Data commit

Task/Cramers-rule/D/cramers-rule.d

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+import std.array : array, uninitializedArray;
+import std.range : iota;
+import std.stdio : writeln;
+import std.typecons : tuple;
+
+alias vector = double[4];
+alias matrix = vector[4];
+
+auto johnsonTrotter(int n) {
+    auto p = iota(n).array;
+    auto q = iota(n).array;
+    auto d = uninitializedArray!(int[])(n);
+    d[] = -1;
+    auto sign = 1;
+    int[][] perms;
+    int[] signs;
+
+    void permute(int k) {
+        if (k >= n) {
+            perms ~= p.dup;
+            signs ~= sign;
+            sign *= -1;
+            return;
+        }
+        permute(k + 1);
+        foreach (i; 0..k) {
+            auto z = p[q[k] + d[k]];
+            p[q[k]] = z;
+            p[q[k] + d[k]] = k;
+            q[z] = q[k];
+            q[k] += d[k];
+            permute(k + 1);
+        }
+        d[k] *= -1;
+    }
+
+    permute(0);
+    return tuple!("sigmas", "signs")(perms, signs);
+}
+
+auto determinant(matrix m) {
+    auto jt = johnsonTrotter(m.length);
+    auto sum = 0.0;
+    foreach (i,sigma; jt.sigmas) {
+        auto prod = 1.0;
+        foreach (j,s; sigma) {
+            prod *= m[j][s];
+        }
+        sum += jt.signs[i] * prod;
+    }
+    return sum;
+}
+
+auto cramer(matrix m, vector d) {
+    auto divisor = determinant(m);
+    auto numerators = uninitializedArray!(matrix[])(m.length);
+    foreach (i; 0..m.length) {
+        foreach (j; 0..m.length) {
+            foreach (k; 0..m.length) {
+                numerators[i][j][k] = m[j][k];
+            }
+        }
+    }
+    vector v;
+    foreach (i; 0..m.length) {
+        foreach (j; 0..m.length) {
+            numerators[i][j][i] = d[j];
+        }
+    }
+    foreach (i; 0..m.length) {
+        v[i] = determinant(numerators[i]) / divisor;
+    }
+    return v;
+}
+
+void main() {
+    matrix m = [
+        [2.0, -1.0,  5.0,  1.0],
+        [3.0,  2.0,  2.0, -6.0],
+        [1.0,  3.0,  3.0, -1.0],
+        [5.0, -2.0, -3.0,  3.0]
+    ];
+    vector d = [-3.0, -32.0, -47.0, 49.0];
+    auto wxyz = cramer(m, d);
+    writeln("w = ", wxyz[0], ", x = ", wxyz[1], ", y = ", wxyz[2], ", z = ", wxyz[3]);
+}