Multiplication of Vector by Scalar, then Matrix, the result added to Second Vector

// mulmatvec0.cpp - Program for testing dynamic memory allocation, version 0. For this purpose,
// this program prompts the user to input the size, N, of an N X N array, [A]. The array is then
// created, as well as two one-dimensional arrays of size N: b1 and b2. The entries for all
// three arrays are input from a text file. This program then multiplies b1 by a scalar, a, to
// create a new vector b1a. It then computes [A](b1a) + (b2).
// 7 April 2006
// Written in Microsoft Visual C++, Version 6

#include <iostream>
#include <fstream>
#include <cctype>
#include <cmath>
#include <new>
#include <float.h>

using namespace std;

void Echo(unsigned int N, double** matrix);

void Echo(unsigned int N, double** matrix) { //Routine to output a SQUARE Matrix
cout << "\n";
for (unsigned int i = 0; i < N; i++){
for (unsigned int j = 0; j < N; j++){
cout << matrix[i][j] << " ";
}
cout << "\n";
} // End for i
cout << "\n";
return;
} // End Echo

int main()
{char rflag = 0; //Readiness flag

cout << " mulmatvec0 (7 April 2006)\n";
cout << "=========================================================================== \n";
cout << "This program does some matrix calculations.\n";
cout << "First, it calculates the result of multiplying vector b1 by scalar a.\n";
cout << "The result is multiplied by matrix [A] and the result added to vector b2.\n";
cout << "The dimension, N, of the [A] matrix, and of the b1 and b2 vectors should \n";
cout << "have been saved beforehand in a file named mulmatvecdat.\n";
cout << "mulmatvecdat should be in the same folder as the mulmatvec executable.\n";
cout << "The next values of mulmatvecdat should be the entries for matrix [A],\n";
cout << "with data for row 1 first, then row 2, then row 3, etc.\n";
cout << "The next N entries should be the values for the b1 vector.\n";
cout << "The next N entries should be the values for the b2 vector.\n";
cout << "The last entry should be the value of the scalar a.\n";
cout << "\nThe data is assumed to be of type double. Variables used within this program\n";
cout << "are type double.\n";
cout << "\nThe output is written to the file mulmatvecout.txt.\n";

cout << "\nIs everything ready (are you ready to continue?)? If yes, Enter y. \n";
cout << "Otherwise Enter any other key. \n";
cin >> rflag;

if (toupper(rflag) == 'Y') {
double** A = NULL; //Pointer to rows of A Matrix
double* b1 = NULL; // b1 vector
double* b2 = NULL; // b2 vector
int i, j, mDim;
double a, temp1;

ifstream in("mulmatvecdat.txt", ios::in);

if (!in) {
cout << "Cannot open the input file.\n";
return 0;
}

in >> mDim; //Input the Matrix dimension from the file
if (mDim < 1) {
cout << "Invalid dimension entered. Program terminated. \n";
in.close(); //Close the input file before terminating
return 0;
}

ofstream out("mulmatvecout.txt", ios::out);
if (!out) {
cout << "Cannot open the output file. Program terminated.\n";
in.close(); //Close the input file before terminating
return 0;
}

//Allocate space for pointers to rows of A matrix
if (!(A = new double*[mDim])){
cout << "Allocation for A failed. \n";
in.close(); //Close the input file before terminating
out.close(); //Close the output file before terminating
return 0;
} //End if

// Allocate space for entries of the columns of the A Matrix
for (i = 0; i < mDim; i++) {
if (!(A[i] = new double[mDim])){//If failure, release memory allocated before ending program
for (j = (i - 1); j >= 0; j--){
delete [] A[j];
}
delete [] A;
cout << "Allocation for columns of A failed.\n";
in.close(); //Close the input file before terminating
out.close(); //Close the output file before terminating
return 0;
} //End if !A
}//End for i

// Allocate space for b1 vector
if (!(b1 = new double[mDim])){
for (i = 0; i < mDim; i++){ //Release all allocated memory before ending program
delete [] A[i];
}
delete [] A;
cout << "Allocation for b1 failed. \n";
in.close(); //Close the input file before terminating
out.close(); //Close the output file before terminating
return 0;
} //End if

// Allocate space for b2 vector
if (!(b2 = new double[mDim])){
for (i = 0; i < mDim; i++) {
delete [] A[i];
} // End for i
delete [] A;
delete [] b1; //Release the memory allocated to b1 before ending program
cout << "Allocation for b2 failed. \n";
in.close(); //Close the input file before terminating
out.close(); //Close the output file before terminating
return 0;
} //End if

for (i = 0; i < mDim; i++){ //Input the A Matrix from the file
for (j = 0; j < mDim; j++){
in >> A[i][j];
}
}//End for i

for (i = 0; i < mDim; i++){ //Input the b1 vector from the file
in >> b1[i];
}//End for i

for (i = 0; i < mDim; i++){ //Input the b2 vector from the file
in >> b2[i];
}//End for i

in >> a; //Input the a scalar from the file

in.close(); //Close the input file

// Echo(mDim, A);

for (i = 0; i < mDim; i++){
temp1 = 0.0;
for (j = 0; j < mDim; j++){
temp1 += A[i][j]*a*b1[j];
}//End for j
b2[i] += temp1;
}//End for i

out.precision(DBL_DIG);

out << "the resulting vector entries follow:\n";
out << "\n";
for (i = 0; i < mDim; i++){
out << b2[i] << " \n";
}

out << "\n";

out.close();
cout << "\nDone! The solution is in the text file mulmatvecout.txt \n";

for (i = 0; i < mDim; i++) {
delete [] A[i]; //Free up memory used by A Matrix before ending program
}
delete [] A;
delete [] b1; //Release the memory allocated to b1 before ending program
delete [] b2;
} //End if rflag = 'Y'
else cout << "\nNot ready. Try again when ready with information. \n";
cout << "\nEnter any key to continue. \n";
cin >> rflag;
return 0;
} // End main program.