--- trunk/src/math/SquareMatrix.hpp	2004/10/13 06:51:09	70
+++ trunk/src/math/SquareMatrix.hpp	2004/10/20 18:07:08	123
@@ -29,10 +29,10 @@
  * @date 10/11/2004
  * @version 1.0
  */
-#ifndef MATH_SQUAREMATRIX_HPP 
+ #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 */
@@ -53,350 +53,53 @@ 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. 
+         * @todo need implementation
+         */
+         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];
-            }
-        }
-
-        /** Returns the determinant of this matrix. */
-        double determinant() const {
+             return result;
+        }        
 
+        /**
+         * Returns the determinant of this matrix.
+         * @todo need implementation
+         */
+        Real determinant() const {
+            Real det;
+            return det;
         }
 
         /** Returns the trace of this matrix. */
-        double trace() const {
-           double tmp = 0;
+        Real trace() const {
+           Real tmp = 0;
            
             for (unsigned int i = 0; i < Dim ; i++)
                 tmp += data_[i][i];
@@ -408,26 +111,26 @@ 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 +142,250 @@ 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;
+        }         
+
+        /** @todo need implementation */
+        void diagonalize() {
+            //jacobi(m, eigenValues, ortMat);
         }
-        
-        protected:
-            double data_[Dim][Dim]; /**< matrix element */            
 
+        /**
+         * Jacobi iteration routines for computing eigenvalues/eigenvectors of 
+         * real symmetric matrix
+         *
+         * @return true if success, otherwise return false
+         * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
+         *     overwritten
+         * @param w will contain the eigenvalues of the matrix On return of this function
+         * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are 
+         *    normalized and mutually orthogonal. 
+         */
+       
+        static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d, 
+                              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();
+/*=========================================================================
 
-        return result;
-    }
-    
-    /**
-    * 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;
+  Program:   Visualization Toolkit
+  Module:    $RCSfile: SquareMatrix.hpp,v $
 
-        result.add(m1, m2);
+  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
+  All rights reserved.
+  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
 
-        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;
+     This software is distributed WITHOUT ANY WARRANTY; without even
+     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+     PURPOSE.  See the above copyright notice for more information.
 
-        result.sub(m1, m2);
+=========================================================================*/
 
-        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;
+#define VTK_ROTATE(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)
 
-        result.mul(m1, m2);
+#define VTK_MAX_ROTATIONS 20
 
-        return result;
-    }
-    
-    /**
-    * 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
-    */
+    // Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
+    // real symmetric matrix. Square nxn matrix a; size of matrix in n;
+    // output eigenvalues in w; and output eigenvectors in v. Resulting
+    // eigenvalues/vectors are sorted in decreasing order; eigenvectors are
+    // normalized.
     template<typename Real, int Dim>
-    inline Vector<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m, 
-                                                                 const SquareMatrix<Real, Dim>& v) {
-        Vector<Real, Dim> result;
+    int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, 
+                                  SquareMatrix<Real, Dim>& v) {
+      const int n = Dim;  
+      int i, j, k, iq, ip, numPos;
+      Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
+      Real bspace[4], zspace[4];
+      Real *b = bspace;
+      Real *z = zspace;
 
-        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;                                                                 
+      // only allocate memory if the matrix is large
+      if (n > 4)
+        {
+        b = new Real[n];
+        z = new Real[n]; 
+        }
+
+      // initialize
+      for (ip=0; ip<n; ip++) 
+        {
+        for (iq=0; iq<n; iq++)
+          {
+          v(ip, iq) = 0.0;
+          }
+        v(ip, ip) = 1.0;
+        }
+      for (ip=0; ip<n; ip++) 
+        {
+        b[ip] = w[ip] = a(ip, ip);
+        z[ip] = 0.0;
+        }
+
+      // begin rotation sequence
+      for (i=0; i<VTK_MAX_ROTATIONS; i++) 
+        {
+        sm = 0.0;
+        for (ip=0; ip<n-1; ip++) 
+          {
+          for (iq=ip+1; iq<n; iq++)
+            {
+            sm += fabs(a(ip, iq));
+            }
+          }
+        if (sm == 0.0)
+          {
+          break;
+          }
+
+        if (i < 3)                                // first 3 sweeps
+          {
+          tresh = 0.2*sm/(n*n);
+          }
+        else
+          {
+          tresh = 0.0;
+          }
+
+        for (ip=0; ip<n-1; ip++) 
+          {
+          for (iq=ip+1; iq<n; iq++) 
+            {
+            g = 100.0*fabs(a(ip, iq));
+
+            // after 4 sweeps
+            if (i > 3 && (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));
+                if (theta < 0.0)
+                  {
+                  t = -t;
+                  }
+                }
+              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;
+
+              // ip already shifted left by 1 unit
+              for (j = 0;j <= ip-1;j++) 
+                {
+                VTK_ROTATE(a,j,ip,j,iq);
+                }
+              // ip and iq already shifted left by 1 unit
+              for (j = ip+1;j <= iq-1;j++) 
+                {
+                VTK_ROTATE(a,ip,j,j,iq);
+                }
+              // iq already shifted left by 1 unit
+              for (j=iq+1; j<n; j++) 
+                {
+                VTK_ROTATE(a,ip,j,iq,j);
+                }
+              for (j=0; j<n; j++) 
+                {
+                VTK_ROTATE(v,j,ip,j,iq);
+                }
+              }
+            }
+          }
+
+        for (ip=0; ip<n; ip++) 
+          {
+          b[ip] += z[ip];
+          w[ip] = b[ip];
+          z[ip] = 0.0;
+          }
+        }
+
+      //// this is NEVER called
+      if ( i >= VTK_MAX_ROTATIONS )
+        {
+           std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
+           return 0;
+        }
+
+      // sort eigenfunctions                 these changes do not affect accuracy 
+      for (j=0; j<n-1; j++)                  // boundary incorrect
+        {
+        k = j;
+        tmp = w[k];
+        for (i=j+1; i<n; i++)                // boundary incorrect, shifted already
+          {
+          if (w[i] >= tmp)                   // why exchage if same?
+            {
+            k = i;
+            tmp = w[k];
+            }
+          }
+        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;
+            }
+          }
+        }
+      // 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 ceil_half_n = (n >> 1) + (n & 1);
+      for (j=0; j<n; j++)
+        {
+        for (numPos=0, i=0; i<n; i++)
+          {
+          if ( v(i, j) >= 0.0 )
+            {
+            numPos++;
+            }
+          }
+    //    if ( numPos < ceil(double(n)/double(2.0)) )
+        if ( numPos < ceil_half_n)
+          {
+          for(i=0; i<n; i++)
+            {
+            v(i, j) *= -1.0;
+            }
+          }
+        }
+
+      if (n > 4)
+        {
+        delete [] b;
+        delete [] z;
+        }
+      return 1;
     }
+
+
 }
 #endif //MATH_SQUAREMATRIX_HPP 
+