Calculus notebook
ML Section
Mix.install([
{:axon, "~> 0.6.1"},
{:nx, "~> 0.7.3"},
{:exla, "~> 0.7.3"},
{:bumblebee, "~> 0.5.3"},
{:explorer, "~> 0.9.1"},
{:kino, "~> 0.13.2"},
{:kino_vega_lite, "~> 0.1.13"},
{:vega_lite, "~> 0.1.9"},
{:tucan, "~> 0.3.0"},
{:stb_image, "~> 0.6.9"},
{:benchee, "~> 1.3"},
{:ecto, "~> 3.12"}
],
config: [
nx: [
default_backend: EXLA.Backend,
default_defn_options: [compiler: EXLA]
]
]
)
alias VegaLite, as: Vl
x = Nx.linspace(-10, 10, n: 100_000)
y = Nx.add(Nx.add(Nx.pow(x, 2), Nx.multiply(2, x)), 2)
data = [ x: x, y: y ]
Tucan.lineplot(data, "x", "y", tooltip: true)
|> Tucan.set_title("Calculus Limits")
in_domain = fn (min, max) -> fn (x) -> x <= max && x >= min end end
flist_filter = fn (t, filter_pred) ->
t
|> Nx.to_flat_list()
|> Enum.filter(filter_pred)
end
[
x: flist_filter.(x, in_domain.(-2, 0)),
y: flist_filter.(y, in_domain.(0, 2))
]
|> Tucan.lineplot("x", "y", tooltip: true)
|> Tucan.set_title("Calculus Limits; (-2, 0), (0, 2)")
[
x: flist_filter.(x, in_domain.(-1.5, -0.5)),
y: flist_filter.(y, in_domain.(0.5, 1.5))
]
|> Tucan.lineplot("x", "y", tooltip: true)
|> Tucan.set_title("Calculus Limits; (-1.5, -0.5), (0.5, 1.5)")
[
x: flist_filter.(x, in_domain.(-1.1, -0.9)),
y: flist_filter.(y, in_domain.(0.9, 1.1))
]
|> Tucan.lineplot("x", "y", tooltip: true)
|> Tucan.set_title("Calculus Limits; (-1.1, -0.9), (0.9, 1.1)")
[
x: flist_filter.(x, in_domain.(-1.01, -0.99)),
y: flist_filter.(y, in_domain.(0.99, 1.01))
]
|> Tucan.lineplot("x", "y", tooltip: true)
|> Tucan.set_title("Calculus Limits; (-1.01, -0.99), (0.99, 1.01)")
defmodule Pkl.Limits do
def limit(1), do: :would_raise_div_by_zero
def limit(n) do
((n ** 2) - 1) / (n - 1)
end
end
Pkl.Limits.limit(2) |> IO.inspect()
Pkl.Limits.limit(0.9) |> IO.inspect()
Pkl.Limits.limit(0.999) |> IO.inspect()
Pkl.Limits.limit(0.999999999) |> IO.inspect()
Pkl.Limits.limit(1.1) |> IO.inspect()
Pkl.Limits.limit(1.01) |> IO.inspect()
Pkl.Limits.limit(1.0000000001) |> IO.inspect()
Pkl.Limits.limit(1)
UUID & Data Structure playground
"""
RFC 4122 A UUID URN Namespace July 2005
4.1.2. Layout and Byte Order
To minimize confusion about bit assignments within octets, the UUID
record definition is defined only in terms of fields that are
integral numbers of octets. The fields are presented with the most
significant one first.
Field Data Type Octet Note
#
time_low unsigned 32 0-3 The low field of the
bit integer timestamp
time_mid unsigned 16 4-5 The middle field of the
bit integer timestamp
time_hi_and_version unsigned 16 6-7 The high field of the
bit integer timestamp multiplexed
with the version number
clock_seq_hi_and_rese unsigned 8 8 The high field of the
rved bit integer clock sequence
multiplexed with the
variant
clock_seq_low unsigned 8 9 The low field of the
bit integer clock sequence
node unsigned 48 10-15 The spatially unique
bit integer node identifier
In the absence of explicit application or presentation protocol
specification to the contrary, a UUID is encoded as a 128-bit object,
as follows:
The fields are encoded as 16 octets, with the sizes and order of the
fields defined above, and with each field encoded with the Most
Significant Byte first (known as network byte order). Note that the
field names, particularly for multiplexed fields, follow historical
practice.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| time_low |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| time_mid | time_hi_and_version |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|clk_seq_hi_res | clk_seq_low | node (0-1) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| node (2-5) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
4.1.3. Version
The version number is in the most significant 4 bits of the time
stamp (bits 4 through 7 of the time_hi_and_version field).
The following table lists the currently-defined versions for this
UUID variant.
Msb0 Msb1 Msb2 Msb3 Version Description
0 0 0 1 1 The time-based version
specified in this document.
0 0 1 0 2 DCE Security version, with
embedded POSIX UIDs.
0 0 1 1 3 The name-based version
specified in this document
that uses MD5 hashing.
-> 0 1 0 0 4 The randomly or pseudo-
randomly generated version
specified in this document.
0 1 0 1 5 The name-based version
specified in this document
that uses SHA-1 hashing.
The version is more accurately a sub-type; again, we retain the term
for compatibility.
Leach, et al. Standards Track [Page 7]
"""
# V4 UUID alt implemention
defmodule Pkl.UUID do
@moduledoc """
[RFC-4122](https://datatracker.ietf.org/doc/html/rfc4122)
4.4. Algorithms for Creating a UUID from Truly Random or
Pseudo-Random Numbers
The version 4 UUID is meant for generating UUIDs from truly-random or
pseudo-random numbers.
The algorithm is as follows:
o Set the two most significant bits (bits 6 and 7) of the
clock_seq_hi_and_reserved to zero and one, respectively.
o Set the four most significant bits (bits 12 through 15) of the
time_hi_and_version field to the 4-bit version number from
Section 4.1.3.
o Set all the other bits to randomly (or pseudo-randomly) chosen
values.
"""
def gen_v4 do
{uuid, _} = for <>, reduce: {"", 0} do
{bits, write_idx} ->
out_str = case write_idx do
12 -> "-4" # 4bit '0 1 0 0 ' version :time_hi_and_version
16 -> "-2" # 4bit '0 0 1 0' :clock_seq_hi_and_reserved
i when i in [8, 20, 32] -> "-#{Integer.to_string(n, 16)}"
_ -> Integer.to_string(n, 16)
end
{Enum.join([bits, out_str]), write_idx + 1}
end
uuid
end
end
uuid = Pkl.UUID.gen_v4()
|> IO.inspect()
Ecto.UUID.cast(uuid)
