ExprEval: add tests for auto-differentiation
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Arne Morten Kvarving
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327a855d1b
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d64d2c642c
218
src/Utility/Test/TestExprAutoDiff.C
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src/Utility/Test/TestExprAutoDiff.C
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//==============================================================================
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//!
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//! \file TestExprAutoDiff.C
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//!
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//! \date Jun 6 2023
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//!
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//! \author Arne Morten Kvarving / SINTEF
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//!
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//! \brief Tests for autodifferentiation of expression functions.
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//!
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//==============================================================================
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#include "ExprFunctions.h"
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#include <autodiff/reverse/var.hpp>
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#include <expreval.h>
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#include <iostream>
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#include "gtest/gtest.h"
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struct ExprAutoDiffImpl {
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using Type = autodiff::var;
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ExprEval::Expression<Type> expr;
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ExprEval::FunctionList<Type> flist;
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ExprEval::ValueList<Type> vlist;
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Type* xval;
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Type* yval;
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ExprAutoDiffImpl(const std::string& func,
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Type xVal, Type yVal)
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{
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flist.AddDefaultFunctions();
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vlist.Add("x", 0.0, false);
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vlist.Add("y", 0.0, false);
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expr.SetFunctionList(&flist);
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expr.SetValueList(&vlist);
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expr.Parse(func);
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xval = vlist.GetAddress("x");
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yval = vlist.GetAddress("y");
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*xval = xVal;
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*yval = yVal;
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}
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};
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struct TestDef {
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std::string name;
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std::string func;
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double x;
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double y;
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std::array<double, 6> vals;
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};
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class TestExprAutoDiff : public testing::Test,
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public testing::WithParamInterface<TestDef>
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{
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};
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TEST_P(TestExprAutoDiff, Derivatives)
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{
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ExprAutoDiffImpl e(GetParam().func, GetParam().x, GetParam().y);
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auto val = e.expr.Evaluate();
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auto [ux, uy] = derivativesx(val, wrt(*e.xval, *e.yval));
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auto [uxx, uxy] = derivativesx(ux, wrt(*e.xval, *e.yval));
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auto [uyx, uyy] = derivativesx(uy, wrt(*e.xval, *e.yval));
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EXPECT_DOUBLE_EQ(val.expr->val, GetParam().vals[0]);
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EXPECT_DOUBLE_EQ(ux.expr->val, GetParam().vals[1]);
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EXPECT_DOUBLE_EQ(uy.expr->val, GetParam().vals[2]);
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EXPECT_DOUBLE_EQ(uxx.expr->val, GetParam().vals[3]);
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EXPECT_DOUBLE_EQ(uxy.expr->val, GetParam().vals[4]);
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EXPECT_DOUBLE_EQ(uyx.expr->val, GetParam().vals[4]);
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EXPECT_DOUBLE_EQ(uyy.expr->val, GetParam().vals[5]);
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}
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INSTANTIATE_TEST_SUITE_P(TestExprAutoDiff, TestExprAutoDiff,
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testing::Values(
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TestDef{"Abs", "abs(x) + abs(y)", 1.0, -2.0,
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{1.0 + 2.0,
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1.0,
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-2.0 / 2.0,
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0.0,
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0.0,
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0.0}},
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TestDef{"ACos", "acos(rad(x)) + acos(y)", 45.0, M_PI / 4.0,
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{acos(45.0 * M_PI / 180.0) + acos(M_PI / 4.0),
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-M_PI / sqrt(32400 - M_PI * M_PI * 45 * 45),
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-1.0 / sqrt(1.0 - M_PI / 4.0 * M_PI / 4.0),
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-pow(M_PI, 3.0) * 45.0 / pow(32400 - M_PI*M_PI*45*45, 3.0 / 2.0),
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0.0,
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-M_PI / (4.0 * pow(1.0 - M_PI / 4.0 * M_PI / 4.0, 3.0 / 2.0))}},
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TestDef{"ASin", "asin(rad(x)) + asin(y)", 45.0, M_PI / 4.0,
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{asin(45.0 * M_PI / 180.0) + asin(M_PI / 4.0),
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M_PI / sqrt(32400 - M_PI * M_PI * 45 * 45),
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1.0 / sqrt(1.0 - M_PI / 4.0 * M_PI / 4.0),
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pow(M_PI, 3.0) * 45.0 / pow(32400 - M_PI * M_PI * 45.0 * 45.0, 3.0 / 2.0),
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0.0,
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M_PI / (4.0 * pow(1.0 - M_PI * M_PI / 4.0 / 4.0, 3.0 / 2.0))}},
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TestDef{"ATan", "atan(2*x) * atan(y)", 1.0, 2.0,
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{atan(2.0 * 1.0) * atan(2.0),
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2.0 / (4.0 * 1.0 * 1.0 + 1.0) * atan(2.0),
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atan(2.0 * 1.0) * 1.0 / (2.0 * 2.0 + 1.0),
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-16.0 * 1.0 / pow(4.0 * 1.0 * 1.0 + 1.0, 2.0) * atan(2.0),
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2.0 / (4.0 * 1.0 * 1.0 + 1.0) * 1.0 / (2.0 * 2.0 + 1.0),
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atan(2.0 * 1.0) * -2.0 * 2.0 / pow(2.0 * 2.0 + 1.0, 2.0)}},
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TestDef{"ATan2", "atan2(x,y)", 1.0, 2.0,
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{atan2(1.0, 2.0),
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2.0 / (1.0 * 1.0 + 2.0 * 2.0),
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-1.0 / (1.0 * 1.0 + 2.0 * 2.0),
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-2.0 * 1.0 * 2.0 / pow(1.0 * 1.0 + 2.0 * 2.0, 2.0),
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(1.0 * 1.0 - 2.0 * 2.0) / pow(1.0 * 1.0 + 2.0 * 2.0, 2.0),
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2.0 * 1.0 * 2.0 / pow(1.0 * 1.0 + 2.0 * 2.0, 2.0)}},
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TestDef{"Cos", "cos(rad(x)) + cos(y)", 45.0, M_PI / 4.0,
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{cos(45 * M_PI / 180.0) + cos(M_PI / 4.0),
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-M_PI / 180.0 * sin(45 * M_PI / 180.0),
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-sin(M_PI / 4.0),
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-M_PI * M_PI / (180.0 * 180.0) * cos(45 * M_PI / 180.0),
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0.0,
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-cos(M_PI / 4.0)}},
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TestDef{"Cosh", "cosh(2*x) * cosh(y)", 1.0, 2.0,
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{cosh(2.0 * 1.0) * cosh(2.0),
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2.0 * sinh(2.0 * 1.0) * cosh(2.0),
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cosh(2.0 * 1.0) * sinh(2.0),
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2.0 * 2.0 * cosh(2.0 * 1.0) * cosh(2.0),
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2.0 * sinh(2.0 * 1.0) * sinh(2.0),
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cosh(2.0 * 1.0) * cosh(2.0)}},
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TestDef{"Deg", "deg(x*x)", 1.0, 2.0,
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{1.0 * 1.0 / M_PI * 180.0,
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360.0 * 1.0 / M_PI,
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0.0,
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360.0 / M_PI,
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0.0,
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0.0}},
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TestDef{"Exp", "exp(2*x) * exp(y)", 1.0, 2.0,
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{exp(2.0 * 1.0) * exp(2.0),
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2.0 * exp(2.0 * 1.0) * exp(2.0),
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exp(2.0 * 1.0) * exp(2.0),
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4.0 * exp(2.0 * 1.0) * exp(2.0),
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2.0 * exp(2.0 * 1.0) * exp(2.0),
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exp(2.0 * 1.0) * exp(2.0)}},
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TestDef{"Ln", "ln(2*x) * ln(y)", 1.0, 2.0,
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{log(2.0 * 1.0) * log(2.0),
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1.0 / 1.0 * log(2.0),
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log(2.0 * 1.0) / 2.0,
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-1.0 / (1.0 * 1.0) * log(2.0),
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1.0 / (1.0) * 1.0 / (2.0),
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log(2.0 * 1.0) * -1.0 / (2.0 * 2.0)}},
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TestDef{"Log", "log(2*x) * log(y)", 1.0, 2.0,
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{log10(2.0 * 1.0) * log10(2.0),
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1.0 / (1.0 * log(10)) * log10(2.0),
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log10(2.0 * 1.0) / (2.0 * log(10)),
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-1.0 / (1.0 * 1.0 * log(10)) * log10(2.0),
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1.0 / (1.0 * log(10)) * 1.0 / (2.0 * log(10)),
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log10(2.0 * 1.0) * -1.0 / (2.0 * 2.0 * log(10))}},
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TestDef{"Logn", "logn(2*x, 5)", 1.0, 2.0,
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{log(2.0 * 1.0) / log(5.0),
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1.0 / (1.0 * log(5.0)),
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0.0,
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-1.0 / (1.0 * 1.0 * log(5.0)),
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0.0,
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0.0}},
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TestDef{"Pow", "pow(x,2) * pow(y,2)", 1.0, 2.0,
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{pow(1.0, 2.0) * pow(2.0, 2.0),
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2.0 * 1.0 * pow(2.0, 2.0),
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pow(1.0, 2.0) * 2.0 * 2.0,
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2.0 * pow(2.0, 2.0),
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2.0 * 1.0 * 2.0 * 2.0,
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pow(1.0, 2.0) * 2.0}},
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TestDef{"Rad", "rad(x*x)", 1.0, 2.0,
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{1.0 * 1.0 * M_PI / 180.0,
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M_PI * 1.0 / 90.0,
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0.0,
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M_PI / 90.0,
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0.0,
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0.0}},
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TestDef{"Sin", "sin(rad(x)) + sin(y)", 45.0, M_PI / 4.0,
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{sin(45 * M_PI / 180.0) + sin(M_PI / 4.0),
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M_PI / 180.0 * cos(45 * M_PI / 180.0),
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cos(M_PI / 4.0),
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-M_PI * M_PI / (180.0 * 180.0) * sin(45 * M_PI / 180.0),
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0.0,
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-sin(M_PI / 4.0)}},
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TestDef{"Sqrt", "sqrt(x) * sqrt(y)", 1.0, 2.0,
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{sqrt(1.0) * sqrt(2.0),
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1.0 / (2.0 * sqrt(1.0)) * sqrt(2.0),
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sqrt(1.0) / (2.0 * sqrt(2.0)),
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-1.0 / 4.0 * sqrt(2.0),
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1.0 / (2.0 * sqrt(1.0)) * 1.0 / (2.0*sqrt(2.0)),
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sqrt(1.0) * -1.0 / (4.0*pow(2.0, 3.0 / 2.0))}},
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TestDef{"Sinh", "sinh(2*x) * sinh(y)", 1.0, 2.0,
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{sinh(2.0 * 1.0) * sinh(2.0),
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2.0*cosh(2.0 * 1.0) * sinh(2.0),
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sinh(2.0 * 1.0) * cosh(2.0),
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2.0 * 2.0 * sinh(2.0 * 1.0) * sinh(2.0),
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2.0 * cosh(2.0 * 1.0) * cosh(2.0),
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sinh(2.0 * 1.0) * sinh(2.0)}},
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TestDef{"Tan", "tan(rad(x)) + tan(y)", 45.0, M_PI / 4.0,
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{tan(45 * M_PI / 180.0) + tan(M_PI / 4.0),
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M_PI / (180.0 * pow(cos(45 * M_PI / 180.0), 2.0)),
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1.0 / pow (cos(M_PI / 4.0), 2.0),
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M_PI * M_PI / (180.0 * 180.0) * 2.0 * sin(45 * M_PI / 180.0) / pow(cos(45 * M_PI / 180.0), 3.0),
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0.0,
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2.0 * sin(M_PI / 4.0) / pow(cos(M_PI / 4.0), 3.0)}},
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TestDef{"Tanh", "tanh(2.0*x) * tanh(y)", 1.0, 2.0,
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{tanh(2.0 * 1.0) * tanh(2.0),
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2.0 / pow(cosh(2.0 * 1.0), 2.0) * tanh(2.0),
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tanh(2.0 * 1.0) / pow(cosh(2.0), 2.0),
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-2.0 * 2.0 * 2.0 * sinh(2.0 * 1.0) / pow(cosh(2.0 * 1.0), 3.0) * tanh(2.0),
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2.0 / pow(cosh(2.0 * 1.0), 2.0) * 1.0 / pow(cosh(2.0), 2.0),
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tanh(2.0 * 1.0) * -2.0 * sinh(2.0) / pow(cosh(2.0), 3.0)}}
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), [](const testing::TestParamInfo<TestDef>& info)
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{
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return info.param.name;
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});
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