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library(TTR)

GetClosePrices=function(stocks, from=20090206, to=20140206){
  # Returns a dataframe whose columns correspond to 
  # the prices of stocks in the input parameter.
  #
  # stocks:  A character vector of ticker symbols  
  # from/to: Dates in YYYYMMDD format, from < to.
  df = xts()
  symbols=c()

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# Using the first two stocks, can solve analytically.

colnames(nyse_prices2)[1:2]
# "A"  "AA"

mu[1:2]
sigma[1:2,1:2]

v = c(-1,1)

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# 1a)

#########################################
# Functions for constructing the spline #
#########################################

# Cubic
f = function(x){
  c(1,x,x^2,x^3)
}

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# Problem 2

h_reimann=function(f,a,b,n){
  x = seq(a,b, length.out=n)
  dx = x[2]-x[1]
  sum(f(x)*dx)
}

h_trapezoid = function(f,a,b,n){
  x = seq(a,b, length.out=n)

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library(igraph)
library(Matrix)

Remap_Node_IDs = function(edgelist){
  # Given an edge list with N nodes, maps the given node ids
  # to values in the range 1-N, returns the converted edge list
  # and a vector whose indexes give the correspondence 
  # transformation
  flat   = sapply(edgelist,c)  
  raw_ids = unique(flat)

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# Problem 3

library(Matrix)
library(igraph)

PowerMethod2 = function(M,w,eps=1e-9){
  w = w/norm(w,type='F')
  last=0
  n=0
  while(norm(last-w, type='F')>eps){

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iris = read.csv('iris.txt', skip=60, header=FALSE)

X = iris[,-5]
Y = iris[,5]

########### Separating Hyperplane Loss Function ###########

Predict_Class=function(beta, X){
  # takes a vector of parameters beta and a design matrix X.
  # Returns a vector of {-1,1} classifications

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David Marx - Math 504 - HW 13
=================================

# Problem 1
  
a = c(
  9.681,0.667,
  9.400,2.041,
  8.025,9.152,
  2.196,0.415,