Question

Instructions

Write a C++ program that performs the following:

1. Accept a list of floating point values on a single line (separated by spaces). This is vector A. The user may enter as many values as they desire.
2. Accept a second list of floating point values on a single line (separated by spaces). This is vector B. The user may enter as many values as they desire. There is no requirement that the two vectors have the same number of elements.
3. Display the norm of each vector.
4. If the vectors have the same number of elements, then
   1. Display the inner product of A and B
   2. Display the outer product of A and B

Design Notes

There is no need to use big integers for this assignment. The elements of the vectors and matrices can be standard C++ floating point data (float, double, or long double).

You should use an "extensible" data structure since you do not know how many elements the user might enter on a line, and therefore can not pre-allocate storage. Vectors or trees are a good choice. Arrays can be used, but are somewhat more complicated because they can not increase or decrease in size once they are allocated.

Example

The following example program was completed on the syccuxas01 server. Your output does not need to look exactly like this - this is just an example. The input used when grading may be different than what is shown here.

-- syccuxas01 > main.exe
Enter vector elements (float, space separated): 1 2 3
Enter vector elements (float, space separated): 4 5 6
Vector: <1,2,3>
Norm: 3.74166

Vector: <4,5,6>
Norm: 8.77496

Inner Product: 32
Outer Product:
Matrix:
      4.00       5.00       6.00
      8.00      10.00      12.00
     12.00      15.00      18.00

-- syccuxas01 >

Answer 1

Code For Above Problem:

#include <iostream>
#include <sstream>
#include <vector>
#include <math.h> 
#include<bits/stdc++.h> 
using namespace std;

//function to calculate norm of vector
double calculateNorm(vector<float>vec)
{
    float sum=0;
    
    for(int i=0;i<vec.size();i++)
    {
        sum+=pow(vec[i],2);
    }
    return sqrt(sum);
}

//function to calculate inner product of vectorA and vectorB
float innerProduct(vector<float>vectorA,vector<float>vectorB)
{
        float x=0;
        for(int i=0;i<vectorA.size();i++)
        {
                x+=vectorA[i]*vectorB[i];
        }
}

int main()
{
    std::string line1;//to read  elements of vectorA
    std::string line2;//to read  elements of vectorB
    int number;
    std::vector<float> vectorA;//declaring vectorA
    std::vector<float> vectorB;//declaring vectorB

        //Asking user to enter values for vectorA space seperated
    std::cout << "Enter vector elements(float,space seperated): ";
    std::getline(std::cin, line1);
    
        //Asking user to enter values for vectorB space seperated
    std::cout << "Enter vector elements(float,space seperated): ";
    std::getline(std::cin, line2);
    
        //storing elements to vectorA from entered line1
    std::istringstream stream(line1);
    while (stream >> number)
        vectorA.push_back(number);
        
        //storing elements to vectorB from entered line2
    std::istringstream stream1(line2);
    while (stream1 >> number)
        vectorB.push_back(number);
        
        //printing vectorA
    cout<<"Vector: ";
    for(int i=0;i<vectorA.size();i++)
    {
        cout<<vectorA[i]<<" ";
    }
    
        //calculating norm of vectorA and print result
    double norm1=calculateNorm(vectorA);
    cout<<"\nNorm: "<<norm1<<endl;
    
    //printing vectorB
    cout<<"\nVector: ";
    for(int i=0;i<vectorB.size();i++)
    {
        cout<<vectorB[i]<<" ";
    }
        //calculating norm of vectorB and print result
    double norm2=calculateNorm(vectorB);
    cout<<"\nNorm: "<<norm2<<endl;

        //if both vector sizes are same
        if(vectorA.size()==vectorB.size())
        {       
                //calculate inner product of vectorA and vectorB
                float x=innerProduct(vectorA,vectorB);
                cout<<"\nInner product:"<<x<<endl;
                
                //calculating and printing outer product
                cout<<"\nOuter product:\nMatrix\n";
                for(int i=0;i<vectorA.size();i++)
                {
                        for(int j=0;j<vectorB.size();j++)
                        {
                                cout<< fixed << setprecision(2)<<vectorA[i]*vectorB[j]<<"\t";
                        }
                        cout<<endl;
                }
        }
    return 0;
}

Sample Run Input/Output Of Code:

Enter vector elements(float,space seperated): 1 2 3
Enter vector elements(float,space seperated): 4 5 6
Vector: 1 2 3 
Norm: 3.74166

Vector: 4 5 6 
Norm: 8.77496

Inner product:32

Outer product:
Matrix
4.00    5.00    6.00    
8.00    10.00   12.00   
12.00   15.00   18.00   

Images Of Code:

} 1 2 #include <iostream> 3 #include <sstream 4 #include <vector> 5 #include <math.h> 6 #include<bits/stdcht.h> 7 using namespace std; 8 9 //function to calculate norm of vector 10 double calculatelorm(vector<float>vec) 11 12 float sum=0; 13 14 for(int i=0; i<vec.size(); i++) 15 { 16 Sum+=pow(vec[i],2); 17 18 return sqrt(sum); 19} 20 21 //function to calculate inner product of vectorA and vector 22 float innerProduct(vector<float>vectorA, vector<float>vectorB) 23 { 24 float x=0; 25 for(int i=0; i<vectorA.size();i) 26 { 27 x+=vectorA[i]*vectorB[i]; 28 29} 30 31 int main() 32 { 33 std::string linel;//to read elements of vectorA 34 std::string line2;//to read elements of vector 35 int number; 36 std::vector<float> vectorA;//declaring vectorA 37 std::vector<float> vectorB;//declaring vectorB 38 39 1/Asking user to enter values for vectorA space seperated 40 std::cout << "Enter vector elements (float, space seperated): "; 41 std::getline(std::cin, linel); 42 43 I/Asking user to enter values for vectorB space seperated 44 std::cout << "Enter vector elements (float, space seperated): "; 45 std::getline(std::cin, line2); 46 47 // storing elements to vectorA from entered linel 48 std::istringstream streamlinel); 49 while (stream >> number) 50 vectorA.push_back(number); 51 }

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 //storing elements to vectors from entered line2 std::istringstream streaml (line); while (streaml >> number) vectorB.push_back(number); 1/printing vector cout<<"Vector: "; for(int i=0; i<vectorA.size(); i++) { cout<<vectorA[i]<<" "; } // calculating norm of vectorA and print result double norml=calculateNorm(vectorA); cout<<"\nNorm: "<<norml<<endl; 1/printing vectorB cout<<"\nVector: "; for(int i=0; i<vector.size(); i++) { cout<<vectorB[i]<<" "; } 1/ calculating norm of vector and print result double norm2=calculateNorm(vector); cout<<"\nNorm: "<<norm2<<endl; //if both vector sizes are same if(vectorA.size()==vectors.size()) // calculate inner product of vectorA and vector float x=inner Product(vectorA, vectorB); cout<<"\nInner product:"<<x<<endl; // calculating and printing outer product cout<<"\nOuter product: InMatrixin"; for(int i=0;i<vectorA.size();i++) for(int j=0; j<vectors.size();j++) { cout<< fixed << setprecision (2)<<vectorA[i]*vectorB[j]<<"\t"; } cout<<endl; } } return 0; { 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97} 98

Image Of Sample Run Input/Output:

Enter vector elements(float,space seperated): 1 2 3 Enter vector elements(float, space seperated): 4 5 6 Vector: 1 2 3 Norm: 3.74166 Vector: 4 5 6 Norm: 8.77496 Inner product:32 Outer product: Matrix 4.00 5.00 8.00 10.00 12.00 15.00 6.00 12.00 18.00