95 lines
2.1 KiB
Mathematica
95 lines
2.1 KiB
Mathematica
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%% Assignment 1
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% Name: ______________
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%
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% Date: 21/2/2019
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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';
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% >> options.outputDir = pwd;
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% >> publish('assignment1.m', options)
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%
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%% Problem 1
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% a)
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x = 5
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% b)
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y = 4.2 * 10 ^ (-2)
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% c)
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r = sqrt(pi)
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% d)
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rate = 0.01
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t = 6
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T = 12
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money = 1000
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interest = money * (exp(rate * t / T) - 1)
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% e)
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a = 1 + i
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b = i
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i = 2
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e = exp(i * pi)
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d = exp(b * pi)
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% \texttt{i} is interpreted as the imaginary unit when assigning to a and b
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% until it is defined to 2. In the subsequent expressions \textit{i} is
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% interpreted as 2.
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c = exp(1i * pi)
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% Here \textit{1i} is interpreted as the imaginary unit, making $c = 1$
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%% Problem 2
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A = [1 -2 0 ; -2 1 -2; 0 -2 1]
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Z = zeros(9,9)
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B = ones(9,9) * 3
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C = (eye(9) - 1) * -1
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D = diag([[1:5],[4:-1:1]])
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E = repmat(transpose(1:9), 1, 5)
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%% Problem 3
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A = fliplr(A)
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B(2, :) = repmat(1, 1, 9)
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C(1, :) = []
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F = E(1:2, 1:2)
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E(:, 1) = flipud(E(:, 1))
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%% Problem 4
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geteps
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getxmin
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getxmax
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function myeps = geteps
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y = 1;
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x = 2 * y;
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while 1 + y ~= 1
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x = y;
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y = y / 2;
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end
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myeps = x;
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end
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function xmin = getxmin
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y = 1;
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x = 2 * y;
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while y ~= 0
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x = y;
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y = y / 2;
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end
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xmin = x;
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end
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function xmax = getxmax
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y = 1;
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x = y;
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while y ~= +inf
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x = y;
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y = y * 2;
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end
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xmax = typecast(bitor(typecast(x, 'uint64'), 0x000FFFFFFFFFFFFF), 'double');
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end
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% geteps does not differ from eps, as getxmax does not differ from realmax.
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% However, getxmin returns the nearest positive floating point value to 0
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% including denormalized numbers, while realmin returns the smallest
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% (ignoring sign) non denormalized floating point number.
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