Stuff

Modellering en simulatie/oefeningen/zitting1/opgave1.m

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+function [Q, R] = opgave1(A)
+    [m, n] = size(A);
+    Q = eye(m);
+    R = A;
+
+    for j = 1:n
+        for i = m:-1:j+1
+            X = [R(i - 1, j); R(i, j)];
+            [G, Y] = planerot(X);
+            R(i - 1, j) = Y(1);
+            R(i, j) = Y(2);
+
+            for k = j+1:n
+                Y = G * [R(i - 1, k); R(i, k)];
+                R(i - 1, k) = Y(1);
+                R(i, k) = Y(2);
+            end
+
+            for k = 1:m
+                Y = [Q(k, i - 1), Q(k, i)] * G.';
+                Q(k, i - 1) = Y(1);
+                Q(k, i) = Y(2);
+            end
+        end
+    end
+end

Modellering en simulatie/oefeningen/zitting1/opgave6.m

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+function N = opgave6(A)
+    [m, n] = size(A);
+
+    for i = 1:n
+        col = A(:, i);
+        s = sum(col);
+        N(:, i) = arrayfun(@(x) x / s, col);
+    end
+end

Modellering en simulatie/oefeningen/zitting1/opgave7.m

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+function B = opgave7(A, q)
+    [m, n] = size(A);
+    c = 1;
+    B = [];
+
+    for i = 1:n
+        A(:, i)
+        q
+        theta = subspace(A(:, i), q)
+        if theta < pi / 4
+            B(c) = i;
+            c = c + 1;
+        end
+    end
+end

Modellering en simulatie/oefeningen/zitting2/notes.md

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+# Opgave 8
+
+De convergentie is in beide gevallen lineair.
+
+# Opgave 9
+
+728 iteraties nodig. Voor $eps^{20}$ zou je dan $728 * 20$ iteraties nodig hebben.

Modellering en simulatie/oefeningen/zitting2/opgave10.m

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+function [eigen, resid] = opgave10(A, tol)
+    [m, _] = size(A);
+    A = hess(A);
+
+    k = 1;
+    resid(k) = norm(tril(A, -1), 'fro');
+
+    for n = m:-1:2
+        while abs(A(n, n - 1)) > tol 
+            kappa = A(n, n);
+            [Q, R] = qr(A - kappa * eye(m));
+            A = R * Q + kappa * eye(m);
+            k = k + 1;
+            resid(k) = norm(tril(A, -1), 'fro');
+        end
+
+        A(n, n - 1) = 0;
+    end
+
+    eigen = diag(A);
+end

Modellering en simulatie/oefeningen/zitting2/opgave4.m

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+[U, S, V] = svd(Z);
+
+i = 1;
+
+for k = 10:10:200
+    Uk = U(:, 1:k);
+    Vk = V(:, 1:k);
+    Sk = S(1:k, 1:k);
+    Zk = Uk * Sk * Vk';
+    %if k == 10
+        %imagesc(Zk)
+    %end
+    images = imagesc(Zk);
+    relDiff(i) = norm(Z - Zk, 'fro') / norm(Z, 'fro');
+    i = i + 1;
+    k
+end
+
+montage(images)
+
+%semilogy(10:10:200, relDiff)

Modellering en simulatie/oefeningen/zitting2/opgave6.m

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+function [Ak, Bk] = testMatrix(k)
+
+    Lk = diag(1:k);
+
+    P1 = orth(rand(k, k));
+    Ak = P1 * Lk * P1';
+
+    P2 = rand(k, k);
+    Bk = P2 * Lk * inv(P2);
+
+end
+
+

Modellering en simulatie/oefeningen/zitting2/opgave7.m

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+function [eigen, resid] = qrAlg(A, tol)
+    k = 1;
+    resid(k) = norm(tril(A, -1), 'fro');
+
+    while resid(k) > tol 
+        [Q, R] = qr(A);
+        A = R * Q;
+        k = k + 1;
+        resid(k) = norm(tril(A, -1), 'fro');
+    end
+
+    eigen = diag(A);
+end

Modellering en simulatie/oefeningen/zitting2/residplot.m

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+function [] = residplot(resid, p)
+    for k = 1:length(resid)-1
+        y(k) = resid(k)/(resid(k+1)^p);
+    end
+
+    plot(y)
+end

Modellering en simulatie/oefeningen/zitting2/testMatrix.m

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+function [Ak, Bk] = testMatrix(k)
+
+    Lk = diag(1:k);
+
+    P1 = orth(rand(k, k));
+    Ak = P1 * Lk * P1';
+
+    P2 = rand(k, k);
+    Bk = P2 * Lk * inv(P2);
+
+end
+
+

Modellering en simulatie/practicum1

@@ -1 +1 @@
-Subproject commit b9148c91208e38281f135e67f75d99e21b4677f7
+Subproject commit c10d1417155f93eac7eff0899243b919af811d4c