151 lines
3.8 KiB
Matlab
151 lines
3.8 KiB
Matlab
%%%% ECE210-B Matlab Seminar, Homework 1.
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% james ryan, 1/24/24
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% <-.0> style point: please ensure files are named so that
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% MATLAB (sorry, i'd rather grade in Octave, but this is not
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% Octave seminar...) can run them! this one had a space in it.
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% preamble
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close all;
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clear;
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clc;
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%% Scale-'ers
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% (1)
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% Takes the absolute value of
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% sin(pi/3)
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% PLUS
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% j divided by secant of (-5/3)*pi
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a = abs(sin(pi ./ 3) ...
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+ ((1 * j) ./ (sec((-5 * pi) / 3))) ...
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);
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% MATLAB interptes complex literals, so you could also write
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% `1j`.
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% (2)
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% n = 3, cubic root
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l = nthroot(8, 3);
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% could also do `8^(1/3)`, if you're mathematically inclined.
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% (3)
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% [1, 2, 3, ..., 79, 80]
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u_mat = 1:80;
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% Sums all the terms from u_mat, scales by 2 / 6!, and takes the square root
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u = sqrt((2 / factorial(6)) * sum(u_mat));
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% q4
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% takes the square
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% of imaginary value
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% of the floor
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% of the log
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% of the square root of 66
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% taken to the power of 7j
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m = (imag(floor(log(sqrt(66).^(7 * j))))).^2;
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% since these are scalars, the `.^` is not strictly necessary,
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% but i see you have a vector bent...
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%% Mother...?
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% (1)
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% Makes a 1x4 matrix from a l u & m,
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% and transposes the formed matrix into a 4x1 matrix
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A = [a; l; u; m];
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% (2)
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% makes a 2x2 matrix using a l u & m.
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F = [a l; u m];
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% (3)
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% takes the non-conjugate transpose of F
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T = F.';
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% (4)
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% takes the inverse of the matrix product of T * F
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B = inv(T * F);
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check = B * (T * F)
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% aaaaaaa no semicolon
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% (5)
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% Makes a square matrix comprised of T and F
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C = [T F; F T];
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%% Cruelty
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meanB = mean(B, "all"); % sums "all" values in matrix B into one scalar
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% squashes every row down into the sum of all elements
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% in a given row
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meanC = mean(C, 2); % ... or takes the mean of every value along a
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% dimension (the 2nd dimension), and squashes
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% the matrix down into one dimension.
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%% Odd Types
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% eval one
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evalOne = T + F;
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%{
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comments:
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evalOne =
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2 5
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5 8
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This makes sense, considering T was [1 3; 2 4] and F was [1 2; 3 4]
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It seems like, at the same index on both matrices, the value occupying
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that spot was taken from both and summed.
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%}
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% eval 2
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evalTwo = T + 1;
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%{
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comments:
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evalTwo =
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2 4
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3 5
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This makes sense, since it seems like 1 was interpreted as a 2x2 matrix
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occupied only by 1's. The same summing algorithm was applied, and every
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value occupying T was incremented by 1.
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This could be confusing if we were multiplying instead of dividing,
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since it would make more intuitive sense to be referring to the
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identity matrix as 1, rather than a matrix filled wuth 1's.
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%}
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% eval kicks
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evalKicks = A + C;
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%{
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comments:
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evalKicks =
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2 5 4 6
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3 6 6 8
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2 4 4 7
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4 6 5 8
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A and C are not the same dimensions. A is 1x4 while C is 4x4.
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It seems that C was sliced by rows in order to let this
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operation make sense.
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so for every Row in C, the value corresponding
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to the matching column in A was added to that value in C.
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Put nicely: Every row in C (a 1x4 matrix) was summed with A,
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and then returned to the row index it previously occupied in C proper.
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%}
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% <+.06> love the extensive commentary.
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%% Not What it Seems...
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for k = [3 5 10 300 1e6]
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% sets up a 1xk matrix of `k` evenly spaced vals that are [0, 1]
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genericMatrix = linspace(0, 1, k);
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% squares every val in the matrix, sums all squared vals together, and divs
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% every element by k.
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% Essentially -- average value of x^2 from 0 to 1
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% Also known as power, according to fred
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genericScalar = sum(genericMatrix.^2) ./ k;
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end
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% right, and what *is* that average, in terms of math objects?
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