91 lines
1.7 KiB
Matlab
91 lines
1.7 KiB
Matlab
%% Assignment 2
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% Name: Claudio Maggioni
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%
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% Date: 19/3/2019
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%
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% This is a template file for the first assignment to get started with running
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% and publishing code in Matlab. Each problem has its own section (delineated
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% by |%%|) and can be run in isolation by clicking into the particular section
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% and pressing |Ctrl| + |Enter| (evaluate current section).
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%
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% To generate a pdf for submission in your current directory, use the following
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% three lines of code at the command window:
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%
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% >> options.format = 'pdf'; options.outputDir = pwd; publish('assignment2.m', options)
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%
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%% Problem 3
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syms x;
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f = exp(x);
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df = diff(f);
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x_0 = 1;
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err = zeros(10, 1);
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h = zeros(10, 1);
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for i = 1:10
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h(i) = 10^(-i);
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err(i) = abs(subs(df,x,x_0) - my_diff(f, x, x_0, h(i)));
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end
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loglog(h, err)
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%% Problem 6
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n = 3000;
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A = rand(n,n);
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B = rand(n,n);
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tic
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[C] = matTimesMat_classical(A, B);
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toc
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norm(C - A * B) / norm(C)
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tic
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[C] = matTimesMat_column(A, B);
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toc
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norm(C - A * B) / norm(C)
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tic
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[C] = matTimesMat_outerProd(A, B);
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toc
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norm(C - A * B) / norm(C)
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%% Problem 3 (functions)
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function approx = my_diff(f, x, x_0, h)
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approx = (subs(f,x,x_0 + h) - subs(f, x, x_0)) / h;
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end
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%% Problem 6 (functions)
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function [C] = matTimesMat_classical(A, B)
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s = size(A);
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n = s(1);
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C = zeros(n);
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for i=1:n
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for j=1:n
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for k=1:n
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C(i,j) = C(i,j) + A(i,k) * B(k,j);
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end
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end
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end
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end
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function [C] = matTimesMat_column(A, B)
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s = size(A);
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n = s(1);
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C = zeros(n);
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for j=1:n
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for k=1:n
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C(:,j) = C(:,j) + B(k,j) * A(:,k);
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end
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end
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end
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function [C] = matTimesMat_outerProd(A, B)
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s = size(A);
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n = s(1);
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C = zeros(n);
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for j=1:n
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C = C + A(:,j) * B(j,:);
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end
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end |