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/**

*

* Java implementation of Matrix fast power

* It can calculate the high power of constant Matrix with O( log(K) )

* where K is the power of the Matrix

*

* In order to do that, Matrix must be square Matrix ( columns equals rows)

*

* Notice : large power of Matrix may cause overflow

*

*

* other Matrix basic operator is based on @author Kyler Smith, 2017

*

* @author DDullahan, 2018

*

*/

class MatrixFastPower {

/**

* Matrix Fast Power

*

* @param matrix : square Matrix

* @param k : power of Matrix

* @return product

*/

public static Matrix FastPower(Matrix matrix, int k) throws RuntimeException {

if(matrix.getColumns() != matrix.getRows())

throw new RuntimeException("Matrix is not square Matrix.");

int[][] newData = new int[matrix.getColumns()][matrix.getRows()];

for(int i = 0; i < matrix.getColumns(); i++)

newData[i][i] = 1;

Matrix newMatrix = new Matrix(newData),

coMatrix = new Matrix(matrix.data);

while(k != 0) {

if((k & 1) != 0)

newMatrix = newMatrix.multiply(coMatrix);

k >>= 1;

coMatrix = coMatrix.multiply(coMatrix);

}

return newMatrix;

}

public static void main(String[] argv) {

int[][] data = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

Matrix matrix = new Matrix(data);

System.out.println("original matrix : ");

System.out.println(matrix.toString());

matrix = MatrixFastPower.FastPower(matrix, 5);

System.out.println("after power : ");

System.out.println(matrix.toString());

matrix = MatrixFastPower.FastPower(matrix, 1000000);

System.out.println("notice, large power may cause overflow : ");

System.out.print(matrix.toString());

System.out.println("you can use mod to fix that :-) ");

}

}

class Matrix {

public int[][] data;

/**

* Constructor for the matrix takes in a 2D array

*

* @param pData

*/

public Matrix(int[][] pData) {

/** Make a deep copy of the data */

if(pData.length != 0) {

int[][] newData = new int[pData.length][pData[0].length];

for(int i = 0; i < pData.length; i++)

for(int j = 0; j < pData[0].length; j++)

newData[i][j] = pData[i][j];

this.data = newData;

} else {

this.data = null;

}

}

/**

* Returns the element specified by the given location

*

* @param x : x cooridinate

* @param y : y cooridinate

* @return int : value at location

*/

public int getElement(int x, int y) {

return data[x][y];

}

/**

* Returns the number of rows in the Matrix

*

* @return rows

*/

public int getRows() {

if(this.data == null)

return 0;

return data.length;

}

/**

* Returns the number of rows in the Matrix

*

* @return columns

*/

public int getColumns() {

if(this.data == null)

return 0;

return data[0].length;

}

/**

* Multiplies this matrix with another matrix.

*

* @param other : Matrix to be multiplied with

* @return product

*/

public Matrix multiply(Matrix other) throws RuntimeException {

int[][] newData = new int[this.data.length][other.getColumns()];

if(this.getColumns() != other.getRows())

throw new RuntimeException("The two matrices cannot be multiplied.");

int sum;

for (int i = 0; i < this.getRows(); ++i)

for(int j = 0; j < other.getColumns(); ++j) {

sum = 0;

for(int k = 0; k < this.getColumns(); ++k) {

sum += this.data[i][k] * other.getElement(k, j);

}

newData[i][j] = sum;

}

return new Matrix(newData);

}

/**

* Returns the Matrix as a String in the following format

*

* [ a b c ] ...

* [ x y z ] ...

* [ i j k ] ...

* ...

*

* @return Matrix as String

* TODO: Work formatting for different digit sizes

*/

public String toString() {

String str = "";

for(int i = 0; i < this.data.length; i++) {

str += "[ ";

for(int j = 0; j < this.data[0].length; j++) {

str += data[i][j];

str += " ";

}

str += "]";

str += "\n";

}

return str;

}

}