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simulatie/oefeningen/zitting1/opgave1.m @@ -0,0 +1,26 @@ +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 diff --git a/Modellering en simulatie/oefeningen/zitting1/opgave6.m b/Modellering en simulatie/oefeningen/zitting1/opgave6.m new file mode 100644 index 0000000..ff2d536 --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting1/opgave6.m @@ -0,0 +1,9 @@ +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 diff --git a/Modellering en simulatie/oefeningen/zitting1/opgave7.m b/Modellering en simulatie/oefeningen/zitting1/opgave7.m new file mode 100644 index 0000000..4860213 --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting1/opgave7.m @@ -0,0 +1,15 @@ +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 diff --git a/Modellering en simulatie/oefeningen/zitting2/.2021-10-04-Note-13-58.autosave.xopp b/Modellering en simulatie/oefeningen/zitting2/.2021-10-04-Note-13-58.autosave.xopp new file mode 100644 index 0000000..9235ed2 Binary files /dev/null and b/Modellering en simulatie/oefeningen/zitting2/.2021-10-04-Note-13-58.autosave.xopp differ diff --git a/Modellering en simulatie/oefeningen/zitting2/2021-10-04-Note-13-58.xopp b/Modellering en simulatie/oefeningen/zitting2/2021-10-04-Note-13-58.xopp new file mode 100644 index 0000000..9235ed2 Binary files /dev/null and b/Modellering en simulatie/oefeningen/zitting2/2021-10-04-Note-13-58.xopp differ diff --git a/Modellering en simulatie/oefeningen/zitting2/Agrigento.mat b/Modellering en simulatie/oefeningen/zitting2/Agrigento.mat new file mode 100644 index 0000000..bb785b3 Binary files /dev/null and b/Modellering en simulatie/oefeningen/zitting2/Agrigento.mat differ diff --git a/Modellering en simulatie/oefeningen/zitting2/notes.md b/Modellering en simulatie/oefeningen/zitting2/notes.md new file mode 100644 index 0000000..eb778bf --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting2/notes.md @@ -0,0 +1,7 @@ +# 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. diff --git a/Modellering en simulatie/oefeningen/zitting2/opgave10.m b/Modellering en simulatie/oefeningen/zitting2/opgave10.m new file mode 100644 index 0000000..7f1783d --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting2/opgave10.m @@ -0,0 +1,21 @@ +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 diff --git a/Modellering en simulatie/oefeningen/zitting2/opgave4.m b/Modellering en simulatie/oefeningen/zitting2/opgave4.m new file mode 100644 index 0000000..cc308a7 --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting2/opgave4.m @@ -0,0 +1,21 @@ +[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) diff --git a/Modellering en simulatie/oefeningen/zitting2/opgave6.m b/Modellering en simulatie/oefeningen/zitting2/opgave6.m new file mode 100644 index 0000000..3b2838a --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting2/opgave6.m @@ -0,0 +1,13 @@ +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 + + diff --git a/Modellering en simulatie/oefeningen/zitting2/opgave7.m b/Modellering en simulatie/oefeningen/zitting2/opgave7.m new file mode 100644 index 0000000..e6c9f64 --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting2/opgave7.m @@ -0,0 +1,13 @@ +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 diff --git a/Modellering en simulatie/oefeningen/zitting2/residplot.m b/Modellering en simulatie/oefeningen/zitting2/residplot.m new file mode 100644 index 0000000..41ec991 --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting2/residplot.m @@ -0,0 +1,7 @@ +function [] = residplot(resid, p) + for k = 1:length(resid)-1 + y(k) = resid(k)/(resid(k+1)^p); + end + + plot(y) +end diff --git a/Modellering en simulatie/oefeningen/zitting2/testMatrix.m b/Modellering en simulatie/oefeningen/zitting2/testMatrix.m new file mode 100644 index 0000000..3b2838a --- /dev/null +++ b/Modellering en simulatie/oefeningen/zitting2/testMatrix.m @@ -0,0 +1,13 @@ +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 + + diff --git a/Modellering en simulatie/practicum1 b/Modellering en simulatie/practicum1 index b9148c9..c10d141 160000 --- a/Modellering en simulatie/practicum1 +++ b/Modellering en simulatie/practicum1 @@ -1 +1 @@ -Subproject commit b9148c91208e38281f135e67f75d99e21b4677f7 +Subproject commit c10d1417155f93eac7eff0899243b919af811d4c diff --git a/Modellering en simulatie/slides_mc.pdf b/Modellering en simulatie/slides_mc.pdf new file mode 100644 index 0000000..c14fa95 Binary files /dev/null and b/Modellering en simulatie/slides_mc.pdf differ diff --git a/Modellering en simulatie/slides_mc.xopp b/Modellering en simulatie/slides_mc.xopp new file mode 100644 index 0000000..2bf625b Binary files /dev/null and b/Modellering en simulatie/slides_mc.xopp differ diff --git a/Modellering en simulatie/slides_rng.pdf b/Modellering en simulatie/slides_rng.pdf new file mode 100644 index 0000000..319372f Binary files /dev/null and b/Modellering en simulatie/slides_rng.pdf differ diff --git a/Modellering en simulatie/slides_rng.xopp b/Modellering en simulatie/slides_rng.xopp new file mode 100644 index 0000000..9aa8dcd Binary files /dev/null and b/Modellering en simulatie/slides_rng.xopp differ diff --git a/Principles of machine learning/.Lecture B7 - 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