`seq`

is a standard generic with a
default method. `seq.int`

is a primitive which can be
much faster but has a few restrictions. `seq_along`

and
`seq_len`

are very fast primitives for two common cases.
```
seq(...)
"seq"(from = 1, to = 1, by = ((to - from)/(length.out - 1)), length.out = NULL, along.with = NULL, ...)
seq.int(from, to, by, length.out, along.with, ...)
seq_along(along.with)
seq_len(length.out)
```

...

arguments passed to or from methods.

from, to

the starting and (maximal) end values of the
sequence. Of length

`1`

unless just `from`

is supplied as
an unnamed argument.by

number: increment of the sequence.

length.out

desired length of the sequence. A
non-negative number, which for

`seq`

and `seq.int`

will be
rounded up if fractional.along.with

take the length from the length of this argument.

`seq.int`

and the default method of `seq`

for numeric
arguments return a vector of type `"integer"`

or `"double"`

:
programmers should not rely on which.`seq_along`

and `seq_len`

return an integer vector, unless
it is a `NaN`

or `NA`

). The interpretation of the unnamed arguments of `seq`

and
`seq.int`

is *not* standard, and it is recommended always to
name the arguments when programming.

`seq`

is generic, and only the default method is described here.
Note that it dispatches on the class of the **first** argument
irrespective of argument names. This can have unintended consequences
if it is called with just one argument intending this to be taken as
`along.with`

: it is much better to use `seg_along`

in that
case.

`seq.int`

is an internal generic which dispatches on
methods for `"seq"`

based on the class of the first supplied
argument (before argument matching).

Typical usages are

seq(from, to) seq(from, to, by= ) seq(from, to, length.out= ) seq(along.with= ) seq(from) seq(length.out= )The first form generates the sequence

`from, from+/-1, ..., to`

(identical to `from:to`

). The second form generates `from, from+by`

, ..., up to the
sequence value less than or equal to `to`

. Specifying ```
to -
from
```

and `by`

of opposite signs is an error. Note that the
computed final value can go just beyond `to`

to allow for
rounding error, but is truncated to `to`

. (‘Just beyond’
is by up to $1e-10$ times `abs(from - to)`

.)

The third generates a sequence of `length.out`

equally spaced
values from `from`

to `to`

. (`length.out`

is usually
abbreviated to `length`

or `len`

, and `seq_len`

is much
faster.)

The fourth form generates the integer sequence ```
1, 2, ...,
length(along.with)
```

. (`along.with`

is usually abbreviated to
`along`

, and `seq_along`

is much faster.)

The fifth form generates the sequence `1, 2, ..., length(from)`

(as if argument `along.with`

had been specified), *unless*
the argument is numeric of length 1 when it is interpreted as
`1:from`

(even for `seq(0)`

for compatibility with S).
Using either `seq_along`

or `seq_len`

is much preferred
(unless strict S compatibility is essential).

The final form generates the integer sequence ```
1, 2, ...,
length.out
```

unless `length.out = 0`

, when it generates
`integer(0)`

.

Very small sequences (with `from - to`

of the order of $10^{-14}$
times the larger of the ends) will return `from`

.

For `seq`

(only), up to two of `from`

, `to`

and
`by`

can be supplied as complex values provided `length.out`

or `along.with`

is specified. More generally, the default method
of `seq`

will handle classed objects with methods for
the `Math`

, `Ops`

and `Summary`

group generics.

`seq.int`

, `seq_along`

and `seq_len`

are
primitive.

`seq.Date`

and `seq.POSIXt`

.```
seq(0, 1, length.out = 11)
seq(stats::rnorm(20)) # effectively 'along'
seq(1, 9, by = 2) # matches 'end'
seq(1, 9, by = pi) # stays below 'end'
seq(1, 6, by = 3)
seq(1.575, 5.125, by = 0.05)
seq(17) # same as 1:17, or even better seq_len(17)
```

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