Latex

1from PIL import ImageFont, Image, ImageDraw
2from matplotlib import pyplot
3
4
5def get_annotation(image_shape: tuple, title: str, font_size: int = 50):
6    frame_height, frame_width = image_shape[:2]
7    times_font = ImageFont.truetype('times-new-roman.ttf', font_size)
8    text_image = Image.new('RGB', (frame_width, frame_height), (255, 255, 255))
9    drawer = ImageDraw.Draw(text_image)
10    w, h = drawer.textsize(title, font=times_font)
11    drawer.text(((frame_width - w) / 2, (frame_height - h) / 2), text=title, fill=(0, 0, 0), font=times_font,
12                align='center')
13    annotation = numpy.array(text_image)
14    return annotation
15
16if __name__ == '__main__':
17    anno = get_annotation((100, 300), 'frame $f_n$')
18    pyplot.imshow(anno)
19    pyplot.show()
20

1import java.util.Arrays;
2import java.util.Random;
3
4public class Solution {
5    static long tc = 0;
6    
7    static void swap(int[] arr, int i, int j) {
8        int temp = arr[i];
9        arr[i] = arr[j];
10        arr[j] = temp;
11    }
12
13    static int kMin(int[] arr, int k) {
14        arr = arr.clone();
15        int pivot = pivot(arr);
16        if(pivot > k) {
17            return kMin(Arrays.copyOfRange(arr, 0, pivot), k);
18        } else if(pivot < k) {
19            return kMin(Arrays.copyOfRange(arr, pivot + 1, arr.length), k - pivot - 1);
20        }
21        return arr[k];
22    }
23
24    static int pivot(int[] arr) {
25        Random rand = new Random();
26        int pivot = rand.nextInt(arr.length);
27    
28        swap(arr, pivot, arr.length - 1);
29    
30        int i = 0;
31        for(int j = 0; j < arr.length - 1; j++) {
32            tc++;
33            if(arr[j] < arr[arr.length - 1]) {
34                swap(arr, i, j);
35                i++;
36            }
37        }
38        swap(arr, i, arr.length - 1);
39        return i;
40    }
41
42    public static void main(String args[]) {
43        int iterations = 10000;
44        int n = 5000;
45        for(int j = 0; j < iterations; j++) {
46            Random rd = new Random(); 
47            int[] arr = new int[n];
48            for (int i = 0; i < arr.length; i++) {
49                arr[i] = rd.nextInt();
50            }
51            int k = rd.nextInt(arr.length - 1);
52            kMin(arr, k);
53        }
54        System.out.println("Actual: " + tc / (double)iterations);
55        
56        double expected = 2.0 * n - 2.0 - (Math.log(n) / Math.log(2));
57        System.out.println("Expected: " + expected);
58    }
59    
60
61}
62

1Rc files read:
2  latexmkrc
3Latexmk: This is Latexmk, John Collins, 20 November 2021, version: 4.76.
4Latexmk: applying rule 'biber main'...
5Rule 'biber main': The following rules & subrules became out-of-date:
6      'biber main'
7------------
8Run number 1 of rule 'biber main'
9------------
10------------
11Running 'biber  "main.bcf"'
12------------
13biber: error while loading shared libraries: libcrypt.so.1: cannot open shared object file: No such file or directory
14Latexmk: Errors, so I did not complete making targets
15Collected error summary (may duplicate other messages):
16  biber main: Could not open biber log file for 'main'
17Latexmk: Use the -f option to force complete processing,
18 unless error was exceeding maximum runs, or warnings treated as errors.
19

1Rc files read:
2  latexmkrc
3Latexmk: This is Latexmk, John Collins, 20 November 2021, version: 4.76.
4Latexmk: applying rule 'biber main'...
5Rule 'biber main': The following rules & subrules became out-of-date:
6      'biber main'
7------------
8Run number 1 of rule 'biber main'
9------------
10------------
11Running 'biber  "main.bcf"'
12------------
13biber: error while loading shared libraries: libcrypt.so.1: cannot open shared object file: No such file or directory
14Latexmk: Errors, so I did not complete making targets
15Collected error summary (may duplicate other messages):
16  biber main: Could not open biber log file for 'main'
17Latexmk: Use the -f option to force complete processing,
18 unless error was exceeding maximum runs, or warnings treated as errors.
19$ pacman -Qo /usr/lib/libcrypt*
20/usr/lib/libcrypto.so is owned by openssl 1.1.1.m-1
21/usr/lib/libcrypto.so.1.1 is owned by openssl 1.1.1.m-1
22/usr/lib/libcryptsetup.so is owned by cryptsetup 2.4.3-2
23/usr/lib/libcryptsetup.so.12 is owned by cryptsetup 2.4.3-2
24/usr/lib/libcryptsetup.so.12.7.0 is owned by cryptsetup 2.4.3-2
25/usr/lib/libcrypt.so is owned by libxcrypt 4.4.28-1
26/usr/lib/libcrypt.so.2 is owned by libxcrypt 4.4.28-1
27/usr/lib/libcrypt.so.2.0.0 is owned by libxcrypt 4.4.28-1
28

1Rc files read:
2  latexmkrc
3Latexmk: This is Latexmk, John Collins, 20 November 2021, version: 4.76.
4Latexmk: applying rule 'biber main'...
5Rule 'biber main': The following rules & subrules became out-of-date:
6      'biber main'
7------------
8Run number 1 of rule 'biber main'
9------------
10------------
11Running 'biber  "main.bcf"'
12------------
13biber: error while loading shared libraries: libcrypt.so.1: cannot open shared object file: No such file or directory
14Latexmk: Errors, so I did not complete making targets
15Collected error summary (may duplicate other messages):
16  biber main: Could not open biber log file for 'main'
17Latexmk: Use the -f option to force complete processing,
18 unless error was exceeding maximum runs, or warnings treated as errors.
19$ pacman -Qo /usr/lib/libcrypt*
20/usr/lib/libcrypto.so is owned by openssl 1.1.1.m-1
21/usr/lib/libcrypto.so.1.1 is owned by openssl 1.1.1.m-1
22/usr/lib/libcryptsetup.so is owned by cryptsetup 2.4.3-2
23/usr/lib/libcryptsetup.so.12 is owned by cryptsetup 2.4.3-2
24/usr/lib/libcryptsetup.so.12.7.0 is owned by cryptsetup 2.4.3-2
25/usr/lib/libcrypt.so is owned by libxcrypt 4.4.28-1
26/usr/lib/libcrypt.so.2 is owned by libxcrypt 4.4.28-1
27/usr/lib/libcrypt.so.2.0.0 is owned by libxcrypt 4.4.28-1
28# ln -s /usr/lib/libcrypt.so /usr/lib/libcrypt.so.1
29$ latexmkrc -pdflua main.ltx
30Rc files read:
31  latexmkrc
32Latexmk: This is Latexmk, John Collins, 20 November 2021, version: 4.76.
33Latexmk: applying rule 'biber main'...
34Rule 'biber main': The following rules & subrules became out-of-date:
35      'biber main'
36------------
37Run number 1 of rule 'biber main'
38------------
39------------
40Running 'biber  "main.bcf"'
41------------
42/tmp/par-716861/cache-0e6aa298f0c2e7a775de99938825b2d56bd2027f/biber: /usr/lib/libcrypt.so.1: version `GLIBC_2.2.5' not found (required by /tmp/par-716861/cache-0e6aa298f0c2e7a775de99938825b2d56bd2027f/biber)
43Latexmk: Errors, so I did not complete making targets
44Collected error summary (may duplicate other messages):
45  biber main: Could not open biber log file for 'main'
46Latexmk: Use the -f option to force complete processing,
47 unless error was exceeding maximum runs, or warnings treated as errors.
48

1Rc files read:
2  latexmkrc
3Latexmk: This is Latexmk, John Collins, 20 November 2021, version: 4.76.
4Latexmk: applying rule 'biber main'...
5Rule 'biber main': The following rules & subrules became out-of-date:
6      'biber main'
7------------
8Run number 1 of rule 'biber main'
9------------
10------------
11Running 'biber  "main.bcf"'
12------------
13biber: error while loading shared libraries: libcrypt.so.1: cannot open shared object file: No such file or directory
14Latexmk: Errors, so I did not complete making targets
15Collected error summary (may duplicate other messages):
16  biber main: Could not open biber log file for 'main'
17Latexmk: Use the -f option to force complete processing,
18 unless error was exceeding maximum runs, or warnings treated as errors.
19$ pacman -Qo /usr/lib/libcrypt*
20/usr/lib/libcrypto.so is owned by openssl 1.1.1.m-1
21/usr/lib/libcrypto.so.1.1 is owned by openssl 1.1.1.m-1
22/usr/lib/libcryptsetup.so is owned by cryptsetup 2.4.3-2
23/usr/lib/libcryptsetup.so.12 is owned by cryptsetup 2.4.3-2
24/usr/lib/libcryptsetup.so.12.7.0 is owned by cryptsetup 2.4.3-2
25/usr/lib/libcrypt.so is owned by libxcrypt 4.4.28-1
26/usr/lib/libcrypt.so.2 is owned by libxcrypt 4.4.28-1
27/usr/lib/libcrypt.so.2.0.0 is owned by libxcrypt 4.4.28-1
28# ln -s /usr/lib/libcrypt.so /usr/lib/libcrypt.so.1
29$ latexmkrc -pdflua main.ltx
30Rc files read:
31  latexmkrc
32Latexmk: This is Latexmk, John Collins, 20 November 2021, version: 4.76.
33Latexmk: applying rule 'biber main'...
34Rule 'biber main': The following rules & subrules became out-of-date:
35      'biber main'
36------------
37Run number 1 of rule 'biber main'
38------------
39------------
40Running 'biber  "main.bcf"'
41------------
42/tmp/par-716861/cache-0e6aa298f0c2e7a775de99938825b2d56bd2027f/biber: /usr/lib/libcrypt.so.1: version `GLIBC_2.2.5' not found (required by /tmp/par-716861/cache-0e6aa298f0c2e7a775de99938825b2d56bd2027f/biber)
43Latexmk: Errors, so I did not complete making targets
44Collected error summary (may duplicate other messages):
45  biber main: Could not open biber log file for 'main'
46Latexmk: Use the -f option to force complete processing,
47 unless error was exceeding maximum runs, or warnings treated as errors.
48$latex='lualatex %O -synctex=1 -interaction=nonstopmode %S';
49#$bibtex='upbibtex %O %B';
50$bibtex='biber %O %B';
51$makeindex='upmendex %O -o %D %S';
52$pdf_mode=3;
53

1par(mfrow = c(2,2))
2
3x <- seq(1,10,0.1)
4y <- sin(x)
5
6plot(x, y, main = expression(sigma[1]))
7plot(x, y, main = expression(sigma[2]))
8

1par(mfrow = c(2,2))
2
3x <- seq(1,10,0.1)
4y <- sin(x)
5
6plot(x, y, main = expression(sigma[1]))
7plot(x, y, main = expression(sigma[2]))
8par(mfrow = c(2,2))
9for (i in 1:2){
10    plot(x, y, main = expression(sigma[i]))
11}
12

1test
2test/man
3test/man/one.Rd
4test/R
5test/R/one.R
6test/DESCRIPTION
7

1test
2test/man
3test/man/one.Rd
4test/R
5test/R/one.R
6test/DESCRIPTION
7\name{one}
8\alias{one}
9\title{Get One}
10\description{Accents are not rendered: \'e \'{e} {\'e} \\'e \\'{e} {\\'e}}
11\usage{
12one()
13}
14

1test
2test/man
3test/man/one.Rd
4test/R
5test/R/one.R
6test/DESCRIPTION
7\name{one}
8\alias{one}
9\title{Get One}
10\description{Accents are not rendered: \'e \'{e} {\'e} \\'e \\'{e} {\\'e}}
11\usage{
12one()
13}
14one <- function() 1
15

1test
2test/man
3test/man/one.Rd
4test/R
5test/R/one.R
6test/DESCRIPTION
7\name{one}
8\alias{one}
9\title{Get One}
10\description{Accents are not rendered: \'e \'{e} {\'e} \\'e \\'{e} {\\'e}}
11\usage{
12one()
13}
14one <- function() 1
15Package: test
16Version: 0.1
17Title: Test
18Author: Nobody
19Maintainer: Nobody <no@body.org>
20Description: Test.
21License: GPL-3
22

1test
2test/man
3test/man/one.Rd
4test/R
5test/R/one.R
6test/DESCRIPTION
7\name{one}
8\alias{one}
9\title{Get One}
10\description{Accents are not rendered: \'e \'{e} {\'e} \\'e \\'{e} {\\'e}}
11\usage{
12one()
13}
14one <- function() 1
15Package: test
16Version: 0.1
17Title: Test
18Author: Nobody
19Maintainer: Nobody <no@body.org>
20Description: Test.
21License: GPL-3
22$ R CMD build test
23$ R CMD check test_0.1.tar.gz
24$ R CMD INSTALL test_0.1.tar.gz
25

1import numpy as np
2import matplotlib.pyplot as plt
3from scipy.stats import norm
4
5
6'''
7We want to get an exponential decay integral approx using importance sampling.
8We will try to integrate x^2exp(-x^2) over the real line.
9Metropolis-hasting alg will generate configuartions (in this case, single numbers) such that 
10the probablity of a given configuration x^a ~ p(x^a) for p(x) propto exp(-x^2).
11
12Once configs  = {x^a} generated, the apporximation, Q_N, of the integral, I, will be given by 
13Q_N = 1/N sum_(configs) x^2
14lim (N-> inf) Q_N -> I
15'''
16
17'''
18Implementing metropolis-hasting algorithm
19'''
20
21#Setting up the initial config for our chain, generating first 2 to generate numpy array
22x_0 = np.random.uniform(-20,-10,2)
23
24#Defining function that generates the next N steps in the chain, given a starting config x
25#Works by iteratively taking the last element in the chain, generating a new candidate configuration from it and accepting/rejecting according to the algorithm
26#Success and failures implemented to see roughly the success rate of each step
27def next_steps(x,N):
28    i = 0
29    Success = 0
30    Failures = 0
31    Data = np.array(x)
32    d = 1.5                       #Spread of (normal) transition function
33    while i < N:
34        r = np.random.uniform(0,1)
35        delta = np.random.normal(0,d)
36        x_old = Data[-1]
37        x_new = x_old + delta
38        hasting_ratio = np.exp(-(x_new**2-x_old**2) )
39        if hasting_ratio > r:
40            i = i+1
41            Data = np.append(Data,x_new)
42            Success = Success +1
43        else:
44            Failures = Failures + 1
45    print(Success)
46    print(Failures)
47    return Data
48
49#Number of steps in the chain
50N_iteration   = 50000
51
52#Generating the data
53Data = next_steps(x_0,N_iteration)
54
55#Plotting data to see convergence of chain to gaussian distribution
56plt.plot(Data)
57plt.show()
58
59#Obtaining tail end data and obtaining the standard deviation of resulting gaussian distribution
60Data = Data[-40000:]
61(mu, sigma) = norm.fit(Data)
62print(sigma)
63
64
65#Plotting a histogram to visually see if guassian
66plt.hist(Data, bins = 300)
67plt.show()
68

1for (int i = 0; i < n; ++i) {
2    for (int j = i + 1; j < n; ++j) {
3        for (int k = j + 1; k < n; ++k) {
4            function(i, j, k);
5        }
6    }
7}
8

1for (int i = 0; i < n; ++i) {
2    for (int j = i + 1; j < n; ++j) {
3        for (int k = j + 1; k < n; ++k) {
4            function(i, j, k);
5        }
6    }
7}
8for (int b = start; b < end; ++b) {
9    // how to calculate i, j, k?
10}
11

1for (int i = 0; i < n; ++i) {
2    for (int j = i + 1; j < n; ++j) {
3        for (int k = j + 1; k < n; ++k) {
4            function(i, j, k);
5        }
6    }
7}
8for (int b = start; b < end; ++b) {
9    // how to calculate i, j, k?
10}
11void calculate(int start, int end) {
12    for (int b = start; b < end; ++b) {
13        int i = ...;
14        int j = ...;
15        int k = ...;
16        function(i, j, k);
17    }
18}
19
20int total = binom(n, 3);
21
22// thread A:
23calculate(0, total / 2);
24
25// thread B:
26calculate(total / 2, total);
27

1---
2title: "Table won't work"
3author: "Exhausted student"
4date: "2022/01/28"
5output: 
6  bookdown::word_document2
7---
8
9```{r table, echo=F, warning=F, message=F}
10library(tidyverse)
11a <- tibble(
12  constants = c("c", "NA", "h", "e", "H2O"),
13  values = c(2.998e8, 6.022e23, 6.626e-34, -1.602e-19, 18.02)
14)
15
16knitr::kable(a, digits = 35)
17```
18