ENH: add new funcs into SquareMatrix

- query func `symmetric()`
    - query func `tridiagonal()`
    - `resize()`
    - `labelpair` identity constructor

    STYLE: add `#if(0 | RUNALL)` to improve test control in Test-Matrix

applications/test/Matrix/Test-Matrix.C

@@ -37,6 +37,7 @@ License
 using namespace Foam;
 using namespace Foam::MatrixTools;
 
+#define RUNALL true
 #define isEqual MatrixTools::equal
 
 void horizontalLine()
@@ -113,7 +114,7 @@ int main(int argc, char *argv[])
 
     Random rndGen(1234);
 
-    #if 1
+    #if (0 | RUNALL)
     {
         horizontalLine();
 
@@ -218,7 +219,7 @@ int main(int argc, char *argv[])
     #endif
 
 
-    #if 1
+    #if (0 | RUNALL)
     {
         horizontalLine();
 
@@ -254,7 +255,7 @@ int main(int argc, char *argv[])
     #endif
 
 
-    #if 1
+    #if (0 | RUNALL)
     {
         horizontalLine();
 
@@ -299,7 +300,7 @@ int main(int argc, char *argv[])
     #endif
 
 
-    #if 1
+    #if (0 | RUNALL)
     {
         horizontalLine();
 
@@ -410,7 +411,7 @@ int main(int argc, char *argv[])
     #endif
 
 
-    #if 1
+    #if (0 | RUNALL)
     {
         horizontalLine();
 
@@ -494,7 +495,7 @@ int main(int argc, char *argv[])
     #endif
 
 
-    #if 1
+    #if (0 | RUNALL)
     {
         horizontalLine();
 
@@ -683,7 +684,7 @@ int main(int argc, char *argv[])
     #endif
 
 
-    #if 1
+    #if (0 | RUNALL)
     {
         horizontalLine();
 
@@ -804,7 +805,7 @@ int main(int argc, char *argv[])
                 << nl;
         }
 
-        #if 1
+        #if (0 | RUNALL)
         {
             Info<< nl << "# Implicit inner/outer products:" << nl;
 
@@ -860,7 +861,65 @@ int main(int argc, char *argv[])
     #endif
 
 
-    #if 1
+    #if (0 | RUNALL)
+    {
+        horizontalLine();
+
+        Info<< "## Query to determine if a square matrix is symmetric:" << nl;
+
+        {
+            const label mRows = 100;
+            SMatrix A(makeRandomMatrix<SMatrix>({mRows, mRows}, rndGen));
+
+            Info<< "# SquareMatrix<scalar>.symmetric():" << nl
+                << A.symmetric() << nl;
+
+            // Symmetrise
+            for (label n = 0; n < A.n() - 1; ++n)
+            {
+                for (label m = A.m() - 1; n < m; --m)
+                {
+                    A(n, m) = A(m, n);
+                }
+            }
+
+            Info<< "# SquareMatrix<scalar>.symmetric():" << nl
+                << A.symmetric() << nl;
+        }
+
+        {
+            const label mRows = 100;
+
+            SCMatrix A(mRows);
+
+            for (auto& val : A)
+            {
+                val.Re() = rndGen.GaussNormal<scalar>();
+                val.Im() = rndGen.GaussNormal<scalar>();
+            }
+
+            Info<< "# SquareMatrix<complex>.symmetric():" << nl
+                << A.symmetric() << nl;
+
+            // Symmetrise
+            for (label n = 0; n < A.n() - 1; ++n)
+            {
+                for (label m = A.m() - 1; n < m; --m)
+                {
+                    A(n, m) = A(m, n);
+                }
+            }
+
+            Info<< "# SquareMatrix<complex>.symmetric():" << nl
+                << A.symmetric() << nl;
+        }
+
+        horizontalLine();
+    }
+    #endif
+
+
+    #if (0 | RUNALL)
     {
         horizontalLine();
 
@@ -898,7 +957,7 @@ int main(int argc, char *argv[])
     #endif
 
 
-    #if 1
+    #if (0 | RUNALL)
     {
         scalarSquareMatrix squareMatrix(3, Zero);
 

src/OpenFOAM/matrices/SquareMatrix/SquareMatrix.H

@@ -85,6 +85,9 @@ public:
         template<class AnyType>
         inline SquareMatrix(const label n, const Identity<AnyType>);
 
+        template<class AnyType>
+        inline SquareMatrix(const labelPair& dims, const Identity<AnyType>);
+
         //- Construct given number of rows/columns (checked to be equal)
         //  For constructor consistency in rectangular matrices
         inline explicit SquareMatrix(const labelPair& dims);
@@ -129,12 +132,23 @@ public:
         //- Resize the matrix preserving the elements
         inline void resize(const label m);
 
+        //- Resize the matrix preserving the elements (compatibility)
+        inline void resize(const label m, const label n);
+
         //- Resize the matrix preserving the elements
         inline void setSize(const label m);
 
         //- Resize the matrix without reallocating storage (unsafe)
         inline void shallowResize(const label m);
 
+    // Check
+
+        //- Return true if the square matrix is effectively symmetric/Hermitian
+        inline bool symmetric() const;
+
+        //- Return true if the square matrix is reduced tridiagonal
+        inline bool tridiagonal() const;
+
 
     // Member Operators
 

src/OpenFOAM/matrices/SquareMatrix/SquareMatrixI.H

@@ -90,6 +90,25 @@ inline Foam::SquareMatrix<Type>::SquareMatrix
 }
 
 
+template<class Type>
+template<class AnyType>
+inline Foam::SquareMatrix<Type>::SquareMatrix
+(
+    const labelPair& dims,
+    const Identity<AnyType>
+)
+:
+    Matrix<SquareMatrix<Type>, Type>(dims, Zero)
+{
+    CHECK_MATRIX_IS_SQUARE(dims.first(), dims.second());
+
+    for (label i = 0; i < dims.first(); ++i)
+    {
+        this->operator()(i, i) = pTraits<Type>::one;
+    }
+}
+
+
 template<class Type>
 inline Foam::SquareMatrix<Type>::SquareMatrix
 (
@@ -206,6 +225,19 @@ inline void Foam::SquareMatrix<Type>::resize(const label m)
 }
 
 
+template<class Type>
+inline void Foam::SquareMatrix<Type>::resize(const label m, const label n)
+{
+    if (m != n)
+    {
+        FatalErrorInFunction<< "Disallowed use of resize() for SquareMatrix"
+            << abort(FatalError);
+    }
+
+    Matrix<SquareMatrix<Type>, Type>::resize(m, m);
+}
+
+
 template<class Type>
 inline void Foam::SquareMatrix<Type>::setSize(const label m)
 {
@@ -220,6 +252,49 @@ inline void Foam::SquareMatrix<Type>::shallowResize(const label m)
 }
 
 
+template<class Type>
+inline bool Foam::SquareMatrix<Type>::symmetric() const
+{
+    for (label n = 0; n < this->n() - 1; ++n)
+    {
+        for (label m = this->m() - 1; n < m; --m)
+        {
+            if (SMALL < mag((*this)(n, m) - (*this)(m, n)))
+            {
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+
+template<class Type>
+inline bool Foam::SquareMatrix<Type>::tridiagonal() const
+{
+    for (label i = 0; i < this->m(); ++i)
+    {
+        for (label j = 0; j < this->n(); ++j)
+        {
+            const Type& val = (*this)(i, j);
+
+            if ((i == j) || (i - 1 == j) || (i + 1 == j))
+            {
+                if (mag(val) < SMALL)
+                {
+                    return false;
+                }
+            }
+            else if (SMALL < mag(val))
+            {
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+
 // * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
 template<class Type>