1593039000

# Statistics for Data Science Part 1: Use of Central Tendency for Data Analysis.

## What is Central Tendency?

Central Tendency is the measure of very basic but very useful statistical functions that represents a central point or typical value of the dataset. It help’s in indicating the point value where the most value in the distribution falls referring to the central location of the distribution. The most common central tendency methods used for the analysis of numerical data are mean, median, and mode.

## Mean

The mean is the most common and well-known method for measuring central tendency and can be used to handle both discrete and continuous data. We can calculate mean as the sum of all the values in the dataset divided by the number of values in the dataset and is denoted as ‘µ’.

Mean is not often one of the actual values that you have observed in your data set but it is one of the most important properties as it minimizes the error to predict the value in any dataset. The reason behind having the lowest error is because it includes every value in your data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.

In the below image we can see the histogram for an array of values and then calculated the mean by summing all the values on the x-axis and just dividing by the number of values i.e 12.

However, the disadvantage of using the mean is that it is particularly susceptible to the influence of outliers. Outliners are the value that is very unusual as compared to the rest of the data, like making a particular value being very small or very large as compared to the rest. Focusing the case when our data is skewed or we can say that when the data is perfectly normal, the mean, median, and mode are identical. In this case, mean lose its ability to provide the best central location for the data because the skewed data is dragging it away from the typical value.

The below histogram shows the image with the skewed dataset and hence all the three mean median and mode will be approx equal to each other.

## Median

Median is the middle value of your observation when the values in the dataset are ordered from the smallest to the largest. If the number of values in the dataset is an odd number then the middle value is the median. But if you have odd number values in the dataset then in order to find median we just take the average of the two middle values.

The below histogram shows the relationship between the mean and mode if we have symmetric data.

#statistics #data-analysis #mean-median-mode #data-science #central-tendency

1653475560

## A Pure PHP Implementation Of The MessagePack Serialization Format

msgpack.php

A pure PHP implementation of the MessagePack serialization format.

## Installation

The recommended way to install the library is through Composer:

``````composer require rybakit/msgpack
``````

## Usage

### Packing

To pack values you can either use an instance of a `Packer`:

``````\$packer = new Packer();
\$packed = \$packer->pack(\$value);
``````

or call a static method on the `MessagePack` class:

``````\$packed = MessagePack::pack(\$value);
``````

In the examples above, the method `pack` automatically packs a value depending on its type. However, not all PHP types can be uniquely translated to MessagePack types. For example, the MessagePack format defines `map` and `array` types, which are represented by a single `array` type in PHP. By default, the packer will pack a PHP array as a MessagePack array if it has sequential numeric keys, starting from `0` and as a MessagePack map otherwise:

``````\$mpArr1 = \$packer->pack([1, 2]);               // MP array [1, 2]
\$mpArr2 = \$packer->pack([0 => 1, 1 => 2]);     // MP array [1, 2]
\$mpMap1 = \$packer->pack([0 => 1, 2 => 3]);     // MP map {0: 1, 2: 3}
\$mpMap2 = \$packer->pack([1 => 2, 2 => 3]);     // MP map {1: 2, 2: 3}
\$mpMap3 = \$packer->pack(['a' => 1, 'b' => 2]); // MP map {a: 1, b: 2}
``````

However, sometimes you need to pack a sequential array as a MessagePack map. To do this, use the `packMap` method:

``````\$mpMap = \$packer->packMap([1, 2]); // {0: 1, 1: 2}
``````

Here is a list of type-specific packing methods:

``````\$packer->packNil();           // MP nil
\$packer->packBool(true);      // MP bool
\$packer->packInt(42);         // MP int
\$packer->packFloat(M_PI);     // MP float (32 or 64)
\$packer->packFloat32(M_PI);   // MP float 32
\$packer->packFloat64(M_PI);   // MP float 64
\$packer->packStr('foo');      // MP str
\$packer->packBin("\x80");     // MP bin
\$packer->packArray([1, 2]);   // MP array
\$packer->packMap(['a' => 1]); // MP map
\$packer->packExt(1, "\xaa");  // MP ext
``````

Check the "Custom types" section below on how to pack custom types.

#### Packing options

The `Packer` object supports a number of bitmask-based options for fine-tuning the packing process (defaults are in bold):

The type detection mode (`DETECT_STR_BIN`/`DETECT_ARR_MAP`) adds some overhead which can be noticed when you pack large (16- and 32-bit) arrays or strings. However, if you know the value type in advance (for example, you only work with UTF-8 strings or/and associative arrays), you can eliminate this overhead by forcing the packer to use the appropriate type, which will save it from running the auto-detection routine. Another option is to explicitly specify the value type. The library provides 2 auxiliary classes for this, `Map` and `Bin`. Check the "Custom types" section below for details.

Examples:

``````// detect str/bin type and pack PHP 64-bit floats (doubles) to MP 32-bit floats
\$packer = new Packer(PackOptions::DETECT_STR_BIN | PackOptions::FORCE_FLOAT32);

// these will throw MessagePack\Exception\InvalidOptionException
\$packer = new Packer(PackOptions::FORCE_STR | PackOptions::FORCE_BIN);
\$packer = new Packer(PackOptions::FORCE_FLOAT32 | PackOptions::FORCE_FLOAT64);
``````

### Unpacking

To unpack data you can either use an instance of a `BufferUnpacker`:

``````\$unpacker = new BufferUnpacker();

\$unpacker->reset(\$packed);
\$value = \$unpacker->unpack();
``````

or call a static method on the `MessagePack` class:

``````\$value = MessagePack::unpack(\$packed);
``````

If the packed data is received in chunks (e.g. when reading from a stream), use the `tryUnpack` method, which attempts to unpack data and returns an array of unpacked messages (if any) instead of throwing an `InsufficientDataException`:

``````while (\$chunk = ...) {
\$unpacker->append(\$chunk);
if (\$messages = \$unpacker->tryUnpack()) {
return \$messages;
}
}
``````

If you want to unpack from a specific position in a buffer, use `seek`:

``````\$unpacker->seek(42); // set position equal to 42 bytes
\$unpacker->seek(-8); // set position to 8 bytes before the end of the buffer
``````

To skip bytes from the current position, use `skip`:

``````\$unpacker->skip(10); // set position to 10 bytes ahead of the current position
``````

To get the number of remaining (unread) bytes in the buffer:

``````\$unreadBytesCount = \$unpacker->getRemainingCount();
``````

To check whether the buffer has unread data:

``````\$hasUnreadBytes = \$unpacker->hasRemaining();
``````

If needed, you can remove already read data from the buffer by calling:

``````\$releasedBytesCount = \$unpacker->release();
``````

With the `read` method you can read raw (packed) data:

``````\$packedData = \$unpacker->read(2); // read 2 bytes
``````

Besides the above methods `BufferUnpacker` provides type-specific unpacking methods, namely:

``````\$unpacker->unpackNil();   // PHP null
\$unpacker->unpackBool();  // PHP bool
\$unpacker->unpackInt();   // PHP int
\$unpacker->unpackFloat(); // PHP float
\$unpacker->unpackStr();   // PHP UTF-8 string
\$unpacker->unpackBin();   // PHP binary string
\$unpacker->unpackArray(); // PHP sequential array
\$unpacker->unpackMap();   // PHP associative array
\$unpacker->unpackExt();   // PHP MessagePack\Type\Ext object
``````

#### Unpacking options

The `BufferUnpacker` object supports a number of bitmask-based options for fine-tuning the unpacking process (defaults are in bold):

1. The binary MessagePack format has unsigned 64-bit as its largest integer data type, but PHP does not support such integers, which means that an overflow can occur during unpacking.

2. Make sure the GMP extension is enabled.

3. Make sure the Decimal extension is enabled.

Examples:

``````\$packedUint64 = "\xcf"."\xff\xff\xff\xff"."\xff\xff\xff\xff";

\$unpacker = new BufferUnpacker(\$packedUint64);
var_dump(\$unpacker->unpack()); // string(20) "18446744073709551615"

\$unpacker = new BufferUnpacker(\$packedUint64, UnpackOptions::BIGINT_AS_GMP);
var_dump(\$unpacker->unpack()); // object(GMP) {...}

\$unpacker = new BufferUnpacker(\$packedUint64, UnpackOptions::BIGINT_AS_DEC);
var_dump(\$unpacker->unpack()); // object(Decimal\Decimal) {...}
``````

### Custom types

In addition to the basic types, the library provides functionality to serialize and deserialize arbitrary types. This can be done in several ways, depending on your use case. Let's take a look at them.

#### Type objects

If you need to serialize an instance of one of your classes into one of the basic MessagePack types, the best way to do this is to implement the CanBePacked interface in the class. A good example of such a class is the `Map` type class that comes with the library. This type is useful when you want to explicitly specify that a given PHP array should be packed as a MessagePack map without triggering an automatic type detection routine:

``````\$packer = new Packer();

\$packedMap = \$packer->pack(new Map([1, 2, 3]));
\$packedArray = \$packer->pack([1, 2, 3]);
``````

More type examples can be found in the src/Type directory.

#### Type transformers

As with type objects, type transformers are only responsible for serializing values. They should be used when you need to serialize a value that does not implement the CanBePacked interface. Examples of such values could be instances of built-in or third-party classes that you don't own, or non-objects such as resources.

A transformer class must implement the CanPack interface. To use a transformer, it must first be registered in the packer. Here is an example of how to serialize PHP streams into the MessagePack `bin` format type using one of the supplied transformers, `StreamTransformer`:

``````\$packer = new Packer(null, [new StreamTransformer()]);

\$packedBin = \$packer->pack(fopen('/path/to/file', 'r+'));
``````

More type transformer examples can be found in the src/TypeTransformer directory.

#### Extensions

In contrast to the cases described above, extensions are intended to handle extension types and are responsible for both serialization and deserialization of values (types).

An extension class must implement the Extension interface. To use an extension, it must first be registered in the packer and the unpacker.

The MessagePack specification divides extension types into two groups: predefined and application-specific. Currently, there is only one predefined type in the specification, Timestamp.

Timestamp

The Timestamp extension type is a predefined type. Support for this type in the library is done through the `TimestampExtension` class. This class is responsible for handling `Timestamp` objects, which represent the number of seconds and optional adjustment in nanoseconds:

``````\$timestampExtension = new TimestampExtension();

\$packer = new Packer();
\$packer = \$packer->extendWith(\$timestampExtension);

\$unpacker = new BufferUnpacker();
\$unpacker = \$unpacker->extendWith(\$timestampExtension);

\$packedTimestamp = \$packer->pack(Timestamp::now());
\$timestamp = \$unpacker->reset(\$packedTimestamp)->unpack();

\$seconds = \$timestamp->getSeconds();
\$nanoseconds = \$timestamp->getNanoseconds();
``````

When using the `MessagePack` class, the Timestamp extension is already registered:

``````\$packedTimestamp = MessagePack::pack(Timestamp::now());
\$timestamp = MessagePack::unpack(\$packedTimestamp);
``````

Application-specific extensions

In addition, the format can be extended with your own types. For example, to make the built-in PHP `DateTime` objects first-class citizens in your code, you can create a corresponding extension, as shown in the example. Please note, that custom extensions have to be registered with a unique extension ID (an integer from `0` to `127`).

More extension examples can be found in the examples/MessagePack directory.

## Exceptions

If an error occurs during packing/unpacking, a `PackingFailedException` or an `UnpackingFailedException` will be thrown, respectively. In addition, an `InsufficientDataException` can be thrown during unpacking.

An `InvalidOptionException` will be thrown in case an invalid option (or a combination of mutually exclusive options) is used.

## Tests

Run tests as follows:

``````vendor/bin/phpunit
``````

Also, if you already have Docker installed, you can run the tests in a docker container. First, create a container:

``````./dockerfile.sh | docker build -t msgpack -
``````

The command above will create a container named `msgpack` with PHP 8.1 runtime. You may change the default runtime by defining the `PHP_IMAGE` environment variable:

``````PHP_IMAGE='php:8.0-cli' ./dockerfile.sh | docker build -t msgpack -
``````

See a list of various images here.

Then run the unit tests:

``````docker run --rm -v \$PWD:/msgpack -w /msgpack msgpack
``````

#### Fuzzing

To ensure that the unpacking works correctly with malformed/semi-malformed data, you can use a testing technique called Fuzzing. The library ships with a help file (target) for PHP-Fuzzer and can be used as follows:

``````php-fuzzer fuzz tests/fuzz_buffer_unpacker.php
``````

#### Performance

To check performance, run:

``````php -n -dzend_extension=opcache.so \
-dpcre.jit=1 -dopcache.enable=1 -dopcache.enable_cli=1 \
tests/bench.php
``````

Example output

``````Filter: MessagePack\Tests\Perf\Filter\ListFilter
Rounds: 3
Iterations: 100000

=============================================
Test/Target            Packer  BufferUnpacker
---------------------------------------------
nil .................. 0.0030 ........ 0.0139
false ................ 0.0037 ........ 0.0144
true ................. 0.0040 ........ 0.0137
7-bit uint #1 ........ 0.0052 ........ 0.0120
7-bit uint #2 ........ 0.0059 ........ 0.0114
7-bit uint #3 ........ 0.0061 ........ 0.0119
5-bit sint #1 ........ 0.0067 ........ 0.0126
5-bit sint #2 ........ 0.0064 ........ 0.0132
5-bit sint #3 ........ 0.0066 ........ 0.0135
8-bit uint #1 ........ 0.0078 ........ 0.0200
8-bit uint #2 ........ 0.0077 ........ 0.0212
8-bit uint #3 ........ 0.0086 ........ 0.0203
16-bit uint #1 ....... 0.0111 ........ 0.0271
16-bit uint #2 ....... 0.0115 ........ 0.0260
16-bit uint #3 ....... 0.0103 ........ 0.0273
32-bit uint #1 ....... 0.0116 ........ 0.0326
32-bit uint #2 ....... 0.0118 ........ 0.0332
32-bit uint #3 ....... 0.0127 ........ 0.0325
64-bit uint #1 ....... 0.0140 ........ 0.0277
64-bit uint #2 ....... 0.0134 ........ 0.0294
64-bit uint #3 ....... 0.0134 ........ 0.0281
8-bit int #1 ......... 0.0086 ........ 0.0241
8-bit int #2 ......... 0.0089 ........ 0.0225
8-bit int #3 ......... 0.0085 ........ 0.0229
16-bit int #1 ........ 0.0118 ........ 0.0280
16-bit int #2 ........ 0.0121 ........ 0.0270
16-bit int #3 ........ 0.0109 ........ 0.0274
32-bit int #1 ........ 0.0128 ........ 0.0346
32-bit int #2 ........ 0.0118 ........ 0.0339
32-bit int #3 ........ 0.0135 ........ 0.0368
64-bit int #1 ........ 0.0138 ........ 0.0276
64-bit int #2 ........ 0.0132 ........ 0.0286
64-bit int #3 ........ 0.0137 ........ 0.0274
64-bit int #4 ........ 0.0180 ........ 0.0285
64-bit float #1 ...... 0.0134 ........ 0.0284
64-bit float #2 ...... 0.0125 ........ 0.0275
64-bit float #3 ...... 0.0126 ........ 0.0283
fix string #1 ........ 0.0035 ........ 0.0133
fix string #2 ........ 0.0094 ........ 0.0216
fix string #3 ........ 0.0094 ........ 0.0222
fix string #4 ........ 0.0091 ........ 0.0241
8-bit string #1 ...... 0.0122 ........ 0.0301
8-bit string #2 ...... 0.0118 ........ 0.0304
8-bit string #3 ...... 0.0119 ........ 0.0315
16-bit string #1 ..... 0.0150 ........ 0.0388
16-bit string #2 ..... 0.1545 ........ 0.1665
32-bit string ........ 0.1570 ........ 0.1756
wide char string #1 .. 0.0091 ........ 0.0236
wide char string #2 .. 0.0122 ........ 0.0313
8-bit binary #1 ...... 0.0100 ........ 0.0302
8-bit binary #2 ...... 0.0123 ........ 0.0324
8-bit binary #3 ...... 0.0126 ........ 0.0327
16-bit binary ........ 0.0168 ........ 0.0372
32-bit binary ........ 0.1588 ........ 0.1754
fix array #1 ......... 0.0042 ........ 0.0131
fix array #2 ......... 0.0294 ........ 0.0367
fix array #3 ......... 0.0412 ........ 0.0472
16-bit array #1 ...... 0.1378 ........ 0.1596
16-bit array #2 ........... S ............. S
32-bit array .............. S ............. S
complex array ........ 0.1865 ........ 0.2283
fix map #1 ........... 0.0725 ........ 0.1048
fix map #2 ........... 0.0319 ........ 0.0405
fix map #3 ........... 0.0356 ........ 0.0665
fix map #4 ........... 0.0465 ........ 0.0497
16-bit map #1 ........ 0.2540 ........ 0.3028
16-bit map #2 ............. S ............. S
32-bit map ................ S ............. S
complex map .......... 0.2372 ........ 0.2710
fixext 1 ............. 0.0283 ........ 0.0358
fixext 2 ............. 0.0291 ........ 0.0371
fixext 4 ............. 0.0302 ........ 0.0355
fixext 8 ............. 0.0288 ........ 0.0384
fixext 16 ............ 0.0293 ........ 0.0359
8-bit ext ............ 0.0302 ........ 0.0439
16-bit ext ........... 0.0334 ........ 0.0499
32-bit ext ........... 0.1845 ........ 0.1888
32-bit timestamp #1 .. 0.0337 ........ 0.0547
32-bit timestamp #2 .. 0.0335 ........ 0.0560
64-bit timestamp #1 .. 0.0371 ........ 0.0575
64-bit timestamp #2 .. 0.0374 ........ 0.0542
64-bit timestamp #3 .. 0.0356 ........ 0.0533
96-bit timestamp #1 .. 0.0362 ........ 0.0699
96-bit timestamp #2 .. 0.0381 ........ 0.0701
96-bit timestamp #3 .. 0.0367 ........ 0.0687
=============================================
Total                  2.7618          4.0820
Skipped                     4               4
Failed                      0               0
Ignored                     0               0
``````

With JIT:

``````php -n -dzend_extension=opcache.so \
-dpcre.jit=1 -dopcache.jit_buffer_size=64M -dopcache.jit=tracing -dopcache.enable=1 -dopcache.enable_cli=1 \
tests/bench.php
``````

Example output

``````Filter: MessagePack\Tests\Perf\Filter\ListFilter
Rounds: 3
Iterations: 100000

=============================================
Test/Target            Packer  BufferUnpacker
---------------------------------------------
nil .................. 0.0005 ........ 0.0054
false ................ 0.0004 ........ 0.0059
true ................. 0.0004 ........ 0.0059
7-bit uint #1 ........ 0.0010 ........ 0.0047
7-bit uint #2 ........ 0.0010 ........ 0.0046
7-bit uint #3 ........ 0.0010 ........ 0.0046
5-bit sint #1 ........ 0.0025 ........ 0.0046
5-bit sint #2 ........ 0.0023 ........ 0.0046
5-bit sint #3 ........ 0.0024 ........ 0.0045
8-bit uint #1 ........ 0.0043 ........ 0.0081
8-bit uint #2 ........ 0.0043 ........ 0.0079
8-bit uint #3 ........ 0.0041 ........ 0.0080
16-bit uint #1 ....... 0.0064 ........ 0.0095
16-bit uint #2 ....... 0.0064 ........ 0.0091
16-bit uint #3 ....... 0.0064 ........ 0.0094
32-bit uint #1 ....... 0.0085 ........ 0.0114
32-bit uint #2 ....... 0.0077 ........ 0.0122
32-bit uint #3 ....... 0.0077 ........ 0.0120
64-bit uint #1 ....... 0.0085 ........ 0.0159
64-bit uint #2 ....... 0.0086 ........ 0.0157
64-bit uint #3 ....... 0.0086 ........ 0.0158
8-bit int #1 ......... 0.0042 ........ 0.0080
8-bit int #2 ......... 0.0042 ........ 0.0080
8-bit int #3 ......... 0.0042 ........ 0.0081
16-bit int #1 ........ 0.0065 ........ 0.0095
16-bit int #2 ........ 0.0065 ........ 0.0090
16-bit int #3 ........ 0.0056 ........ 0.0085
32-bit int #1 ........ 0.0067 ........ 0.0107
32-bit int #2 ........ 0.0066 ........ 0.0106
32-bit int #3 ........ 0.0063 ........ 0.0104
64-bit int #1 ........ 0.0072 ........ 0.0162
64-bit int #2 ........ 0.0073 ........ 0.0174
64-bit int #3 ........ 0.0072 ........ 0.0164
64-bit int #4 ........ 0.0077 ........ 0.0161
64-bit float #1 ...... 0.0053 ........ 0.0135
64-bit float #2 ...... 0.0053 ........ 0.0135
64-bit float #3 ...... 0.0052 ........ 0.0135
fix string #1 ....... -0.0002 ........ 0.0044
fix string #2 ........ 0.0035 ........ 0.0067
fix string #3 ........ 0.0035 ........ 0.0077
fix string #4 ........ 0.0033 ........ 0.0078
8-bit string #1 ...... 0.0059 ........ 0.0110
8-bit string #2 ...... 0.0063 ........ 0.0121
8-bit string #3 ...... 0.0064 ........ 0.0124
16-bit string #1 ..... 0.0099 ........ 0.0146
16-bit string #2 ..... 0.1522 ........ 0.1474
32-bit string ........ 0.1511 ........ 0.1483
wide char string #1 .. 0.0039 ........ 0.0084
wide char string #2 .. 0.0073 ........ 0.0123
8-bit binary #1 ...... 0.0040 ........ 0.0112
8-bit binary #2 ...... 0.0075 ........ 0.0123
8-bit binary #3 ...... 0.0077 ........ 0.0129
16-bit binary ........ 0.0096 ........ 0.0145
32-bit binary ........ 0.1535 ........ 0.1479
fix array #1 ......... 0.0008 ........ 0.0061
fix array #2 ......... 0.0121 ........ 0.0165
fix array #3 ......... 0.0193 ........ 0.0222
16-bit array #1 ...... 0.0607 ........ 0.0479
16-bit array #2 ........... S ............. S
32-bit array .............. S ............. S
complex array ........ 0.0749 ........ 0.0824
fix map #1 ........... 0.0329 ........ 0.0431
fix map #2 ........... 0.0161 ........ 0.0189
fix map #3 ........... 0.0205 ........ 0.0262
fix map #4 ........... 0.0252 ........ 0.0205
16-bit map #1 ........ 0.1016 ........ 0.0927
16-bit map #2 ............. S ............. S
32-bit map ................ S ............. S
complex map .......... 0.1096 ........ 0.1030
fixext 1 ............. 0.0157 ........ 0.0161
fixext 2 ............. 0.0175 ........ 0.0183
fixext 4 ............. 0.0156 ........ 0.0185
fixext 8 ............. 0.0163 ........ 0.0184
fixext 16 ............ 0.0164 ........ 0.0182
8-bit ext ............ 0.0158 ........ 0.0207
16-bit ext ........... 0.0203 ........ 0.0219
32-bit ext ........... 0.1614 ........ 0.1539
32-bit timestamp #1 .. 0.0195 ........ 0.0249
32-bit timestamp #2 .. 0.0188 ........ 0.0260
64-bit timestamp #1 .. 0.0207 ........ 0.0281
64-bit timestamp #2 .. 0.0212 ........ 0.0291
64-bit timestamp #3 .. 0.0207 ........ 0.0295
96-bit timestamp #1 .. 0.0222 ........ 0.0358
96-bit timestamp #2 .. 0.0228 ........ 0.0353
96-bit timestamp #3 .. 0.0210 ........ 0.0319
=============================================
Total                  1.6432          1.9674
Skipped                     4               4
Failed                      0               0
Ignored                     0               0
``````

You may change default benchmark settings by defining the following environment variables:

For example:

``````export MP_BENCH_TARGETS=pure_p
export MP_BENCH_ITERATIONS=1000000
export MP_BENCH_ROUNDS=5
# a comma separated list of test names
export MP_BENCH_TESTS='complex array, complex map'
# or a group name
# export MP_BENCH_TESTS='-@slow' // @pecl_comp
# or a regexp
# export MP_BENCH_TESTS='/complex (array|map)/'
``````

Another example, benchmarking both the library and the PECL extension:

``````MP_BENCH_TARGETS=pure_p,pure_u,pecl_p,pecl_u \
php -n -dextension=msgpack.so -dzend_extension=opcache.so \
-dpcre.jit=1 -dopcache.enable=1 -dopcache.enable_cli=1 \
tests/bench.php
``````

Example output

``````Filter: MessagePack\Tests\Perf\Filter\ListFilter
Rounds: 3
Iterations: 100000

===========================================================================
Test/Target            Packer  BufferUnpacker  msgpack_pack  msgpack_unpack
---------------------------------------------------------------------------
nil .................. 0.0031 ........ 0.0141 ...... 0.0055 ........ 0.0064
false ................ 0.0039 ........ 0.0154 ...... 0.0056 ........ 0.0053
true ................. 0.0038 ........ 0.0139 ...... 0.0056 ........ 0.0044
7-bit uint #1 ........ 0.0061 ........ 0.0110 ...... 0.0059 ........ 0.0046
7-bit uint #2 ........ 0.0065 ........ 0.0119 ...... 0.0042 ........ 0.0029
7-bit uint #3 ........ 0.0054 ........ 0.0117 ...... 0.0045 ........ 0.0025
5-bit sint #1 ........ 0.0047 ........ 0.0103 ...... 0.0038 ........ 0.0022
5-bit sint #2 ........ 0.0048 ........ 0.0117 ...... 0.0038 ........ 0.0022
5-bit sint #3 ........ 0.0046 ........ 0.0102 ...... 0.0038 ........ 0.0023
8-bit uint #1 ........ 0.0063 ........ 0.0174 ...... 0.0039 ........ 0.0031
8-bit uint #2 ........ 0.0063 ........ 0.0167 ...... 0.0040 ........ 0.0029
8-bit uint #3 ........ 0.0063 ........ 0.0168 ...... 0.0039 ........ 0.0030
16-bit uint #1 ....... 0.0092 ........ 0.0222 ...... 0.0049 ........ 0.0030
16-bit uint #2 ....... 0.0096 ........ 0.0227 ...... 0.0042 ........ 0.0046
16-bit uint #3 ....... 0.0123 ........ 0.0274 ...... 0.0059 ........ 0.0051
32-bit uint #1 ....... 0.0136 ........ 0.0331 ...... 0.0060 ........ 0.0048
32-bit uint #2 ....... 0.0130 ........ 0.0336 ...... 0.0070 ........ 0.0048
32-bit uint #3 ....... 0.0127 ........ 0.0329 ...... 0.0051 ........ 0.0048
64-bit uint #1 ....... 0.0126 ........ 0.0268 ...... 0.0055 ........ 0.0049
64-bit uint #2 ....... 0.0135 ........ 0.0281 ...... 0.0052 ........ 0.0046
64-bit uint #3 ....... 0.0131 ........ 0.0274 ...... 0.0069 ........ 0.0044
8-bit int #1 ......... 0.0077 ........ 0.0236 ...... 0.0058 ........ 0.0044
8-bit int #2 ......... 0.0087 ........ 0.0244 ...... 0.0058 ........ 0.0048
8-bit int #3 ......... 0.0084 ........ 0.0241 ...... 0.0055 ........ 0.0049
16-bit int #1 ........ 0.0112 ........ 0.0271 ...... 0.0048 ........ 0.0045
16-bit int #2 ........ 0.0124 ........ 0.0292 ...... 0.0057 ........ 0.0049
16-bit int #3 ........ 0.0118 ........ 0.0270 ...... 0.0058 ........ 0.0050
32-bit int #1 ........ 0.0137 ........ 0.0366 ...... 0.0058 ........ 0.0051
32-bit int #2 ........ 0.0133 ........ 0.0366 ...... 0.0056 ........ 0.0049
32-bit int #3 ........ 0.0129 ........ 0.0350 ...... 0.0052 ........ 0.0048
64-bit int #1 ........ 0.0145 ........ 0.0254 ...... 0.0034 ........ 0.0025
64-bit int #2 ........ 0.0097 ........ 0.0214 ...... 0.0034 ........ 0.0025
64-bit int #3 ........ 0.0096 ........ 0.0287 ...... 0.0059 ........ 0.0050
64-bit int #4 ........ 0.0143 ........ 0.0277 ...... 0.0059 ........ 0.0046
64-bit float #1 ...... 0.0134 ........ 0.0281 ...... 0.0057 ........ 0.0052
64-bit float #2 ...... 0.0141 ........ 0.0281 ...... 0.0057 ........ 0.0050
64-bit float #3 ...... 0.0144 ........ 0.0282 ...... 0.0057 ........ 0.0050
fix string #1 ........ 0.0036 ........ 0.0143 ...... 0.0066 ........ 0.0053
fix string #2 ........ 0.0107 ........ 0.0222 ...... 0.0065 ........ 0.0068
fix string #3 ........ 0.0116 ........ 0.0245 ...... 0.0063 ........ 0.0069
fix string #4 ........ 0.0105 ........ 0.0253 ...... 0.0083 ........ 0.0077
8-bit string #1 ...... 0.0126 ........ 0.0318 ...... 0.0075 ........ 0.0088
8-bit string #2 ...... 0.0121 ........ 0.0295 ...... 0.0076 ........ 0.0086
8-bit string #3 ...... 0.0125 ........ 0.0293 ...... 0.0130 ........ 0.0093
16-bit string #1 ..... 0.0159 ........ 0.0368 ...... 0.0117 ........ 0.0086
16-bit string #2 ..... 0.1547 ........ 0.1686 ...... 0.1516 ........ 0.1373
32-bit string ........ 0.1558 ........ 0.1729 ...... 0.1511 ........ 0.1396
wide char string #1 .. 0.0098 ........ 0.0237 ...... 0.0066 ........ 0.0065
wide char string #2 .. 0.0128 ........ 0.0291 ...... 0.0061 ........ 0.0082
8-bit binary #1 ........... I ............. I ........... F ............. I
8-bit binary #2 ........... I ............. I ........... F ............. I
8-bit binary #3 ........... I ............. I ........... F ............. I
16-bit binary ............. I ............. I ........... F ............. I
32-bit binary ............. I ............. I ........... F ............. I
fix array #1 ......... 0.0040 ........ 0.0129 ...... 0.0120 ........ 0.0058
fix array #2 ......... 0.0279 ........ 0.0390 ...... 0.0143 ........ 0.0165
fix array #3 ......... 0.0415 ........ 0.0463 ...... 0.0162 ........ 0.0187
16-bit array #1 ...... 0.1349 ........ 0.1628 ...... 0.0334 ........ 0.0341
16-bit array #2 ........... S ............. S ........... S ............. S
32-bit array .............. S ............. S ........... S ............. S
complex array ............. I ............. I ........... F ............. F
fix map #1 ................ I ............. I ........... F ............. I
fix map #2 ........... 0.0345 ........ 0.0391 ...... 0.0143 ........ 0.0168
fix map #3 ................ I ............. I ........... F ............. I
fix map #4 ........... 0.0459 ........ 0.0473 ...... 0.0151 ........ 0.0163
16-bit map #1 ........ 0.2518 ........ 0.2962 ...... 0.0400 ........ 0.0490
16-bit map #2 ............. S ............. S ........... S ............. S
32-bit map ................ S ............. S ........... S ............. S
complex map .......... 0.2380 ........ 0.2682 ...... 0.0545 ........ 0.0579
fixext 1 .................. I ............. I ........... F ............. F
fixext 2 .................. I ............. I ........... F ............. F
fixext 4 .................. I ............. I ........... F ............. F
fixext 8 .................. I ............. I ........... F ............. F
fixext 16 ................. I ............. I ........... F ............. F
8-bit ext ................. I ............. I ........... F ............. F
16-bit ext ................ I ............. I ........... F ............. F
32-bit ext ................ I ............. I ........... F ............. F
32-bit timestamp #1 ....... I ............. I ........... F ............. F
32-bit timestamp #2 ....... I ............. I ........... F ............. F
64-bit timestamp #1 ....... I ............. I ........... F ............. F
64-bit timestamp #2 ....... I ............. I ........... F ............. F
64-bit timestamp #3 ....... I ............. I ........... F ............. F
96-bit timestamp #1 ....... I ............. I ........... F ............. F
96-bit timestamp #2 ....... I ............. I ........... F ............. F
96-bit timestamp #3 ....... I ............. I ........... F ............. F
===========================================================================
Total                  1.5625          2.3866        0.7735          0.7243
Skipped                     4               4             4               4
Failed                      0               0            24              17
Ignored                    24              24             0               7
``````

With JIT:

``````MP_BENCH_TARGETS=pure_p,pure_u,pecl_p,pecl_u \
php -n -dextension=msgpack.so -dzend_extension=opcache.so \
-dpcre.jit=1 -dopcache.jit_buffer_size=64M -dopcache.jit=tracing -dopcache.enable=1 -dopcache.enable_cli=1 \
tests/bench.php
``````

Example output

``````Filter: MessagePack\Tests\Perf\Filter\ListFilter
Rounds: 3
Iterations: 100000

===========================================================================
Test/Target            Packer  BufferUnpacker  msgpack_pack  msgpack_unpack
---------------------------------------------------------------------------
nil .................. 0.0001 ........ 0.0052 ...... 0.0053 ........ 0.0042
false ................ 0.0007 ........ 0.0060 ...... 0.0057 ........ 0.0043
true ................. 0.0008 ........ 0.0060 ...... 0.0056 ........ 0.0041
7-bit uint #1 ........ 0.0031 ........ 0.0046 ...... 0.0062 ........ 0.0041
7-bit uint #2 ........ 0.0021 ........ 0.0043 ...... 0.0062 ........ 0.0041
7-bit uint #3 ........ 0.0022 ........ 0.0044 ...... 0.0061 ........ 0.0040
5-bit sint #1 ........ 0.0030 ........ 0.0048 ...... 0.0062 ........ 0.0040
5-bit sint #2 ........ 0.0032 ........ 0.0046 ...... 0.0062 ........ 0.0040
5-bit sint #3 ........ 0.0031 ........ 0.0046 ...... 0.0062 ........ 0.0040
8-bit uint #1 ........ 0.0054 ........ 0.0079 ...... 0.0062 ........ 0.0050
8-bit uint #2 ........ 0.0051 ........ 0.0079 ...... 0.0064 ........ 0.0044
8-bit uint #3 ........ 0.0051 ........ 0.0082 ...... 0.0062 ........ 0.0044
16-bit uint #1 ....... 0.0077 ........ 0.0094 ...... 0.0065 ........ 0.0045
16-bit uint #2 ....... 0.0077 ........ 0.0094 ...... 0.0063 ........ 0.0045
16-bit uint #3 ....... 0.0077 ........ 0.0095 ...... 0.0064 ........ 0.0047
32-bit uint #1 ....... 0.0088 ........ 0.0119 ...... 0.0063 ........ 0.0043
32-bit uint #2 ....... 0.0089 ........ 0.0117 ...... 0.0062 ........ 0.0039
32-bit uint #3 ....... 0.0089 ........ 0.0118 ...... 0.0063 ........ 0.0044
64-bit uint #1 ....... 0.0097 ........ 0.0155 ...... 0.0063 ........ 0.0045
64-bit uint #2 ....... 0.0095 ........ 0.0153 ...... 0.0061 ........ 0.0045
64-bit uint #3 ....... 0.0096 ........ 0.0156 ...... 0.0063 ........ 0.0047
8-bit int #1 ......... 0.0053 ........ 0.0083 ...... 0.0062 ........ 0.0044
8-bit int #2 ......... 0.0052 ........ 0.0080 ...... 0.0062 ........ 0.0044
8-bit int #3 ......... 0.0052 ........ 0.0080 ...... 0.0062 ........ 0.0043
16-bit int #1 ........ 0.0089 ........ 0.0097 ...... 0.0069 ........ 0.0046
16-bit int #2 ........ 0.0075 ........ 0.0093 ...... 0.0063 ........ 0.0043
16-bit int #3 ........ 0.0075 ........ 0.0094 ...... 0.0062 ........ 0.0046
32-bit int #1 ........ 0.0086 ........ 0.0122 ...... 0.0063 ........ 0.0044
32-bit int #2 ........ 0.0087 ........ 0.0120 ...... 0.0066 ........ 0.0046
32-bit int #3 ........ 0.0086 ........ 0.0121 ...... 0.0060 ........ 0.0044
64-bit int #1 ........ 0.0096 ........ 0.0149 ...... 0.0060 ........ 0.0045
64-bit int #2 ........ 0.0096 ........ 0.0157 ...... 0.0062 ........ 0.0044
64-bit int #3 ........ 0.0096 ........ 0.0160 ...... 0.0063 ........ 0.0046
64-bit int #4 ........ 0.0097 ........ 0.0157 ...... 0.0061 ........ 0.0044
64-bit float #1 ...... 0.0079 ........ 0.0153 ...... 0.0056 ........ 0.0044
64-bit float #2 ...... 0.0079 ........ 0.0152 ...... 0.0057 ........ 0.0045
64-bit float #3 ...... 0.0079 ........ 0.0155 ...... 0.0057 ........ 0.0044
fix string #1 ........ 0.0010 ........ 0.0045 ...... 0.0071 ........ 0.0044
fix string #2 ........ 0.0048 ........ 0.0075 ...... 0.0070 ........ 0.0060
fix string #3 ........ 0.0048 ........ 0.0086 ...... 0.0068 ........ 0.0060
fix string #4 ........ 0.0050 ........ 0.0088 ...... 0.0070 ........ 0.0059
8-bit string #1 ...... 0.0081 ........ 0.0129 ...... 0.0069 ........ 0.0062
8-bit string #2 ...... 0.0086 ........ 0.0128 ...... 0.0069 ........ 0.0065
8-bit string #3 ...... 0.0086 ........ 0.0126 ...... 0.0115 ........ 0.0065
16-bit string #1 ..... 0.0105 ........ 0.0137 ...... 0.0128 ........ 0.0068
16-bit string #2 ..... 0.1510 ........ 0.1486 ...... 0.1526 ........ 0.1391
32-bit string ........ 0.1517 ........ 0.1475 ...... 0.1504 ........ 0.1370
wide char string #1 .. 0.0044 ........ 0.0085 ...... 0.0067 ........ 0.0057
wide char string #2 .. 0.0081 ........ 0.0125 ...... 0.0069 ........ 0.0063
8-bit binary #1 ........... I ............. I ........... F ............. I
8-bit binary #2 ........... I ............. I ........... F ............. I
8-bit binary #3 ........... I ............. I ........... F ............. I
16-bit binary ............. I ............. I ........... F ............. I
32-bit binary ............. I ............. I ........... F ............. I
fix array #1 ......... 0.0014 ........ 0.0059 ...... 0.0132 ........ 0.0055
fix array #2 ......... 0.0146 ........ 0.0156 ...... 0.0155 ........ 0.0148
fix array #3 ......... 0.0211 ........ 0.0229 ...... 0.0179 ........ 0.0180
16-bit array #1 ...... 0.0673 ........ 0.0498 ...... 0.0343 ........ 0.0388
16-bit array #2 ........... S ............. S ........... S ............. S
32-bit array .............. S ............. S ........... S ............. S
complex array ............. I ............. I ........... F ............. F
fix map #1 ................ I ............. I ........... F ............. I
fix map #2 ........... 0.0148 ........ 0.0180 ...... 0.0156 ........ 0.0179
fix map #3 ................ I ............. I ........... F ............. I
fix map #4 ........... 0.0252 ........ 0.0201 ...... 0.0214 ........ 0.0167
16-bit map #1 ........ 0.1027 ........ 0.0836 ...... 0.0388 ........ 0.0510
16-bit map #2 ............. S ............. S ........... S ............. S
32-bit map ................ S ............. S ........... S ............. S
complex map .......... 0.1104 ........ 0.1010 ...... 0.0556 ........ 0.0602
fixext 1 .................. I ............. I ........... F ............. F
fixext 2 .................. I ............. I ........... F ............. F
fixext 4 .................. I ............. I ........... F ............. F
fixext 8 .................. I ............. I ........... F ............. F
fixext 16 ................. I ............. I ........... F ............. F
8-bit ext ................. I ............. I ........... F ............. F
16-bit ext ................ I ............. I ........... F ............. F
32-bit ext ................ I ............. I ........... F ............. F
32-bit timestamp #1 ....... I ............. I ........... F ............. F
32-bit timestamp #2 ....... I ............. I ........... F ............. F
64-bit timestamp #1 ....... I ............. I ........... F ............. F
64-bit timestamp #2 ....... I ............. I ........... F ............. F
64-bit timestamp #3 ....... I ............. I ........... F ............. F
96-bit timestamp #1 ....... I ............. I ........... F ............. F
96-bit timestamp #2 ....... I ............. I ........... F ............. F
96-bit timestamp #3 ....... I ............. I ........... F ............. F
===========================================================================
Total                  0.9642          1.0909        0.8224          0.7213
Skipped                     4               4             4               4
Failed                      0               0            24              17
Ignored                    24              24             0               7
``````

Note that the msgpack extension (v2.1.2) doesn't support ext, bin and UTF-8 str types.

The library is released under the MIT License. See the bundled LICENSE file for details.

Author: rybakit
Source Code: https://github.com/rybakit/msgpack.php

1648641360

## Treebender

A symbolic natural language parsing library for Rust, inspired by HDPSG.

## What is this?

This is a library for parsing natural or constructed languages into syntax trees and feature structures. There's no machine learning or probabilistic models, everything is hand-crafted and deterministic.

You can find out more about the motivations of this project in this blog post.

### But what are you using it for?

I'm using this to parse a constructed language for my upcoming xenolinguistics game, Themengi.

## Motivation

Using a simple 80-line grammar, introduced in the tutorial below, we can parse a simple subset of English, checking reflexive pronoun binding, case, and number agreement.

``````\$ cargo run --bin cli examples/reflexives.fgr
> she likes himself
Parsed 0 trees

> her likes herself
Parsed 0 trees

> she like herself
Parsed 0 trees

> she likes herself
Parsed 1 tree
(0..3: S
(0..1: N (0..1: she))
(1..2: TV (1..2: likes))
(2..3: N (2..3: herself)))
[
child-2: [
case: acc
pron: ref
needs_pron: #0 she
num: sg
child-0: [ word: herself ]
]
child-1: [
tense: nonpast
child-0: [ word: likes ]
num: #1 sg
]
child-0: [
child-0: [ word: she ]
case: nom
pron: #0
num: #1
]
]
``````

Low resource language? Low problem! No need to train on gigabytes of text, just write a grammar using your brain. Let's hypothesize that in American Sign Language, topicalized nouns (expressed with raised eyebrows) must appear first in the sentence. We can write a small grammar (18 lines), and plug in some sentences:

``````\$ cargo run --bin cli examples/asl-wordorder.fgr -n
> boy sit
Parsed 1 tree
(0..2: S
(0..1: NP ((0..1: N (0..1: boy))))
(1..2: IV (1..2: sit)))

> boy throw ball
Parsed 1 tree
(0..3: S
(0..1: NP ((0..1: N (0..1: boy))))
(1..2: TV (1..2: throw))
(2..3: NP ((2..3: N (2..3: ball)))))

> ball nm-raised-eyebrows boy throw
Parsed 1 tree
(0..4: S
(0..2: NP
(0..1: N (0..1: ball))
(1..2: Topic (1..2: nm-raised-eyebrows)))
(2..3: NP ((2..3: N (2..3: boy))))
(3..4: TV (3..4: throw)))

> boy throw ball nm-raised-eyebrows
Parsed 0 trees
``````

## Tutorial

As an example, let's say we want to build a parser for English reflexive pronouns (himself, herself, themselves, themself, itself). We'll also support number ("He likes X" v.s. "They like X") and simple embedded clauses ("He said that they like X").

Grammar files are written in a custom language, similar to BNF, called Feature GRammar (.fgr). There's a VSCode syntax highlighting extension for these files available as `fgr-syntax`.

We'll start by defining our lexicon. The lexicon is the set of terminal symbols (symbols in the actual input) that the grammar will match. Terminal symbols must start with a lowercase letter, and non-terminal symbols must start with an uppercase letter.

``````// pronouns
N -> he
N -> him
N -> himself
N -> she
N -> her
N -> herself
N -> they
N -> them
N -> themselves
N -> themself

// names, lowercase as they are terminals
N -> mary
N -> sue
N -> takeshi
N -> robert

// complementizer
Comp -> that

// verbs -- intransitive, transitive, and clausal
IV -> falls
IV -> fall
IV -> fell

TV -> likes
TV -> like
TV -> liked

CV -> says
CV -> say
CV -> said
``````

Next, we can add our sentence rules (they must be added at the top, as the first rule in the file is assumed to be the top-level rule):

``````// sentence rules
S -> N IV
S -> N TV N
S -> N CV Comp S

// ... previous lexicon ...
``````

Assuming this file is saved as `examples/no-features.fgr` (which it is :wink:), we can test this file with the built-in CLI:

``````\$ cargo run --bin cli examples/no-features.fgr
> he falls
Parsed 1 tree
(0..2: S
(0..1: N (0..1: he))
(1..2: IV (1..2: falls)))
[
child-1: [ child-0: [ word: falls ] ]
child-0: [ child-0: [ word: he ] ]
]

> he falls her
Parsed 0 trees

> he likes her
Parsed 1 tree
(0..3: S
(0..1: N (0..1: he))
(1..2: TV (1..2: likes))
(2..3: N (2..3: her)))
[
child-2: [ child-0: [ word: her ] ]
child-1: [ child-0: [ word: likes ] ]
child-0: [ child-0: [ word: he ] ]
]

> he likes
Parsed 0 trees

> he said that he likes her
Parsed 1 tree
(0..6: S
(0..1: N (0..1: he))
(1..2: CV (1..2: said))
(2..3: Comp (2..3: that))
(3..6: S
(3..4: N (3..4: he))
(4..5: TV (4..5: likes))
(5..6: N (5..6: her))))
[
child-0: [ child-0: [ word: he ] ]
child-2: [ child-0: [ word: that ] ]
child-1: [ child-0: [ word: said ] ]
child-3: [
child-2: [ child-0: [ word: her ] ]
child-1: [ child-0: [ word: likes ] ]
child-0: [ child-0: [ word: he ] ]
]
]

> he said that he
Parsed 0 trees
``````

This grammar already parses some correct sentences, and blocks some trivially incorrect ones. However, it doesn't care about number, case, or reflexives right now:

``````> she likes himself  // unbound reflexive pronoun
Parsed 1 tree
(0..3: S
(0..1: N (0..1: she))
(1..2: TV (1..2: likes))
(2..3: N (2..3: himself)))
[
child-0: [ child-0: [ word: she ] ]
child-2: [ child-0: [ word: himself ] ]
child-1: [ child-0: [ word: likes ] ]
]

> him like her  // incorrect case on the subject pronoun, should be nominative
// (he) instead of accusative (him)
Parsed 1 tree
(0..3: S
(0..1: N (0..1: him))
(1..2: TV (1..2: like))
(2..3: N (2..3: her)))
[
child-0: [ child-0: [ word: him ] ]
child-1: [ child-0: [ word: like ] ]
child-2: [ child-0: [ word: her ] ]
]

> he like her  // incorrect verb number agreement
Parsed 1 tree
(0..3: S
(0..1: N (0..1: he))
(1..2: TV (1..2: like))
(2..3: N (2..3: her)))
[
child-2: [ child-0: [ word: her ] ]
child-1: [ child-0: [ word: like ] ]
child-0: [ child-0: [ word: he ] ]
]
``````

To fix this, we need to add features to our lexicon, and restrict the sentence rules based on features.

Features are added with square brackets, and are key: value pairs separated by commas. `**top**` is a special feature value, which basically means "unspecified" -- we'll come back to it later. Features that are unspecified are also assumed to have a `**top**` value, but sometimes explicitly stating top is more clear.

``````/// Pronouns
// The added features are:
// * num: sg or pl, whether this noun wants a singular verb (likes) or
//   a plural verb (like). note this is grammatical number, so for example
//   singular they takes plural agreement ("they like X", not *"they likes X")
// * case: nom or acc, whether this noun is nominative or accusative case.
//   nominative case goes in the subject, and accusative in the object.
//   e.g., "he fell" and "she likes him", not *"him fell" and *"her likes he"
// * pron: he, she, they, or ref -- what type of pronoun this is
// * needs_pron: whether this is a reflexive that needs to bind to another
//   pronoun.
N[ num: sg, case: nom, pron: he ]                    -> he
N[ num: sg, case: acc, pron: he ]                    -> him
N[ num: sg, case: acc, pron: ref, needs_pron: he ]   -> himself
N[ num: sg, case: nom, pron: she ]                   -> she
N[ num: sg, case: acc, pron: she ]                   -> her
N[ num: sg, case: acc, pron: ref, needs_pron: she]   -> herself
N[ num: pl, case: nom, pron: they ]                  -> they
N[ num: pl, case: acc, pron: they ]                  -> them
N[ num: pl, case: acc, pron: ref, needs_pron: they ] -> themselves
N[ num: sg, case: acc, pron: ref, needs_pron: they ] -> themself

// Names
// The added features are:
// * num: sg, as people are singular ("mary likes her" / *"mary like her")
// * case: **top**, as names can be both subjects and objects
//   ("mary likes her" / "she likes mary")
// * pron: whichever pronoun the person uses for reflexive agreement
//   mary    pron: she  => mary likes herself
//   sue     pron: they => sue likes themself
//   takeshi pron: he   => takeshi likes himself
N[ num: sg, case: **top**, pron: she ]  -> mary
N[ num: sg, case: **top**, pron: they ] -> sue
N[ num: sg, case: **top**, pron: he ]   -> takeshi
N[ num: sg, case: **top**, pron: he ]   -> robert

// Complementizer doesn't need features
Comp -> that

// Verbs -- intransitive, transitive, and clausal
// The added features are:
// * num: sg, pl, or **top** -- to match the noun numbers.
//   **top** will match either sg or pl, as past-tense verbs in English
//   don't agree in number: "he fell" and "they fell" are both fine
// * tense: past or nonpast -- this won't be used for agreement, but will be
//   copied into the final feature structure, and the client code could do
//   something with it
IV[ num:      sg, tense: nonpast ] -> falls
IV[ num:      pl, tense: nonpast ] -> fall
IV[ num: **top**, tense: past ]    -> fell

TV[ num:      sg, tense: nonpast ] -> likes
TV[ num:      pl, tense: nonpast ] -> like
TV[ num: **top**, tense: past ]    -> liked

CV[ num:      sg, tense: nonpast ] -> says
CV[ num:      pl, tense: nonpast ] -> say
CV[ num: **top**, tense: past ]    -> said
``````

Now that our lexicon is updated with features, we can update our sentence rules to constrain parsing based on those features. This uses two new features, tags and unification. Tags allow features to be associated between nodes in a rule, and unification controls how those features are compatible. The rules for unification are:

1. A string feature can unify with a string feature with the same value
2. A top feature can unify with anything, and the nodes are merged
3. A complex feature ([ ... ] structure) is recursively unified with another complex feature.

If unification fails anywhere, the parse is aborted and the tree is discarded. This allows the programmer to discard trees if features don't match.

``````// Sentence rules
// Intransitive verb:
// * Subject must be nominative case
// * Subject and verb must agree in number (copied through #1)
S -> N[ case: nom, num: #1 ] IV[ num: #1 ]
// Transitive verb:
// * Subject must be nominative case
// * Subject and verb must agree in number (copied through #2)
// * If there's a reflexive in the object position, make sure its `needs_pron`
//   feature matches the subject's `pron` feature. If the object isn't a
//   reflexive, then its `needs_pron` feature will implicitly be `**top**`, so
//   will unify with anything.
S -> N[ case: nom, pron: #1, num: #2 ] TV[ num: #2 ] N[ case: acc, needs_pron: #1 ]
// Clausal verb:
// * Subject must be nominative case
// * Subject and verb must agree in number (copied through #1)
// * Reflexives can't cross clause boundaries (*"He said that she likes himself"),
//   so we can ignore reflexives and delegate to inner clause rule
S -> N[ case: nom, num: #1 ] CV[ num: #1 ] Comp S
``````

Now that we have this augmented grammar (available as `examples/reflexives.fgr`), we can try it out and see that it rejects illicit sentences that were previously accepted, while still accepting valid ones:

``````> he fell
Parsed 1 tree
(0..2: S
(0..1: N (0..1: he))
(1..2: IV (1..2: fell)))
[
child-1: [
child-0: [ word: fell ]
num: #0 sg
tense: past
]
child-0: [
pron: he
case: nom
num: #0
child-0: [ word: he ]
]
]

> he like him
Parsed 0 trees

> he likes himself
Parsed 1 tree
(0..3: S
(0..1: N (0..1: he))
(1..2: TV (1..2: likes))
(2..3: N (2..3: himself)))
[
child-1: [
num: #0 sg
child-0: [ word: likes ]
tense: nonpast
]
child-2: [
needs_pron: #1 he
num: sg
child-0: [ word: himself ]
pron: ref
case: acc
]
child-0: [
child-0: [ word: he ]
pron: #1
num: #0
case: nom
]
]

> he likes herself
Parsed 0 trees

> mary likes herself
Parsed 1 tree
(0..3: S
(0..1: N (0..1: mary))
(1..2: TV (1..2: likes))
(2..3: N (2..3: herself)))
[
child-0: [
pron: #0 she
num: #1 sg
case: nom
child-0: [ word: mary ]
]
child-1: [
tense: nonpast
child-0: [ word: likes ]
num: #1
]
child-2: [
child-0: [ word: herself ]
num: sg
pron: ref
case: acc
needs_pron: #0
]
]

> mary likes themself
Parsed 0 trees

> sue likes themself
Parsed 1 tree
(0..3: S
(0..1: N (0..1: sue))
(1..2: TV (1..2: likes))
(2..3: N (2..3: themself)))
[
child-0: [
pron: #0 they
child-0: [ word: sue ]
case: nom
num: #1 sg
]
child-1: [
tense: nonpast
num: #1
child-0: [ word: likes ]
]
child-2: [
needs_pron: #0
case: acc
pron: ref
child-0: [ word: themself ]
num: sg
]
]

> sue likes himself
Parsed 0 trees
``````

If this is interesting to you and you want to learn more, you can check out my blog series, the excellent textbook Syntactic Theory: A Formal Introduction (2nd ed.), and the DELPH-IN project, whose work on the LKB inspired this simplified version.

## Using from code

I need to write this section in more detail, but if you're comfortable with Rust, I suggest looking through the codebase. It's not perfect, it started as one of my first Rust projects (after migrating through F# -> TypeScript -> C in search of the right performance/ergonomics tradeoff), and it could use more tests, but overall it's not too bad.

Basically, the processing pipeline is:

1. Make a `Grammar` struct
• `Grammar` is defined in `rules.rs`.
• The easiest way to make a `Grammar` is `Grammar::parse_from_file`, which is mostly a hand-written recusive descent parser in `parse_grammar.rs`. Yes, I recognize the irony here.
1. It takes input (in `Grammar::parse`, which does everything for you, or `Grammar::parse_chart`, which just does the chart)
2. The input is first chart-parsed in `earley.rs`
3. Then, a forest is built from the chart, in `forest.rs`, using an algorithm I found in a very useful blog series I forget the URL for, because the algorithms in the academic literature for this are... weird.
4. Finally, the feature unification is used to prune the forest down to only valid trees. It would be more efficient to do this during parsing, but meh.

The most interesting thing you can do via code and not via the CLI is probably getting at the raw feature DAG, as that would let you do things like pronoun coreference. The DAG code is in `featurestructure.rs`, and should be fairly approachable -- there's a lot of Rust ceremony around `Rc<RefCell<...>>` because using an arena allocation crate seemed too harlike overkill, but that is somewhat mitigated by the `NodeRef` type alias. Hit me up at https://vgel.me/contact if you need help with anything here!

Author: vgel
Source Code: https://github.com/vgel/treebender

1667488080

## Py-rouge

A full Python implementation of the ROUGE metric, producing same results as in the official perl implementation.

Important remarks

• The original Porter stemmer in NLTK is slightly different than the one use in the official ROUGE perl script as it has been written by end. Therefore, there might be slightly different stems for certain words. For DUC2004 dataset, I have identified these words and this script produces same stems.
• The official ROUGE perl script use resampling strategy to compute the average with confidence intervals. Therefore, we might have a difference `<3e-5` for ROUGE-L as well as ROUGE-W and `<4e-5` for ROUGE-N.
• Finally, ROUGE-1.5.5. has a bug: should have \$tmpTextLen += \$sLen at line 2101. Here, the last sentence, \$limitBytes is taken instead of \$limitBytes-\$tmpTextLen (as \$tmpTextLen is never updated with bytes length limit). It has been fixed in this code. This bug does not have a consequence for the default evaluation `-b 665`.

In case of doubts, please see all the implemented tests to compare outputs between the official ROUGE-1.5.5 and this script.

## Installation

Package is uploaded on `PyPI <https://pypi.org/project/py-rouge>`_.

You can install it with pip:

``````pip install py-rouge
``````

or do it manually:

``````git clone https://github.com/Diego999/py-rouge
cd py-rouge
python setup.py install
``````

Issues/Pull Requests/Feedbacks

Don't hesitate to contact for any feedback or create issues/pull requests (especially if you want to rewrite the stemmer implemented in ROUGE-1.5.5 in python ;)).

Example

``````import rouge

def prepare_results(m, p, r, f):
return '\t{}:\t{}: {:5.2f}\t{}: {:5.2f}\t{}: {:5.2f}'.format(m, 'P', 100.0 * p, 'R', 100.0 * r, 'F1', 100.0 * f)

for aggregator in ['Avg', 'Best', 'Individual']:
print('Evaluation with {}'.format(aggregator))
apply_avg = aggregator == 'Avg'
apply_best = aggregator == 'Best'

evaluator = rouge.Rouge(metrics=['rouge-n', 'rouge-l', 'rouge-w'],
max_n=4,
limit_length=True,
length_limit=100,
length_limit_type='words',
apply_avg=apply_avg,
apply_best=apply_best,
alpha=0.5, # Default F1_score
weight_factor=1.2,
stemming=True)

hypothesis_1 = "King Norodom Sihanouk has declined requests to chair a summit of Cambodia 's top political leaders , saying the meeting would not bring any progress in deadlocked negotiations to form a government .\nGovernment and opposition parties have asked King Norodom Sihanouk to host a summit meeting after a series of post-election negotiations between the two opposition groups and Hun Sen 's party to form a new government failed .\nHun Sen 's ruling party narrowly won a majority in elections in July , but the opposition _ claiming widespread intimidation and fraud _ has denied Hun Sen the two-thirds vote in parliament required to approve the next government .\n"
references_1 = ["Prospects were dim for resolution of the political crisis in Cambodia in October 1998.\nPrime Minister Hun Sen insisted that talks take place in Cambodia while opposition leaders Ranariddh and Sam Rainsy, fearing arrest at home, wanted them abroad.\nKing Sihanouk declined to chair talks in either place.\nA U.S. House resolution criticized Hun Sen's regime while the opposition tried to cut off his access to loans.\nBut in November the King announced a coalition government with Hun Sen heading the executive and Ranariddh leading the parliament.\nLeft out, Sam Rainsy sought the King's assurance of Hun Sen's promise of safety and freedom for all politicians.",
"Cambodian prime minister Hun Sen rejects demands of 2 opposition parties for talks in Beijing after failing to win a 2/3 majority in recent elections.\nSihanouk refuses to host talks in Beijing.\nOpposition parties ask the Asian Development Bank to stop loans to Hun Sen's government.\nCCP defends Hun Sen to the US Senate.\nFUNCINPEC refuses to share the presidency.\nHun Sen and Ranariddh eventually form a coalition at summit convened by Sihanouk.\nHun Sen remains prime minister, Ranariddh is president of the national assembly, and a new senate will be formed.\nOpposition leader Rainsy left out.\nHe seeks strong assurance of safety should he return to Cambodia.\n",
]

hypothesis_2 = "China 's government said Thursday that two prominent dissidents arrested this week are suspected of endangering national security _ the clearest sign yet Chinese leaders plan to quash a would-be opposition party .\nOne leader of a suppressed new political party will be tried on Dec. 17 on a charge of colluding with foreign enemies of China '' to incite the subversion of state power , '' according to court documents given to his wife on Monday .\nWith attorneys locked up , harassed or plain scared , two prominent dissidents will defend themselves against charges of subversion Thursday in China 's highest-profile dissident trials in two years .\n"
references_2 = "Hurricane Mitch, category 5 hurricane, brought widespread death and destruction to Central American.\nEspecially hard hit was Honduras where an estimated 6,076 people lost their lives.\nThe hurricane, which lingered off the coast of Honduras for 3 days before moving off, flooded large areas, destroying crops and property.\nThe U.S. and European Union were joined by Pope John Paul II in a call for money and workers to help the stricken area.\nPresident Clinton sent Tipper Gore, wife of Vice President Gore to the area to deliver much needed supplies to the area, demonstrating U.S. commitment to the recovery of the region.\n"

all_hypothesis = [hypothesis_1, hypothesis_2]
all_references = [references_1, references_2]

scores = evaluator.get_scores(all_hypothesis, all_references)

for metric, results in sorted(scores.items(), key=lambda x: x[0]):
if not apply_avg and not apply_best: # value is a type of list as we evaluate each summary vs each reference
for hypothesis_id, results_per_ref in enumerate(results):
nb_references = len(results_per_ref['p'])
for reference_id in range(nb_references):
print('\tHypothesis #{} & Reference #{}: '.format(hypothesis_id, reference_id))
print('\t' + prepare_results(metric,results_per_ref['p'][reference_id], results_per_ref['r'][reference_id], results_per_ref['f'][reference_id]))
print()
else:
print(prepare_results(metric, results['p'], results['r'], results['f']))
print()
``````

It produces the following output:

``````Evaluation with Avg
rouge-1:    P: 28.62    R: 26.46    F1: 27.49
rouge-2:    P:  4.21    R:  3.92    F1:  4.06
rouge-3:    P:  0.80    R:  0.74    F1:  0.77
rouge-4:    P:  0.00    R:  0.00    F1:  0.00
rouge-l:    P: 30.52    R: 28.57    F1: 29.51
rouge-w:    P: 15.85    R:  8.28    F1: 10.87

Evaluation with Best
rouge-1:    P: 30.44    R: 28.36    F1: 29.37
rouge-2:    P:  4.74    R:  4.46    F1:  4.59
rouge-3:    P:  1.06    R:  0.98    F1:  1.02
rouge-4:    P:  0.00    R:  0.00    F1:  0.00
rouge-l:    P: 31.54    R: 29.71    F1: 30.60
rouge-w:    P: 16.42    R:  8.82    F1: 11.47

Evaluation with Individual
Hypothesis #0 & Reference #0:
rouge-1:    P: 38.54    R: 35.58    F1: 37.00
Hypothesis #0 & Reference #1:
rouge-1:    P: 45.83    R: 43.14    F1: 44.44
Hypothesis #1 & Reference #0:
rouge-1:    P: 15.05    R: 13.59    F1: 14.29

Hypothesis #0 & Reference #0:
rouge-2:    P:  7.37    R:  6.80    F1:  7.07
Hypothesis #0 & Reference #1:
rouge-2:    P:  9.47    R:  8.91    F1:  9.18
Hypothesis #1 & Reference #0:
rouge-2:    P:  0.00    R:  0.00    F1:  0.00

Hypothesis #0 & Reference #0:
rouge-3:    P:  2.13    R:  1.96    F1:  2.04
Hypothesis #0 & Reference #1:
rouge-3:    P:  1.06    R:  1.00    F1:  1.03
Hypothesis #1 & Reference #0:
rouge-3:    P:  0.00    R:  0.00    F1:  0.00

Hypothesis #0 & Reference #0:
rouge-4:    P:  0.00    R:  0.00    F1:  0.00
Hypothesis #0 & Reference #1:
rouge-4:    P:  0.00    R:  0.00    F1:  0.00
Hypothesis #1 & Reference #0:
rouge-4:    P:  0.00    R:  0.00    F1:  0.00

Hypothesis #0 & Reference #0:
rouge-l:    P: 42.11    R: 39.39    F1: 40.70
Hypothesis #0 & Reference #1:
rouge-l:    P: 46.19    R: 43.92    F1: 45.03
Hypothesis #1 & Reference #0:
rouge-l:    P: 16.88    R: 15.50    F1: 16.16

Hypothesis #0 & Reference #0:
rouge-w:    P: 22.27    R: 11.49    F1: 15.16
Hypothesis #0 & Reference #1:
rouge-w:    P: 24.56    R: 13.60    F1: 17.51
Hypothesis #1 & Reference #0:
rouge-w:    P:  8.29    R:  4.04    F1:  5.43``````

Author: Diego999
Source Code: https://github.com/Diego999/py-rouge

1656856140

## A Plugin for D3.js That Allows You to Easy Use Context-menus

This is a plugin for d3.js that allows you to easy use context-menus in your visualizations. It's 100% d3 based and done in the "d3 way", so you don't need to worry about including additional frameworks.

### Install with Bower

``````bower install d3-context-menu
``````

### Basic usage:

``````// Define your menu
var menu = [
{
title: 'Item #1',
action: function(d) {
console.log('Item #1 clicked!');
console.log('The data for this circle is: ' + d);
},
disabled: false // optional, defaults to false
},
{
title: 'Item #2',
action: function(d) {
console.log('You have clicked the second item!');
console.log('The data for this circle is: ' + d);
}
}
]

var data = [1, 2, 3];

var g = d3.select('body').append('svg')
.attr('width', 200)
.attr('height', 400)
.append('g');

g.selectAll('circles')
.data(data)
.enter()
.append('circle')
.attr('r', 30)
.attr('fill', 'steelblue')
.attr('cx', function(d) {
return 100;
})
.attr('cy', function(d) {
return d * 100;
})
});
``````

#### Headers and Dividers

Menus can have Headers and Dividers. To specify a header simply don't define an "action" property. To specify a divider, simply add a "divider: true" property to the menu item, and it'll be considered a divider. Example menu definition:

``````var menu = [
{
},
{
title: 'Normal item',
action: function() {}
},
{
divider: true
},
{
title: 'Last item',
action: function() {}
}
];
``````

Menus can have Nested Menu. To specify a nested menu, simply add "children" property. Children has item of array.

``````var menu = [
{
title: 'Parent',
children: [
{
title: 'Child',
children: [
{
title: 'Grand-Child1'
},
{
// normal
title: 'Grand-Child2',
action: function() {}
},
{
// divider
divider: true
},
{
// disable
title: 'Grand-Child3',
action: function() {}
}
]
}
]
},
];
``````

See the index.htm file in the example folder to see this in action.

#### Pre-show callback

You can pass in a callback that will be executed before the context menu appears. This can be useful if you need something to close tooltips or perform some other task before the menu appears:

``````    ...
console.log('Quick! Before the menu appears!');
})); // attach menu to element
``````

#### Post-show callback

You can pass in a callback that will be executed after the context menu appears using the onClose option:

``````    ...
onOpen: function() {
console.log('Quick! Before the menu appears!');
},
onClose: function() {
console.log('Menu has been closed.');
}
})); // attach menu to element
``````

#### Context-sensitive menu items

You can use information from your context in menu names, simply specify a function for title which returns a string:

``````var menu = [
{
title: function(d) {
return 'Delete circle '+d.circleName;
},
action: function(d) {
// delete it
}
},
{
title: function(d) {
return 'Item 2';
},
action: function(d) {
// do nothing interesting
}
}
];

// Menu shown is:

[Delete Circle MyCircle]
[Item 2]
``````

#### Dynamic menu list

You can also have different lists of menu items for different nodes if `menu` is a function:

``````var menu = function(data) {
if (data.x > 100) {
return [{
title: 'Item #1',
action: function(d) {
console.log('Item #1 clicked!');
console.log('The data for this circle is: ' + d);
}
}];
} else {
return [{
title: 'Item #1',
action: function(d) {
console.log('Item #1 clicked!');
console.log('The data for this circle is: ' + d);
}
}, {
title: 'Item #2',
action: function(d) {
console.log('Item #2 clicked!');
console.log('The data for this circle is: ' + d);
}
}];
}
};

// Menu shown for nodes with x < 100 contains 1 item, while other nodes have 2 menu items
``````

#### Deleting Nodes Example

The following example shows how to add a right click menu to a tree diagram:

http://plnkr.co/edit/bDBe0xGX1mCLzqYGOqOS?p=info

#### Explicitly set menu position

Default position can be overwritten by providing a `position` option (either object or function returning an object):

``````    ...
onOpen: function() {
...
},
onClose: function() {
...
},
position: {
top: 100,
left: 200
}
})); // attach menu to element
``````

or

``````    ...
onOpen: function() {
...
},
onClose: function() {
...
},
position: function(d) {
var elm = this;
var bounds = elm.getBoundingClientRect();

// eg. align bottom-left
return {
top: bounds.top + bounds.height,
left: bounds.left
}
}
})); // attach menu to element
``````

#### Set your own CSS class as theme (make sure to style it)

``````d3.contextMenu(menu, {
...
theme: 'my-awesome-theme'
});
``````

or

``````d3.contextMenu(menu, {
...
theme: function () {
if (foo) {
return 'my-foo-theme';
}
else {
return 'my-awesome-theme';
}
}
});
``````

#### Close the context menu programatically (can be used as cleanup, as well)

``````d3.contextMenu('close');
``````

The following example shows how to add a right click menu to a tree diagram:

http://plnkr.co/edit/bDBe0xGX1mCLzqYGOqOS?p=info

#### Additional callback arguments

Depending on the D3 library version used the callback functions can provide an additional argument:

• for D3 6.x or above it will be the event, since the global d3.event is not available.
``````var menu = [
{
title: 'Item #1',
action: function(d, event) {
console.log('Item #1 clicked!');
console.log('The data for this circle is: ' + d);
console.log('The event is: ' + event);
}
}
]
``````
• for D3 5.x or below it will be the index, for backward compatibility reasons.
``````var menu = [
{
title: 'Item #1',
action: function(d, index) {
console.log('Item #1 clicked!');
console.log('The data for this circle is: ' + d);
console.log('The index is: ' + index);
}
}
]
``````

### What's new in version 2.1.0

• Added support for accessing event information in with D3 6.x.

### What's new in version 2.0.0

• Added support for D3 6.x
• The `index` parameter of callbacks are undefined when using D3 6.x or above. See the index.htm file in the example folder to see how to get the proper `index` value in that case.
• Added class property for menu items that allows specifying CSS classes (see: https://github.com/patorjk/d3-context-menu/pull/56).

### What's new in version 1.1.2

• Menu updated so it wont go off bottom or right of screen when window is smaller.

### What's new in version 1.1.1

• Menu close bug fix.

### What's new in version 1.1.0

• Nested submenus are now supported.

### What's new in version 1.0.1

• Default theme styles extracted to their own CSS class (`d3-context-menu-theme`)
• Ability to specify own theme css class via the `theme` configuration option (as string or function returning string)
• onOpen/onClose callbacks now have consistent signature (they receive `data` and `index`, and `this` argument refers to the DOM element the context menu is related to)
• all other functions (eg. `position`, `menu`) have the same signature and `this` object as `onClose`/`onOpen`
• Context menu now closes on `mousedown` outside of the menu, instead of `click` outside (to mimic behaviour of the native context menu)
• `disabled` and `divider` can now be functions as well and have the same signature and `this` object as explained above
• Close the context menu programatically using `d3.contextMenu('close');`

### What's new in version 0.2.1

• Ability to set menu position
• Minified css and js versions

### What's new in version 0.1.3

• Fixed issue where context menu element is never removed from DOM
• Fixed issue where `<body>` click event is never removed
• Fixed issue where the incorrect `onClose` callback was called when menu was closed as a result of clicking outside

### What's new in version 0.1.2

• If contextmenu is clicked twice it will close rather than open the browser's context menu.

### What's new in version 0.1.1

• Header and Divider items.
• Ability to disable items.

It's written to be very light weight and customizable. You can see it in action here:

http://plnkr.co/edit/hAx36JQhb0RsvVn7TomS?p=info

Author: Patorjk

1593039000

## What is Central Tendency?

Central Tendency is the measure of very basic but very useful statistical functions that represents a central point or typical value of the dataset. It help’s in indicating the point value where the most value in the distribution falls referring to the central location of the distribution. The most common central tendency methods used for the analysis of numerical data are mean, median, and mode.

## Mean

The mean is the most common and well-known method for measuring central tendency and can be used to handle both discrete and continuous data. We can calculate mean as the sum of all the values in the dataset divided by the number of values in the dataset and is denoted as ‘µ’.

Mean is not often one of the actual values that you have observed in your data set but it is one of the most important properties as it minimizes the error to predict the value in any dataset. The reason behind having the lowest error is because it includes every value in your data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.

In the below image we can see the histogram for an array of values and then calculated the mean by summing all the values on the x-axis and just dividing by the number of values i.e 12.

However, the disadvantage of using the mean is that it is particularly susceptible to the influence of outliers. Outliners are the value that is very unusual as compared to the rest of the data, like making a particular value being very small or very large as compared to the rest. Focusing the case when our data is skewed or we can say that when the data is perfectly normal, the mean, median, and mode are identical. In this case, mean lose its ability to provide the best central location for the data because the skewed data is dragging it away from the typical value.

The below histogram shows the image with the skewed dataset and hence all the three mean median and mode will be approx equal to each other.

## Median

Median is the middle value of your observation when the values in the dataset are ordered from the smallest to the largest. If the number of values in the dataset is an odd number then the middle value is the median. But if you have odd number values in the dataset then in order to find median we just take the average of the two middle values.

The below histogram shows the relationship between the mean and mode if we have symmetric data.

#statistics #data-analysis #mean-median-mode #data-science #central-tendency