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