--- trunk/OOPSE-3.0/src/math/SquareMatrix.hpp	2004/10/13 06:51:09	1563
+++ trunk/OOPSE-3.0/src/math/SquareMatrix.hpp	2004/10/17 01:19:11	1586
@@ -32,7 +32,7 @@
 #ifndef MATH_SQUAREMATRIX_HPP 
 #define MATH_SQUAREMATRIX_HPP 
 
-#include "Vector3d.hpp"
+#include "math/RectMatrix.hpp"
 
 namespace oopse {
 
@@ -43,7 +43,7 @@ namespace oopse {
      * @template Dim the dimension of the square matrix
      */
     template<typename Real, int Dim>
-    class SquareMatrix{
+    class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
         public:
 
         /** default constructor */
@@ -53,345 +53,42 @@ namespace oopse {
                     data_[i][j] = 0.0;
          }
 
-        /** Constructs and initializes every element of this matrix to a scalar */ 
-        SquareMatrix(double s) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)
-                    data_[i][j] = s;
-        }
-
         /** copy constructor */
-        SquareMatrix(const SquareMatrix<Real, Dim>& m) {
-            *this = m;
+        SquareMatrix(const RectMatrix<Real, Dim, Dim>& m)  : RectMatrix<Real, Dim, Dim>(m) {
         }
         
-        /** destructor*/
-        ~SquareMatrix() {}
-
         /** copy assignment operator */
-        SquareMatrix<Real, Dim>& operator =(const SquareMatrix<Real, Dim>& m) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)
-                    data_[i][j] = m.data_[i][j];
-        }
-        
-        /**
-         * Return the reference of a single element of this matrix.
-         * @return the reference of a single element of this matrix 
-         * @param i row index
-         * @param j colum index
-         */
-        double& operator()(unsigned int i, unsigned int j) {
-            return data_[i][j];
-        }
-
-        /**
-         * Return the value of a single element of this matrix.
-         * @return the value of a single element of this matrix 
-         * @param i row index
-         * @param j colum index
-         */        
-        double operator()(unsigned int i, unsigned int j) const  {
-            return data_[i][j];  
-        }
-
-        /**
-         * Returns a row of  this matrix as a vector.
-         * @return a row of  this matrix as a vector 
-         * @param row the row index
-         */                
-        Vector<Real, Dim> getRow(unsigned int row) {
-            Vector<Real, Dim> v;
-
-            for (unsigned int i = 0; i < Dim; i++)
-                v[i] = data_[row][i];
-
-            return v;
-        }
-
-        /**
-         * Sets a row of  this matrix
-         * @param row the row index
-         * @param v the vector to be set
-         */                
-         void setRow(unsigned int row, const Vector<Real, Dim>& v) {
-            Vector<Real, Dim> v;
-
-            for (unsigned int i = 0; i < Dim; i++)
-                data_[row][i] = v[i];
-         }
-
-        /**
-         * Returns a column of  this matrix as a vector.
-         * @return a column of  this matrix as a vector 
-         * @param col the column index
-         */                
-        Vector<Real, Dim> getColum(unsigned int col) {
-            Vector<Real, Dim> v;
-
-            for (unsigned int i = 0; i < Dim; i++)
-                v[i] = data_[i][col];
-
-            return v;
-        }
-
-        /**
-         * Sets a column of  this matrix
-         * @param col the column index
-         * @param v the vector to be set
-         */                
-         void setColum(unsigned int col, const Vector<Real, Dim>& v){
-            Vector<Real, Dim> v;
-
-            for (unsigned int i = 0; i < Dim; i++)
-                data_[i][col] = v[i];
-         }         
-
-        /** Negates the value of this matrix in place. */           
-        inline void negate() {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)
-                    data_[i][j] = -data_[i][j];
-        }
-        
-        /**
-        * Sets the value of this matrix to the negation of matrix m.
-        * @param m the source matrix
-        */
-        inline void negate(const SquareMatrix<Real, Dim>& m) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)
-                    data_[i][j] = -m.data_[i][j];        
-        }
-        
-        /**
-        * Sets the value of this matrix to the sum of itself and m (*this += m).
-        * @param m the other matrix
-        */
-        inline void add( const SquareMatrix<Real, Dim>& m ) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)        
-                data_[i][j] += m.data_[i][j];
-            }
-        
-        /**
-        * Sets the value of this matrix to the sum of m1 and m2 (*this = m1 + m2).
-        * @param m1 the first matrix
-        * @param m2 the second matrix
-        */
-        inline void add( const SquareMatrix<Real, Dim>& m1, const SquareMatrix<Real, Dim>& m2 ) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)        
-                data_[i][j] = m1.data_[i][j] + m2.data_[i][j];
-        }
-        
-        /**
-        * Sets the value of this matrix to the difference  of itself and m (*this -= m).
-        * @param m the other matrix
-        */
-        inline void sub( const SquareMatrix<Real, Dim>& m ) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)        
-                data_[i][j] -= m.data_[i][j];
-        }
-        
-        /**
-        * Sets the value of this matrix to the difference of matrix m1 and m2 (*this = m1 - m2).
-        * @param m1 the first matrix
-        * @param m2 the second matrix
-        */
-        inline void sub( const SquareMatrix<Real, Dim>& m1, const Vector  &m2){
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)        
-                data_[i][j] = m1.data_[i][j] - m2.data_[i][j];
-        }
-        
-        /**
-        * Sets the value of this matrix to the scalar multiplication of itself (*this *= s).
-        * @param s the scalar value
-        */
-        inline void mul( double s ) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)  
-                    data_[i][j] *= s;
-        }
-
-        /**
-        * Sets the value of this matrix to the scalar multiplication of matrix m  (*this = s * m).
-        * @param s the scalar value
-        * @param m the matrix
-        */
-        inline void mul( double s, const SquareMatrix<Real, Dim>& m ) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)  
-                    data_[i][j] = s * m.data_[i][j];
-        }
-
-        /**
-        * Sets the value of this matrix to the  multiplication of this matrix and matrix m
-        * (*this = *this * m).
-        * @param m the matrix
-        */
-        inline void mul(const SquareMatrix<Real, Dim>& m ) {
-            SquareMatrix<Real, Dim> tmp(*this);
-            
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++) {  
-                    
-                    data_[i][j] = 0.0;
-                    for (unsigned int k = 0; k < Dim; k++)
-                        data_[i][j]  = tmp.data_[i][k] * m.data_[k][j]
-                }
-        }
-        
-        /**
-        * Sets the value of this matrix to the  left multiplication of matrix m into itself
-        * (*this = m *  *this).
-        * @param m the matrix
-        */
-        inline void leftmul(const SquareMatrix<Real, Dim>& m ) {
-            SquareMatrix<Real, Dim> tmp(*this);
-            
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++) {  
-                    
-                    data_[i][j] = 0.0;
-                    for (unsigned int k = 0; k < Dim; k++)
-                        data_[i][j]  = m.data_[i][k] * tmp.data_[k][j]
-                }
-        }
-
-        /**
-        * Sets the value of this matrix to the  multiplication of matrix m1 and matrix m2
-        * (*this = m1 * m2).
-        * @param m1 the first  matrix
-        * @param m2 the second matrix
-        */
-        inline void mul(const SquareMatrix<Real, Dim>& m1, 
-                                  const SquareMatrix<Real, Dim>& m2 ) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++) {  
-                    
-                    data_[i][j] = 0.0;
-                    for (unsigned int k = 0; k < Dim; k++)
-                        data_[i][j]  = m1.data_[i][k] * m2.data_[k][j]
-                }
-
-        }
-        
-        /**
-        * Sets the value of this matrix to the scalar division of itself  (*this /= s ).
-        * @param s the scalar value
-        */             
-        inline void div( double s) {
-            for (unsigned int i = 0; i < Dim; i++)
-                for (unsigned int j = 0; j < Dim; j++)  
-                    data_[i][j] /= s;
-        }
-        
-        inline SquareMatrix<Real, Dim>& operator=(const SquareMatrix<Real, Dim>& v) {
-            if (this == &v)
-                return *this;
-            
-            for (unsigned int i = 0; i < Dim; i++)            
-                data_[i] = v[i];
-            
+        SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
+            RectMatrix<Real, Dim, Dim>::operator=(m);
             return *this;
         }
-        
-        /**
-        * Sets the value of this matrix to the scalar division of matrix v1  (*this = v1 / s ).
-        * @paran v1 the source matrix
-        * @param s the scalar value
-        */                         
-        inline void div( const SquareMatrix<Real, Dim>& v1, double s ) {
-            for (unsigned int i = 0; i < Dim; i++)
-                data_[i] = v1.data_[i] / s;
-        }
+                               
+        /** Retunrs  an identity matrix*/
 
-        /**
-         *  Multiples a scalar into every element of this matrix.
-         * @param s the scalar value
-         */
-        SquareMatrix<Real, Dim>& operator *=(const double s) {
-            this->mul(s);
-            return *this;
-        }
-
-        /**
-         *  Divides every element of this matrix by a scalar.
-         * @param s the scalar value
-         */
-        SquareMatrix<Real, Dim>& operator /=(const double s) {
-            this->div(s);
-            return *this;
-        }
-
-        /**
-         * Sets the value of this matrix to the sum of the other matrix and itself (*this += m).
-         * @param m the other matrix
-         */
-        SquareMatrix<Real, Dim>& operator += (const SquareMatrix<Real, Dim>& m) {
-            add(m);
-            return *this;
-         }
-
-        /**
-         * Sets the value of this matrix to the differerence of itself and the other matrix (*this -= m) 
-         * @param m the other matrix
-         */
-        SquareMatrix<Real, Dim>& operator -= (const SquareMatrix<Real, Dim>& m){
-            sub(m);
-            return *this;
-        }
-
-        /** set this matrix to an identity matrix*/
-
-       void identity() {
+       static SquareMatrix<Real, Dim> identity() {
+            SquareMatrix<Real, Dim> m;
+            
             for (unsigned int i = 0; i < Dim; i++) 
-                for (unsigned int i = 0; i < Dim; i++) 
+                for (unsigned int j = 0; j < Dim; j++) 
                     if (i == j)
-                        data_[i][j] = 1.0;
+                        m(i, j) = 1.0;
                     else
-                        data_[i][j] = 0.0;
-        }
+                        m(i, j) = 0.0;
 
-        /** Sets the value of this matrix to  the inversion of itself. */
-        void  inverse() {
-            inverse(*this);
+            return m;
         }
 
-        /**
-         * Sets the value of this matrix to  the inversion of other matrix.
-         * @ param m the source matrix
-         */        
-        void inverse(const SquareMatrix<Real, Dim>& m);
-        
-        /** Sets the value of this matrix to  the transpose of itself. */
-        void transpose() {
-            for (unsigned int i = 0; i < Dim - 1; i++)
-                for (unsigned int j = i; j < Dim; j++)
-                    std::swap(data_[i][j], data_[j][i]);
-        }
+        /** Retunrs  the inversion of this matrix. */
+         SquareMatrix<Real, Dim>  inverse() {
+             SquareMatrix<Real, Dim> result;
 
-        /**
-         * Sets the value of this matrix to  the transpose of other matrix.
-         * @ param m the source matrix
-         */        
-        void transpose(const SquareMatrix<Real, Dim>& m) {
-            
-            if (this == &m) {
-                transpose();
-            } else {
-                for (unsigned int i = 0; i < Dim; i++)
-                    for (unsigned int j =0; j < Dim; j++)
-                        data_[i][j] = m.data_[i][j];
-            }
-        }
+             return result;
+        }        
 
         /** Returns the determinant of this matrix. */
         double determinant() const {
-
+            double det;
+            return det;
         }
 
         /** Returns the trace of this matrix. */
@@ -408,26 +105,26 @@ namespace oopse {
         bool isSymmetric() const {
             for (unsigned int i = 0; i < Dim - 1; i++)
                 for (unsigned int j = i; j < Dim; j++)
-                    if (fabs(data_[i][j] - data_[j][i]) > epsilon) 
+                    if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) 
                         return false;
                     
             return true;
         }
 
-        /** Tests if this matrix is orthogona. */            
-        bool isOrthogonal() const {
-            SquareMatrix<Real, Dim> t(*this);
+        /** Tests if this matrix is orthogonal. */            
+        bool isOrthogonal() {
+            SquareMatrix<Real, Dim> tmp;
 
-            t.transpose();
+            tmp = *this * transpose();
 
-            return isUnitMatrix(*this * t);
+            return tmp.isDiagonal();
         }
 
         /** Tests if this matrix is diagonal. */
         bool isDiagonal() const {
             for (unsigned int i = 0; i < Dim ; i++)
                 for (unsigned int j = 0; j < Dim; j++)
-                    if (i !=j && fabs(data_[i][j]) > epsilon) 
+                    if (i !=j && fabs(data_[i][j]) > oopse::epsilon) 
                         return false;
                     
             return true;
@@ -439,92 +136,182 @@ namespace oopse {
                 return false;
             
             for (unsigned int i = 0; i < Dim ; i++)
-                if (fabs(data_[i][i] - 1) > epsilon)
+                if (fabs(data_[i][i] - 1) > oopse::epsilon)
                     return false;
                 
             return true;
+        }         
+
+        void diagonalize() {
+            jacobi(m, eigenValues, ortMat);
         }
-        
-        protected:
-            double data_[Dim][Dim]; /**< matrix element */            
 
+        /**
+         * Finds the eigenvalues and eigenvectors of a symmetric matrix
+         * @param eigenvals a reference to a vector3 where the
+         * eigenvalues will be stored. The eigenvalues are ordered so
+         * that eigenvals[0] <= eigenvals[1] <= eigenvals[2].
+         * @return an orthogonal matrix whose ith column is an
+         * eigenvector for the eigenvalue eigenvals[i]
+         */
+        SquareMatrix<Real, Dim>  findEigenvectors(Vector<Real, Dim>& eigenValues) {
+            SquareMatrix<Real, Dim> ortMat;
+            
+            if ( !isSymmetric()){
+                throw();
+            }
+            
+            SquareMatrix<Real, Dim> m(*this);
+            jacobi(m, eigenValues, ortMat);
+
+            return ortMat;
+        }
+        /**
+         * Jacobi iteration routines for computing eigenvalues/eigenvectors of 
+         * real symmetric matrix
+         *
+         * @return true if success, otherwise return false
+         * @param a source matrix
+         * @param w output eigenvalues 
+         * @param v output eigenvectors 
+         */
+        bool jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, 
+                              SquareMatrix<Real, Dim>& v);
     };//end SquareMatrix
 
-    
-    /** Negate the value of every element of this matrix. */
-    template<typename Real, int Dim>
-    inline SquareMatrix<Real, Dim> operator -(const SquareMatrix& m) {
-        SquareMatrix<Real, Dim> result(m);
 
-        result.negate();
+#define ROT(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);a(k, l)=h+s*(g-h*tau)
+#define MAX_ROTATIONS 60
 
-        return result;
+template<typename Real, int Dim>
+bool SquareMatrix<Real, Dim>::jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, 
+                              SquareMatrix<Real, Dim>& v) {
+    const int N = Dim;                                                                       
+    int i, j, k, iq, ip;
+    double tresh, theta, tau, t, sm, s, h, g, c;
+    double tmp;
+    Vector<Real, Dim> b, z;
+
+    // initialize
+    for (ip=0; ip<N; ip++) {
+        for (iq=0; iq<N; iq++)
+            v(ip, iq) = 0.0;
+        v(ip, ip) = 1.0;
     }
     
-    /**
-    * Return the sum of two matrixes  (m1 + m2). 
-    * @return the sum of two matrixes
-    * @param m1 the first matrix
-    * @param m2 the second matrix
-    */ 
-    template<typename Real, int Dim>
-    inline SquareMatrix<Real, Dim> operator + (const SquareMatrix<Real, Dim>& m1,
-                                                                                         const SquareMatrix<Real, Dim>& m2) {
-        SquareMatrix<Real, Dim>result;
+    for (ip=0; ip<N; ip++) {
+        b(ip) = w(ip) = a(ip, ip);
+        z(ip) = 0.0;
+    }
 
-        result.add(m1, m2);
+    // begin rotation sequence
+    for (i=0; i<MAX_ROTATIONS; i++) {
+        sm = 0.0;
+        for (ip=0; ip<2; ip++) {
+            for (iq=ip+1; iq<N; iq++)
+                sm += fabs(a(ip, iq));
+        }
+        
+        if (sm == 0.0)
+            break;
 
-        return result;
-    }
-    
-    /**
-    * Return the difference of two matrixes  (m1 - m2). 
-    * @return the sum of two matrixes
-    * @param m1 the first matrix
-    * @param m2 the second matrix
-    */
-    template<typename Real, int Dim>
-    inline SquareMatrix<Real, Dim> operator - (const SquareMatrix<Real, Dim>& m1, 
-                                                                                        const SquareMatrix<Real, Dim>& m2) {
-        SquareMatrix<Real, Dim>result;
+        if (i < 4)
+            tresh = 0.2*sm/(9);
+        else
+            tresh = 0.0;
 
-        result.sub(m1, m2);
+        for (ip=0; ip<2; ip++) {
+            for (iq=ip+1; iq<N; iq++) {
+                g = 100.0*fabs(a(ip, iq));
+                if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip))
+                    && (fabs(w(iq))+g) == fabs(w(iq))) {
+                    a(ip, iq) = 0.0;
+                } else if (fabs(a(ip, iq)) > tresh) {
+                    h = w(iq) - w(ip);
+                    if ( (fabs(h)+g) == fabs(h)) {
+                        t = (a(ip, iq)) / h;
+                    } else {
+                        theta = 0.5*h / (a(ip, iq));
+                        t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
 
-        return result;
-    }
-    
-    /**
-    * Return the multiplication of two matrixes  (m1 * m2). 
-    * @return the multiplication of two matrixes
-    * @param m1 the first matrix
-    * @param m2 the second matrix
-    */
-    template<typename Real, int Dim>
-    inline SquareMatrix<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m1,
-                                                                                       const SquareMatrix<Real, Dim>& m2) {
-        SquareMatrix<Real, Dim> result;
+                        if (theta < 0.0)
+                            t = -t;
+                    }
 
-        result.mul(m1, m2);
+                    c = 1.0 / sqrt(1+t*t);
+                    s = t*c;
+                    tau = s/(1.0+c);
+                    h = t*a(ip, iq);
+                    z(ip) -= h;
+                    z(iq) += h;
+                    w(ip) -= h;
+                    w(iq) += h;
+                    a(ip, iq)=0.0;
+                    
+                    for (j=0;j<ip-1;j++) 
+                        ROT(a,j,ip,j,iq);
 
-        return result;
-    }
+                    for (j=ip+1;j<iq-1;j++) 
+                        ROT(a,ip,j,j,iq);
+
+                    for (j=iq+1; j<N; j++) 
+                        ROT(a,ip,j,iq,j);
+                    for (j=0; j<N; j++) 
+                        ROT(v,j,ip,j,iq);
+                }
+            }
+        }//for (ip=0; ip<2; ip++) 
+
+        for (ip=0; ip<N; ip++) {
+            b(ip) += z(ip);
+            w(ip) = b(ip);
+            z(ip) = 0.0;
+        }
+        
+    } // end for (i=0; i<MAX_ROTATIONS; i++) 
+
+    if ( i >= MAX_ROTATIONS )
+        return false;
+
+    // sort eigenfunctions
+    for (j=0; j<N; j++) {
+        k = j;
+        tmp = w(k);
+        for (i=j; i<N; i++) {
+            if (w(i) >= tmp) {
+            k = i;
+            tmp = w(k);
+            }
+        }
     
-    /**
-    * Return the multiplication of  matrixes m  and vector v (m * v). 
-    * @return the multiplication of matrixes and vector
-    * @param m the matrix
-    * @param v the vector
-    */
-    template<typename Real, int Dim>
-    inline Vector<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m, 
-                                                                 const SquareMatrix<Real, Dim>& v) {
-        Vector<Real, Dim> result;
+        if (k != j) {
+            w(k) = w(j);
+            w(j) = tmp;
+            for (i=0; i<N; i++)  {
+                tmp = v(i, j);
+                v(i, j) = v(i, k);
+                v(i, k) = tmp;
+            }
+        }
+    }
 
-        for (unsigned int i = 0; i < Dim ; i++)
-            for (unsigned int j = 0; j < Dim ; j++)            
-                result[i] += m(i, j) * v[j];
-            
-        return result;                                                                 
+    //    insure eigenvector consistency (i.e., Jacobi can compute
+    //    vectors that are negative of one another (.707,.707,0) and
+    //    (-.707,-.707,0). This can reek havoc in
+    //    hyperstreamline/other stuff. We will select the most
+    //    positive eigenvector.
+    int numPos;
+    for (j=0; j<N; j++) {
+        for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++;
+        if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0;
     }
+
+    return true;
 }
+
+#undef ROT
+#undef MAX_ROTATIONS
+
+}
+
 #endif //MATH_SQUAREMATRIX_HPP