Adding the first moment analytical integration of a lin-lin panel

src/scion/integration/FirstMomentLinearLinear.hpp

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+#ifndef NJOY_SCION_INTEGRATION_LINEARLINEAR
+#define NJOY_SCION_INTEGRATION_LINEARLINEAR
+
+// system includes
+
+// other includes
+#include "scion/integration/IntegratorBase.hpp"
+
+namespace njoy {
+namespace scion {
+namespace integration {
+
+  /**
+   *  @class
+   *  @brief First raw moment of a Linear-linear panel (y is linear in x)
+   *
+   *  The first raw moment or mean is defined as the integral of x * f(x)
+   */
+  class FirstMomentLinearLinear : public IntegratorBase< FirstMomentLinearLinear > {
+
+    /* friend declarations */
+    friend class IntegratorBase< FirstMomentLinearLinear >;
+
+    /* interface implementation functions */
+
+    /**
+     *  @brief Perform first raw moment integration of a linear-linear panel (y is linear in x)
+     *
+     *  @param[in] xLeft    the left value on the x interval
+     *  @param[in] xRight   the right value on the x interval
+     *  @param[in] yLeft    the left value on the y interval
+     *  @param[in] yRight   the right value on the y interval
+     */
+    template < typename X, typename Y,
+               typename I = decltype( std::declval< X >() * std::declval< X >() * std::declval< Y >() ) >
+    I integrate( const X& xLeft, const X& xRight,
+                 const Y& yLeft, const Y& yRight ) const noexcept {
+
+      auto delta = ( xRight - xLeft );
+      auto slope = ( yRight - yLeft ) / delta / 3.;
+      auto constant = 0.5 * ( xRight * yLeft - xLeft * yRight ) / delta;
+      return xRight * xRight * ( slope * xRight + constant )
+             - xLeft * xLeft * ( slope * yLeft + constant );
+    }
+
+  public:
+
+    using IntegratorBase::operator();
+  };
+
+  // integration function
+  static constexpr FirstMomentLinearLinear firstMomentLinLin;
+
+} // integration namespace
+} // scion namespace
+} // njoy namespace
+
+#endif

src/scion/integration/FirstMomentLinearLinear/test/CMakeLists.txt

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+add_cpp_test( integration.FirstMomentLinearLinear FirstMomentLinearLinear.test.cpp )

src/scion/integration/FirstMomentLinearLinear/test/FirstMomentLinearLinear.test.cpp

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+// include Catch2
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers_floating_point.hpp>
+using Catch::Matchers::WithinRel;
+
+// what we are testing
+#include "scion/integration/FirstMomentLinearLinear.hpp"
+
+// other includes
+
+// convenience typedefs
+using namespace njoy::scion;
+
+SCENARIO( "MeanLinearLinear" ) {
+
+  GIVEN( "MeanLinearLinear integration object" ) {
+
+    WHEN( "integrating an interval" ) {
+
+      integration::FirstMomentLinearLinear integrator{};
+
+      THEN( "the integration is performed correctly" ) {
+
+        double xLeft = 1.0;
+        double xRight = 2.0;
+        double yLeft = 1.0;
+        double yRight = 4.0;
+
+        // both y values are the same
+        CHECK_THAT( 1.5, WithinRel( integrator( xLeft, xRight, yLeft, yLeft ) ) );
+
+        // the y values are different
+        CHECK_THAT( 4.0, WithinRel( integrator( xLeft, xRight, yLeft, yRight ) ) );
+      } // THEN
+    } // WHEN
+  } // GIVEN
+
+  GIVEN( "linlin integration function" ) {
+
+    WHEN( "integrating an interval" ) {
+
+      THEN( "the integration is performed correctly" ) {
+
+        double xLeft = 1.0;
+        double xRight = 2.0;
+        double yLeft = 1.0;
+        double yRight = 4.0;
+
+        // both y values are the same
+        CHECK_THAT( 1.5, WithinRel( integration::firstMomentLinLin( xLeft, xRight, yLeft, yLeft ) ) );
+
+        // the y values are different
+        CHECK_THAT( 4.0, WithinRel( integration::firstMomentLinLin( xLeft, xRight, yLeft, yRight ) ) );
+      } // THEN
+    } // WHEN
+  } // GIVEN
+} // SCENARIO