.3)));
}
void TestExp() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal y = exp(x0 * x0 + x1);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx1x1 = GetAdjoint(x1, x1);
NearEqualAssert(dydx0, Real(2.0) * x0.val * exp(x0.val * x0.val + x1.val));
NearEqualAssert(dydx1, exp(x0.val * x0.val + x1.val));
NearEqualAssert(dydx0x0, Real(2.0) * (Real(2.0) * x0.val * x0.val + Real(1.0)) * exp(x0.val * x0.val + x1.val));
NearEqualAssert(dydx0x1, Real(2.0) * x0.val * exp(x0.val * x0.val + x1.val));
NearEqualAssert(dydx1x1, exp(x0.val * x0.val + x1.val));
}
void TestLog() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal y = log(x0 * x0 + x1);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx1x1 = GetAdjoint(x1, x1);
NearEqualAssert(dydx0, Real(2.0) * x0.val / (x0.val * x0.val + x1.val));
NearEqualAssert(dydx1, Real(1.0) / (x0.val * x0.val + x1.val));
NearEqualAssert(dydx0x0, - Real(2.0) * (x0.val * x0.val - x1.val) / ((x0.val * x0.val + x1.val) * (x0.val * x0.val + x1.val)));
NearEqualAssert(dydx0x1, - Real(2.0) * x0.val / ((x0.val * x0.val + x1.val) * (x0.val * x0.val + x1.val)));
NearEqualAssert(dydx1x1, - Real(1.0) / ((x0.val * x0.val + x1.val) * (x0.val * x0.val + x1.val)));
}
void TestSin() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal y = sin(x0) * sin(x1);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx1x1 = GetAdjoint(x1, x1);
NearEqualAssert(dydx0, cos(x0.val) * sin(x1.val));
NearEqualAssert(dydx1, sin(x0.val) * cos(x1.val));
NearEqualAssert(dydx0x0, - sin(x0.val) * sin(x1.val));
NearEqualAssert(dydx0x1, cos(x0.val) * cos(x1.val));
NearEqualAssert(dydx1x1, - sin(x0.val) * sin(x1.val));
}
void TestCos() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal y = cos(x0) * cos(x1);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx1x1 = GetAdjoint(x1, x1);
NearEqualAssert(dydx0, - sin(x0.val) * cos(x1.val));
NearEqualAssert(dydx1, - cos(x0.val) * sin(x1.val));
NearEqualAssert(dydx0x0, - cos(x0.val) * cos(x1.val));
NearEqualAssert(dydx0x1, sin(x0.val) * sin(x1.val));
NearEqualAssert(dydx1x1, - cos(x0.val) * cos(x1.val));
}
void TestTan() {
ADGraph adGraph;
AReal x0 = AReal(Real(1.0));
AReal x1 = AReal(Real(2.0));
AReal y = tan(x0) * tan(x1);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx1x1 = GetAdjoint(x1, x1);
NearEqualAssert(dydx0, tan(x1.val) / (cos(x0.val) * cos(x0.val)));
NearEqualAssert(dydx1, tan(x0.val) / (cos(x1.val) * cos(x1.val)));
NearEqualAssert(dydx0x0, Real(2.0) * tan(x0.val) * tan(x1.val) / (cos(x0.val) * cos(x0.val)));
NearEqualAssert(dydx0x1, Real(1.0) / (cos(x0.val) * cos(x0.val) * cos(x1.val) * cos(x1.val)));
NearEqualAssert(dydx1x1, Real(2.0) * tan(x0.val) * tan(x1.val) / (cos(x1.val) * cos(x1.val)));
}
void TestASin() {
ADGraph adGraph;
AReal x0 = AReal(Real(0.3));
AReal x1 = AReal(Real(0.6));
AReal y = asin(x0) * asin(x1);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx1x1 = GetAdjoint(x1, x1);
NearEqualAssert(dydx0, asin(x1.val) / sqrt(Real(1.0) - x0.val * x0.val));
NearEqualAssert(dydx1, asin(x0.val) / sqrt(Real(1.0) - x1.val * x1.val));
NearEqualAssert(dydx0x0, x0.val * asin(x1.val) / pow(Real(1.0) - x0.val * x0.val, Real(3.0) / Real(2.0)));
NearEqualAssert(dydx0x1, Real(1.0) / (sqrt(Real(1.0) - x0.val * x0.val) * sqrt(Real(1.0) - x1.val * x1.val)));
NearEqualAssert(dydx1x1, x1.val * asin(x0.val) / pow(Real(1.0) - x1.val * x1.val, Real(3.0) / Real(2.0)));
}
void TestACos() {
ADGraph adGraph;
AReal x0 = AReal(Real(0.3));
AReal x1 = AReal(Real(0.6));
AReal y = acos(x0) * acos(x1);
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx0 = GetAdjoint(x0);
Real dydx1 = GetAdjoint(x1);
Real dydx0x0 = GetAdjoint(x0, x0);
Real dydx0x1 = GetAdjoint(x0, x1);
Real dydx1x1 = GetAdjoint(x1, x1);
NearEqualAssert(dydx0, - acos(x1.val) / sqrt(Real(1.0) - x0.val * x0.val));
NearEqualAssert(dydx1, - acos(x0.val) / sqrt(Real(1.0) - x1.val * x1.val));
NearEqualAssert(dydx0x0, - x0.val * acos(x1.val) / pow(Real(1.0) - x0.val * x0.val, Real(3.0) / Real(2.0)));
NearEqualAssert(dydx0x1, Real(1.0) / (sqrt(Real(1.0) - x0.val * x0.val) * sqrt(Real(1.0) - x1.val * x1.val)));
NearEqualAssert(dydx1x1, - x1.val * acos(x0.val) / pow(Real(1.0) - x1.val * x1.val, Real(3.0) / Real(2.0)));
}
void TestCopy() {
ADGraph adGraph;
AReal x = AReal(Real(0.3));
AReal tmp = x;
AReal y = x * tmp; // y = x^2
SetAdjoint(y, Real(1.0));
PropagateAdjoint();
Real dydx = GetAdjoint(x);
Real dydxx = GetAdjoint(x, x);
NearEqualAssert(dydx, Real(2.0) * x.val);
NearEqualAssert(dydxx, Real(2.0));
}
int main(int argc, char *argv[]) {
TestAdd();
TestMinus();
TestMultiply();
TestDivision();
TestSqrt();
TestPow();
TestExp();
TestLog();
TestSin();
TestCos();
TestTan();
TestASin();
TestACos();
TestCopy();
return 0;
}