Question: Programming in C++ Inverse of a Matrix, use 1D array format to represent the Matrix array (do not use 2D array format) Write a program
Programming in C++
Inverse of a Matrix, use 1D array format to represent the Matrix array (do not use 2D array format)
Write a program to invert a 3x3 matrix
2 1 1
3 2 1
2 1 2
Utilizing structured programming write a new module to invert a matrix
A*A^-1= IdentMatrix
Declare two matrices A and InvA ( do not declare ident matrix)
Figure out how to appended matrix C with A and Identity Matrix
Run steps to convert the fist half of matrix into identity matrix to get inverse matrix
Push values back form Matrix C into InvA and Display Matrix InvA similar to what is done above?
Please help with generating this code in C++
I have how to do standard Gauss Jordan, I just don't understand how to make an invers by making an identity matrix. Here is the Code I have.
#include
struct Matrix{ //declaring a structure for Matrix
double *X;
int n_rows, n_columns;
};
struct Vector{ //declaring a structure for Vector
double *x;
int dimension;
};
void DefineVector(Vector &z, int dimension){
z.dimension = dimension;
z.x = (double*)calloc(z.dimension, sizeof(double));
}
void DefineMatrix(Matrix &Z, int rows, int columns){
Z.n_rows = rows;
Z.n_columns = columns;
Z.X = (double*)calloc(Z.n_rows*Z.n_columns, sizeof(double));
}
void SpecifyVectorElements(Vector &z){
for (int i = 0; i < z.dimension; i++){
std::cout <<"specify vector element x[" << i << "] " << std::endl;
std::cin >> z.x[i];
}
}
void DisplayVector(Vector z){
std::cout << "The elements of the vector are" << std::endl;
for (int i = 0; i < z.dimension; i++){
std::cout <<"x[" << i << "] = " << z.x[i] << std::endl;
} //Displays Vector Elements
}
void SpecifyMatrixElements(Matrix &Z){
for (int i = 0; i < Z.n_rows; i++){
for (int k = 0; k < Z.n_columns; k++){
std::cout <<"specify Matrix element X[" << i << "][" << k << "] " <
std::cin >> Z.X[k*Z.n_rows+i];//in takes the Matrix elements
}
}
}
void DisplayMatrix(Matrix Z){
std::cout << "The elements of the Matrix are" << std::endl;
for (int i = 0; i < Z.n_rows; i++){
for (int k = 0; k < Z.n_columns; k++){
std::cout <<"X[" << i << "][" << k << "] = " << Z.X[k*Z.n_rows+i] << "\t"; //displays Matrix elements of a row with tab spacing
}
std::cout << std::endl; //adds a new line for next row elements
}
}
void MatrixVectorProduct(Matrix Z, Vector x, Vector &y){
if (Z.n_columns == x.dimension){
for(int i=0; i < Z.n_rows; i++){
y.x[i] = 0;
for (int k = 0; k < Z.n_columns; k++){
y.x[i] += Z.X[k*Z.n_rows + i] * x.x[k];
}
}
}
else std::cout<<"Matrix-Vector Multiplication not supported due to dimensions mismatch"<
}
void MatrixMatrixProduct(Matrix A, Matrix B, Matrix &Y){
if (A.n_columns == B.n_rows){
for (int i = 0; i < A.n_rows; i++){
for(int j = 0; j < B.n_columns; j++){
Y.X[j*Y.n_rows +i] = 0;
for (int k = 0; k < A.n_columns; k++){ //B.n_rows can also be used
Y.X[j*Y.n_rows +i] += A.X[k*A.n_rows+i]* B.X[k+ j*B.n_rows];
}
}
}
}
else std::cout<<"Matrix-Vector Multiplication not supported due to dimensions mismatch"<
}
void Convert_ith_DiagonalElementToOne(Matrix C, int x){
double cii = 0;
cii = C.X[x*(C.n_rows+1)]; //Diagonal element
for (int i = 0; i < C.n_columns; i++){
C.X[i*C.n_rows+ x] /= cii;
}
}
void ReadRow(Matrix C, Vector &c, int x){
for ( int i = 0; i < C.n_columns; i++){
c.x[i] = C.X[i*C.n_rows + x];
}
}
void convertColumnElements_ij_ToZero_ForwardPath(Matrix &C, int x, int y){
double Cij = 0;
Vector c;
DefineVector(c, C.n_columns);
ReadRow(C, c, x);
Cij = C.X[x*C.n_rows + y];
for (int i = x+1; i< C.n_columns; i++){
C.X[i*C.n_rows +y] -= Cij*c.x[i];
} C.X[x*C.n_rows +y] = 0;
}
void ConverColumElements_ij_ToZero_BackwardPath(Matrix &C, int x, int y){
double Cij = 0;
int size = C.n_columns - C.n_rows;
Cij = C.X[x*C.n_rows +y];
for(int i = 0; C.n_columns; i++){
C.X[C.n_rows*C.n_rows + i *C.n_rows +y] -= Cij*C.X[C.n_rows*C.n_rows + i * C.n_rows +x];
} C.X[x*C.n_rows +y] =0;
}
void GaussJordanElimination(Matrix A, Vector y, Vector &x){
Matrix C;
DefineMatrix (C, A.n_rows, A.n_columns +1);
for (int i = 0; i < A.n_rows; i++ ){
for (int k = 0; k < A.n_columns; k++){
C.X[k*A.n_rows + i] = A.X[k*A.n_rows + i];
}
C.X[A.n_rows*A.n_columns + i] = y.x[i];
}
DisplayMatrix(C);
for (int i =0; i< A.n_rows; i ++){
Convert_ith_DiagonalElementToOne(C, i);
for (int j= i+1; j < A.n_rows; j++){
convertColumnElements_ij_ToZero_ForwardPath(C, i, j);
}
} DisplayMatrix(C);
for (int i = A.n_rows -1; i > 0; i--){
for (int j = i-1; j>= 0; j--){
convertColumnElements_ij_ToZero_ForwardPath(C, i, j);
}
} DisplayMatrix(C);
for (int i = 0; i < A.n_columns; i ++){
for (int j=i -1; j>= 0 ; j--){
ConverColumElements_ij_ToZero_BackwardPath(C, i, j);
}
} DisplayMatrix(C);
for (int i = 0; i < C.n_rows; i++){
x.x[i] = C.X[C.n_rows*C.n_rows+i];
}
}
int main() {
Matrix A, B, Y;
Vector x, y;
int A_rows = 3, A_columns =3;// B_rows = 3, B_columns = 3;
int x_dimension =3;//can ask user for inputs as well
DefineVector (x, A_columns); //DMA for x vector
DefineVector (y, A_rows); //y = A*x //DMA for y vector
DefineMatrix (A, A_rows, A_columns); //DMA for A Matrix
SpecifyMatrixElements(A); //User inputs Matrix A elements
DisplayMatrix (A); // User displays Matrix A elements
SpecifyVectorElements(y);//User inputs vector elements
DisplayVector(y); // Displays vector y
GaussJordanElimination(A, y, x);
DisplayVector(x);
}
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts
Study Help