# Series Progression

Is there any package to determine series progression in R?
like Arithmatic progression,Geometric progression,Harmonic,fourier series..etc..

i want to know weather a vector say as
v<-1,2,3,4... is in arithmatic progression by differencing 1
like wise i want for all mathematic series ....

in other word i want to mine number pattern in R for large dataset.

I don't know whether there are any packages or not. But for AP, Gp or HP, this shouldn't be too difficult.

``````# defining functions to check AP, GP or HP
is_AP <- function(given_sequence)
{
successive_differences <- diff(x = given_sequence)
ifelse(test = (length(x = unique(x = successive_differences)) == 1),
yes = TRUE,
no = FALSE)
}

is_GP <- function(given_sequence)
{
successive_ratios <- sapply(X = 2:length(x = given_sequence),
FUN = function(t)
{
given_sequence[t] / given_sequence[t - 1]
})
ifelse(test = (length(x = unique(x = successive_ratios)) == 1),
yes = TRUE,
no = FALSE)
}

is_HP <- function(given_sequence)
{
reciprocal_sequence <- (1 / given_sequence)
is_AP(given_sequence = reciprocal_sequence)
}

# examples
ap_example <- seq(from = 1,
to = 19,
by = 2)
gp_example <- 2 ^ (1:10)
hp_example <- (1 / (1:10))

is_AP(ap_example)
#>  TRUE
is_GP(ap_example)
#>  FALSE
is_HP(ap_example)
#>  FALSE
is_AP(gp_example)
#>  FALSE
is_GP(gp_example)
#>  TRUE
is_HP(gp_example)
#>  FALSE
is_AP(hp_example)
#>  FALSE
is_GP(hp_example)
#>  FALSE
is_HP(hp_example)
#>  TRUE
``````

Created on 2019-02-09 by the reprex package (v0.2.1)

Obviously, we don't need to check all differences or ratios. You can modify suitably.

I don't think that real life datasets will represent such simple patterns. You'll need to plot and check for patterns visually.

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