Function1s::Polynomial: Simplification

The coefficients in the polynomial are now specified in order of
increasing exponent, starting from the constant coefficient (i.e., zero
exponent). Exponents are no longer specified. This better fits the
definition of a polynomial, and it prevents the strange scenario when if
exponents are given as a vector or tensor or similar then the units of
the coefficients are not the same across the different components.

For example, polynomial y = -1 + x^2 + 2x^3 can be specified as:

    <name>  polynomial (-1 0 1 2);

Or, alternatively:

    <name>
    {
        type    polynomial;
        coeffs  (-1 0 1 2);
    }

applications/test/Function1/polynomial

@@ -0,0 +1,5 @@
+function polynomial (0 4 -4 1);
+
+x0 -0.5;
+x1 2.5;
+nX 51;

src/OpenFOAM/primitives/functions/Function1/Polynomial1/Polynomial1.C

@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2023 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2024 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -27,45 +27,6 @@ License
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-template<class Type>
-Foam::Function1s::Polynomial<Type>::Polynomial
-(
-    const word& name,
-    const List<Tuple2<Type, Type>>& coeffs
-)
-:
-    FieldFunction1<Type, Polynomial<Type>>(name),
-    coeffs_(coeffs),
-    integrable_(true)
-{
-    if (!coeffs_.size())
-    {
-        FatalErrorInFunction
-            << "Polynomial coefficients for entry " << this->name_
-            << " are invalid (empty)" << nl << exit(FatalError);
-    }
-
-    forAll(coeffs_, i)
-    {
-        if (mag(coeffs_[i].second() + pTraits<Type>::one) < rootVSmall)
-        {
-            integrable_ = false;
-            break;
-        }
-    }
-
-    if (debug)
-    {
-        if (!integrable_)
-        {
-            WarningInFunction
-                << "Polynomial " << this->name_ << " cannot be integrald"
-                << endl;
-        }
-    }
-}
-
-
 template<class Type>
 Foam::Function1s::Polynomial<Type>::Polynomial
 (
@@ -73,8 +34,17 @@ Foam::Function1s::Polynomial<Type>::Polynomial
     const dictionary& dict
 )
 :
-    Polynomial<Type>(name, dict.lookup("coeffs"))
+    FieldFunction1<Type, Polynomial<Type>>(name),
-{}
+    coeffs_(dict.lookup("coeffs"))
+{
+    if (!coeffs_.size())
+    {
+        FatalIOErrorInFunction(dict)
+            << typeName.capitalise() << ' ' << name
+            << " must have at least one coefficient"
+            << exit(FatalError);
+    }
+}
 
 
 template<class Type>
@@ -84,16 +54,24 @@ Foam::Function1s::Polynomial<Type>::Polynomial
     Istream& is
 )
 :
-    Polynomial<Type>(name, List<Tuple2<Type, Type>>(is))
+    FieldFunction1<Type, Polynomial<Type>>(name),
-{}
+    coeffs_(is)
+{
+    if (!coeffs_.size())
+    {
+        FatalIOErrorInFunction(is)
+            << typeName.capitalise() << ' ' << name
+            << " must have at least one coefficient"
+            << exit(FatalError);
+    }
+}
 
 
 template<class Type>
 Foam::Function1s::Polynomial<Type>::Polynomial(const Polynomial& poly)
 :
     FieldFunction1<Type, Polynomial<Type>>(poly),
-    coeffs_(poly.coeffs_),
+    coeffs_(poly.coeffs_)
-    integrable_(poly.integrable_)
 {}
 
 
@@ -109,14 +87,11 @@ Foam::Function1s::Polynomial<Type>::~Polynomial()
 template<class Type>
 Type Foam::Function1s::Polynomial<Type>::value(const scalar x) const
 {
-    Type y(Zero);
+    Type y = coeffs_[coeffs_.size() - 1];
-    forAll(coeffs_, i)
+
+    for (label i = coeffs_.size() - 2; i >= 0; i --)
     {
-        y += cmptMultiply
+        y = y*x + coeffs_[i];
-        (
-            coeffs_[i].first(),
-            cmptPow(pTraits<Type>::one*x, coeffs_[i].second())
-        );
     }
 
     return y;
@@ -130,34 +105,15 @@ Type Foam::Function1s::Polynomial<Type>::integral
     const scalar x2
 ) const
 {
-    Type intx(Zero);
+    Type Sy1 = coeffs_[coeffs_.size() - 1]/coeffs_.size(), Sy2 = Sy1;
 
-    if (integrable_)
+    for (label i = coeffs_.size() - 2; i >= 0; i --)
     {
-        forAll(coeffs_, i)
+        Sy1 = Sy1*x1 + coeffs_[i]/(i + 1);
-        {
+        Sy2 = Sy2*x2 + coeffs_[i]/(i + 1);
-            intx += cmptMultiply
-            (
-                cmptDivide
-                (
-                    coeffs_[i].first(),
-                    coeffs_[i].second() + pTraits<Type>::one
-                ),
-                cmptPow
-                (
-                    pTraits<Type>::one*x2,
-                    coeffs_[i].second() + pTraits<Type>::one
-                )
-              - cmptPow
-                (
-                    pTraits<Type>::one*x1,
-                    coeffs_[i].second() + pTraits<Type>::one
-                )
-            );
-        }
     }
 
-    return intx;
+    return x2*Sy2 - x1*Sy1;
 }
 
 

src/OpenFOAM/primitives/functions/Function1/Polynomial1/Polynomial1.H

@@ -27,15 +27,23 @@ Class
 Description
     Arbitrary order polynomial Function1.
 
-    The coefficients and exponents of the terms in the polynomial are specified
+    The coefficients in the polynomial are specified in order of increasing
-    as a list of Tuple2's e.g. for the polynomial y = x^2 + 2x^3
+    exponent, starting from the constant coefficient (i.e., zero exponent).
+
+    For example, the polynomial y = -1 + x^2 + 2x^3 can be specified as:
 
     \verbatim
-        <name>  polynomial
+        <name>  polynomial (-1 0 1 2);
-        (
+    \endverbatim
-            (1    2)
+
-            (2    3)
+    Or, alternatively:
-        );
+
+    \verbatim
+        <name>
+        {
+            type    polynomial;
+            coeffs  (-1 0 1 2);
+        }
     \endverbatim
 
 SourceFiles
@@ -47,7 +55,6 @@ SourceFiles
 #define Polynomial1_H
 
 #include "Function1.H"
-#include "Tuple2.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
@@ -67,14 +74,8 @@ class Polynomial
 {
     // Private Data
 
-        //- Polynomial coefficients - list of prefactor, exponent
+        //- Polynomial coefficients
-        const List<Tuple2<Type, Type>> coeffs_;
+        const List<Type> coeffs_;
-
-        //- Flag to indicate whether the function can be integrated
-        bool integrable_;
-
-
-    // Private member functions
 
 
 public:
@@ -85,13 +86,6 @@ public:
 
     // Constructors
 
-        //- Construct from components
-        Polynomial
-        (
-            const word& name,
-            const List<Tuple2<Type, Type>>&
-        );
-
         //- Construct from name and dictionary
         Polynomial(const word& name, const dictionary& dict);
 

tutorials/incompressibleFluid/TJunctionFan/system/createBafflesDict

@@ -99,7 +99,7 @@ baffles
                     patchType   cyclic;
                     jump        uniform 0;
                     value       uniform 0;
-                    jumpTable   polynomial 1((100 0));
+                    jumpTable   polynomial (100);
                 }
             }
         }

tutorials/incompressibleFluid/TJunctionFan/system/createNonConformalCouplesDict

@@ -32,7 +32,7 @@ nonConformalCouples
                     patchType   nonConformalCyclic;
                     jump        uniform 0;
                     value       uniform 0;
-                    jumpTable   polynomial 1((100 0));
+                    jumpTable   polynomial (100);
                 }
             }
         }