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LU decomposition: Difference between revisions
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3 17 18 1
2 5 7 1</lang>
=={{header|Java}}==
Translation of [[#Common_Lisp|Common Lisp]] via [[#D|D]]
{{works with|Java|8}}
<lang java>import static java.util.Arrays.stream;
import java.util.Locale;
import static java.util.stream.IntStream.range;
public class Test {
static double dotProduct(double[] a, double[] b) {
return range(0, a.length).mapToDouble(i -> a[i] * b[i]).sum();
}
static double[][] matrixMul(double[][] A, double[][] B) {
double[][] result = new double[A.length][B[0].length];
double[] aux = new double[B.length];
for (int j = 0; j < B[0].length; j++) {
for (int k = 0; k < B.length; k++)
aux[k] = B[k][j];
for (int i = 0; i < A.length; i++)
result[i][j] = dotProduct(A[i], aux);
}
return result;
}
static double[][] pivotize(double[][] m) {
int n = m.length;
double[][] id = range(0, n).mapToObj(j -> range(0, n)
.mapToDouble(i -> i == j ? 1 : 0).toArray())
.toArray(double[][]::new);
for (int i = 0; i < n; i++) {
double maxm = m[i][i];
int row = i;
for (int j = i; j < n; j++)
if (m[j][i] > maxm) {
maxm = m[j][i];
row = j;
}
if (i != row) {
double[] tmp = id[i];
id[i] = id[row];
id[row] = tmp;
}
}
return id;
}
static double[][][] lu(double[][] A) {
int n = A.length;
double[][] L = new double[n][n];
double[][] U = new double[n][n];
double[][] P = pivotize(A);
double[][] A2 = matrixMul(P, A);
for (int j = 0; j < n; j++) {
L[j][j] = 1;
for (int i = 0; i < j + 1; i++) {
double s1 = 0;
for (int k = 0; k < i; k++)
s1 += U[k][j] * L[i][k];
U[i][j] = A2[i][j] - s1;
}
for (int i = j; i < n; i++) {
double s2 = 0;
for (int k = 0; k < j; k++)
s2 += U[k][j] * L[i][k];
L[i][j] = (A2[i][j] - s2) / U[j][j];
}
}
return new double[][][]{L, U, P};
}
static void print(double[][] m) {
stream(m).forEach(a -> {
stream(a).forEach(n -> System.out.printf(Locale.US, "%5.1f ", n));
System.out.println();
});
System.out.println();
}
public static void main(String[] args) {
double[][] a = {{1.0, 3, 5}, {2.0, 4, 7}, {1.0, 1, 0}};
double[][] b = {{11.0, 9, 24, 2}, {1.0, 5, 2, 6}, {3.0, 17, 18, 1},
{2.0, 5, 7, 1}};
for (double[][] m : lu(a))
print(m);
System.out.println();
for (double[][] m : lu(b))
print(m);
}
}</lang>
<pre> 1.0 0.0 0.0
0.5 1.0 0.0
0.5 -1.0 1.0
2.0 4.0 7.0
0.0 1.0 1.5
0.0 0.0 -2.0
0.0 1.0 0.0
1.0 0.0 0.0
0.0 0.0 1.0
1.0 0.0 0.0 0.0
0.3 1.0 0.0 0.0
0.1 0.3 1.0 0.0
0.2 0.2 0.0 1.0
11.0 9.0 24.0 2.0
0.0 14.5 11.5 0.5
0.0 0.0 -3.5 5.7
0.0 0.0 0.0 0.5
1.0 0.0 0.0 0.0
0.0 0.0 1.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 0.0 1.0 </pre>
=={{header|jq}}==
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