You're technically trying to index an uninitialized array. You have to first initialize the outer list with lists before adding items; Python calls this "list comprehension".

# Creates a list containing 5 lists, each of 8 items, all set to 0
w, h = 8, 5
Matrix = [[0 for x in range(w)] for y in range(h)] 

#You can now add items to the list:

Matrix[0][0] = 1
Matrix[6][0] = 3 # error! range... 
Matrix[0][6] = 3 # valid

Note that the matrix is "y" address major, in other words, the "y index" comes before the "x index".

print Matrix[0][0] # prints 1
x, y = 0, 6 
print Matrix[x][y] # prints 3; be careful with indexing! 

Although you can name them as you wish, I look at it this way to avoid some confusion that could arise with the indexing, if you use "x" for both the inner and outer lists, and want a non-square Matrix.

We need to cover at least these aspects to provide a comprehensive answer/comparison (in no particular order of importance): Speed, Memory usage, Syntax and Features.

My intent is to cover each one of these as clearly as possible from data.table perspective.

Note: unless explicitly mentioned otherwise, by referring to dplyr, we refer to dplyr's data.frame interface whose internals are in C++ using Rcpp.

The data.table syntax is consistent in its form - DT[i, j, by]. To keep i, j and by together is by design. By keeping related operations together, it allows to easily optimise operations for speed and more importantly memory usage, and also provide some powerful features, all while maintaining the consistency in syntax.

1. Speed

Quite a few benchmarks (though mostly on grouping operations) have been added to the question already showing data.table gets faster than dplyr as the number of groups and/or rows to group by increase, including benchmarks by Matt on grouping from 10 million to 2 billion rows (100GB in RAM) on 100 - 10 million groups and varying grouping columns, which also compares pandas. See also updated benchmarks, which include Spark and pydatatable as well.

On benchmarks, it would be great to cover these remaining aspects as well:

• Grouping operations involving a subset of rows - i.e., DT[x > val, sum(y), by = z] type operations.

• Benchmark other operations such as update and joins.

• Also benchmark memory footprint for each operation in addition to runtime.

2. Memory usage

1. Operations involving filter() or slice() in dplyr can be memory inefficient (on both data.frames and data.tables). See this post.

   Note that Hadley's comment talks about speed (that dplyr is plentiful fast for him), whereas the major concern here is memory.

2. data.table interface at the moment allows one to modify/update columns by reference (note that we don't need to re-assign the result back to a variable).

    # sub-assign by reference, updates 'y' in-place
    DT[x >= 1L, y := NA]
   

   But dplyr will never update by reference. The dplyr equivalent would be (note that the result needs to be re-assigned):

    # copies the entire 'y' column
    ans <- DF %>% mutate(y = replace(y, which(x >= 1L), NA))
   

   A concern for this is referential transparency. Updating a data.table object by reference, especially within a function may not be always desirable. But this is an incredibly useful feature: see this and this posts for interesting cases. And we want to keep it.

   Therefore we are working towards exporting shallow() function in data.table that will provide the user with both possibilities. For example, if it is desirable to not modify the input data.table within a function, one can then do:

    foo <- function(DT) {
        DT = shallow(DT)          ## shallow copy DT
        DT[, newcol := 1L]        ## does not affect the original DT 
        DT[x > 2L, newcol := 2L]  ## no need to copy (internally), as this column exists only in shallow copied DT
        DT[x > 2L, x := 3L]       ## have to copy (like base R / dplyr does always); otherwise original DT will 
                                  ## also get modified.
    }
   

   By not using shallow(), the old functionality is retained:

    bar <- function(DT) {
        DT[, newcol := 1L]        ## old behaviour, original DT gets updated by reference
        DT[x > 2L, x := 3L]       ## old behaviour, update column x in original DT.
    }
   

   By creating a shallow copy using shallow(), we understand that you don't want to modify the original object. We take care of everything internally to ensure that while also ensuring to copy columns you modify only when it is absolutely necessary. When implemented, this should settle the referential transparency issue altogether while providing the user with both possibilties.

   Also, once shallow() is exported dplyr's data.table interface should avoid almost all copies. So those who prefer dplyr's syntax can use it with data.tables.

   But it will still lack many features that data.table provides, including (sub)-assignment by reference.

3. Aggregate while joining:

   Suppose you have two data.tables as follows:

    DT1 = data.table(x=c(1,1,1,1,2,2,2,2), y=c("a", "a", "b", "b"), z=1:8, key=c("x", "y"))
    #    x y z
    # 1: 1 a 1
    # 2: 1 a 2
    # 3: 1 b 3
    # 4: 1 b 4
    # 5: 2 a 5
    # 6: 2 a 6
    # 7: 2 b 7
    # 8: 2 b 8
    DT2 = data.table(x=1:2, y=c("a", "b"), mul=4:3, key=c("x", "y"))
    #    x y mul
    # 1: 1 a   4
    # 2: 2 b   3
   

   And you would like to get sum(z) * mul for each row in DT2 while joining by columns x,y. We can either:

   • 1. aggregate DT1 to get sum(z), 2) perform a join and 3) multiply (or)

        data.table way

        DT1[, .(z = sum(z)), keyby = .(x,y)][DT2][, z := z*mul][]

        dplyr equivalent

        DF1 %>% group_by(x, y) %>% summarise(z = sum(z)) %>% right_join(DF2) %>% mutate(z = z * mul)

   • 2. do it all in one go (using by = .EACHI feature):

        DT1[DT2, list(z=sum(z) * mul), by = .EACHI]

   What is the advantage?

   • We don't have to allocate memory for the intermediate result.

   • We don't have to group/hash twice (one for aggregation and other for joining).

   • And more importantly, the operation what we wanted to perform is clear by looking at j in (2).

   Check this post for a detailed explanation of by = .EACHI. No intermediate results are materialised, and the join+aggregate is performed all in one go.

   Have a look at this, this and this posts for real usage scenarios.

   In dplyr you would have to join and aggregate or aggregate first and then join, neither of which are as efficient, in terms of memory (which in turn translates to speed).

4. Update and joins:

   Consider the data.table code shown below:

    DT1[DT2, col := i.mul]
   

   adds/updates DT1's column col with mul from DT2 on those rows where DT2's key column matches DT1. I don't think there is an exact equivalent of this operation in dplyr, i.e., without avoiding a *_join operation, which would have to copy the entire DT1 just to add a new column to it, which is unnecessary.

   Check this post for a real usage scenario.

To summarise, it is important to realise that every bit of optimisation matters. As Grace Hopper would say, Mind your nanoseconds!

3. Syntax

Let's now look at syntax. Hadley commented here:

Data tables are extremely fast but I think their concision makes it harder to learn and code that uses it is harder to read after you have written it ...

I find this remark pointless because it is very subjective. What we can perhaps try is to contrast consistency in syntax. We will compare data.table and dplyr syntax side-by-side.

We will work with the dummy data shown below:

DT = data.table(x=1:10, y=11:20, z=rep(1:2, each=5))
DF = as.data.frame(DT)

1. Basic aggregation/update operations.

    # case (a)
    DT[, sum(y), by = z]                       ## data.table syntax
    DF %>% group_by(z) %>% summarise(sum(y)) ## dplyr syntax
    DT[, y := cumsum(y), by = z]
    ans <- DF %>% group_by(z) %>% mutate(y = cumsum(y))
   
    # case (b)
    DT[x > 2, sum(y), by = z]
    DF %>% filter(x>2) %>% group_by(z) %>% summarise(sum(y))
    DT[x > 2, y := cumsum(y), by = z]
    ans <- DF %>% group_by(z) %>% mutate(y = replace(y, which(x > 2), cumsum(y)))
   
    # case (c)
    DT[, if(any(x > 5L)) y[1L]-y[2L] else y[2L], by = z]
    DF %>% group_by(z) %>% summarise(if (any(x > 5L)) y[1L] - y[2L] else y[2L])
    DT[, if(any(x > 5L)) y[1L] - y[2L], by = z]
    DF %>% group_by(z) %>% filter(any(x > 5L)) %>% summarise(y[1L] - y[2L])
   

   • data.table syntax is compact and dplyr's quite verbose. Things are more or less equivalent in case (a).

   • In case (b), we had to use filter() in dplyr while summarising. But while updating, we had to move the logic inside mutate(). In data.table however, we express both operations with the same logic - operate on rows where x > 2, but in first case, get sum(y), whereas in the second case update those rows for y with its cumulative sum.

     This is what we mean when we say the DT[i, j, by] form is consistent.

   • Similarly in case (c), when we have if-else condition, we are able to express the logic "as-is" in both data.table and dplyr. However, if we would like to return just those rows where the if condition satisfies and skip otherwise, we cannot use summarise() directly (AFAICT). We have to filter() first and then summarise because summarise() always expects a single value.

     While it returns the same result, using filter() here makes the actual operation less obvious.

     It might very well be possible to use filter() in the first case as well (does not seem obvious to me), but my point is that we should not have to.

2. Aggregation / update on multiple columns

    # case (a)
    DT[, lapply(.SD, sum), by = z]                     ## data.table syntax
    DF %>% group_by(z) %>% summarise_each(funs(sum)) ## dplyr syntax
    DT[, (cols) := lapply(.SD, sum), by = z]
    ans <- DF %>% group_by(z) %>% mutate_each(funs(sum))
   
    # case (b)
    DT[, c(lapply(.SD, sum), lapply(.SD, mean)), by = z]
    DF %>% group_by(z) %>% summarise_each(funs(sum, mean))
   
    # case (c)
    DT[, c(.N, lapply(.SD, sum)), by = z]     
    DF %>% group_by(z) %>% summarise_each(funs(n(), mean))
   

   • In case (a), the codes are more or less equivalent. data.table uses familiar base function lapply(), whereas dplyr introduces *_each() along with a bunch of functions to funs().

   • data.table's := requires column names to be provided, whereas dplyr generates it automatically.

   • In case (b), dplyr's syntax is relatively straightforward. Improving aggregations/updates on multiple functions is on data.table's list.

   • In case (c) though, dplyr would return n() as many times as many columns, instead of just once. In data.table, all we need to do is to return a list in j. Each element of the list will become a column in the result. So, we can use, once again, the familiar base function c() to concatenate .N to a list which returns a list.

   Note: Once again, in data.table, all we need to do is return a list in j. Each element of the list will become a column in result. You can use c(), as.list(), lapply(), list() etc... base functions to accomplish this, without having to learn any new functions.

   You will need to learn just the special variables - .N and .SD at least. The equivalent in dplyr are n() and .

3. Joins

   dplyr provides separate functions for each type of join where as data.table allows joins using the same syntax DT[i, j, by] (and with reason). It also provides an equivalent merge.data.table() function as an alternative.

    setkey(DT1, x, y)
   
    # 1. normal join
    DT1[DT2]            ## data.table syntax
    left_join(DT2, DT1) ## dplyr syntax
   
    # 2. select columns while join    
    DT1[DT2, .(z, i.mul)]
    left_join(select(DT2, x, y, mul), select(DT1, x, y, z))
   
    # 3. aggregate while join
    DT1[DT2, .(sum(z) * i.mul), by = .EACHI]
    DF1 %>% group_by(x, y) %>% summarise(z = sum(z)) %>% 
        inner_join(DF2) %>% mutate(z = z*mul) %>% select(-mul)
   
    # 4. update while join
    DT1[DT2, z := cumsum(z) * i.mul, by = .EACHI]
    ??
   
    # 5. rolling join
    DT1[DT2, roll = -Inf]
    ??
   
    # 6. other arguments to control output
    DT1[DT2, mult = "first"]
    ??
   

• Some might find a separate function for each joins much nicer (left, right, inner, anti, semi etc), whereas as others might like data.table's DT[i, j, by], or merge() which is similar to base R.

• However dplyr joins do just that. Nothing more. Nothing less.

• data.tables can select columns while joining (2), and in dplyr you will need to select() first on both data.frames before to join as shown above. Otherwise you would materialiase the join with unnecessary columns only to remove them later and that is inefficient.

• data.tables can aggregate while joining using by = .EACHI feature (3) and also update while joining (4). Why materialize the entire join result to add/update just a few columns?

• data.table is capable of rolling joins (5) - roll forward, LOCF, roll backward, NOCB, nearest.

• data.table also has mult = argument which selects first, last or all matches (6).

• data.table has allow.cartesian = TRUE argument to protect from accidental invalid joins.

Once again, the syntax is consistent with DT[i, j, by] with additional arguments allowing for controlling the output further.

4. do()...

   dplyr's summarise is specially designed for functions that return a single value. If your function returns multiple/unequal values, you will have to resort to do(). You have to know beforehand about all your functions return value.

    DT[, list(x[1], y[1]), by = z]                 ## data.table syntax
    DF %>% group_by(z) %>% summarise(x[1], y[1]) ## dplyr syntax
    DT[, list(x[1:2], y[1]), by = z]
    DF %>% group_by(z) %>% do(data.frame(.$x[1:2], .$y[1]))
   
    DT[, quantile(x, 0.25), by = z]
    DF %>% group_by(z) %>% summarise(quantile(x, 0.25))
    DT[, quantile(x, c(0.25, 0.75)), by = z]
    DF %>% group_by(z) %>% do(data.frame(quantile(.$x, c(0.25, 0.75))))
   
    DT[, as.list(summary(x)), by = z]
    DF %>% group_by(z) %>% do(data.frame(as.list(summary(.$x))))
   

• .SD's equivalent is .

• In data.table, you can throw pretty much anything in j - the only thing to remember is for it to return a list so that each element of the list gets converted to a column.

• In dplyr, cannot do that. Have to resort to do() depending on how sure you are as to whether your function would always return a single value. And it is quite slow.

Once again, data.table's syntax is consistent with DT[i, j, by]. We can just keep throwing expressions in j without having to worry about these things.

Have a look at this SO question and this one. I wonder if it would be possible to express the answer as straightforward using dplyr's syntax...

To summarise, I have particularly highlighted several instances where dplyr's syntax is either inefficient, limited or fails to make operations straightforward. This is particularly because data.table gets quite a bit of backlash about "harder to read/learn" syntax (like the one pasted/linked above). Most posts that cover dplyr talk about most straightforward operations. And that is great. But it is important to realise its syntax and feature limitations as well, and I am yet to see a post on it.

data.table has its quirks as well (some of which I have pointed out that we are attempting to fix). We are also attempting to improve data.table's joins as I have highlighted here.

But one should also consider the number of features that dplyr lacks in comparison to data.table.

4. Features

I have pointed out most of the features here and also in this post. In addition:

• fread - fast file reader has been available for a long time now.

• fwrite - a parallelised fast file writer is now available. See this post for a detailed explanation on the implementation and #1664 for keeping track of further developments.

• Automatic indexing - another handy feature to optimise base R syntax as is, internally.

• Ad-hoc grouping: dplyr automatically sorts the results by grouping variables during summarise(), which may not be always desirable.

• Numerous advantages in data.table joins (for speed / memory efficiency and syntax) mentioned above.

• Non-equi joins: Allows joins using other operators <=, <, >, >= along with all other advantages of data.table joins.

• Overlapping range joins was implemented in data.table recently. Check this post for an overview with benchmarks.

• setorder() function in data.table that allows really fast reordering of data.tables by reference.

• dplyr provides interface to databases using the same syntax, which data.table does not at the moment.

• data.table provides faster equivalents of set operations (written by Jan Gorecki) - fsetdiff, fintersect, funion and fsetequal with additional all argument (as in SQL).

• data.table loads cleanly with no masking warnings and has a mechanism described here for [.data.frame compatibility when passed to any R package. dplyr changes base functions filter, lag and [ which can cause problems; e.g. here and here.

Finally:

• On databases - there is no reason why data.table cannot provide similar interface, but this is not a priority now. It might get bumped up if users would very much like that feature.. not sure.

• On parallelism - Everything is difficult, until someone goes ahead and does it. Of course it will take effort (being thread safe).

  • Progress is being made currently (in v1.9.7 devel) towards parallelising known time consuming parts for incremental performance gains using OpenMP.