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https://github.com/jokergoo/list-vectorize

vectorized functions in perl
https://github.com/jokergoo/list-vectorize

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vectorized functions in perl

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## functions to make vectorized calculation easy



### INSTALL



```

cpan -i List::Vectorize

```



### SYNOPSIS



```perl

use List::Vectorize;               # export all functions

use List::Vectorize qw(:apply);    # export apply family functions

use List::Vectorize qw(:list);     # export functions that manuplate lists/vectors

use List::Vectorize qw(:set);      # export functions that manuplate sets

use List::Vectorize qw(:stat);     # export functions that do statistical things

use List::Vectorize qw(:io);       # export functions that print or read data

```



### DESCRIPTION



The module implements some functions in R style. The motivation is to help perl programming vectorized. And the module also provides a lot of functions to do basic statistic work.



#### Apply family functions



Apply family functions in R are used to apply functions on categories of data. In this module, four apply functions are implemented. It can easily vectorize perl programming where the vectors are represented as array references. However, the code may be a little hard to read.



##### `sapply(ARRAY_REF, CODE_REF)`



To apply a function on every element in the array. Maybe it is more proper to name this function as apply. But to be consistent with the function name in R where `apply` is used to apply functions on certain dimension of matrix and `sapply` function is used to apply function on every element of a vector, so we name the function as `sapply` here.



```perl

my $a = [1..10];

my $b = sapply($a, sub {1/$_[0]});

print_ref $b;

```



The function returns an array reference with same length of the input vector.



Since `sapply` can reduce the amount of for or foreach, it would sometimes make the source code more readable. For example, when we write a blogging software, we want to get all post ids, post titles and post times of some author, the code can be written as:



```perl

my $post_id = get_post_id_by_author($author);

my $post_title = get_post_title_by_author($author);

my $post_createtime = get_post_createtime_by_author($author);

```



And `$post_id`, `$post_title` and `$post_createtime` are all array references and can be sent to some template software such as `Template`.



##### `mapply(ARRAY_REF, ARRAY_REF, ..., CODE_REF)`



To apply a function on every element of the arrays parallel. This function is an extension of `sapply` and it can implement most of the vectorized calculation.



```perl

my $x = [1..26];

my $y = [1..26];

# if you think x and y are all vectors, then z is also a vector

# z = x^2 + 1/y + x*y

my $z = mapply($x, $y, sub{$_[0]**2 + 1/$_[1] + $_[0]*$_[1]});

print_ref $z;

```



We will show how to translate algorithms in R code into perl. The following code is to calculate false discovery rate (FDR, BH process) in multiple test problem (see source code of `p.adjust` function).



```perl

# source code of BH part in p.adjust

lp <- length(p)

n <- length(p)

i <- lp:1

o <- order(p, decreasing = TRUE)

ro <- order(o)

pmin(1, cummin(n/i * p[o]))[ro]

```



To translate, we need to define a new function cummin which is a cummulative minimum of the elements in the vector. Anyway, we have already a function `cumf` in this module that can calculate cummulative values in the vector. Then the translation looks like:



```perl

# p-values are stored in @$p

# lp <- length(p)

my $lp = len($p);

 

# n <- length(p)

my $n = $lp;

 

# i <- 1p:1

my $i = seq($lp, 1);

 

# o <- order(p, decreasing = TRUE)

my $o = order($p, sub {$_[1] <=> $_[0]});  # descreasing

 

# ro <- order(o)

my $ro = order($o);

 

# n/i * p[o]

my $foo1 = mapply($i, subset($p, $o), sub {$n/$_[0]*$_[1]})

 

# cummin(n/i * p[o])

my $foo2 = cumf($foo1, \&min);

 

# pmin(1, cummin(n/i * p[o])), pmin means parallel min

my $foo3 = mapply(1, $foo2, sub {min(\@_)});

# or just

my $foo3 = sapply($foo2, sub{min([$_[0], 1])});

 

# ok, the finnal pmin(1, cummin(n/i * p[o]))[ro]

my $adjp = subset($foo3, $ro);

# well, you can also use

my $adjp = \@$foo3[@$ro];

```



Although the translation is longer than source R code, but it would help to implement algorithms from R to perl more conviniently.



##### `happly(ARRAY_REF, CODE_REF)`



To apply a function on every element of the hash. If you take the hash as a named array, then it is similar to the sapply function. The function returns a hash reference.



```perl

my $h = {"a" => 1, "b" => 2, "c" => 3};

my $b = happly($h, sub {$_[0]**2});

print_ref $b;

```



##### `tapply(ARRAY_REF, ARRAY_REF, ..., CODE_REF)`



To apply a function on the elements of every catelogy according to the tabulation. The first argument is the value array reference, the last argument is the code reference, and the others are the array reference for tabulation. The function returns a hash reference. If the amount of the tabulation array is more than one, the strings of different tabulations are seperated by `|`.



```perl

my $x = [1..10];

my $t1 = ["a", "a", "a", "a", "a", "b", "b", "b", "b", "b"];

my $y = tapply($x, $t1, sub {sum(\@_)});

print_ref $y;

 

# or there may be more catogiry variables

my $t2 = ["c", "c", "d", "d", "e", "e", "f", "f", "g", "g"];

my $z = tapply($x, $t1, $t2, sub {sum(\@_)});

print_ref $z;

```



#### List functions



Functions to manuplate lists/vectors. Lists/vectors are represented as array references.



##### `len(ARRAY_REF | HASH_REF | SCALAR)`



If the argument is an array reference, then it returns the array's length. If it is a hash reference, then returns the hash's value's length. If the argument is not defined, then returns 0, or else 1. The function returns a number.



```perl

print len([1..10]);

print len({"a" => 1, "b" => 2});

print len(undef);

print len(1);

print len([]);

print len({});

```



##### `initial_array(SCALAR (size), SCALAR | CODE_REF | ARRAY_REF | HASH_REF (value) )`



Initialize an array with some values. The first argument is the size of the array and the second argument is either a scalar or code reference. If it is a scalar, the value of the scalar will be repeated to fill the array. If it is a code refence, the value of the array will be generated by the code. If it is an array reference or hash reference, the value would be copyed instead of just repeat the address of the reference. By default, the second argument is undef. The functions returns an array reference.



```perl

my $x = initial_array(10);

my $x = initial_array(10, 1);

my $x = initial_array(10, sub{rand});

my $x = initial_array(10, [1, 2]);

my $x = initial_array(10, {a => 1, b => 2});

print_ref $x;

```



##### `initial_matrix(SCALAR (n_row), SCALAR (n_col), SCALAR | CODE_REF (value) )`



Initial a matrix. The arguments are similar to `initial_array`.



The functions returns a matrix (reference of a two dimensional array reference).



```perl

# a 2x2 matrix initialized with random numbers from a uniform distribution in (0, 1)

my $x = initial_matrix(10, 10, sub{rand});

print_matrix $x;

```



##### `order(ARRAY_REF (value), CODE_REF (sorting function) )`



Returns the order of the elements in the array. The function returns an array reference. By default, the sorting function is to sort numbers from smallest to largest. Variables `$a` and `$b` are replaces with `$_[0]` and `$_[1]`.



```perl

my $x = [3, 1, 14, 6, 26];

my $o = order($x);

print_ref $o;

# if you want to sort the array descreasingly

$o = order($x, sub {$_[1] <=> $_[0]});

 

# sort as they are strings

$o = order($x, sub {$_[0] cmp $_[1]);

print_ref $o;

```



##### `rank(ARRAY_REF (value), CODE_REF (sorting function) )`



Returns the rank of the elements in the array. The function returns an array reference. The argument is same as `order`



##### `sort_array(ARRAY_REF (value), CODE_REF (sorting function) )`



Sort the array. Arguments are similar to the `order`. The function returns an array reference.



##### `reverse_array(ARRAY_REF (value) )`



Reverse the array.



##### `repeat(SCALAR (value), SCALAR (size), SCALAR (need_copy) )`



Repeat a value or data structure. If the first argument is a reference, then the third argumetn is to specify whether make a copy of the real data that the reference refer to or just repeat the address.



```perl

my $x = repeat(1, 10);

my $v = [1..10];   # reference

$x = repeat($v, 10, 0);  # ten items all refer to a same address.

$x = repeat($v, 10, 1);  # ten items have same values and independent.

```



##### `rep(SCALAR (value), SCALAR (size), SCALAR (need_copy) )`



Same as `repeat`.



##### `copy(REF)`



Copy a new data from a reference. The new data has the same values as the old data but locates at different address.



```perl

my $x = {a => [1, 2], b => [3, 4]};

my $y = copy($x);  # change $y will not affect $x.

```



##### `paste(ARRAY_REF | SCALAR, ARRAY_REF | SCALAR, ..., SCALAR (seperation) )`



Paste strings in arrays in parallel. If the last argument is a scalar and not a reference, it is used as the seperation character. The default seperation character is `|`.



```perl

my $x1 = "a";

my $x2 = [1..10];

my $x3 = ["+", "+", "+", "+", "+", "-", "-", "-", "-", "-"];

my $y = paste($x1, $x2, $x3, "");

```



##### `seq(SCALAR (from), SCALAR (to), SCALAR (by) )`



Generate a list of numbers.



```perl

my $x = seq(1, 10);

my $x = seq(1, 10, 3);

my $x = seq(10, 1);

```



##### `c(ARRAY_REF | SCALAR, ...)`



combine values into an array, only array reference and scalar is permitted.



```perl

my $x = c([1..10], 11, [12..15]);

```



##### `test(ARRAY_REF, CODE_REF)`



Test whether the values meet the condition of the function. The function returns an array reference. The values in the returned array is 0 or 1;



```perl

my $x = seq(-5, 5);

my $l = test($x, sub {$_[0] > 0});

```



##### `unique(ARRAY_REF)`



unify the array



##### `subset(ARRAY_REF, ARRAY_REF | CODE_REF)`



Get the subset of an array. If the second argument is number, positive number means to get the value and negative number means to drop the value. The second argument can also be function to test whether the values in the array meet the condition. Note using `0|1` as the value of the array in the second argument does not means take values in the corresponding posotion or not. Using `0|1` directly only means take values in the first or the second position of the array. If you want to take `0|1` as logical variable, use `which` function.



```perl

my $x = seq(-5, 5);

my $s = subset($x, sub{$_[0] > 0});

$s = subset($x, [1, 2, 3]);

$s = subset($x, [1, 1, 2, 2, 3, 3]);

$s = subset($x, [-1, -2, -3]);

$s = subset($x, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]);

$s = subset($x, which([1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]));

````



##### `subset_value(ARRAY_REF, ARRAY_REF | CODE_REF, ARRAY_REF | SCALAR)`



Change subset values. The first and the second arguments are similar to the `subset`, and the third argument is the value that will replace the value in the origin array. It can be either an array reference having the same length as the values to be replaced or a scalar.



```perl

my $x = seq(-5, 5);

subset_value($x, sub{$_[0] > 0}, 0);

print_ref $x;

```



##### `del_array_item(ARRAY_REF, SCALAR | ARRAY_REF)`



Delete items in an array. The second argument refers to single position or multiple positions.



```perl

my $x = [1..10];

del_array_item($x, 2);

del_array_item($x, [1, 3, 5]);

```



##### `which(ARRAY_REF)`



Return the index of the elements in the array that have true values.



```perl

my $x = seq(-5, 5);

my $l = test($x, sub {$_[0] > 0});

my $w = which($l);

```

##### `all(ARRAY_REF)`



Test whether all items are true. Return 1 or 0.



##### `any(ARRAY_REF)`



Test whether at least one of the items is true. Return 1 or 0.



##### `match(ARRAY_REF, ARRAY_REF)`



Find the index of the first array that can be found in the second array.



```perl

my $x1 = ["a", "b", "c"];

my $x2 = ["b", "c", "d"];

my $m = match($x1, $x2);

$m = match($x2, $x1);

```



##### `dim(ARRAY_REF)`



Dimensions of the matrix



```perl

my $m = [[1,2],[3,4]];

print dim($m);

```



##### `t(ARRAY_REF)`



Transpose the matrix.



```perl

my $m = [[1,2],[3,4]];

print_matrix $m;

my $t = t($m);

print_matrix($t);

```



##### `matrix_prod(ARRAY_REF,ARRAY_REF, ...)`



Product a list of matrixes.



```perl

my $m = [[1,2],[3,4]];

print_matrix matrix_prod($m, $m, $m);

````



##### `inner(ARRAY_REF, ARRAY_REF, CODE_REF)`



Inner function on two arrays. The same as the sum of mapply with two arrays. The default function is production.



##### `outer(ARRAY_REF, ARRAY_REF, CODE_REF)`



Outer function on two arrays. The default function is production.



```perl

my $x = [1..10];

my $y = [1..10];

# z = sin(xy)

my $z = outer($x, $y, sub {sin($_[0]*$_[1])});

print_matrix $z;

```



##### `is_array_identical(ARRAY_REF,ARRAY_REF)`



whether the two arrays are similarly same.



##### `is_matrix_identical(ARRAY_REF,ARRAY_REF)`



whether the two matrixes are similarly same.



##### `is_empty(ARRAY_REF | HASH_REF | SCALAR)`



whether the reference or value is empty. If the array reference or hash reference has length under len is 0 (note the reference itself is logically true), then it returns 0;



##### `plus(ARRAY_REF | SCALAR_REF, ARRAY_REF | SCALAR_REF, ...)`



plus of arrays



```perl

my $r = plus([1..10], [2..11], 2);

```



##### `minus(ARRAY_REF | SCALAR_REF, ARRAY_REF | SCALAR_REF, ...)`



minus of arrays



##### `multiply(ARRAY_REF | SCALAR_REF, ARRAY_REF | SCALAR_REF, ...)`



multiply of arrays



##### `divide(ARRAY_REF | SCALAR_REF, ARRAY_REF | SCALAR_REF, ...)`



divide of arrays



#### Set operation functions



##### `intersect(ARRAY_REF, ARRAY_REF, ...)`



Intersection of a list of arrays.



```perl

my $x = ["a", "b", "c", "d"];

my $y = ["b", "c", d", "e"];

my $x = ["c", "d", "a", "g"];

my $d = intersect($x, $y, $z);

```



##### `union(ARRAY_REF, ARRAY_REF, ...)`



Union of a list of arrays.



```perl

my $x = ["a", "b", "c", "d"];

my $y = ["b", "c", d", "e"];

my $x = ["c", "d", "a", "g"];

my $d = union($x, $y, $z);

```



##### `setdiff(ARRAY_REF, ARRAY_REF)`



Items exist in the first set while not in the second set.



```perl

my $x = ["a", "b", "c", "d"];

my $y = ["b", "c", d", "e"];

my $d = setdiff($x, $y);

```



##### `setequal(ARRAY_REF, ARRAY_REF)`



whether the two sets are equal. Sets are arrays that have been unified.



##### `is_element(SCALAR, ARRAY_REF)`



whether the element is in the set



```perl

my $x = ["a", "b", "c", "d"];

print is_element("a", $x);

```



#### Input and output functions



##### `print_ref(REF)`



print the data structure of the reference.



```perl

print_ref [1..10];

print_ref {a => 1, b => 2};

print_ref \1;

print_ref \\1;

print_ref sub {1};

```



##### `print_matrix(ARRAY_REF)`



print the content of the matrix.



##### `read_table(SCALAR, HASH)`



read matrix from file. The first argument is the path of the file. The other arguments are as follows.



```

quote       charector to quote the value (no quoting)

sep         seperation character (\t)

col.names   whether take first column as column names

row.names   whether take first row as row names

```



The function return a list with three elements: the data matrix, colnames, rownames in a list context. While in a scalar context, it only returns the data matrix.



```perl

my ($mat, $cn, $rn) = read_table('some_file_as_table');

my $mat = read_table('some_file_as_table');

```



##### `write_table(ARRAY_REF, HASH)`



write data to file. The first argument is a data matrix. The other arguments are as follows.



```

quote       charector to quote the value (no quoting)

sep         seperation character (\t)

col.names   array reference of the column names (optional)

row.names   array reference of the row names (optional)

file        file name

```



For example



```perl

my $x = [[1,2], [3,4]];

my $colnames = ["c1", "c2"];

my $rownames = ["r1", "r2"];

write_table($x, "file" => "file.txt",

                "quote" => "\"",

                "sep" => "\t",

                "col.names" => $colnames,

                "row.names" => $rownames,);

```



#### Statistical functions



Simple functions but used very frequently.



##### `abs($value)`



return the absolute value



##### `sign($value)`



return the sign of a value (`1|0|-1`)



##### `sum(ARRAY_REF)`



Summmation of a list of numbers.



##### `mean(ARRAY_REF)`



Mean value of a list of numbers.



##### `geometric_mean(ARRAY_REF)`



Geometric mean value of a list of numbers.



##### `sd(ARRAY_REF, SCALAR)`



Standard deviation of a list of numbers. The second argument is the mean value (optional)



##### `var(ARRAY_REF, SCALAR)`



Variance of a list of numbers. The second argument is the mean value (optional)



##### `cov(ARRAY_REF, ARRAY_REF)`



Coviarance of two vectors.



##### `cor(ARRAY_REF, ARRAY_REF, SCALAR)`



Correlation coefficient of two vectors. The third argument is "pearson" (by default) or "spearman".



##### `dist(ARRAY_REF, ARRAY_REF, SCALAR)`



Distance between two vectors. Several definition of the distance are provided.



```

euclidean  Euclidean distance (by default)

person     Person correlation coefficient

spearman   Spearman correlation coefficient

logical    It is defined as 1/(1+k) where k is the number of items that are both ture in two vectors.

```



##### `freq(ARRAY_REF, ARRAY_REF, ...)`



Frequency of the items in an array or arrays. Returns a hash reference. Different catelogical strings are seperated by `|`.



```perl

my $a = ["a", "a", "a", "a", "b", "b", "b", "b"];

my $b = ["1", "2", "1", "2", "1", "2", "1", "2"];

print_ref freq($a);

print_ref freq($a, $b);

```



##### `table(ARRAY_REF, ARRAY_REF, ...)`



The same as freq, to be consist with R



##### `scale(ARRAY_REF, SCALAR)`



Scale the vector based on some criterion.



```

zvalue        vector has mean value of 0 and variance of 1 (by default)

              formula: (x-mean)/sd

percentage    values in the vector are between 0 - 1

              formula: (x-min)/(max-min)

sphere        format the n-dimensional point on the surface of the unit super sphere

              formula: x/radius

```



##### `sample(ARRAY_REF, SCALAR (size), HASH)`



Random samplings and permutations. The third argument is



```

p         probability for each sampling, values will be scaled into [0, 1]

replace   whether sampling with replacement. 1|0

```



```perl

my $x = ["a".."g"];

# sample without replacement

sample($x, 5);

# permutation

sample($x, len($x));

# sample with replacement

sample($x, 5, "replace" => 1);

# sample with unequal probability

# normalization of the p-values will be done automatically

sample($x, 5, "p" => [10, 1, 1, 1, 1, 1, 1]);

```



##### `rnorm(SCALAR (size), SCALAR (mean), SCALAR (sd))`



Generate random numbers from normal distribution. Default mean value is 0 and default standard deviation is 1.



```perl

my $x = rnorm(10);

$x = rnorm(10, 1, 2);

```



##### `rbinom(SCALAR (size), SCALAR (p-value for success))`



Generate random numbers from binominal distribution. P-value is 0.5 by default.



```perl

my $x = rbinom(10, 0.1)

```



##### `max(ARRAY_REF)`



Maximum value in a vector



##### `min(ARRAY_REF)`



Minimum value in a vector



##### `which_max(ARRAY_REF)`



Find the index of the maximum value in the array. If there are several maximum values, only the take the first one.



##### `which_min(ARRAY_REF)`



Find the index of the minimum value in the array. If there are several minimum values, only the take the first one.



##### `median(ARRAY_REF)`



Median value in a vector.



##### `quantile(ARRAY_REF, ARRAY_REF | SCALAR_REF )`



quantile, the second argument can be a single percentage or a list of percentages storted in an array reference. The return value type is same as the second argument. If the second argumet is not specified, it will take `[0, 0.25, 0.5, 0.75, 1]`.



```perl

my $x = rnorm(100);

my $q = quantile($x, 0.5);

$q = quantile($x, [0.25, 0.75]);

```



##### `iqr(ARRAY_REF)`



Inter quantile range. It is the distance between the 25th and the 75th quantiles.



##### `cumf(ARRAY_REF, CODE_REF)`



cummulative function on an array.



```perl

my $x = rnorm(10);

my $sum = sum($x);

my $ecdf = cumf($x, sub {sum($_[0])/$sum});

```