R/summer.R

In mlanier/summer: summer

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if (!require('pander')) {
  devtools::install_github('Rapporter/pander')
}

if (!require('stringr')) {
  install.packages('stringr')
}


if(!require('pracma')){
  install.packages('pracma')
}



library(pracma)
library(pander)
library(stringr)



devtools::use_package("pracma")
devtools::use_package("stringr")
devtools::use_package("pander")


summation_notation=function(i=1,n=10,formula)
{
  if(i>n)
  {print("It appears your bounds are mixed. i<n")
    return()}
  
  
  if(grepl("x+",toString(formula))==FALSE)
  {
    print("Your expression doesn't appear to be in terms of x. Please make sure it is only in terms of x.")
    
  }else{
    form=toString(str_replace_all(toString(formula), "x", "i"))
    
    
    sum=0
    
    for(j in i:n)
    {
      
      formula_temp=toString(str_replace_all(toString(form), "i", toString(j)))
      
      sum=sum+as.numeric(pander::evals(formula_temp)[[1]]$result)
      
      
    }
    
    return(sum)
  }
  
}



product_notation=function(i=1,n=10,formula)
{
  if(i>n)
  {print("It appears your bounds are mixed. i<n")
    return()}
  if(grepl("x+",toString(formula))==FALSE)
  {
    print("Your expression doesn't appear to be in terms of x. Please make sure it is only in terms of x.")
    
  }else{
    form=toString(str_replace_all(toString(formula), "x", "i"))
    product=1
    
    for(j in i:n)
    {
      
      formula_temp=toString(str_replace_all(toString(form), "i", toString(j)))
      
      product=product*as.numeric(pander::evals(formula_temp)[[1]]$result)
      
      
    }
    
    return(product)
  }
  
}



Zeta=function(s,fun=summation_notation)
{
  
  
  if(s<0)
  {
    B=-1*bernoulli(abs(s)+1)/(abs(s)+1)
    
    return(B[length(B)])
    
    
  }else{
    
    
    
    
    
    if(s==0)
    {
      return(-.5)
      
    }else{
      if(s==1)
      {
        print("Your series is divergent.")
        return()
        
      }else{
        if(round((1/.000000001)^(1/abs(s)))>1000)
        {num=700}else{num=round((1/.0000001)^(1/abs(s)))}
        
        Z=fun(i=1,n=num,formula=paste("1/x^",s))
        return(Z)
      }
    }
    
  }
  
}

#Complex exponentiation, Note that this is multivalued ie a^bi

c_Expo=function(a=1,b=1)
{
  if(a>0)
  {
    arg=cos(b*log(a))+complex(imaginary=1)*sin(b*log(a))
    return(arg)
  }else{
    if(a<0)
    {
      a=abs(a)
      arg=cos(log(a))+complex(imaginary=1)*sin(log(a))*exp(-1*pi)
      return(arg)
      
    }else{
      print("0 to the i is undefined")        
      
      
    }
    
  }
  
}


#We will attempt an implementations of a complex zeta function

c_Zeta=function(a,b,x_Expo)
{
  s=complex(real=a,imaginary=b)
  G=gammaz(s)^-1
  rand=runif(10000)
  num=(1/rand-1)^Re(s)*c_Expo(a=(1/rand-1),b=Im(s))*(1/rand-1)^-1
  den=rand^2*(exp((1/rand)-1)-1)
  value=G*mean(num/den)
  return(value)
  
}