/*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++*//*                                                                           *//*                                                                           *//*                   MV++ Numerical Matrix/Vector C++ Library                *//*                             MV++ Version 1.5                              *//*                                                                           *//*                                  R. Pozo                                  *//*               National Institute of Standards and Technology              *//*                                                                           *//*                                  NOTICE                                   *//*                                                                           *//* Permission to use, copy, modify, and distribute this software and         *//* its documentation for any purpose and without fee is hereby granted       *//* provided that this permission notice appear in all copies and             *//* supporting documentation.                                                 *//*                                                                           *//* Neither the Institution (National Institute of Standards and Technology)  *//* nor the author makes any representations about the suitability of this    *//* software for any purpose.  This software is provided ``as is''without     *//* expressed or implied warranty.                                            *//*                                                                           *//*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++*/#include <iostream>#include <math.h>#include <stdlib.h>#include "mvvd.h"MV_Vector_double& operator*=(MV_Vector_double &x, const double &a){      int N = x.size();      for (int i=0;i<N;i++)         x(i) *= a;      return x;}MV_Vector_double operator*(const double &a, const MV_Vector_double &x){      int N = x.size();      MV_Vector_double result(N);      for (int i=0;i<N;i++)         result(i) = x(i)*a;      return result;}MV_Vector_double operator*(const MV_Vector_double &x, const double &a){    // This is the other commutative case of vector*scalar.    // It should be just defined to be    // "return operator*(a,x);"    // but some compilers (e.g. Turbo C++ v.3.0) have trouble    // determining the proper template match.  For the moment,    // we'll just duplicate the code in the scalar * vector     // case above.      int N = x.size();      MV_Vector_double result(N);      for (int i=0;i<N;i++)         result(i) = x(i)*a;      return result;}MV_Vector_double operator+(const MV_Vector_double &x, const MV_Vector_double &y){      int N = x.size();      if (N != y.size())      {         std::cout << "Incompatible vector lengths in +." << "\n";         exit(1);      }            MV_Vector_double result(N);      for (int i=0;i<N; i++)         result(i) = x(i) + y(i);      return result;}          MV_Vector_double operator-(const MV_Vector_double &x, const MV_Vector_double &y){      int N = x.size();      if (N != y.size())      {         std::cout << "Incompatible vector lengths in -." << "\n";         exit(1);      }            MV_Vector_double result(N);      for (int i=0;i<N; i++)         result(i) = x(i) - y(i);      return result;}          MV_Vector_double& operator+=(MV_Vector_double &x, const MV_Vector_double &y){      int N = x.size();      if (N != y.size())      {         std::cout << "Incompatible vector lengths in -." << "\n";         exit(1);      }            for (int i=0;i<N; i++)         x(i) += y(i);      return x;}                MV_Vector_double& operator-=(MV_Vector_double &x, const MV_Vector_double &y){      int N = x.size();      if (N != y.size())      {         std::cout << "Incompatible vector lengths in -." << "\n";         exit(1);      }            for (int i=0;i<N; i++)         x(i) -= y(i);      return x;}                //  norm and dot product functions for the MV_Vector<> classdouble dot(const MV_Vector_double &x, const MV_Vector_double &y){          //  Check for compatible dimensions:  if (x.size() != y.size())      {         std::cout << "Incompatible dimensions in dot(). " << "\n";         exit(1);      }      double temp =  0;      for (int i=0; i<x.size();i++)           temp += x(i)*y(i);      return temp;}double norm(const MV_Vector_double &x){      double temp = dot(x,x);      return sqrt(temp);}