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Copy pathMatrixFastPower.java
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191 lines (149 loc) · 4.49 KB
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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;
}
}