{
"cells": [
{
"cell_type": "markdown",
"id": "accurate-paint",
"metadata": {},
"source": [
"\n",
"# R Introduction\n",
"\n",
"-----------------------\n",
"\n",
"BIO401-01/598-02 \n",
" \n",
"Mar. 17 2021\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "deluxe-moisture",
"metadata": {},
"source": [
"\n",
"\n",
" R is a script language for statistical data analysis and manipulation. \n",
" \n",
" home page : https://cran.r-project.org/"
]
},
{
"cell_type": "markdown",
"id": "marine-trail",
"metadata": {},
"source": [
"## How to run \n",
"\n",
"1. batch mode\n",
"\n",
" $ R CMD BATCH script.R\n",
" \n",
"help for the batch mode \n",
"\n",
" $ R CMD command --help \n",
"\n",
"for example \n",
"\n",
" $ R CMD INSTALL --help \n",
"\n",
"2. interactive mode\n",
"\n",
"console : \">\" as the R prompt\n",
"\n",
"common IDE (integrated development environment) for R \n",
"\n",
"- R studio \n",
"- Jupyter-notebook \n",
"- ESS(emacs speaks statistics) \n",
"- R commander, etc."
]
},
{
"cell_type": "markdown",
"id": "swedish-ensemble",
"metadata": {},
"source": [
"## Installing packages\n",
"\n",
" > install.packages(\"package_name\")\n",
" \n",
" > install.packages(c(\"ggplot2\",\"sp\",\"raster\"))"
]
},
{
"cell_type": "markdown",
"id": "focused-consideration",
"metadata": {},
"source": [
"## Interfacing with the system\n",
"\n",
" > dir() # show files in the current directory\n",
"\n",
" > getwd() # is asking for the current working directory"
]
},
{
"cell_type": "markdown",
"id": "understanding-engagement",
"metadata": {},
"source": [
"## Getting help\n",
"\n",
"R provides help with function and commands. On-line help gives useful \n",
"information as well. Getting used to R help is a key to successful \n",
"statistical modelling. The online help can be accessed in HTML format by \n",
"typing:\n",
"\n",
" > help.start()\n",
" \n",
"A keyword search is possible using the Search Engine and Keywords link.\n",
"You can also use the help() or ? functions.\n",
"\n",
" > help(dir)\n",
"\n",
"or \n",
"\n",
" > ? dir "
]
},
{
"cell_type": "markdown",
"id": "moral-point",
"metadata": {},
"source": [
"## As a caculator"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "tough-madrid",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"8"
],
"text/latex": [
"8"
],
"text/markdown": [
"8"
],
"text/plain": [
"[1] 8"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"3 + 5 "
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "sensitive-character",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"1"
],
"text/latex": [
"1"
],
"text/markdown": [
"1"
],
"text/plain": [
"[1] 1"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sin(pi/2)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "chubby-water",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"8"
],
"text/latex": [
"8"
],
"text/markdown": [
"8"
],
"text/plain": [
"[1] 8"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"2^3"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "ready-sacrifice",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"1.66666666666667"
],
"text/latex": [
"1.66666666666667"
],
"text/markdown": [
"1.66666666666667"
],
"text/plain": [
"[1] 1.666667"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"5/3"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "legal-annex",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"2"
],
"text/latex": [
"2"
],
"text/markdown": [
"2"
],
"text/plain": [
"[1] 2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"5%%3"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "suburban-lexington",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"1"
],
"text/latex": [
"1"
],
"text/markdown": [
"1"
],
"text/plain": [
"[1] 1"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"5%/%3"
]
},
{
"cell_type": "markdown",
"id": "artistic-clone",
"metadata": {},
"source": [
"## Logic Operations\n",
"\n",
"- AND operator &\n",
"- OR operator |\n",
"- NOT operator !"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "abroad-sword",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"TRUE"
],
"text/latex": [
"TRUE"
],
"text/markdown": [
"TRUE"
],
"text/plain": [
"[1] TRUE"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"12 > 5 & 12 < 15"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "formal-principal",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"FALSE"
],
"text/latex": [
"FALSE"
],
"text/markdown": [
"FALSE"
],
"text/plain": [
"[1] FALSE"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"! TRUE"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "military-citation",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"TRUE"
],
"text/latex": [
"TRUE"
],
"text/markdown": [
"TRUE"
],
"text/plain": [
"[1] TRUE"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"TRUE | FALSE"
]
},
{
"cell_type": "markdown",
"id": "treated-recycling",
"metadata": {},
"source": [
"## Data structures \n",
"\n",
"R objects\n",
" \n",
"The entities R operates on are technically known as objects. \n",
"Examples are \"vectors of numeric (real)\" or \"complex values\", \"vectors of \n",
"logical\" values and \"vectors of character strings\". \n",
"These are known as “atomic” structures since their components are all of \n",
"the same type, or mode, namely numeric, complex, logical, character and raw.\n",
"R also operates on objects called \"lists\", which are of mode list. \n",
"These are ordered sequences of objects which individually can be of any mode. \n",
"Lists are known as “recursive” rather than atomic structures since their \n",
"components can themselves be lists in their own right.\n",
"The other recursive structures are those of mode function and expression. \n",
"\n",
"By the \"mode\" of an object we mean the basic type of its fundamental \n",
"constituents. This is a special case of a “property” of an object. Another\n",
"property of every object is its \"length.\" The functions mode(object) and \n",
"length(object) can be used \n",
"to find out the mode and length of any defined structure 10.\n",
"\n",
"Further properties of an object are usually provided by attributes(object). \n",
"Because of this, mode and length are also called “intrinsic attributes” of an object. \n",
"For example, if z is a complex vector of length 100, then in an expression mode(z) \n",
"is the character string \"complex\" and length(z) is 100."
]
},
{
"cell_type": "markdown",
"id": "moral-scotland",
"metadata": {},
"source": [
"### vectors : the heart of R\n",
"\n",
"Vectors are combinations of scalars in a string structure. Vectors must have \n",
"all values of the same mode. Thus any given vector must be unambiguously \n",
"either logical, numeric, complex, character or raw. (The only apparent \n",
"exception to this rule is the special “value” listed as NA for quantities not\n",
"available, but in fact there are several types of NA). Note that a vector can\n",
"be empty and still have a mode. For example the empty character string vector\n",
"is listed as character(0) and the empty numeric vector as numeric(0). \n",
"\n",
" > help(vector)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "future-standard",
"metadata": {},
"outputs": [],
"source": [
"# \"<-\" is the assignment operator in R.\n",
"# \"c\" stands for concatenate. \n",
"\n",
"x <- c(1,5,8)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "verified-pixel",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"1"
],
"text/latex": [
"1"
],
"text/markdown": [
"1"
],
"text/plain": [
"[1] 1"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"- 5
- 8
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 5\n",
"\\item 8\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 5\n",
"2. 8\n",
"\n",
"\n"
],
"text/plain": [
"[1] 5 8"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# subsetting operation\n",
"# \"[]\" used to retrieve vector elements \n",
"# \":\" used to give a range for retrieval\n",
"x[1]\n",
"x[2:3]"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "adjacent-kansas",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"3"
],
"text/latex": [
"3"
],
"text/markdown": [
"3"
],
"text/plain": [
"[1] 3"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"length(x)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "intense-dealer",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'numeric'"
],
"text/latex": [
"'numeric'"
],
"text/markdown": [
"'numeric'"
],
"text/plain": [
"[1] \"numeric\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mode(x)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "fewer-single",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"3.5"
],
"text/latex": [
"3.5"
],
"text/markdown": [
"3.5"
],
"text/plain": [
"[1] 3.5"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"3.5"
],
"text/latex": [
"3.5"
],
"text/markdown": [
"3.5"
],
"text/plain": [
"[1] 3.5"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# scalar not really exist in R \n",
"# individual numbers actually single element vectors \n",
"\n",
"x <- 3.5\n",
"x\n",
"x[1]"
]
},
{
"cell_type": "markdown",
"id": "turkish-collar",
"metadata": {},
"source": [
"Two common functions we can use to generate a sequence. \n",
"\n",
"The seq() function \"seq(from = number, to = number, by = number)\" allow to \n",
"create a vector starting from a value to another by a defined increment:\n",
" \n",
"The replicate function \"rep(x,times)\" enables you to replicate a vector \n",
"several times in a more complex vector. Calculations can be included to \n",
"form vectors as well and functions can be combined in the same command."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "intellectual-advocacy",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 4\n",
"\\item 5\n",
"\\item 6\n",
"\\item 7\n",
"\\item 8\n",
"\\item 9\n",
"\\item 10\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 2\n",
"3. 3\n",
"4. 4\n",
"5. 5\n",
"6. 6\n",
"7. 7\n",
"8. 8\n",
"9. 9\n",
"10. 10\n",
"\n",
"\n"
],
"text/plain": [
" [1] 1 2 3 4 5 6 7 8 9 10"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"1:10"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "practical-entrepreneur",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 1.25
- 1.5
- 1.75
- 2
- 2.25
- 2.5
- 2.75
- 3
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 1.25\n",
"\\item 1.5\n",
"\\item 1.75\n",
"\\item 2\n",
"\\item 2.25\n",
"\\item 2.5\n",
"\\item 2.75\n",
"\\item 3\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 1.25\n",
"3. 1.5\n",
"4. 1.75\n",
"5. 2\n",
"6. 2.25\n",
"7. 2.5\n",
"8. 2.75\n",
"9. 3\n",
"\n",
"\n"
],
"text/plain": [
"[1] 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"seq(1,3,0.25)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "derived-lewis",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 2
- 3
- 1
- 2
- 3
- 1
- 2
- 3
- 1
- 2
- 3
- 1
- 2
- 3
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 2\n",
"3. 3\n",
"4. 1\n",
"5. 2\n",
"6. 3\n",
"7. 1\n",
"8. 2\n",
"9. 3\n",
"10. 1\n",
"11. 2\n",
"12. 3\n",
"13. 1\n",
"14. 2\n",
"15. 3\n",
"\n",
"\n"
],
"text/plain": [
" [1] 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"one2three <- 1:3 \n",
"rep(one2three,5) "
]
},
{
"cell_type": "markdown",
"id": "thrown-milton",
"metadata": {},
"source": [
"### Missing Values\n",
"\n",
"In some cases the components of a vector or of an R object more in general, \n",
"may not be completely known. When an element or value is “not available” \n",
"or a “missing value” in the statistical sense, a place within a vector may\n",
"be reserved for it by assigning it the special value NA. Any operation on \n",
"an NA becomes an NA. \n",
"\n",
"The function is.na(x) gives a logical vector of the same size as x with \n",
"value TRUE if and only if the corresponding element in x is NA.\n",
"\n",
"Functions : dealing with NAs\n",
"\n",
"na.fail returns the object if it does not contain any missing values, and signals an error otherwise. \n",
"\n",
"na.omit returns the object with incomplete cases removed. \n",
"\n",
"na.pass returns the object unchanged."
]
},
{
"cell_type": "code",
"execution_count": 90,
"id": "colonial-ridge",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- FALSE
- FALSE
- FALSE
- TRUE
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item FALSE\n",
"\\item FALSE\n",
"\\item FALSE\n",
"\\item TRUE\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. FALSE\n",
"2. FALSE\n",
"3. FALSE\n",
"4. TRUE\n",
"\n",
"\n"
],
"text/plain": [
"[1] FALSE FALSE FALSE TRUE"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"z <- c(1:3,NA)\n",
"ind <- is.na(z)\n",
"ind"
]
},
{
"cell_type": "markdown",
"id": "applicable-hamilton",
"metadata": {},
"source": [
"There is a second kind of “missing” values which are produced by numerical \n",
"computation, the so-called Not a Number, NaN , values. \n",
"\n",
"Examples are 0/0 \n",
"or Inf - Inf which both give NaN since the result cannot be defined sensibly."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "serial-breath",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"NaN"
],
"text/latex": [
"NaN"
],
"text/markdown": [
"NaN"
],
"text/plain": [
"[1] NaN"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"NaN"
],
"text/latex": [
"NaN"
],
"text/markdown": [
"NaN"
],
"text/plain": [
"[1] NaN"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Inf-Inf\n",
"0/0"
]
},
{
"cell_type": "markdown",
"id": "cardiac-regression",
"metadata": {},
"source": [
"is.na(xx) is TRUE both for NA and NaN values. To differentiate \n",
"these, is.nan(xx) is only TRUE for NaNs. Missing values are sometimes printed\n",
"as when character vectors are printed without quotes. "
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "touched-defendant",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- FALSE
- FALSE
- FALSE
- FALSE
- TRUE
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item FALSE\n",
"\\item FALSE\n",
"\\item FALSE\n",
"\\item FALSE\n",
"\\item TRUE\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. FALSE\n",
"2. FALSE\n",
"3. FALSE\n",
"4. FALSE\n",
"5. TRUE\n",
"\n",
"\n"
],
"text/plain": [
"[1] FALSE FALSE FALSE FALSE TRUE"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"- FALSE
- FALSE
- FALSE
- TRUE
- TRUE
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item FALSE\n",
"\\item FALSE\n",
"\\item FALSE\n",
"\\item TRUE\n",
"\\item TRUE\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. FALSE\n",
"2. FALSE\n",
"3. FALSE\n",
"4. TRUE\n",
"5. TRUE\n",
"\n",
"\n"
],
"text/plain": [
"[1] FALSE FALSE FALSE TRUE TRUE"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"z <- c(1:3,NA,0/0)\n",
"is.not.available <- is.na(z) \n",
"is.not.a.number <-is.nan(z)\n",
"\n",
"is.not.a.number\n",
"is.not.available "
]
},
{
"cell_type": "markdown",
"id": "czech-azerbaijan",
"metadata": {},
"source": [
"On the other hand, NULL represent the value does not exit. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "criminal-thing",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<NA>"
],
"text/latex": [
""
],
"text/markdown": [
"<NA>"
],
"text/plain": [
"[1] NA"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x <- c(1,2,3,NA)\n",
"mean(x)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "pediatric-cause",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"2"
],
"text/latex": [
"2"
],
"text/markdown": [
"2"
],
"text/plain": [
"[1] 2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mean(x,na.rm=TRUE)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "statutory-roommate",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"2"
],
"text/latex": [
"2"
],
"text/markdown": [
"2"
],
"text/plain": [
"[1] 2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"y <- c(1,2,3,NULL)\n",
"mean(y)"
]
},
{
"cell_type": "code",
"execution_count": 99,
"id": "liquid-correlation",
"metadata": {},
"outputs": [
{
"ename": "ERROR",
"evalue": "Error in na.fail.default(x): missing values in object\n",
"output_type": "error",
"traceback": [
"Error in na.fail.default(x): missing values in object\nTraceback:\n",
"1. na.fail(x)",
"2. na.fail.default(x)",
"3. stop(\"missing values in object\")"
]
}
],
"source": [
"na.fail(x)"
]
},
{
"cell_type": "code",
"execution_count": 100,
"id": "behavioral-ladder",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 2
- 3
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 2\n",
"3. 3\n",
"\n",
"\n"
],
"text/plain": [
"[1] 1 2 3"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"na.fail(y)"
]
},
{
"cell_type": "markdown",
"id": "equal-regard",
"metadata": {},
"source": [
"#### Exercise\n",
"\n",
"creat a sequence as below and compute its mean\n",
"\n",
"```\n",
"10 20 30 10 20 30 50 50 50 NA NA NA 10 10 10 \n",
"```"
]
},
{
"cell_type": "markdown",
"id": "linear-hawaiian",
"metadata": {},
"source": [
"### Working with strings\n",
"\n",
"character strings : single element vectors \n",
"\n",
"mode : check datatype "
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "divided-craft",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'character'"
],
"text/latex": [
"'character'"
],
"text/markdown": [
"'character'"
],
"text/plain": [
"[1] \"character\""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"1"
],
"text/latex": [
"1"
],
"text/markdown": [
"1"
],
"text/plain": [
"[1] 1"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x <- \"hello\"\n",
"mode(x)\n",
"length(x)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "sophisticated-heater",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'hello world'"
],
"text/latex": [
"'hello world'"
],
"text/markdown": [
"'hello world'"
],
"text/plain": [
"[1] \"hello world\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# concatenate strings \n",
"\n",
"paste(\"hello\",\"world\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "complex-roads",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'helloworld'"
],
"text/latex": [
"'helloworld'"
],
"text/markdown": [
"'helloworld'"
],
"text/plain": [
"[1] \"helloworld\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# if you don't want any space between the strings, you can use paste0\n",
"\n",
"paste0 (\"hello\",\"world\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "underlying-series",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"' world'"
],
"text/latex": [
"' world'"
],
"text/markdown": [
"' world'"
],
"text/plain": [
"[1] \" world\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# substr is used to get parts of a string \n",
"\n",
"substr(\"Hello world\", 6,11)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "requested-montana",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 3
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 3\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 3\n",
"\n",
"\n"
],
"text/plain": [
"[1] 1 3"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# grep : retrieval based on certain pattern \n",
"\n",
"timespan <- c(\"day\",\"month\",\"year\")\n",
"grep('y', timespan)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "handmade-jacket",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"2"
],
"text/latex": [
"2"
],
"text/markdown": [
"2"
],
"text/plain": [
"[1] 2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# ^ : start with\n",
"\n",
"grep('^m', timespan)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "stopped-island",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 50
- 45
- 40
- 35
- 30
- 25
- 20
- 15
- 10
- 5
- 5
- 6
- 50
- 45
- 40
- 35
- 30
- 25
- 20
- 15
- 10
- 5
- 5
- 6
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 50\n",
"\\item 45\n",
"\\item 40\n",
"\\item 35\n",
"\\item 30\n",
"\\item 25\n",
"\\item 20\n",
"\\item 15\n",
"\\item 10\n",
"\\item 5\n",
"\\item 5\n",
"\\item 6\n",
"\\item 50\n",
"\\item 45\n",
"\\item 40\n",
"\\item 35\n",
"\\item 30\n",
"\\item 25\n",
"\\item 20\n",
"\\item 15\n",
"\\item 10\n",
"\\item 5\n",
"\\item 5\n",
"\\item 6\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 50\n",
"2. 45\n",
"3. 40\n",
"4. 35\n",
"5. 30\n",
"6. 25\n",
"7. 20\n",
"8. 15\n",
"9. 10\n",
"10. 5\n",
"11. 5\n",
"12. 6\n",
"13. 50\n",
"14. 45\n",
"15. 40\n",
"16. 35\n",
"17. 30\n",
"18. 25\n",
"19. 20\n",
"20. 15\n",
"21. 10\n",
"22. 5\n",
"23. 5\n",
"24. 6\n",
"\n",
"\n"
],
"text/plain": [
" [1] 50 45 40 35 30 25 20 15 10 5 5 6 50 45 40 35 30 25 20 15 10 5 5 6"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"numeric.vector <- c(rep(c (5*10:1, 5, 6), 2))\n",
"numeric.vector"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "sitting-minority",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- '50'
- '45'
- '40'
- '35'
- '30'
- '25'
- '20'
- '15'
- '10'
- '5'
- '5'
- '6'
- '50'
- '45'
- '40'
- '35'
- '30'
- '25'
- '20'
- '15'
- '10'
- '5'
- '5'
- '6'
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item '50'\n",
"\\item '45'\n",
"\\item '40'\n",
"\\item '35'\n",
"\\item '30'\n",
"\\item '25'\n",
"\\item '20'\n",
"\\item '15'\n",
"\\item '10'\n",
"\\item '5'\n",
"\\item '5'\n",
"\\item '6'\n",
"\\item '50'\n",
"\\item '45'\n",
"\\item '40'\n",
"\\item '35'\n",
"\\item '30'\n",
"\\item '25'\n",
"\\item '20'\n",
"\\item '15'\n",
"\\item '10'\n",
"\\item '5'\n",
"\\item '5'\n",
"\\item '6'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. '50'\n",
"2. '45'\n",
"3. '40'\n",
"4. '35'\n",
"5. '30'\n",
"6. '25'\n",
"7. '20'\n",
"8. '15'\n",
"9. '10'\n",
"10. '5'\n",
"11. '5'\n",
"12. '6'\n",
"13. '50'\n",
"14. '45'\n",
"15. '40'\n",
"16. '35'\n",
"17. '30'\n",
"18. '25'\n",
"19. '20'\n",
"20. '15'\n",
"21. '10'\n",
"22. '5'\n",
"23. '5'\n",
"24. '6'\n",
"\n",
"\n"
],
"text/plain": [
" [1] \"50\" \"45\" \"40\" \"35\" \"30\" \"25\" \"20\" \"15\" \"10\" \"5\" \"5\" \"6\" \"50\" \"45\" \"40\"\n",
"[16] \"35\" \"30\" \"25\" \"20\" \"15\" \"10\" \"5\" \"5\" \"6\" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"character.vector <- as.character(numeric.vector)\n",
"character.vector"
]
},
{
"cell_type": "markdown",
"id": "deluxe-daily",
"metadata": {},
"source": [
"#### Exercise\n",
"\n",
"retreive the position of the 2nd \"to\" in the quatation in the sentence below, replace it with \"T\" and reprint the whole sentence.\n",
"\n",
"```\n",
"“All we have to decide is what to do with the time that is given us.”\n",
"\n",
"― J.R.R. Tolkien, The Fellowship of the Ring\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "respiratory-railway",
"metadata": {},
"source": [
"### Factors\n",
"\n",
"A factor is a variable to represent categories of a set. They can created using the function as.factor(). "
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "australian-thirty",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- Korea
- China
- UK
- UK
- USA
- Japan
- Korea
\n",
"\n",
"\n",
"\t\n",
"\t\tLevels:\n",
"\t
\n",
"\t\n",
"\t- 'China'
- 'Japan'
- 'Korea'
- 'UK'
- 'USA'
\n",
" "
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item Korea\n",
"\\item China\n",
"\\item UK\n",
"\\item UK\n",
"\\item USA\n",
"\\item Japan\n",
"\\item Korea\n",
"\\end{enumerate*}\n",
"\n",
"\\emph{Levels}: \\begin{enumerate*}\n",
"\\item 'China'\n",
"\\item 'Japan'\n",
"\\item 'Korea'\n",
"\\item 'UK'\n",
"\\item 'USA'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. Korea\n",
"2. China\n",
"3. UK\n",
"4. UK\n",
"5. USA\n",
"6. Japan\n",
"7. Korea\n",
"\n",
"\n",
"\n",
"**Levels**: 1. 'China'\n",
"2. 'Japan'\n",
"3. 'Korea'\n",
"4. 'UK'\n",
"5. 'USA'\n",
"\n",
"\n"
],
"text/plain": [
"[1] Korea China UK UK USA Japan Korea\n",
"Levels: China Japan Korea UK USA"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"countries <- c(\"Korea\", \"China\", \"UK\", \"UK\", \"USA\", \"Japan\", \"Korea\")\n",
"as.factor(countries)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "radical-evanescence",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 2
- 3
- 2
- 3
- 4
- 5
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
\n",
"\n",
"\n",
"\t\n",
"\t\tLevels:\n",
"\t
\n",
"\t\n",
"\t- '1'
- '2'
- '3'
- '4'
- '5'
- '6'
- '7'
- '8'
\n",
" "
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 2\n",
"\\item 3\n",
"\\item 4\n",
"\\item 5\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 4\n",
"\\item 5\n",
"\\item 6\n",
"\\item 7\n",
"\\item 8\n",
"\\end{enumerate*}\n",
"\n",
"\\emph{Levels}: \\begin{enumerate*}\n",
"\\item '1'\n",
"\\item '2'\n",
"\\item '3'\n",
"\\item '4'\n",
"\\item '5'\n",
"\\item '6'\n",
"\\item '7'\n",
"\\item '8'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 2\n",
"3. 3\n",
"4. 2\n",
"5. 3\n",
"6. 4\n",
"7. 5\n",
"8. 1\n",
"9. 2\n",
"10. 3\n",
"11. 4\n",
"12. 5\n",
"13. 6\n",
"14. 7\n",
"15. 8\n",
"\n",
"\n",
"\n",
"**Levels**: 1. '1'\n",
"2. '2'\n",
"3. '3'\n",
"4. '4'\n",
"5. '5'\n",
"6. '6'\n",
"7. '7'\n",
"8. '8'\n",
"\n",
"\n"
],
"text/plain": [
" [1] 1 2 3 2 3 4 5 1 2 3 4 5 6 7 8\n",
"Levels: 1 2 3 4 5 6 7 8"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# factor can work on numbers also. \n",
"fnum <- c(1:3,2:5,1:8)\n",
"as.factor(fnum)"
]
},
{
"cell_type": "markdown",
"id": "athletic-force",
"metadata": {},
"source": [
"### Set Operations \n",
"\n",
" union(x,y) \n",
" intersect(x,y)\n",
" setdiff(x,y) : all elements of x NOT in y\n",
" setequal(x,y)\n",
" c %in% x : membership testing "
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "moral-toronto",
"metadata": {},
"outputs": [],
"source": [
"x <- c(1, 3, 5, 8, 10)\n",
"y <- c(3, 4, 5, 6, 7)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "complicated-girlfriend",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 3
- 5
- 8
- 10
- 4
- 6
- 7
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 3\n",
"\\item 5\n",
"\\item 8\n",
"\\item 10\n",
"\\item 4\n",
"\\item 6\n",
"\\item 7\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 3\n",
"3. 5\n",
"4. 8\n",
"5. 10\n",
"6. 4\n",
"7. 6\n",
"8. 7\n",
"\n",
"\n"
],
"text/plain": [
"[1] 1 3 5 8 10 4 6 7"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"- 3
- 5
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 3\n",
"\\item 5\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 3\n",
"2. 5\n",
"\n",
"\n"
],
"text/plain": [
"[1] 3 5"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"- 1
- 8
- 10
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 8\n",
"\\item 10\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 8\n",
"3. 10\n",
"\n",
"\n"
],
"text/plain": [
"[1] 1 8 10"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"FALSE"
],
"text/latex": [
"FALSE"
],
"text/markdown": [
"FALSE"
],
"text/plain": [
"[1] FALSE"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"union(x,y)\n",
"intersect(x,y)\n",
"setdiff(x,y)\n",
"setequal(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "intimate-wyoming",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"FALSE"
],
"text/latex": [
"FALSE"
],
"text/markdown": [
"FALSE"
],
"text/plain": [
"[1] FALSE"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"7 %in% x"
]
},
{
"cell_type": "markdown",
"id": "vocal-leonard",
"metadata": {},
"source": [
"### List : contains that can hold different types \n",
"\n",
"Lists are a general form of vector in which the various elements need not be \n",
"of the same type, and are often themselves vectors or lists. Lists provide a \n",
"convenient way to return the results of a statistical computation."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "tight-florist",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- $w
\n",
"\t\t- 2
\n",
"\t- $v
\n",
"\t\t- 'GIS'
\n",
"
\n"
],
"text/latex": [
"\\begin{description}\n",
"\\item[\\$w] 2\n",
"\\item[\\$v] 'GIS'\n",
"\\end{description}\n"
],
"text/markdown": [
"$w\n",
": 2\n",
"$v\n",
": 'GIS'\n",
"\n",
"\n"
],
"text/plain": [
"$w\n",
"[1] 2\n",
"\n",
"$v\n",
"[1] \"GIS\"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x <- list(w=2, v=\"GIS\")\n",
"x"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "convinced-statement",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"2"
],
"text/latex": [
"2"
],
"text/markdown": [
"2"
],
"text/plain": [
"[1] 2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# $ sign used to access list elements by names\n",
"x$w"
]
},
{
"cell_type": "code",
"execution_count": 62,
"id": "hindu-korea",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'list'"
],
"text/latex": [
"'list'"
],
"text/markdown": [
"'list'"
],
"text/plain": [
"[1] \"list\""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"'character'"
],
"text/latex": [
"'character'"
],
"text/markdown": [
"'character'"
],
"text/plain": [
"[1] \"character\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mode(x)\n",
"mode(c(x$w,x$v))"
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "fixed-solution",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'character'"
],
"text/latex": [
"'character'"
],
"text/markdown": [
"'character'"
],
"text/plain": [
"[1] \"character\""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"'character'"
],
"text/latex": [
"'character'"
],
"text/markdown": [
"'character'"
],
"text/plain": [
"[1] \"character\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x <- c(2,\"GIS\")\n",
"mode(x)\n",
"mode(x[1])"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "magnetic-allen",
"metadata": {},
"outputs": [],
"source": [
"# show internal datasets \n",
"\n",
"data()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "exotic-departure",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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nvvXfrmx5xFSN0hpIDoh7R67mCV13TF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",
"text/plain": [
"Plot with title “Histogram of Nile”"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"hn <- hist(Nile)"
]
},
{
"cell_type": "code",
"execution_count": 67,
"id": "lucky-african",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"$breaks\n",
" [1] 400 500 600 700 800 900 1000 1100 1200 1300 1400\n",
"\n",
"$counts\n",
" [1] 1 0 5 20 25 19 12 11 6 1\n",
"\n",
"$density\n",
" [1] 0.0001 0.0000 0.0005 0.0020 0.0025 0.0019 0.0012 0.0011 0.0006 0.0001\n",
"\n",
"$mids\n",
" [1] 450 550 650 750 850 950 1050 1150 1250 1350\n",
"\n",
"$xname\n",
"[1] \"Nile\"\n",
"\n",
"$equidist\n",
"[1] TRUE\n",
"\n",
"attr(,\"class\")\n",
"[1] \"histogram\"\n"
]
}
],
"source": [
"print (hn)"
]
},
{
"cell_type": "code",
"execution_count": 68,
"id": "christian-airfare",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"List of 6\n",
" $ breaks : int [1:11] 400 500 600 700 800 900 1000 1100 1200 1300 ...\n",
" $ counts : int [1:10] 1 0 5 20 25 19 12 11 6 1\n",
" $ density : num [1:10] 0.0001 0 0.0005 0.002 0.0025 0.0019 0.0012 0.0011 0.0006 0.0001\n",
" $ mids : num [1:10] 450 550 650 750 850 950 1050 1150 1250 1350\n",
" $ xname : chr \"Nile\"\n",
" $ equidist: logi TRUE\n",
" - attr(*, \"class\")= chr \"histogram\"\n"
]
}
],
"source": [
"# str : structure\n",
"str(hn)"
]
},
{
"cell_type": "code",
"execution_count": 69,
"id": "protecting-superior",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'list'"
],
"text/latex": [
"'list'"
],
"text/markdown": [
"'list'"
],
"text/plain": [
"[1] \"list\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mode(hn)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "lesser-canyon",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" Length Class Mode \n",
"breaks 11 -none- numeric \n",
"counts 10 -none- numeric \n",
"density 10 -none- numeric \n",
"mids 10 -none- numeric \n",
"xname 1 -none- character\n",
"equidist 1 -none- logical "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# summary is a generic function in R. It outputs a concise and more friendly representation of a list. \n",
"summary(hn)"
]
},
{
"cell_type": "markdown",
"id": "ceramic-traffic",
"metadata": {},
"source": [
"Matrices\n",
"\n",
"Matrices, or more generally arrays, are multi-dimensional generalizations of \n",
"vectors. In fact, they are vectors that can be indexed by two or more indices\n",
"and will be printed in a special way.\n",
"\n",
"The matrix() function creates a matrix from the given set of values. We use \n",
"the matrix(x, nrow=, ncol=) function to set the matrix cell values, the \n",
"number of rows and the number of columns. We can use the colnames() and \n",
"rownames() functions to set the column and row names of the matrix-like \n",
"object."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "solar-administration",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 2 × 3 of type lgl\n",
"\n",
"\t| NA | NA | NA |
\n",
"\t| NA | NA | NA |
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 2 × 3 of type lgl\n",
"\\begin{tabular}{lll}\n",
"\t NA & NA & NA\\\\\n",
"\t NA & NA & NA\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A matrix: 2 × 3 of type lgl\n",
"\n",
"| NA | NA | NA |\n",
"| NA | NA | NA |\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3]\n",
"[1,] NA NA NA \n",
"[2,] NA NA NA "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"matrix(data = NA, nrow = 2, ncol = 3) "
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "caroline-things",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 2 × 3 of type int\n",
"\n",
"\t| 1 | 3 | 5 |
\n",
"\t| 2 | 4 | 6 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 2 × 3 of type int\n",
"\\begin{tabular}{lll}\n",
"\t 1 & 3 & 5\\\\\n",
"\t 2 & 4 & 6\\\\\n",
"\\end{tabular}\n"
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"\n",
"A matrix: 2 × 3 of type int\n",
"\n",
"| 1 | 3 | 5 |\n",
"| 2 | 4 | 6 |\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3]\n",
"[1,] 1 3 5 \n",
"[2,] 2 4 6 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"example.matrix <- matrix(1:6,2,3)\n",
"example.matrix"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "durable-custody",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 2 × 3 of type int\n",
"\n",
"\t| 1 | 2 | 3 |
\n",
"\t| 4 | 5 | 6 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 2 × 3 of type int\n",
"\\begin{tabular}{lll}\n",
"\t 1 & 2 & 3\\\\\n",
"\t 4 & 5 & 6\\\\\n",
"\\end{tabular}\n"
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"\n",
"A matrix: 2 × 3 of type int\n",
"\n",
"| 1 | 2 | 3 |\n",
"| 4 | 5 | 6 |\n",
"\n"
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"text/plain": [
" [,1] [,2] [,3]\n",
"[1,] 1 2 3 \n",
"[2,] 4 5 6 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# data distributed by columns by default, can be changed using the keyword byrow \n",
"example.matrix <- matrix(1:6,2,3, byrow=TRUE)\n",
"example.matrix"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "searching-limit",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 2
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],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 2\n",
"3. 3\n",
"\n",
"\n"
],
"text/plain": [
"[1] 1 2 3"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# retrieval by rows\n",
"example.matrix[1,]"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "rocky-consideration",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 2
- 5
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 2\n",
"\\item 5\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 2\n",
"2. 5\n",
"\n",
"\n"
],
"text/plain": [
"[1] 2 5"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# retrival by columns\n",
"example.matrix[,2]"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "abandoned-measure",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 2 × 3 of type dbl\n",
"\n",
"\t| 1 | 2 | 3 |
\n",
"\t| 5 | 10 | 4 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 2 × 3 of type dbl\n",
"\\begin{tabular}{lll}\n",
"\t 1 & 2 & 3\\\\\n",
"\t 5 & 10 & 4\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A matrix: 2 × 3 of type dbl\n",
"\n",
"| 1 | 2 | 3 |\n",
"| 5 | 10 | 4 |\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3]\n",
"[1,] 1 2 3 \n",
"[2,] 5 10 4 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# changing values\n",
"\n",
"example.matrix[1,] <- 1:3\n",
"example.matrix[2,] <- c(5,10,4)\n",
"example.matrix"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "pressing-fields",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 6
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\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 6\n",
"\\item 12\n",
"\\item 7\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 6\n",
"2. 12\n",
"3. 7\n",
"\n",
"\n"
],
"text/plain": [
"[1] 6 12 7"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# apply () function is a machanism to apply a function across a vector. \n",
"\n",
"# by column\n",
"apply(example.matrix,2,sum)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"id": "passing-trinity",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 6
- 19
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 6\n",
"\\item 19\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 6\n",
"2. 19\n",
"\n",
"\n"
],
"text/plain": [
"[1] 6 19"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# by row\n",
"apply(example.matrix,1,sum)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "acoustic-consultancy",
"metadata": {},
"outputs": [],
"source": [
"matrix.head <- c(\"col a\",\"col b\",\"column c\")\n",
"matrix.side <- c(\"first raw\",\"second raw\")"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "qualified-senior",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 2 × 3 of type dbl\n",
"\n",
"\t | col a | col b | column c |
|---|
\n",
"\n",
"\n",
"\t| first raw | 1 | 2 | 3 |
|---|
\n",
"\t| second raw | 5 | 10 | 4 |
|---|
\n",
"\n",
"
\n"
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"text/latex": [
"A matrix: 2 × 3 of type dbl\n",
"\\begin{tabular}{r|lll}\n",
" & col a & col b & column c\\\\\n",
"\\hline\n",
"\tfirst raw & 1 & 2 & 3\\\\\n",
"\tsecond raw & 5 & 10 & 4\\\\\n",
"\\end{tabular}\n"
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"text/markdown": [
"\n",
"A matrix: 2 × 3 of type dbl\n",
"\n",
"| | col a | col b | column c |\n",
"|---|---|---|---|\n",
"| first raw | 1 | 2 | 3 |\n",
"| second raw | 5 | 10 | 4 |\n",
"\n"
],
"text/plain": [
" col a col b column c\n",
"first raw 1 2 3 \n",
"second raw 5 10 4 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"colnames(example.matrix) = matrix.head\n",
"rownames(example.matrix) = matrix.side\n",
"example.matrix"
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "basic-routine",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" num [1:2, 1:3] 1 5 2 10 3 4\n",
" - attr(*, \"dimnames\")=List of 2\n",
" ..$ : chr [1:2] \"first raw\" \"second raw\"\n",
" ..$ : chr [1:3] \"col a\" \"col b\" \"column c\"\n"
]
}
],
"source": [
"# The structure function str(object.name) informs you of the structure of a\n",
"# specific object\n",
"\n",
"str(example.matrix)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "annoying-monitoring",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A matrix: 4 × 3 of type int\n",
"\n",
"\t| 1 | 3 | 5 |
\n",
"\t| 2 | 4 | 6 |
\n",
"\t| 11 | 13 | 15 |
\n",
"\t| 12 | 14 | 16 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A matrix: 4 × 3 of type int\n",
"\\begin{tabular}{lll}\n",
"\t 1 & 3 & 5\\\\\n",
"\t 2 & 4 & 6\\\\\n",
"\t 11 & 13 & 15\\\\\n",
"\t 12 & 14 & 16\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A matrix: 4 × 3 of type int\n",
"\n",
"| 1 | 3 | 5 |\n",
"| 2 | 4 | 6 |\n",
"| 11 | 13 | 15 |\n",
"| 12 | 14 | 16 |\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3]\n",
"[1,] 1 3 5 \n",
"[2,] 2 4 6 \n",
"[3,] 11 13 15 \n",
"[4,] 12 14 16 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"A matrix: 2 × 6 of type int\n",
"\n",
"\t| 1 | 3 | 5 | 11 | 13 | 15 |
\n",
"\t| 2 | 4 | 6 | 12 | 14 | 16 |
\n",
"\n",
"
\n"
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"text/latex": [
"A matrix: 2 × 6 of type int\n",
"\\begin{tabular}{llllll}\n",
"\t 1 & 3 & 5 & 11 & 13 & 15\\\\\n",
"\t 2 & 4 & 6 & 12 & 14 & 16\\\\\n",
"\\end{tabular}\n"
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"text/markdown": [
"\n",
"A matrix: 2 × 6 of type int\n",
"\n",
"| 1 | 3 | 5 | 11 | 13 | 15 |\n",
"| 2 | 4 | 6 | 12 | 14 | 16 |\n",
"\n"
],
"text/plain": [
" [,1] [,2] [,3] [,4] [,5] [,6]\n",
"[1,] 1 3 5 11 13 15 \n",
"[2,] 2 4 6 12 14 16 "
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# combine matrix using rbind (by row) and cbind (by column)\n",
"\n",
"matrix1 <- matrix(1:6,2,3)\n",
"matrix2 <- matrix(11:16,2,3)\n",
"rbind(matrix1,matrix2)\n",
"cbind(matrix1,matrix2)"
]
},
{
"cell_type": "markdown",
"id": "wound-expansion",
"metadata": {},
"source": [
"### Exercise \n",
"\n",
"create a matrix with the following elements and then change the first column values to all 0.\n",
"\n",
"```\n",
"1 1 1 \n",
"2 2 2 \n",
"3 3 3 \n",
"```"
]
},
{
"cell_type": "markdown",
"id": "lovely-effect",
"metadata": {},
"source": [
"Arrays\n",
"\n",
"An array can be considered a multiple subscripted collection of data \n",
"entries, for example numeric. R allows simple facilities for creating \n",
"and handling arrays, and in particular the special case of matrices. \n",
"\n",
"As well as giving a vector structure a dim attribute, arrays can be \n",
"constructed from vectors by the array function, which has the form \n",
"array(data_vector, dim_vector)"
]
},
{
"cell_type": "code",
"execution_count": 60,
"id": "large-frederick",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
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],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 4\n",
"\\item 5\n",
"\\item 6\n",
"\\item 7\n",
"\\item 8\n",
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"\\item 21\n",
"\\item 22\n",
"\\item 23\n",
"\\item 24\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 2\n",
"3. 3\n",
"4. 4\n",
"5. 5\n",
"6. 6\n",
"7. 7\n",
"8. 8\n",
"9. 9\n",
"10. 10\n",
"11. 11\n",
"12. 12\n",
"13. 13\n",
"14. 14\n",
"15. 15\n",
"16. 16\n",
"17. 17\n",
"18. 18\n",
"19. 19\n",
"20. 20\n",
"21. 21\n",
"22. 22\n",
"23. 23\n",
"24. 24\n",
"\n",
"\n"
],
"text/plain": [
", , 1\n",
"\n",
" [,1] [,2] [,3] [,4]\n",
"[1,] 1 4 7 10\n",
"[2,] 2 5 8 11\n",
"[3,] 3 6 9 12\n",
"\n",
", , 2\n",
"\n",
" [,1] [,2] [,3] [,4]\n",
"[1,] 13 16 19 22\n",
"[2,] 14 17 20 23\n",
"[3,] 15 18 21 24\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Z <- array(1:24, c(3,4,2))\n",
"Z"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "lined-messaging",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" int [1:3, 1:4, 1:2] 1 2 3 4 5 6 7 8 9 10 ...\n"
]
}
],
"source": [
"str(Z)"
]
},
{
"cell_type": "markdown",
"id": "brown-tsunami",
"metadata": {},
"source": [
"## list and delete R objects \n",
"\n",
"The list function ls() outputs a list of existing R objects.\n",
"\n",
"rm() removes the object."
]
},
{
"cell_type": "code",
"execution_count": 57,
"id": "convertible-essex",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 'character.vector'
- 'example.matrix'
- 'hn'
- 'ind'
- 'is.not.a.number'
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\n"
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"\\begin{enumerate*}\n",
"\\item 'character.vector'\n",
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"\\item 'x'\n",
"\\item 'z'\n",
"\\item 'Z'\n",
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"text/markdown": [
"1. 'character.vector'\n",
"2. 'example.matrix'\n",
"3. 'hn'\n",
"4. 'ind'\n",
"5. 'is.not.a.number'\n",
"6. 'is.not.available'\n",
"7. 'matrix.head'\n",
"8. 'matrix.side'\n",
"9. 'numeric.vector'\n",
"10. 'one2three'\n",
"11. 'x'\n",
"12. 'z'\n",
"13. 'Z'\n",
"\n",
"\n"
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" [5] \"is.not.a.number\" \"is.not.available\" \"matrix.head\" \"matrix.side\" \n",
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"[13] \"Z\" "
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"source": [
"ls()"
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{
"cell_type": "code",
"execution_count": 61,
"id": "subjective-library",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 'character.vector'
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"1. 'character.vector'\n",
"2. 'example.matrix'\n",
"3. 'hn'\n",
"4. 'ind'\n",
"5. 'is.not.a.number'\n",
"6. 'is.not.available'\n",
"7. 'matrix.head'\n",
"8. 'matrix.side'\n",
"9. 'numeric.vector'\n",
"10. 'one2three'\n",
"11. 'x'\n",
"12. 'z'\n",
"\n",
"\n"
],
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" [9] \"numeric.vector\" \"one2three\" \"x\" \"z\" "
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"metadata": {},
"output_type": "display_data"
}
],
"source": [
"rm(Z)\n",
"ls()"
]
},
{
"cell_type": "markdown",
"id": "infectious-myanmar",
"metadata": {},
"source": [
"## Data Frames\n",
"\n",
"Data frames are matrix-like structures, in which the columns can be \n",
"of different types. Think of data frames as data matrices with one row per \n",
"observational unit but with (possibly) both numerical and categorical \n",
"variables. Many experiments are best described by data frames: the treatments\n",
"are categorical but the response is numeric. \n",
"\n",
"As a result R dataframes are tightly coupled collections of variables which \n",
"share many of the properties of matrices and of lists. Data frames are used \n",
"as the fundamental data structure by most of R's modeling software.\n",
"\n",
"A data frame is a list with class \"data.frame\". There are restrictions on \n",
"lists that may be made into data frames, namely :\n",
"\n",
"The components must be vectors (numeric, character, or logical), factors, \n",
"numeric matrices, lists, or other data frames.\n",
"Matrices, lists, and data frames provide as many variables to the new data \n",
"frame as they have columns, elements, or variables, respectively.\n",
"Numeric vectors, logicals and factors are included, and character vectors \n",
"are coerced to be factors, whose levels are the unique values appearing in\n",
"the vector.\n",
"Vector structures appearing as variables of the data frame must all have the\n",
"same length, and matrix structures must all have the same row size. "
]
},
{
"cell_type": "markdown",
"id": "compliant-bride",
"metadata": {},
"source": [
"### Dataframe construction "
]
},
{
"cell_type": "code",
"execution_count": 62,
"id": "loaded-feeding",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 4 × 3\n",
"\n",
"\t| v | ch | n |
|---|
\n",
"\t| <int> | <chr> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 1 | a | 10 |
\n",
"\t| 2 | b | 10 |
\n",
"\t| 3 | c | 10 |
\n",
"\t| 4 | d | 10 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 4 × 3\n",
"\\begin{tabular}{lll}\n",
" v & ch & n\\\\\n",
" & & \\\\\n",
"\\hline\n",
"\t 1 & a & 10\\\\\n",
"\t 2 & b & 10\\\\\n",
"\t 3 & c & 10\\\\\n",
"\t 4 & d & 10\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 4 × 3\n",
"\n",
"| v <int> | ch <chr> | n <dbl> |\n",
"|---|---|---|\n",
"| 1 | a | 10 |\n",
"| 2 | b | 10 |\n",
"| 3 | c | 10 |\n",
"| 4 | d | 10 |\n",
"\n"
],
"text/plain": [
" v ch n \n",
"1 1 a 10\n",
"2 2 b 10\n",
"3 3 c 10\n",
"4 4 d 10"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"my.data.frame = data.frame(v = 1:4, ch = c(\"a\", \"b\", \"c\", \"d\"), n = 10)\n",
"my.data.frame"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "bright-trainer",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 4 × 3\n",
"\n",
"\t | vector | character | const.vector |
|---|
\n",
"\t | <int> | <chr> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| data1 | 1 | a | 10 |
|---|
\n",
"\t| data2 | 2 | b | 10 |
|---|
\n",
"\t| data3 | 3 | c | 10 |
|---|
\n",
"\t| data4 | 4 | d | 10 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 4 × 3\n",
"\\begin{tabular}{r|lll}\n",
" & vector & character & const.vector\\\\\n",
" & & & \\\\\n",
"\\hline\n",
"\tdata1 & 1 & a & 10\\\\\n",
"\tdata2 & 2 & b & 10\\\\\n",
"\tdata3 & 3 & c & 10\\\\\n",
"\tdata4 & 4 & d & 10\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 4 × 3\n",
"\n",
"| | vector <int> | character <chr> | const.vector <dbl> |\n",
"|---|---|---|---|\n",
"| data1 | 1 | a | 10 |\n",
"| data2 | 2 | b | 10 |\n",
"| data3 | 3 | c | 10 |\n",
"| data4 | 4 | d | 10 |\n",
"\n"
],
"text/plain": [
" vector character const.vector\n",
"data1 1 a 10 \n",
"data2 2 b 10 \n",
"data3 3 c 10 \n",
"data4 4 d 10 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Or:\n",
"\n",
"my.data.frame = data.frame(vector = 1:4,\n",
" character = c(\"a\", \"b\", \"c\", \"d\"),\n",
" const.vector = 10,\n",
" row.names =c(\"data1\", \"data2\", \"data3\", \"data4\"))\n",
"my.data.frame"
]
},
{
"cell_type": "markdown",
"id": "finished-bridge",
"metadata": {},
"source": [
"### Data selection and manipulation"
]
},
{
"cell_type": "code",
"execution_count": 64,
"id": "angry-intermediate",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 'a'
- 'b'
- 'c'
- 'd'
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'a'\n",
"\\item 'b'\n",
"\\item 'c'\n",
"\\item 'd'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'a'\n",
"2. 'b'\n",
"3. 'c'\n",
"4. 'd'\n",
"\n",
"\n"
],
"text/plain": [
"[1] \"a\" \"b\" \"c\" \"d\""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"- 'a'
- 'b'
- 'c'
- 'd'
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'a'\n",
"\\item 'b'\n",
"\\item 'c'\n",
"\\item 'd'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'a'\n",
"2. 'b'\n",
"3. 'c'\n",
"4. 'd'\n",
"\n",
"\n"
],
"text/plain": [
"[1] \"a\" \"b\" \"c\" \"d\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# You can extract data from dataframes using the [ [ ] ] and $ sign:\n",
"\n",
"my.data.frame[[\"character\"]]\n",
"\n",
"my.data.frame[[2]]"
]
},
{
"cell_type": "code",
"execution_count": 66,
"id": "excess-patrol",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"'c'"
],
"text/latex": [
"'c'"
],
"text/markdown": [
"'c'"
],
"text/plain": [
"[1] \"c\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Call the 3rd value of the character vector:\n",
"\n",
"my.data.frame[[2]][3]"
]
},
{
"cell_type": "code",
"execution_count": 67,
"id": "athletic-fitness",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 1
- 2
- 3
- 4
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 1\n",
"\\item 2\n",
"\\item 3\n",
"\\item 4\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 1\n",
"2. 2\n",
"3. 3\n",
"4. 4\n",
"\n",
"\n"
],
"text/plain": [
"[1] 1 2 3 4"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"- 'b'
- 'c'
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'b'\n",
"\\item 'c'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'b'\n",
"2. 'c'\n",
"\n",
"\n"
],
"text/plain": [
"[1] \"b\" \"c\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Or using the $ syntax:\n",
" \n",
"my.data.frame$vector\n",
" \n",
"my.data.frame$character[2:3]"
]
},
{
"cell_type": "code",
"execution_count": 68,
"id": "secondary-multiple",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"NULL"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"A data.frame: 4 × 4\n",
"\n",
"\t | vector | character | const.vector | new |
|---|
\n",
"\t | <int> | <chr> | <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| data1 | 1 | a | 10 | 10 |
|---|
\n",
"\t| data2 | 2 | b | 10 | 11 |
|---|
\n",
"\t| data3 | 3 | c | 10 | 20 |
|---|
\n",
"\t| data4 | 4 | d | 10 | 40 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 4 × 4\n",
"\\begin{tabular}{r|llll}\n",
" & vector & character & const.vector & new\\\\\n",
" & & & & \\\\\n",
"\\hline\n",
"\tdata1 & 1 & a & 10 & 10\\\\\n",
"\tdata2 & 2 & b & 10 & 11\\\\\n",
"\tdata3 & 3 & c & 10 & 20\\\\\n",
"\tdata4 & 4 & d & 10 & 40\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 4 × 4\n",
"\n",
"| | vector <int> | character <chr> | const.vector <dbl> | new <dbl> |\n",
"|---|---|---|---|---|\n",
"| data1 | 1 | a | 10 | 10 |\n",
"| data2 | 2 | b | 10 | 11 |\n",
"| data3 | 3 | c | 10 | 20 |\n",
"| data4 | 4 | d | 10 | 40 |\n",
"\n"
],
"text/plain": [
" vector character const.vector new\n",
"data1 1 a 10 10 \n",
"data2 2 b 10 11 \n",
"data3 3 c 10 20 \n",
"data4 4 d 10 40 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# You can add single arguments to a data frame, query information, select and \n",
"# manipulate arguments or single values from a dataframe \n",
" \n",
"my.data.frame$new\n",
"\n",
"my.data.frame$new = c(10,11,20,40)\n",
"my.data.frame"
]
},
{
"cell_type": "code",
"execution_count": 69,
"id": "civil-language",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"4"
],
"text/latex": [
"4"
],
"text/markdown": [
"4"
],
"text/plain": [
"[1] 4"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# length(object.name) returns the number of elements in an object such as \n",
"# matrix vector or dataframes:\n",
" \n",
"length(my.data.frame$new) "
]
},
{
"cell_type": "code",
"execution_count": 70,
"id": "ongoing-world",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"4"
],
"text/latex": [
"4"
],
"text/markdown": [
"4"
],
"text/plain": [
"[1] 4"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"3"
],
"text/latex": [
"3"
],
"text/markdown": [
"3"
],
"text/plain": [
"[1] 3"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# which(object.name) and which.max(object.name) return the index of a specific\n",
"# or of the greatest element of an object\n",
" \n",
"which.max(my.data.frame$new) \n",
"\n",
"which(my.data.frame$new == 20) "
]
},
{
"cell_type": "code",
"execution_count": 71,
"id": "acceptable-allen",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"40"
],
"text/latex": [
"40"
],
"text/markdown": [
"40"
],
"text/plain": [
"[1] 40"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# max(object.name) returns the value of the greatest element\n",
" \n",
"max(my.data.frame$new) "
]
},
{
"cell_type": "code",
"execution_count": 72,
"id": "smart-temple",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 10
- 11
- 20
- 40
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 10\n",
"\\item 11\n",
"\\item 20\n",
"\\item 40\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 10\n",
"2. 11\n",
"3. 20\n",
"4. 40\n",
"\n",
"\n"
],
"text/plain": [
"[1] 10 11 20 40"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# sort(object.name) sort from small to big \n",
" \n",
"sort(my.data.frame$new) "
]
},
{
"cell_type": "code",
"execution_count": 73,
"id": "chinese-president",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"- 40
- 20
- 11
- 10
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 40\n",
"\\item 20\n",
"\\item 11\n",
"\\item 10\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 40\n",
"2. 20\n",
"3. 11\n",
"4. 10\n",
"\n",
"\n"
],
"text/plain": [
"[1] 40 20 11 10"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# rev(object.name) sorts from big to small\n",
" \n",
"rev(sort(my.data.frame$new)) "
]
},
{
"cell_type": "code",
"execution_count": 74,
"id": "separated-fifty",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 1 × 4\n",
"\n",
"\t | vector | character | const.vector | new |
|---|
\n",
"\t | <int> | <chr> | <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| data3 | 3 | c | 10 | 20 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 1 × 4\n",
"\\begin{tabular}{r|llll}\n",
" & vector & character & const.vector & new\\\\\n",
" & & & & \\\\\n",
"\\hline\n",
"\tdata3 & 3 & c & 10 & 20\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 1 × 4\n",
"\n",
"| | vector <int> | character <chr> | const.vector <dbl> | new <dbl> |\n",
"|---|---|---|---|---|\n",
"| data3 | 3 | c | 10 | 20 |\n",
"\n"
],
"text/plain": [
" vector character const.vector new\n",
"data3 3 c 10 20 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# subset(object.name, ...) returns a selection of an R-object with respect to \n",
"# criteria (typically comparisons: x$V1 < 10). \n",
" \n",
"subset(my.data.frame, my.data.frame$new == 20)"
]
},
{
"cell_type": "code",
"execution_count": 79,
"id": "wireless-compact",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 4 × 3\n",
"\n",
"\t | character | const.vector | new |
|---|
\n",
"\t | <chr> | <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| data1 | a | 10 | 10 |
|---|
\n",
"\t| data2 | b | 10 | 11 |
|---|
\n",
"\t| data3 | c | 10 | 20 |
|---|
\n",
"\t| data4 | d | 10 | 40 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 4 × 3\n",
"\\begin{tabular}{r|lll}\n",
" & character & const.vector & new\\\\\n",
" & & & \\\\\n",
"\\hline\n",
"\tdata1 & a & 10 & 10\\\\\n",
"\tdata2 & b & 10 & 11\\\\\n",
"\tdata3 & c & 10 & 20\\\\\n",
"\tdata4 & d & 10 & 40\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 4 × 3\n",
"\n",
"| | character <chr> | const.vector <dbl> | new <dbl> |\n",
"|---|---|---|---|\n",
"| data1 | a | 10 | 10 |\n",
"| data2 | b | 10 | 11 |\n",
"| data3 | c | 10 | 20 |\n",
"| data4 | d | 10 | 40 |\n",
"\n"
],
"text/plain": [
" character const.vector new\n",
"data1 a 10 10 \n",
"data2 b 10 11 \n",
"data3 c 10 20 \n",
"data4 d 10 40 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# If the R-object is a data frame,\n",
"# the option select gives the variables to be kept or dropped using a minus \n",
"# sign\n",
"\n",
"my.data.frame[-1]"
]
},
{
"cell_type": "markdown",
"id": "emotional-target",
"metadata": {},
"source": [
"## Reading and Writing Files\n",
"\n",
"read.table(\"filename\")** Reads a file in table format and creates a data \n",
"frame from it, with cases corresponding to lines and variables to fields \n",
"within the file. The default separator sep=\"\" is any whitespace. \n",
"You might need sep=\",\" or \";\" and so on. \n",
"Use header=TRUE to read the first line as a header of column names. \n",
"The **as.is=TRUE** specification is used to prevent character vectors from\n",
"being converted to factors. \n",
"\n",
"The comment.char=\"\" specification is used to prevent \"#\" from being \n",
"interpreted as a comment and use \"skip=n\" to skip n lines before reading \n",
"data. For more details:\n",
"?read.table\n",
"\n",
"read.csv(\"filename\") is set to read comma separated files. Example usage is:\n",
"read.csv(file.name, header = TRUE, sep = \",\", quote=\"\\\"\", dec=\".\", \n",
"fill =TRUE, comment.char=\"\", ...)\n",
"\n",
"read.delim(\"filename\") is used for reading tab-delimited files\n",
"\n",
"read.fwf() reads a table of fixed width formatted data into a ’data.frame’.\n",
"Widths is an integer vector, giving the widths of the fixed-width fields\n",
"\n",
"write.table(Robj, \"filename\", sep=\",\", row.names=FALSE, quote=FALSE)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "brave-popularity",
"metadata": {},
"outputs": [],
"source": [
"df <- read.csv(\"./geodata/shp/point_stat.csv\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "complimentary-ground",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 6 × 4\n",
"\n",
"\t | FID | mean | stdev | min |
|---|
\n",
"\t | <int> | <dbl> | <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 1 | 0 | 2.550725 | 0.25891342 | 2.396264 |
|---|
\n",
"\t| 2 | 1 | 2.550725 | 0.25891342 | 2.396264 |
|---|
\n",
"\t| 3 | 2 | 2.550725 | 0.25891342 | 2.396264 |
|---|
\n",
"\t| 4 | 3 | 2.383711 | 0.12381761 | 2.050272 |
|---|
\n",
"\t| 5 | 4 | 2.383137 | 0.09662122 | 2.133288 |
|---|
\n",
"\t| 6 | 5 | 2.383137 | 0.09662122 | 2.133288 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 6 × 4\n",
"\\begin{tabular}{r|llll}\n",
" & FID & mean & stdev & min\\\\\n",
" & & & & \\\\\n",
"\\hline\n",
"\t1 & 0 & 2.550725 & 0.25891342 & 2.396264\\\\\n",
"\t2 & 1 & 2.550725 & 0.25891342 & 2.396264\\\\\n",
"\t3 & 2 & 2.550725 & 0.25891342 & 2.396264\\\\\n",
"\t4 & 3 & 2.383711 & 0.12381761 & 2.050272\\\\\n",
"\t5 & 4 & 2.383137 & 0.09662122 & 2.133288\\\\\n",
"\t6 & 5 & 2.383137 & 0.09662122 & 2.133288\\\\\n",
"\\end{tabular}\n"
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"text/markdown": [
"\n",
"A data.frame: 6 × 4\n",
"\n",
"| | FID <int> | mean <dbl> | stdev <dbl> | min <dbl> |\n",
"|---|---|---|---|---|\n",
"| 1 | 0 | 2.550725 | 0.25891342 | 2.396264 |\n",
"| 2 | 1 | 2.550725 | 0.25891342 | 2.396264 |\n",
"| 3 | 2 | 2.550725 | 0.25891342 | 2.396264 |\n",
"| 4 | 3 | 2.383711 | 0.12381761 | 2.050272 |\n",
"| 5 | 4 | 2.383137 | 0.09662122 | 2.133288 |\n",
"| 6 | 5 | 2.383137 | 0.09662122 | 2.133288 |\n",
"\n"
],
"text/plain": [
" FID mean stdev min \n",
"1 0 2.550725 0.25891342 2.396264\n",
"2 1 2.550725 0.25891342 2.396264\n",
"3 2 2.550725 0.25891342 2.396264\n",
"4 3 2.383711 0.12381761 2.050272\n",
"5 4 2.383137 0.09662122 2.133288\n",
"6 5 2.383137 0.09662122 2.133288"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"head(df)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "alike-tender",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 2 × 4\n",
"\n",
"\t | FID | mean | stdev | min |
|---|
\n",
"\t | <int> | <dbl> | <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 106 | 105 | 7.536515 | 0.1895011 | 7.16515 |
|---|
\n",
"\t| 107 | 106 | 7.536515 | 0.1895011 | 7.16515 |
|---|
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 2 × 4\n",
"\\begin{tabular}{r|llll}\n",
" & FID & mean & stdev & min\\\\\n",
" & & & & \\\\\n",
"\\hline\n",
"\t106 & 105 & 7.536515 & 0.1895011 & 7.16515\\\\\n",
"\t107 & 106 & 7.536515 & 0.1895011 & 7.16515\\\\\n",
"\\end{tabular}\n"
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"text/markdown": [
"\n",
"A data.frame: 2 × 4\n",
"\n",
"| | FID <int> | mean <dbl> | stdev <dbl> | min <dbl> |\n",
"|---|---|---|---|---|\n",
"| 106 | 105 | 7.536515 | 0.1895011 | 7.16515 |\n",
"| 107 | 106 | 7.536515 | 0.1895011 | 7.16515 |\n",
"\n"
],
"text/plain": [
" FID mean stdev min \n",
"106 105 7.536515 0.1895011 7.16515\n",
"107 106 7.536515 0.1895011 7.16515"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# subsetting \n",
"dfSel <- df[which(df$mean>7),]\n",
"dfSel"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "informal-frontier",
"metadata": {},
"outputs": [],
"source": [
"write.csv(dfSel,\"./geodata/shp/point_stat_sel.csv\", row.names=FALSE)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "israeli-first",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"A data.frame: 2 × 4\n",
"\n",
"\t| FID | mean | stdev | min |
|---|
\n",
"\t| <int> | <dbl> | <dbl> | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 105 | 7.536515 | 0.1895011 | 7.16515 |
\n",
"\t| 106 | 7.536515 | 0.1895011 | 7.16515 |
\n",
"\n",
"
\n"
],
"text/latex": [
"A data.frame: 2 × 4\n",
"\\begin{tabular}{llll}\n",
" FID & mean & stdev & min\\\\\n",
" & & & \\\\\n",
"\\hline\n",
"\t 105 & 7.536515 & 0.1895011 & 7.16515\\\\\n",
"\t 106 & 7.536515 & 0.1895011 & 7.16515\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 2 × 4\n",
"\n",
"| FID <int> | mean <dbl> | stdev <dbl> | min <dbl> |\n",
"|---|---|---|---|\n",
"| 105 | 7.536515 | 0.1895011 | 7.16515 |\n",
"| 106 | 7.536515 | 0.1895011 | 7.16515 |\n",
"\n"
],
"text/plain": [
" FID mean stdev min \n",
"1 105 7.536515 0.1895011 7.16515\n",
"2 106 7.536515 0.1895011 7.16515"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df <- read.csv(\"./geodata/shp/point_stat_sel.csv\")\n",
"df"
]
},
{
"cell_type": "markdown",
"id": "concrete-filing",
"metadata": {},
"source": [
"### Exercise \n",
"\n",
"Print the data rows with the column min value less than 1. Do NOT use the \"which\" function in R. "
]
},
{
"cell_type": "markdown",
"id": "phantom-courtesy",
"metadata": {},
"source": [
"## Functions\n",
"\n",
"Functions are themselves objects in R which can be stored in the project's \n",
"workspace. This provides a simple and convenient way to extend R. \n",
"\n",
"Usage: in writing your own function you provide one or more arguments or \n",
"names for the function, an expression and a value \n",
"is produced equal to the output function result.\n",
"\n",
"function(arglist) expr function definition \n",
"return(value) "
]
},
{
"cell_type": "code",
"execution_count": 112,
"id": "jewish-light",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"243"
],
"text/latex": [
"243"
],
"text/markdown": [
"243"
],
"text/plain": [
"[1] 243"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Example\n",
"\n",
"myfunction <- function(x) x^5\n",
"myfunction(3)"
]
},
{
"cell_type": "code",
"execution_count": 115,
"id": "recent-romance",
"metadata": {},
"outputs": [],
"source": [
"# oddcount function \n",
"\n",
"oddcount <- function(x){\n",
" k <- 0 \n",
" for (i in x) {\n",
" if (i %% 2 == 1) k <- k + 1\n",
" }\n",
" return (k)\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": 116,
"id": "brown-syndicate",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"4"
],
"text/latex": [
"4"
],
"text/markdown": [
"4"
],
"text/plain": [
"[1] 4"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"oddcount(c(1,3,5,7))"
]
},
{
"cell_type": "code",
"execution_count": 117,
"id": "incorrect-carroll",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"3"
],
"text/latex": [
"3"
],
"text/markdown": [
"3"
],
"text/plain": [
"[1] 3"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"oddcount(c(1,3,5,8))"
]
},
{
"cell_type": "markdown",
"id": "thick-theta",
"metadata": {},
"source": [
"### break and next \n",
" break : break out of a loop \n",
" next : skip a step "
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "reduced-dispatch",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] 2\n",
"[1] 4\n",
"[1] 6\n",
"[1] 8\n"
]
}
],
"source": [
"for (i in 1:10){\n",
" if (i %in% c(1,3,5,7)) {\n",
" next\n",
" }\n",
" else if (i > 8){\n",
" break\n",
" } \n",
" print (i)\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "answering-draft",
"metadata": {},
"source": [
"### Exercise \n",
"\n",
"write a function to test if a number is a prime number, a natural number that is NOT a multiplication of two smaller numbers. "
]
},
{
"cell_type": "markdown",
"id": "moved-appearance",
"metadata": {},
"source": [
"## Basic Graphs\n",
"\n",
"The plot() function forms the foundation for much of R based graphing operations. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "approved-occasion",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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h0HJl14IjTclHu7y4mEBJ/xFNLYaiPM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\nRK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(c(1,3,5,7),c(2,4,6,8))"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "diverse-stuff",
"metadata": {},
"outputs": [],
"source": [
"x <- seq(0,10,length.out=100)\n",
"y <- exp(-x)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "neutral-hanging",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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O+Y+PqNx6dKzwTsGkKy7juPm+blauN9hWcCdg0hWde2lWWZmGmFshMB+4aQrAsf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\n+sCMHVgjAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "desperate-preliminary",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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PuQxpiQHnE5C2Ah9iE9YkL6ictZAAux\nD+kNE9K5LmcBLMQ+pM9KRLo7HAWwEfuQgr1F2jscBbAR/5C+wvPf8C/+If3APEia6XAWwEL8\nQ/qpCel3DmcBLMQ/pMdNSKMczgJYiH9I80xIZzicBbAQ/5DW7iByhMNZAAvxDyk4TKRynbtZ\nAAsJCKmvObd7190sgIUEhHSNCelJd7MAFhIQ0m/42j54l4CQZnDZBniXgJBWl4p0dTcLYCEB\nIQU1Irs5GwWwkYSQeplzu4+dzQJYSEJIl5mQXnA2C2AhCSHdbUKa6GwWwEISQvqbCelSZ7MA\nFpIQ0hIT0inOZgEsJCGkYHeRakeTAFYSEVLm28Zy+gVAWSJCGmzO7aa7mgWwkIiQxpmQfu1q\nFsBCIkJ6yoQ00tUsgIVEhLTQhNTH1SyAhUSEtK61yKGuZgEsJCKk4EiRinpHswAWkhFSP3Nu\nN9fRLICFZIR0vQnpD45mASwkI6SHTUhjHM0CWEhGSG+akAY6mgWwkIyQPm8hcrSjWQALyQgp\nOFBkpwY3swAWEhLSN8y53b/dzAJYSEhIw01IU93MAlhISEj3mpDucDMLYCEhIb1iQhrqZhbA\nQkJCWmFC6ulmFsBCQkIK9uK7zeFTUkL6qjkkLXcyC2AhKSENMSG94mQWwEJSQrrdhHSfk1kA\nC0kJ6S8mpOFOZgEsJCWkf5uQvuFkFsBCUkIKdhHZ38UogI3EhNRVpGSFi1kAC4kJ6QJzbvd3\nF7MAFhIT0p0mpLtdzAJYSExIme92ucjFLICFxIS0vETkKy5mASwkJqSgg8iuDkYBbCQnpP82\n53YfOJgFsJCckDIfkn3awSyAheSE9KAJ6acOZgEsJCekN0xIA/RHAWwkJ6TPK0Q6O5gFsJCc\nkIJDRXZYqz8LYCFBIZ1uzu3e0Z8FsJCgkEabkB7WnwWwkKCQHjchXaM/C2AhQSFlvkn22/qz\nABYSFFLDTiIH6M8CWEhQSMGxIqWr1GcBLCQppMHm3O5V9VkAC0kKKXNJrnvUZwEsJCmk501I\nl6rPAlhIUkhLuZI+fElSSEF7kT20RwFsJCqkk80h6SPtWQALPkKqn/XSwvAt8gzpChPSX/L5\nRaBA0Yb04oXmjzt2M/f3Q58L2y7PkH5ldnxrPr8IFCjSkF6oqGoIJsqOfS48ubQi7BWfPEN6\n3YQ0KM/ZgEJEGlLPdguCYN+a/5ib/6j875AN8wyproXIUfmNBhQk0pB2uTIIlsvt2duDdwnZ\nMM+QgkNEWq3L6zeBgkQaUuurzVGj5PfZ26N2CNkw35D6mnO7eXn9JlCQSEPqetDqIDjuyszN\ntZ2PCNkw35CuNyFNzus3gYJEGtJT0uXp+untfv35mld6yi9CNsw3pEdNSKPymw0oRLRPf/+q\nSioPrZayMim5siFku3xDmm9C6pPfaEAhIn5B9uNbelXv2HLXLhfPCN0s35DW7ShycF6/CRQk\nUW8RCoL/EilbrTsLYCFhIZ1jzu2m6c4CWEhYSLeZkMKexQDc8BXS/J5bfnLo3T3abNAq35Be\nNCFdWPBwQK58hTRDttzLuj9O2uAH+Ya0slTkmIKHA3LlK6Ta2bND/jbvU7vMm4Qq6/P8XSBv\nCXuMFPQz53ZhiQJORB1Sw4IpkydPXdTMVvmHdLMJ6f48fxfIW7QhLR7WVrKqR4VeyTH/kKaa\nnQ/L83eBvEUa0gc10nHANWPHjuzXXjotD9kw/5CWlYh0z/N3gbxFGtKg8oeabq29o+SSkA3z\nDynYT2QnPpKEqEUaUruzN94+rUPIhgWE9F1zbvd/+f4ykKdIQ6oYvfH2dRUhGxYQ0g0mpN/l\n+8tAniINqXqTjzj0rgnZsICQnjQhXZXvLwN5ijSkYSU31zXeWjki9N5eQEgfmpC+lu8vA3mK\nNKTlnaWqx8ChQ/p3q5Tun4VsWEBImesW75b3LwP5ifZ1pNpxXUozLyO1OO7u0PfxFBJSb7P/\n9/L+bSAvkb9FqG7utOnz1jSzUSEhXW1Ceizv3wbykrT32gXBZBPStXqjADaSF9I/TUinKs4C\nWEheSMHuInvrjQLYSGBIJ5lD0od6swAWEhjSlSakp/RmASwkMKSHTEijm98MUJTAkOZyuVVE\nLoEhNewssr/eLICFBIYUnCBSskxtFsBCEkO6xJzbPas2C2AhiSHdZ0L6qdosgIUkhjTLhPR9\ntVkAC0kMaW0rkS+ozQJYSGJImS93KS1oB0COEhnS+ebcLvf/WkD+EhnSRBPS7VqzABYSGdJr\nJqSzm98MUJPIkOoqRA7VmgWwkMiQss82rFCaBbCQzJAuMud2U5VmASwkM6QHTUg3Ks0CWEhm\nSPNMSN9UmgWwkMyQGnYX2VNpFsBCMkMKeplDUnNfCwjoSWhI15mQJunMAlhIaEhPmZAu15kF\nsJDQkJaWiHTVmQWwkNCQggNFdmjuCuOAmqSGdKY5t5uuMgtgIakh3W5CulNlFsBCUkN61YQ0\nQGMUwEZSQ1pTKXKIyiyAhaSGFBzLxe0QocSGdKk5t3tGYxbAQmJDylxK/8caswAWEhvSuyak\n3hqzABYSG1LQVmQPhVEAG8kNqbc5JL2rMAtgodCQjpmwXG+YDTRC+rEJ6SGFWQALhYbUQirP\neGad3jyNNEJ6xoR0qcIsgIVCQ1oysWeZdBgxT2+iDI2QlpeKHKMwC2BB4THSx3f1KJOuv/xU\naaIMjZCCQ0Ra1hW+G8CCzpMNH93eWVoNnqsxUJZKSAPMud2rhe8GsKAS0upJfVtJdXmLEVoP\nllRCupMrgCMyCiG9eO5OUnnWC8Gi78gNSlOphDTdhHRm4bsBLBQa0ns3HChy5M8bnwM/qZ3S\nVCohrWklcmDhuwEsFBpSqex8wevr/8NtlRojBUohBV1FSpYo7AdoVqEhdfvV6o3/Ye5jhQ+U\npRPSFebc7g8K+wGaldy3CAXBoyakHyrsB2hWkkNaXMJLsohIkkMKviBS/pnGjoBmJDqkwebc\n7lmNHQHNSHRID5iQRmnsCGhGokP6pwnpRI0dAc1IdEjBviKtuXAxIpDskPrxvlVEI9kh3WVC\nukVlT0CoZIf0pgnpWyp7AkIlO6SG3UR2b1DZFRAm2SEF3zCHpLd1dgWESHhIY01Id+vsCgiR\n8JD+bkI6S2dXQIiEh5T5cF+Nzq6AEAkPKehhDknvKe0L2K6kh3SNCek3SvsCtivpIU0xIV2g\ntC9gu5Ie0qpykcOU9gVsV9JDCo7iCiiIQOJDusyc2z2utTNgOxIfEldAQRQSHxJXQEEUEh8S\nV0BBFJIfUuYKKM+p7Q3YpuSHxBVQEIHkh5S5Akp3tb0B25T8kIKOIhWr9HYHbEMKQso8SHpa\nb3fANqQgpN+ZkK7U2x2wDSkIaUmpSGe93QHbkIKQgiNEShcr7g/YShpCynzh2MOK+wO2koaQ\nnjIhna+4P2AraQjps5Z8KzMcS0NIwQnmkLRQc4fAFlIR0igT0j2aOwS2kIqQXjQh9dPcIbAF\nPyGtGB5+HWHlkOp3EmnLJcDhkJ+Q3pcnQv9eOaSgtzkkzVbdI7CZSEM6Z70z5GvnnBOyoXZI\nt5qQxqvuEdhMpCHJZkI21A5pllnuVNU9ApuJNKRhZZ2e/iTjLfntJ5+EbKgdUkM7kSq+TBbu\nRPsY6bUjSi/OJBL1Y6TgDHNIyv2/KGAr4icb6sdUdvijh5B+aUK6XneXwCYif9Zufk857cPI\nQ1rE583hlIenv+/dtc3YqEMKDuDz5nDJx+tIH50ukYd0njkk/Vl5n8AGfl6QffLyOaF/rx/S\nJK5cDJdS8V67oPHz5kcq7xPYIC0hBZ1FSj/U3inQxFdI83v23OKfNDw/ZYNL9EMabs7t7tPe\nKdDEV0gztnqL0ILKTd8/9KnCGpt5wez0e9o7BZr4Cql2dti7sR2c2tXvIrIz7xKCI6l5jBR8\nzxySXlDfK5AVdUgNC6ZMnjx1UTNbuQjpPhPScPW9AlnRhrR4WNvGh0DVo0LfZuAipI9L+X5z\nOBNpSB/USMcB14wdO7Jfe+m0PGRDFyEF/2UC/qf+boEg4pAGlT/UdGvtHSWXhGzoJKTrTEh3\n6e8WCCIOqd3ZG2+f1iFkQychvcrHZOFMpCFVjN54+7qKkA2dhLSunUjlav39AhGHVN1n4+3e\nNSEbOgkpGGgOSU852C8Q8TUbSm6ua7y1coRcFbKhm5Ay7wC/yMF+gWhDWt5ZqnoMHDqkf7dK\n6f5ZyIZuQlpRLrKfg/0CEb+OVDuuS2nmZaQWx91dH7adm5CC7mbpd1zsGKkX+VuE6uZOmz6v\nufe8OQrpJyakW1zsGKmXnvfaGW+akLb89AagIVUhBTUi5WHvqADylK6QLjCHpMlO9oyUS1dI\nT5iQznWyZ6RcukJa3UpkL74oCfrSFVLQyxySXneza6RaykK6nWuAw4mUhbTQhHSEm10j1VIW\nUnCkKWm+o30jxdIW0o9NSGMd7RsplraQ3jEhHeNo30ixtIUUfEGk5D1XO0dqpS6kkeaQdLur\nnSO1UhfS6yakHq52jtRKXUjB/iJlHznbO1IqfSFdbg5Jv3C2d6RU+kJ6yYTUy9nekVLpC6lh\nH5HyZc52j3RKX0jBEHNIetDd7pFKKQxpqgnpO+52j1RKYUhr9xBpFfplGECuUhhSMMgckn7v\ncP9IoTSG9EcTUj+H+0cKpTGkup1FqmodLoD0SWNIQT9zSPqTywWQOqkM6fcmpHNcLoDUSWVI\nq1qJ7N7cZZOBHKQypOA75pD0hNMVkDLpDOlhE9IZTldAyqQzpNpdRFp96nQJpEs6Q8q+Jnu/\n2yWQKikNKfN+u5PdLoFUSWlI6/YRKfuP2zWQJikNKbjCHJLGO14DKZLWkGaYkI5yvAZSJK0h\nBYfxxcxQlNqQRpuQrnW9CFIjtSEtKhHpyHeOQUlqQwq6mkPSK85XQUqkN6S7TEgXOV8FKZHe\nkJa2FNmj3vkySIf0hhR8wxySnnS/DFIhxSH9zoT0fffLIBVSHFLtziKtI1gHaZDikIKBvAUc\nWtIc0hQT0gkRrIMUSHNI62pMSXMiWAjJl+aQgutNSFdEsRASL9Uh/atMZPe6KFZC0qU6pKC3\nOSRNimQlJFy6Q/qDCelrkayEhEt3SPV7i5TMj2QpJFu6QwpGmEPSyGiWQqKlPKR3S0X24p2r\nKFjKQwpOMoekxyNaCwmW9pAy71w9NaK1kGBpD+nzPUXK3otoMSRX2kMKLjeHpB9HtRgSK/Uh\nvVMisu/aqFZDUqU+pKCbOSQ9HdlqSChCesCE9N3IVkNCEdLqNiIteLoBhSGkYJg5JA2Pbjkk\nEiEFC8tE2qyKbj0kESEFwbfMIemuCNdDAhFSEDxnQjqIy4CjEIRkHGFK+nOUCyJxCMm414TU\nK8oFkTiEZNS1EynhckIoACFlXGsOSRdEuiIShpAyPtpBpNWSSJdEshBSVn9zSPpJtEsiUQgp\n63UT0t5rol0TSUJIjU7gCncoBCE1esSEdHzEayJBCKnR2swF9f8R8aJIDkJq8lMT0reiXhSJ\nQUhNVuwiUjIr6lWRFIS03tXmkHRG5KsiIQhpvaVVImVzI18WyUBIG1xhDkmDol8WiUBIG3xY\nKVK+MPp1kQSEtNEQc0ga4mFdJAAhbfRehUjLf3tYGPFHSJsYxJczI0+EtIn5LURaf+xjZcQd\nIW3qDHNIutrLyog5byEtWxjyl75CeqtUZOdPvCyNeIs2pL+eUt1lfOPHfoaH7cVXSMG3zSFp\ntJ+lEWuRhjSjXFqVy/FLM7eLM6TXTEi7ckhCziIN6dvljzbUjSv/cub6wMUZUvB1U9JVntZG\njEUaUoezMn9Orei9rmhDesM8Sqp839PiiK9IQ9rhmuyP++Wyog0p+8Tdeb4WR2xFGtLB32j8\n+T9yS9GG9G6FSBkXi0SOIg1pWMnP6zM/GwbIFRcXaUjBheaQ1Nfb6oipSENavJ+cnL3RcLG5\nt4Zs6DOkj6pESl7xtjziKdrXkZYMvazp1iMdizWkYKSJ/Cv+lkcs8RahrXy6pylpir/1EUeE\ntLVbTEhd+OIx5IKQtvb5flx2FTnyFdL8nj23+CefDBm8QTevIWW/eOwgrgSOHPgKacZWz9ot\nOavvBl38hrT2UFPSrT4nQNz4Cql29uyQv/V7ahcEfzAh7fyh1xEQLzxG2qZTTEln+x0BsRJ1\nSA0LpkyePHVRM1t5D2lOuUjJ3/3OgDiJNqTFw9pKVvWoVWHbeQ8puCzzFPg6z0MgPiIN6YMa\n6TjgmrFjR/ZrL52Wh2zoP6RP9zIl/cLzEIiPSEMaVP5Q0621d5RcErKh/5CC+0xIu/H9zLAU\naUjtNnn8flqHkA2LIKSGbqaki3xPgbiINKSKTa4rcl1FyIZFEFLweplI2UzfUyAmIg2pus/G\n271rQjYshpCCweaQ1JW33MFKxB/su7mu8dbKEaGXGCmKkBbvakr6je8pEA+RhrS8s1T1GDh0\nSP9uldL9s5ANiyKk4OcmpD15vgE2on0dqXZcl9LMy0gtjru7Pmy74ghp7RFm1DN9T4FYiPwt\nQnVzp02f19w7q4sjpMwFLUUe8z0F4oD32oUZbkJqz4VX0TxCClP3RVPSYN9TIAYIKdTL5iFd\nyTO+p0DxI6RwF5lDUk2xDIPiRUjhPutoSrrU9xQoeoTUjKklIqV/8z0Fih0hNSfzDc1fWO17\nChQ5QmrOJ+1NSRf6ngJFjpCa9bjwsiyaQ0jNO8+E1Ka5y0wg3QipebWHm5JOWOt7DBQzQrLw\nZqUp6UbfU6CYEZKN2zLvWH/Z9xQoYoRko+EbpqT9wq57hJQjJCuL2/OFmAhDSHb+kvlA4j2+\np0DRIiRLmY8m7fCq7ylQrAjJ0pr/MiXtwzdUYNsIydYHmYsYH/e57zFQnAjJ2osVpqShvqdA\ncSIke5lXk+SXvqdAUSKkHJyTecLhH76nQDEipBzUHmVK2uvfvsdAESKkXLy3pympW53vMVB8\nCCknz2cuGXk63+SHLRFSbrJPOFzuewoUHULK0SWZkm71PQWKDSHlaF0fE1Lpw77HQJEhpFzV\nds08Cc4FurAZQsrZ0kNMSTvP8j0Gigoh5W5h5l13NbychE0QUh6mV5mSDv6P7zFQRAgpH1Mr\nKAmbIaS8PJD5wOzhfL8s1iOk/NybKakTJaEJIeXpnkxJRy7zPQaKBCHl6xclpqRjVvgeA8WB\nkPJ2a+bNQsdyTEIGIeVvbCj/PjsAAAwcSURBVKakw3g9CQEhFeTGTEn7zfM9BooAIRViXOZx\nUruZvseAf4RUkAcyH/Tb5a++x4B3hFSYxzPf+NJysu8x4BshFej5nUxJ5RN9jwHPCKlQ0zMX\nRJFL+EK/dCOkgs2tzpR0Ct+elGqEVLjF3TIlHfiO7zngESEpqOufKWnXZ33PAX8ISUPDDZkX\nlCru9D0HvCEkHb9vnTkonfGp7zngCSEpeWPfTEkH8S6HlCIkLR9kLtMllXztSzoRkpr6azOf\n9ZMzYzg6CkZIiv64W6akL7zmew5Ej5A0LTo2U1KLa9f4HgRRIyRVTad3X5rhexBEjJCUPd42\nU9IOY/kOpXQhJG0ffzdTknSd63sQRImQ9E3KPudQPrzW9yCIDiE58K9TsgelA5/xPQgiQ0gu\nNEysyqZ0+ge+J0FECMmNfzU+Utr5Np4JTwdCcmXqwdmUDprkexBEgZCcWf2jimxKPab7ngTu\nEZJDc76SLam0//u+J4FrhOTU5IOyKVVe9pHvSeAWIbm15mfZF5Wk9RWklGiE5Nonw3doTOli\nviozwQjJvXfPKsumtOMP/+V7FLhCSFFYMLgxpfK+fFYpoQgpGm+dnv18hZSc8hffo8AFQorK\nm6c1HpXkyHs+8z0L1BFSdN69uHVjSjsNnu17FigjpCgtHrVnY0olX32YN+ElCiFFa/WEQxpT\nkj0v5fPoCUJIUWuY2qe8qaVO4z70PQ2UEJIH/x61d1NKLXrfv8L3NNBASF7UP3rq+sPSDt98\nkCuGxx8h+fLRrZ1kfUvfvn+J73FQGELyaOalbde3VHbCzVx2KM4Iyau1U8/fY31LcvDlT6/2\nPRDyREi+rfvbxRuOS1J54phpDb4nQh4IqQjUP3fZARtakvbfv5uzvNghpCIx5yfHl22Maa8z\nJszhyBQnhFQ8lkwavO/GlqTqxGsfX+Z7JlgipOLy1rheO24SU1mncye89rnvodA8Qio69S/f\ndErVJjFJxZfPm/D3Vb7HQqioQ2pYMGXy5KmLmtkq1SFl1L/y02+32zQmKT2w7w1/mM+XxRSr\naENaPKzpmd7qUaH/D5v6kLLefXBo5/LNapLKI79/46Pv8AmM4hNpSB/USMcB14wdO7Jfe+m0\nPGRDQlqv9pU7zv5Si81rkhYHfv2yCVP/udb3cNgo0pAGlT/UdGvtHSWXhGxISJv57OW7zjt2\nR9lSxUG9hox79PWlvsdDEHFI7c7eePu0DiEbEtLW1s17+Nq+h5ZvlZNI1WG9Lxx9/3P/xxeb\neRRpSBWjN96+riJkQ0LanjVzHh79/aN22UZOxh5f6jVwxO2TX1rA1VUiF2lI1X023u5dE7Ih\nITXjo7/+8qq+XbbTk9H6gOO/df7I8b9+ZuZ7RBWJSEMaVnJzXeOtlSPkqpANCcnOkld/O3ZI\n78OqthtU9pm+fQ7v0Wfw8DETJ02ZNu9jXt11I9KQlneWqh4Dhw7p361Suof9PyUh5WbpzCfu\nHNG/x8GtQ4tq6mqvQ4468bsDL/rRmLvuf2TKP2YtWMIxS0G0ryPVjuuSveBoi+Purg/bjpDy\ntPLt5x8cd0X/Uw7fq6y5oDa1c7v9Ox11Yu++5wwe/qMx4ybeN+mxKS9Mm7ng3WXLeIrdUuRv\nEaqbO236vOZeUSSkgjV89NYLj9x5/cX9Tv5yTfipX3NHsDZt9t//i126fOXEE/v2PX3w4AuG\nD/+fMWPG/HzixP+dNGnSn6ZMmfLStGnTZi0wli5btiyt13LhvXZp8PmHb7/8pwdvv/7yc/uc\n+OUD96wsJCwrbTLa7p91RJeMo05sdErfJmcP3mD4JsZsbsLErdwzKcQTU/Lw4jR72/tCEUJK\no/plC2b89alJvxg/evh5A/qe1LVLx33abOsVKmyldMK2/5X6Cml+z55b/JOFbdts0Ep4s3Pk\nGpb9Z8Hsac9Nefh3EyeOGXPV8PMH9+t76olf6dLl4P33bdOmpe97cLE4dNv/9nyFNEO23Mva\nxzceoK8XnqUtPiuWLTMPhMzpjTkbemzSpF+b06xbzdnXSHNCdok5QTs3c8J2aub0rVv2ZO6A\n7Ild+8b/a/R999fTf9v/cnyFVDs77AsZXiKkZKpf1mTBBjM3Pv54ZfOHLr/f6hHQPVs/Ymp0\n5xh7o4YXYvx2LvRUnI+RCAkxU5wf7CMkxExxfrCPkBAzxfnBPkJCzBTnB/sICTFTnB/sIyTE\nTHF+sI+QEDPF+cE+QkLMFOcH+wgJMVOcH+wjJMRMcX6wj5AQM8X5wT5CQszwXjtAASEBCggJ\nUEBIgAJCAhQQEqCAkAAFhAQoKM6QXvN5mRggH6/lfDd3H1Iwc3sXujzlhAe8OoH1073+Kdu7\nZ87M/V4eQUjbNXCgx8VZn/U11yck1md9BYTE+qyvgJBYn/UVEBLrs74CQmJ91ldASKzP+goI\nifVZXwEhsT7rKyAk1md9BT5DGjzY4+Ksz/qa6/sMadkyj4uzPutrru8zJCAxCAlQQEiAAkIC\nFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJECBv5CWD6uu2Ouc/3hb\nf/Flh1RWf2eWt/Uzhsk5/hZ/qtuObU58wdvyCwcdsENN3zwuV1+4NVeVdmm8pXcn9BZSbWf5\n7g1nt9hviaf1l+xfcurVZ5VXvOhp/YzXyjyGdL8cOPKH7Vrm/k1AOmZV7XbtA6P3Lp8a/dJz\nOlc1haR4J/QW0jj5ifnzIbnM0/pD5efmz0ell6f1jfojDvcX0uKqIz8LggVVF3ha/zR51vw5\nS7pHvvKKyi/Pa9kYkuKd0FtIXapqMz86tm3ws/6wk+vNnw2tqv0snzGm9Gl/Id0if8788PRv\nPwiOlrrMj6qayFdeevmaoCkkxTuhr5DqSntkfw6QBZ4maByjvIu3tedXXvyJv5B6VdYHdSt8\nrR4EAyXz8HSxpzOCxpA074S+QporjRcVu0ameJog62cyztvaPTus9BhS9aGvH18i1ff4Wn/O\nLodPef/vX231ipfVG0PSvBP6CmmaDM3+vFke8TRBxvMVx3r7puh75YnAY0g7Vre9/OHb9pU7\nfQ3w5iEi0sHTcx2NIWneCX2HNFYme5rA+E3LLr6eNAw+2vW0wGdILeVB8+e/d9yt3s/6c6r3\nvfXxCV+q8nNCsnlIGndCXyHNk/7ZnyPFw/OfjRquka+v9LV4cHqbD72GtGtZ9sF+H/H0Stqx\nrReZPz/tsLeXU4LGkDTvhL5CWtOiW/ZnP1nkaYKGQTJsnae1g+BJGfv++++/JWe87+kBf5ey\nNZkfF4qfk6uVTc97n+kn5MaQNO+E3p7+PrbVKvPn2vbVvga4RG72tbRxuaw33M8AF0n2Yf7J\nstDL8h/L0dmf35FpPpZvevpb8U7oLaSJcrX58+cyytP6j3h7KThrzhMZv5WvPfG2nwGml/Q0\n53avlX7Rz/LB/hWZ/+JLd2t8JSdqTSEp3gm9hbSmq5x63eklnVZ5Wr+jXDw8y+eV3D0+RjLH\nxMN/dF4rH2/RyXq0dLcR997UUe6KfOXnzf/oZe3MH0s074T+3rS66srqin0u/sTX8htOrRb6\nmiDwG1LDxE4td+7l52WcjBe/uUdZm5P+FP3CN63/X36e5p2Qj1EACggJUEBIgAJCAhQQEqCA\nkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCA\nkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCA\nkOJpSskZmR+9Sv/mexJkEVJMnS9TguD3Msz3HGhESDG1subAulUdDlrtew40IqS4erbk2itK\nX/Y9BZoQUmxd2LL8h75nwHqEFFvTRWb7ngHrEVJcrTu27W7dGnxPgSaEFFc3y2/vlfG+p0AT\nQoqpuZX/HQQ9Wv2f7znQiJDiad2xrf9pamp5/DrfkyCLkOLppzIu8+N6ucX3JMgiJEABIQEK\nCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEK\nCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAX/D4ZLYV3DSZT3\nAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(x,y,type=\"l\",lwd=3)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "optional-compact",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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NKRkCLdzT7beV8tAPyTkCKNZSKN5lULAC5ISJEWM5Hu4FULAC4wTCR3bfSHMonO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\nIEukTyqRzaVbwmOfIglto9+cSZTl/Hufvm38yFebL0mkbdWIUuq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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot(x,y,type=\"l\",lwd=3, xlab=\"time\", cex.lab=1.5,cex.axis=1.5)\n",
"grid(lwd=3)"
]
},
{
"cell_type": "markdown",
"id": "herbal-drawing",
"metadata": {},
"source": [
"## Assignment \n",
"\n",
"- individual effort or collaboration by maximum two people \n",
"- if in collaboration, please specify the contribution of each contributor \n",
"- please turn in a set of .pdf and .ipynb files\n",
"- please label the question number before giving the answer\n",
"\n",
"Q1. Read in file \"./geodata/shp/point_stat.csv\" and output the rows that their values in the \"stdev\" column are less than those in their \"min\" column and their \"mean\" values are all greater than 7. (20%)\n",
"\n",
"\n",
"Q2. Create a 3x3 matrix with element values in the range of 1 to 9 and then change the diagonal elements to 0. (20%)\n",
"\n",
"```\n",
"1\t4\t7 0\t4\t7\n",
"2\t5\t8 ==> 2\t0\t8\n",
"3\t6\t9 3\t6\t0\n",
"```\n",
"\n",
"\n",
"Q3. Create a dataframe to store the calendar of March 2021 with the day of the week as the column name. (20%) \n",
"\n",
"```\n",
"Mo Tu We Th Fr Sa Su \n",
" 1 2 3 4 5 6 7 \n",
" 8 9 10 11 12 13 14 \n",
"15 16 17 18 19 20 21 \n",
"22 23 24 25 26 27 28 \n",
"29 30 31\n",
"```\n",
"QB (bonus) (10%)\n",
"\n",
"According to Gregorian calendar, leap years can be determined by the criteria below. \n",
"```\n",
"Years that are divisible by 4 and not divisible by 100 are leap years. \n",
"Years that are divisible by 100 but not divisible by 400 are NOT leap years. \n",
"Years that are divisible by 400 are leap years. \n",
"```\n",
"Please write a R script to print all the leap years between 1800 and 2020 into a file named \"leap_years.dat\" and calculate the ratio of the number of leap years over this period of time."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.6.3"
}
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"nbformat": 4,
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}