import java.util.*;
public class Algorithm {
public class Matrix{
private Double[][] x;
}
public static Scanner scan = new Scanner(System.in);
private static String str;
public static void read_data(Double[] degrees, Double[] l) {
l[0] = 0.0;
int i;
for (i = 0; i < 9; i++) {
str = scan.next(); //passem la primera columna
str = scan.next(); //agafem el valor del desplaçament
str = str.substring(0, str.length()-1); //traiem la coma
l[i+1] = Double.parseDouble(str);
str = scan.next(); //passem la primera columna
str = scan.next(); //agafem el valor del desplaçament
str = str.substring(0, str.length()-1); //traiem la coma
degrees[i] = Double.parseDouble(str);
}
degrees[i] = 0.0;
}
public static void init_Matrix(Double[][] M, int i, Double[] degrees, Double[] l) {
M[0][3] = l[i];
M[0][0] = Math.cos(degrees[i]);
M[0][1] = -Math.sin(degrees[i]);
M[1][0] = Math.sin(degrees[i]);
M[1][1] = Math.cos(degrees[i]);
for (int k = 0; i < 4; k++) {
for (int j = 0; j < 4; j++) {
if (k == j && (M[k][j] == null)) M[k][j] = 1.0;
else if(M[k][j] == null) M[k][j] = 0.0;
}
}
}
public static void init_Ultima_Matrix(Double[][] M, int i, Double[] l) {
M[0][3] = l[i];
for (int k = 0; k < 4; k++) {
for (int j = 0; j < 4; j++) {
if (k == j) M[k][j] = 1.0;
else if(M[k][j] == null) M[k][j] = 0.0;
}
}
}
public static void init_Derivada(Double[][] M, int i, Double[] degrees) {
M[0][0] = -Math.sin(degrees[i]);
M[0][1] = -Math.cos(degrees[i]);
M[1][0] = Math.cos(degrees[i]);
M[1][1] = -Math.sin(degrees[i]);
for (int k = 0; k < 4; k++) {
for (int j = 0; j < 4; j++) {
if(M[k][j] == null) M[k][j] = 0.0;
}
}
}
public static void init_Ultima_Derivada(Double[][] M, int i) {
for (int k = 0; k < 4; k++) {
for (int j = 0; j < 4; j++) {
M[k][j] = 0.0;
}
}
}
public static void fulfill_Ts(Matrix[] Ts, Double[] degrees, Double[] l) {
int i;
for (i = 0; i < 9; i++) {
Ts[i].x = new Double[4][4];
init_Matrix(Ts[i].x, i, degrees, l);
}
init_Ultima_Matrix(Ts[i].x, i, l);
}
public static void fulfill_Ds(Matrix[] Ds, Double[] degrees) {
int i;
for (i = 0; i < 9; i++) {
Ds[i].x = new Double[4][4];
init_Derivada(Ds[i].x, i, degrees);
}
init_Ultima_Derivada(Ds[i].x, i);
}
private static Double[][] product(Double[][] A, Double[][] B){
Double suma = 0.0;
Double result[][] = new Double[4][4];
for(int i = 0; i < 4; i++){
for(int j = 0; j < 4; j++){
suma = 0.0;
for(int k = 0; k < 4; k++){
suma += A[i][k] * B[k][j];
}
result[i][j] = suma;
}
}
return result;
}
private static void calc_Jacobian(Matrix[] Ts, Matrix[] Ds, int i, Double[][] jacobian) {
Double[][] tmp;
if (i == 0) tmp = Ds[0].x;
else tmp = Ts[0].x;
for (int j = 1; j < 10; j++) {
if (j == i) tmp = product(tmp, Ds[j].x);
else tmp = product(tmp, Ts[j].x);
}
jacobian[0][i] = tmp[0][3];
jacobian[1][i] = tmp[1][3];
jacobian[2][i] = tmp[0][0];
}
public static void main(String[] args) {
Matrix[] Ts = new Matrix[10];
Matrix[] Ds = new Matrix[10];
for (int i = 0; i < 10; i++) {
Ts[i].x = new Double[4][4];
Ds[i].x = new Double[4][4];
}
Double[] degrees = new Double[10];
Double[] l = new Double[10];
read_data(degrees, l);
fulfill_Ts(Ts, degrees, l);
fulfill_Ds(Ds, degrees);
Matrix jacobian = new Matrix();
jacobian.x = new Double[3][9];
for (int j=0; j<9; j++)
calc_Jacobian(Ts, Ds, j, jacobian.x);
//La matriu Jacobiana hauria d'estar acabada
}
}
Well, this is my code. The error is in the first line where says "Matrix jacobian = new Matrix();". Have I declared it wrong? The definition of Matrix is at the beginning of the code.
It says: No enclosing instance of type Algorithm is accessible. Must qualify the allocation with an enclosing instance of type Algorithm (e.g. x.new A() where x is an instance of Algorithm).
Moreover, I get an Exception with this: "Matrix[] Ts = new Matrix[10];". Can't I declare an array of elements Matrix?
Thank you very much.
Yes, try this: Matrix M = new Matrix();
This one Matrix[] Ts = new Matrix[10]; is valid but you should also loop through the array elements and initialize them by calling the constructor. Otherwise, they will remain having null values.
Change
public class Matrix
to
public static class Matrix
Creating a nested class without the static modifier creates a closure, which allows you to reference non-static members of the enclosing instance. If you don't declare it static, you need an enclosing instance (ie, a this) to create it, which you don't have in static void main().
Explaining a closure is beyond the scope of this answer, but it would be a private member Algorithm _closure in Matrix, which is implicitly referenced (the same way this is), when you mention a non-static member of Algorithm.
I'm having trouble with this polynomial class, specifically the checkZero and differentiate methods. The checkZero class is supposed to see if there are any leading coefficients in the polynomial, and if so, it should resize the coefficient array. The differentiate method should find the derivative of a polynomial, but I keep getting ArrayIndexOutOfBounds errors.
public class Polynomial {
private float[] coefficients;
public static void main (String[] args){
float[] fa = {3, 2, 4};
Polynomial test = new Polynomial(fa);
}
public Polynomial() {
coefficients = new float[1];
coefficients[0] = 0;
}
public Polynomial(int degree) {
coefficients = new float[degree+1];
for (int i = 0; i <= degree; i++)
coefficients[i] = 0;
}
public Polynomial(float[] a) {
coefficients = new float[a.length];
for (int i = 0; i < a.length; i++)
coefficients[i] = a[i];
}
public int getDegree() {
return coefficients.length-1;
}
public float getCoefficient(int i) {
return coefficients[i];
}
public void setCoefficient(int i, float value) {
coefficients[i] = value;
}
public Polynomial add(Polynomial p) {
int n = getDegree();
int m = p.getDegree();
Polynomial result = new Polynomial(Polynomial.max(n, m));
int i;
for (i = 0; i <= Polynomial.min(n, m); i++)
result.setCoefficient(i, coefficients[i] + p.getCoefficient(i));
if (i <= n) {
//we have to copy the remaining coefficients from this object
for ( ; i <= n; i++)
result.setCoefficient(i, coefficients[i]);
} else {
// we have to copy the remaining coefficients from p
for ( ; i <= m; i++)
result.setCoefficient(i, p.getCoefficient(i));
}
return result;
}
public void displayPolynomial () {
for (int i=0; i < coefficients.length; i++)
System.out.print(" "+coefficients[i]);
System.out.println();
}
private static int max (int n, int m) {
if (n > m)
return n;
return m;
}
private static int min (int n, int m) {
if (n > m)
return m;
return n;
}
public Polynomial multiplyCon (double c){
int n = getDegree();
Polynomial results = new Polynomial(n);
for (int i =0; i <= n; i++){ // can work when multiplying only 1 coefficient
results.setCoefficient(i, (float)(coefficients[i] * c)); // errors ArrayIndexOutOfBounds for setCoefficient
}
return results;
}
public Polynomial multiplyPoly (Polynomial p){
int n = getDegree();
int m = p.getDegree();
Polynomial result = null;
for (int i = 0; i <= n; i++){
Polynomial tmpResult = p.multiByConstantWithDegree(coefficients[i], i); //Calls new method
if (result == null){
result = tmpResult;
} else {
result = result.add(tmpResult);
}
}
return result;
}
public void checkZero(){
int newDegree = getDegree();
int length = coefficients.length;
float testArray[] = coefficients;
for (int i = coefficients.length-1; i>0; i--){
if (coefficients[i] != 0){
testArray[i] = coefficients[i];
}
}
for (int j = 0; j < testArray.length; j++){
coefficients[j] = testArray[j];
}
}
public Polynomial differentiate(){
int n = getDegree();
int newPolyDegree = n - 1;
Polynomial newResult = new Polynomial();
if (n == 0){
newResult.setCoefficient(0, 0);
}
for (int i =0; i<= n; i++){
newResult.setCoefficient(i, coefficients[i+1] * (i+1));
}
return newResult;
}
}
There might be more problems, but one is a problem with your differentiate method:
int n = getDegree();
...
Polynomial newResult = new Polynomial();
...
for (int i = 0; i <= n; i++)
{
newResult.setCoefficient(i, coefficients[i + 1] * (i + 1)); //This line
}
Your paramaterless constructor initializes an array with length 1, so "newResult" will only have 1 index, and you try to put something into place i, which goes above 1 if the Polynomial you are in have an array of greater length than 1.
First, a few code notes:
New arrays are automatically initialized to 0 in Java. This is not needed.
coefficients = new float[degree+1];
for (int i = 0; i <= degree; i++)
coefficients[i] = 0;
I also see many lines which might become more readable and compact if you use the trinary operator, for example:
int i;
for (i = 0; i <= Polynomial.min(n, m); i++)
result.setCoefficient(i, coefficients[i] + p.getCoefficient(i));
if (i <= n) {
//we have to copy the remaining coefficients from this object
for ( ; i <= n; i++)
result.setCoefficient(i, coefficients[i]);
} else {
// we have to copy the remaining coefficients from p
for ( ; i <= m; i++)
result.setCoefficient(i, p.getCoefficient(i));
}
Could become something like
for (int i = 0; i <= result.getDegree(); i++)
result.setCoefficient(i,
i>n?0:coefficients[i] +
i>m?0:p.getCoefficient(i));
The one bug I did spot was here:
int n = getDegree();
....
for (int i =0; i<= n; i++){
newResult.setCoefficient(i, coefficients[i+1] * (i+1));
}
This will always call coefficients[coefficients.length] on the last iteration, which will always fail.
The stack trace of the exception when you ran this program should tell you exactly where the error is, by the way.
I'm trying to make two methods for a Polynomial class but I'm having troubles.
The first method checkZeros is supposed to check if there are any leading zeros in the coefficients of a polynomial. The method should resize the coefficient array if there are leading zeros. The second method should find the derivative of a polynomial, but I keep getting ArrayIndexOutOfBounds errors.
Here they are:
public class Poly {
private float[] coefficients;
public static void main (String[] args){
float[] fa = {3, 2, 4};
Poly test = new Poly(fa);
}
public Poly() {
coefficients = new float[1];
coefficients[0] = 0;
}
public Poly(int degree) {
coefficients = new float[degree+1];
for (int i = 0; i <= degree; i++)
coefficients[i] = 0;
}
public Poly(float[] a) {
coefficients = new float[a.length];
for (int i = 0; i < a.length; i++)
coefficients[i] = a[i];
}
public int getDegree() {
return coefficients.length-1;
}
public float getCoefficient(int i) {
return coefficients[i];
}
public void setCoefficient(int i, float value) {
coefficients[i] = value;
}
public Poly add(Poly p) {
int n = getDegree();
int m = p.getDegree();
Poly result = new Poly(Poly.max(n, m));
int i;
for (i = 0; i <= Poly.min(n, m); i++)
result.setCoefficient(i, coefficients[i] + p.getCoefficient(i));
if (i <= n) {
//we have to copy the remaining coefficients from this object
for ( ; i <= n; i++)
result.setCoefficient(i, coefficients[i]);
} else {
// we have to copy the remaining coefficients from p
for ( ; i <= m; i++)
result.setCoefficient(i, p.getCoefficient(i));
}
return result;
}
public void displayPoly () {
for (int i=0; i < coefficients.length; i++)
System.out.print(" "+coefficients[i]);
System.out.println();
}
private static int max (int n, int m) {
if (n > m)
return n;
return m;
}
private static int min (int n, int m) {
if (n > m)
return m;
return n;
}
public void checkForZeros(){
int newDegree = getDegree();
int length = coefficients.length;
double testArray[] = coefficients;
for (int i = length - 1; i >0; i--) {
if (coefficients[i] != 0) {
testArray[i] = coefficients[i];
}
}
for (int j = 0; j < testArray.length; j++){
coefficients[j] = testArray[j];
}
}
public Poly differentiate(){
int n = getDegree();
int newPolyDegree = n - 1;
Poly newResult = new Poly();
if (n == 0){
newResult.setCoefficient(0, 0);
}
for (int i =0; i<= n; i++){
newResult.setCoefficient(i, coefficients[i+1] * (i+1));
}
return newResult;
}
}
I would suspect the problem is here
for (int i =0; i<= n; i++){
newResult.setCoefficient(i, coefficients[i+1] * (i+1));
}
Since n = getDegree();, let's assume the polynomial is of 1st degree (1+x for example). Then n=1 I would guess, and coefficients has a length of 2. But you are going to be checking coefficients[2] (since you have i+1) which is out of bounds. I'm guessing you want
for (i=0; i<=newPolyDegree; i++){
newResult.setCoefficient(i, coefficients[i] * (i+1));
}
or something... It's hard to tell with the amount of code you gave.
You are most probably getting ArrayIndexOutofBounds because you've implemented checkzeroes in a wrong manner and hence getdegree() is returning a size less than the coefficient array. Consider the following polynomial:
f(x) = 2x^3 + 5x + 1
The coefficient array will be
[2,0,5,1]
After checkzeroes, it becomes
[2,5,1] (because you're removing all zeroes, not just leading zeroes.)
I suppose the degree function will still return 3 and you'll run out of array bounds in differentiate()
The error is in the loop.
for (int i =0; i<= n; i++){
newResult.setCoefficient(i, coefficients[i+1] * (i+1));
Base on little information, I assume:
1. setCoefficient(power of x, coefficient of x)
So in this case, we have a polynomial of degree n for differentiation, which have n+1 term, starting from 0->n (x^0 -> x^n)
Look at the loop, when i=n, it have to fetch the coefficient of x^(n+1) which is not exist.
You should do.
for (int i =0; i< n; i++){
newResult.setCoefficient(i, coefficients[i+1] * (i+1));
I am trying to calculate the determinant of a matrix (of any size), for self coding / interview practice. My first attempt is using recursion and that leads me to the following implementation:
import java.util.Scanner.*;
public class Determinant {
double A[][];
double m[][];
int N;
int start;
int last;
public Determinant (double A[][], int N, int start, int last){
this.A = A;
this.N = N;
this.start = start;
this.last = last;
}
public double[][] generateSubArray (double A[][], int N, int j1){
m = new double[N-1][];
for (int k=0; k<(N-1); k++)
m[k] = new double[N-1];
for (int i=1; i<N; i++){
int j2=0;
for (int j=0; j<N; j++){
if(j == j1)
continue;
m[i-1][j2] = A[i][j];
j2++;
}
}
return m;
}
/*
* Calculate determinant recursively
*/
public double determinant(double A[][], int N){
double res;
// Trivial 1x1 matrix
if (N == 1) res = A[0][0];
// Trivial 2x2 matrix
else if (N == 2) res = A[0][0]*A[1][1] - A[1][0]*A[0][1];
// NxN matrix
else{
res=0;
for (int j1=0; j1<N; j1++){
m = generateSubArray (A, N, j1);
res += Math.pow(-1.0, 1.0+j1+1.0) * A[0][j1] * determinant(m, N-1);
}
}
return res;
}
}
So far it is all good and it gives me a correct result. Now I would like to optimise my code by making use of multiple threads to calculate this determinant value.
I tried to parallelize it using the Java Fork/Join model. This is my approach:
#Override
protected Double compute() {
if (N < THRESHOLD) {
result = computeDeterminant(A, N);
return result;
}
for (int j1 = 0; j1 < N; j1++){
m = generateSubArray (A, N, j1);
ParallelDeterminants d = new ParallelDeterminants (m, N-1);
d.fork();
result += Math.pow(-1.0, 1.0+j1+1.0) * A[0][j1] * d.join();
}
return result;
}
public double computeDeterminant(double A[][], int N){
double res;
// Trivial 1x1 matrix
if (N == 1) res = A[0][0];
// Trivial 2x2 matrix
else if (N == 2) res = A[0][0]*A[1][1] - A[1][0]*A[0][1];
// NxN matrix
else{
res=0;
for (int j1=0; j1<N; j1++){
m = generateSubArray (A, N, j1);
res += Math.pow(-1.0, 1.0+j1+1.0) * A[0][j1] * computeDeterminant(m, N-1);
}
}
return res;
}
/*
* Main function
*/
public static void main(String args[]){
double res;
ForkJoinPool pool = new ForkJoinPool();
ParallelDeterminants d = new ParallelDeterminants();
d.inputData();
long starttime=System.nanoTime();
res = pool.invoke (d);
long EndTime=System.nanoTime();
System.out.println("Seq Run = "+ (EndTime-starttime)/100000);
System.out.println("the determinant valaue is " + res);
}
However after comparing the performance, I found that the performance of the Fork/Join approach is very bad, and the higher the matrix dimension, the slower it becomes (as compared to the first approach). Where is the overhead? Can anyone shed a light on how to improve this?
Using This class you can calculate the determinant of a matrix with any dimension
This class uses many different methods to make the matrix triangular and then, calculates the determinant of it. It can be used for matrix of high dimension like 500 x 500 or even more. the bright side of the this class is that you can get the result in BigDecimal so there is no infinity and you'll have always the accurate answer. By the way, using many various methods and avoiding recursion resulted in much faster way with higher performance to the answer. hope it would be helpful.
import java.math.BigDecimal;
public class DeterminantCalc {
private double[][] matrix;
private int sign = 1;
DeterminantCalc(double[][] matrix) {
this.matrix = matrix;
}
public int getSign() {
return sign;
}
public BigDecimal determinant() {
BigDecimal deter;
if (isUpperTriangular() || isLowerTriangular())
deter = multiplyDiameter().multiply(BigDecimal.valueOf(sign));
else {
makeTriangular();
deter = multiplyDiameter().multiply(BigDecimal.valueOf(sign));
}
return deter;
}
/* receives a matrix and makes it triangular using allowed operations
on columns and rows
*/
public void makeTriangular() {
for (int j = 0; j < matrix.length; j++) {
sortCol(j);
for (int i = matrix.length - 1; i > j; i--) {
if (matrix[i][j] == 0)
continue;
double x = matrix[i][j];
double y = matrix[i - 1][j];
multiplyRow(i, (-y / x));
addRow(i, i - 1);
multiplyRow(i, (-x / y));
}
}
}
public boolean isUpperTriangular() {
if (matrix.length < 2)
return false;
for (int i = 0; i < matrix.length; i++) {
for (int j = 0; j < i; j++) {
if (matrix[i][j] != 0)
return false;
}
}
return true;
}
public boolean isLowerTriangular() {
if (matrix.length < 2)
return false;
for (int j = 0; j < matrix.length; j++) {
for (int i = 0; j > i; i++) {
if (matrix[i][j] != 0)
return false;
}
}
return true;
}
public BigDecimal multiplyDiameter() {
BigDecimal result = BigDecimal.ONE;
for (int i = 0; i < matrix.length; i++) {
for (int j = 0; j < matrix.length; j++) {
if (i == j)
result = result.multiply(BigDecimal.valueOf(matrix[i][j]));
}
}
return result;
}
// when matrix[i][j] = 0 it makes it's value non-zero
public void makeNonZero(int rowPos, int colPos) {
int len = matrix.length;
outer:
for (int i = 0; i < len; i++) {
for (int j = 0; j < len; j++) {
if (matrix[i][j] != 0) {
if (i == rowPos) { // found "!= 0" in it's own row, so cols must be added
addCol(colPos, j);
break outer;
}
if (j == colPos) { // found "!= 0" in it's own col, so rows must be added
addRow(rowPos, i);
break outer;
}
}
}
}
}
//add row1 to row2 and store in row1
public void addRow(int row1, int row2) {
for (int j = 0; j < matrix.length; j++)
matrix[row1][j] += matrix[row2][j];
}
//add col1 to col2 and store in col1
public void addCol(int col1, int col2) {
for (int i = 0; i < matrix.length; i++)
matrix[i][col1] += matrix[i][col2];
}
//multiply the whole row by num
public void multiplyRow(int row, double num) {
if (num < 0)
sign *= -1;
for (int j = 0; j < matrix.length; j++) {
matrix[row][j] *= num;
}
}
//multiply the whole column by num
public void multiplyCol(int col, double num) {
if (num < 0)
sign *= -1;
for (int i = 0; i < matrix.length; i++)
matrix[i][col] *= num;
}
// sort the cols from the biggest to the lowest value
public void sortCol(int col) {
for (int i = matrix.length - 1; i >= col; i--) {
for (int k = matrix.length - 1; k >= col; k--) {
double tmp1 = matrix[i][col];
double tmp2 = matrix[k][col];
if (Math.abs(tmp1) < Math.abs(tmp2))
replaceRow(i, k);
}
}
}
//replace row1 with row2
public void replaceRow(int row1, int row2) {
if (row1 != row2)
sign *= -1;
double[] tempRow = new double[matrix.length];
for (int j = 0; j < matrix.length; j++) {
tempRow[j] = matrix[row1][j];
matrix[row1][j] = matrix[row2][j];
matrix[row2][j] = tempRow[j];
}
}
//replace col1 with col2
public void replaceCol(int col1, int col2) {
if (col1 != col2)
sign *= -1;
System.out.printf("replace col%d with col%d, sign = %d%n", col1, col2, sign);
double[][] tempCol = new double[matrix.length][1];
for (int i = 0; i < matrix.length; i++) {
tempCol[i][0] = matrix[i][col1];
matrix[i][col1] = matrix[i][col2];
matrix[i][col2] = tempCol[i][0];
}
} }
This Class Receives a matrix of n x n from the user then calculates it's determinant. It also shows the solution and the final triangular matrix.
import java.math.BigDecimal;
import java.text.NumberFormat;
import java.util.Scanner;
public class DeterminantTest {
public static void main(String[] args) {
String determinant;
//generating random numbers
/*int len = 300;
SecureRandom random = new SecureRandom();
double[][] matrix = new double[len][len];
for (int i = 0; i < len; i++) {
for (int j = 0; j < len; j++) {
matrix[i][j] = random.nextInt(500);
System.out.printf("%15.2f", matrix[i][j]);
}
}
System.out.println();*/
/*double[][] matrix = {
{1, 5, 2, -2, 3, 2, 5, 1, 0, 5},
{4, 6, 0, -2, -2, 0, 1, 1, -2, 1},
{0, 5, 1, 0, 1, -5, -9, 0, 4, 1},
{2, 3, 5, -1, 2, 2, 0, 4, 5, -1},
{1, 0, 3, -1, 5, 1, 0, 2, 0, 2},
{1, 1, 0, -2, 5, 1, 2, 1, 1, 6},
{1, 0, 1, -1, 1, 1, 0, 1, 1, 1},
{1, 5, 5, 0, 3, 5, 5, 0, 0, 6},
{1, -5, 2, -2, 3, 2, 5, 1, 1, 5},
{1, 5, -2, -2, 3, 1, 5, 0, 0, 1}
};
*/
double[][] matrix = menu();
DeterminantCalc deter = new DeterminantCalc(matrix);
BigDecimal det = deter.determinant();
determinant = NumberFormat.getInstance().format(det);
for (int i = 0; i < matrix.length; i++) {
for (int j = 0; j < matrix.length; j++) {
System.out.printf("%15.2f", matrix[i][j]);
}
System.out.println();
}
System.out.println();
System.out.printf("%s%s%n", "Determinant: ", determinant);
System.out.printf("%s%d", "sign: ", deter.getSign());
}
public static double[][] menu() {
Scanner scanner = new Scanner(System.in);
System.out.print("Matrix Dimension: ");
int dim = scanner.nextInt();
double[][] inputMatrix = new double[dim][dim];
System.out.println("Set the Matrix: ");
for (int i = 0; i < dim; i++) {
System.out.printf("%5s%d%n", "row", i + 1);
for (int j = 0; j < dim; j++) {
System.out.printf("M[%d][%d] = ", i + 1, j + 1);
inputMatrix[i][j] = scanner.nextDouble();
}
System.out.println();
}
scanner.close();
return inputMatrix;
}}
The main reason the ForkJoin code is slower is that it's actually serialized with some thread overhead thrown in. To benefit from fork/join, you need to 1) fork all instances first, then 2) wait for the results. Split your loop in "compute" into two loops: one to fork (storing instances of ParallelDeterminants in, say, an array) and another to collect the results.
Also, I suggest to only fork at the outermost level and not in any of the inner ones. You don't want to be creating O(N^2) threads.
There is a new method of calculating the determinant of the matrix you can read more from here
and I've implemented a simple version of this with no fancy optimization techniques or library in plain simple java and I've tested against methods described previously and it was faster on average by a factor of 10
public class Test {
public static double[][] reduce(int row , int column , double[][] mat){
int n=mat.length;
double[][] res = new double[n- 1][n- 1];
int r=0,c=0;
for (int i = 0; i < n; i++) {
c=0;
if(i==row)
continue;
for (int j = 0; j < n; j++) {
if(j==column)
continue;
res[r][c] = mat[i][j];
c++;
}
r++;
}
return res;
}
public static double det(double mat[][]){
int n = mat.length;
if(n==1)
return mat[0][0];
if(n==2)
return mat[0][0]*mat[1][1] - (mat[0][1]*mat[1][0]);
//TODO : do reduce more efficiently
double[][] m11 = reduce(0,0,mat);
double[][] m1n = reduce(0,n-1,mat);
double[][] mn1 = reduce(n-1 , 0 , mat);
double[][] mnn = reduce(n-1,n-1,mat);
double[][] m11nn = reduce(0,0,reduce(n-1,n-1,mat));
return (det(m11)*det(mnn) - det(m1n)*det(mn1))/det(m11nn);
}
public static double[][] randomMatrix(int n , int range){
double[][] mat = new double[n][n];
for (int i=0; i<mat.length; i++) {
for (int j=0; j<mat[i].length; j++) {
mat[i][j] = (Math.random()*range);
}
}
return mat;
}
public static void main(String[] args) {
double[][] mat = randomMatrix(10,100);
System.out.println(det(mat));
}
}
there is a little fault in the case of the determinant of m11nn if happen to be zero it will blow up and you should check for that. I've tested on 100 random samples it rarely happens but I think it worth mentioning and also using a better indexing scheme can also improve the efficiency
This is a part of my Matrix class which uses a double[][] member variable called data to store the matrix data.
The _determinant_recursivetask_impl() function uses a RecursiveTask<Double> object with the ForkJoinPool to try to use multiple threads for calculation.
This method performs very slow compared to matrix operations to get an upper/lower triangular matrix. Try to compute the determinant of a 13x13 matrix for example.
public class Matrix
{
// Dimensions
private final int I,J;
private final double[][] data;
private Double determinant = null;
static class MatrixEntry
{
public final int I,J;
public final double value;
private MatrixEntry(int i, int j, double value) {
I = i;
J = j;
this.value = value;
}
}
/**
* Calculates determinant of this Matrix recursively and caches it for future use.
* #return determinant
*/
public double determinant()
{
if(I!=J)
throw new IllegalStateException(String.format("Can't calculate determinant of (%d,%d) matrix, not a square matrix.", I,J));
if(determinant==null)
determinant = _determinant_recursivetask_impl(this);
return determinant;
}
private static double _determinant_recursivetask_impl(Matrix m)
{
class determinant_recurse extends RecursiveTask<Double>
{
private final Matrix m;
determinant_recurse(Matrix m) {
this.m = m;
}
#Override
protected Double compute() {
// Base cases
if(m.I==1 && m.J==1)
return m.data[0][0];
else if(m.I==2 && m.J==2)
return m.data[0][0]*m.data[1][1] - m.data[0][1]*m.data[1][0];
else
{
determinant_recurse[] tasks = new determinant_recurse[m.I];
for (int i = 0; i <m.I ; i++) {
tasks[i] = new determinant_recurse(m.getSubmatrix(0, i));
}
for (int i = 1; i <m.I ; i++) {
tasks[i].fork();
}
double ret = m.data[0][0]*tasks[0].compute();
for (int i = 1; i < m.I; i++) {
if(i%2==0)
ret += m.data[0][i]*tasks[i].join();
else
ret -= m.data[0][i]*tasks[i].join();
}
return ret;
}
}
}
return ForkJoinPool.commonPool().invoke(new determinant_recurse(m));
}
private static void _map_impl(Matrix ret, Function<Matrix.MatrixEntry, Double> operator)
{
for (int i = 0; i <ret.I ; i++) {
for (int j = 0; j <ret.J ; j++) {
ret.data[i][j] = operator.apply(new Matrix.MatrixEntry(i,j,ret.data[i][j]));
}
}
}
/**
* Returns a new Matrix that is sub-matrix without the given row and column.
* #param removeI row to remove
* #param removeJ col. to remove
* #return new Matrix.
*/
public Matrix getSubmatrix(int removeI, int removeJ)
{
if(removeI<0 || removeJ<0 || removeI>=this.I || removeJ>=this.J)
throw new IllegalArgumentException(String.format("Invalid element position (%d,%d) for matrix(%d,%d).", removeI,removeJ,this.I,this.J));
Matrix m = new Matrix(this.I-1, this.J-1);
_map_impl(m, (e)->{
int i = e.I, j = e.J;
if(e.I >= removeI) ++i;
if(e.J >= removeJ) ++j;
return this.data[i][j];
});
return m;
}
// Constructors
public Matrix(int i, int j) {
if(i<1 || j<1)
throw new IllegalArgumentException(String.format("Invalid array dimensions: (%d,%d)", i, j));
I = i;
J = j;
data = new double[I][J];
}
}
int det(int[][] mat) {
if (mat.length == 1)
return mat[0][0];
if (mat.length == 2)
return mat[0][0] * mat[1][1] - mat[1][0] * mat[0][1];
int sum = 0, sign = 1;
int newN = mat.length - 1;
int[][] temp = new int[newN][newN];
for (int t = 0; t < newN; t++) {
int q = 0;
for (int i = 0; i < newN; i++) {
for (int j = 0; j < newN; j++) {
temp[i][j] = mat[1 + i][q + j];
}
if (q == i)
q = 1;
}
sum += sign * mat[0][t] * det(temp);
sign *= -1;
}
return sum;
}
I am trying to run my code so it prints cyclic permutations, though I can only get it to do the first one at the moment. It runs correctly up to the point which I have marked but I can't see what is going wrong. I think it has no break in the while loop, but I'm not sure. Really could do with some help here.
package permutation;
public class Permutation {
static int DEFAULT = 100;
public static void main(String[] args) {
int n = DEFAULT;
if (args.length > 0)
n = Integer.parseInt(args[0]);
int[] OA = new int[n];
for (int i = 0; i < n; i++)
OA[i] = i + 1;
System.out.println("The original array is:");
for (int i = 0; i < OA.length; i++)
System.out.print(OA[i] + " ");
System.out.println();
System.out.println("A permutation of the original array is:");
OA = generateRandomPermutation(n);
printArray(OA);
printPemutation(OA);
}
static int[] generateRandomPermutation(int n)// (a)
{
int[] A = new int[n];
for (int i = 0; i < n; i++)
A[i] = i + 1;
for (int i = 0; i < n; i++) {
int r = (int) (Math.random() * (n));
int swap = A[r];
A[r] = A[i];
A[i] = swap;
}
return A;
}
static void printArray(int A[]) {
for (int i = 0; i < A.length; i++)
System.out.print(A[i] + " ");
System.out.println();
}
static void printPemutation(int p[])// (b)
{
System.out
.println("The permutation is represented by the cyclic notation:");
int[] B = new int[p.length];
int m = 0;
while (m < p.length)// this is the point at which my code screws up
{
if (!check(B, m)) {
B = parenthesis(p, m);
printParenthesis(B);
m++;
} else
m++;
}// if not there are then repeat
}
static int[] parenthesis(int p[], int i) {
int[] B = new int[p.length];
for (int a = p[i], j = 0; a != B[0]; a = p[a - 1], j++) {
B[j] = a;
}
return B;
}
static void printParenthesis(int B[]) {
System.out.print("( ");
for (int i = 0; i < B.length && B[i] != 0; i++)
System.out.print(B[i] + " ");
System.out.print(")");
}
static boolean check(int B[], int m) {
int i = 0;
boolean a = false;
while (i < B.length || !a) {
if ((ispresent(m, B, i))){
a = true;
break;
}
else
i++;
}
return a;
}
static boolean ispresent(int m, int B[], int i) {
return m == B[i] && m < B.length;
}
}
Among others you should check p[m] in check(B, p[m]) instead of m:
in static void printPemutation(int p[]):
while (m < p.length){
if (!check(B, p[m])) {
B = parenthesis(p, m);
printParenthesis(B);
}
m++;
}
then
static boolean check(int B[], int m) {
int i = 0;
while (i < B.length) {
if (m == B[i]) {
return true;
}
i++;
}
return false;
}
this does somehow more what you want, but not always i fear...