ArrayViews.jl: A Julia Package to Explore A New System Of Array Views

ArrayViews.jl

A Julia package to explore a new system of array views.


For users of julia 0.4 or higher

By and large, this package is no longer necessary: base julia now has efficient SubArrays (i.e., sub and slice). In choosing whether to use SubArrays or the ArrayViews package, here are some considerations:

Reasons to prefer SubArrays:

ArrayViews can only make a view of an Array, whereas SubArrays can create a view of any AbstractArray.

The views created by ArrayViews are most efficient for ContiguousViews such as column slices. In contrast, the views created by SubArrays are efficient for any type of view (e.g., also row slices), in some cases resulting in a 3- to 10-fold advantage. In either case, it's generally recommended to write functions using cartesian indexing rather than linear indexing (e.g., for I in eachindex(S) rather than for i = 1:length(S)), although in both cases there are some view types that are also efficient under linear indexing.

SubArrays allow more general slicing behavior, e.g., you can make a view with S = sub(A, [1,3,17], :).

By default, SubArrays check bounds upon construction whereas ArrayViews do not: V = view(A, -5:10, :) does not generate an error, and if V is used in a function with an @inbounds declaration you are likely to get a segfault. (You can bypass bounds checking with Base._sub and Base._slice, in cases where you want out-of-bounds construction for SubArrays.)

Reasons to prefer ArrayViews:

  • Construction of SubArrays is frequently (but not always) 2-4 times slower than construction of views. If you are constructing many column views, ArrayViews may still be the better choice.

Main Features

  • An efficient aview function that implements array views
  • Support of arrays of arbitrary dimension and arbitrary combinations of indexers
  • Support aview composition (i.e. construct views over views)
  • Special attention to ensure type stability in most cases
  • Efficient indexing (both cartesian and linear)
  • Light weight array view construction
  • A systematic approach to detect contiguous views (statically)
  • Views work with linear algebra functions

Overview

The key function in this package is aview. This function is similar to sub in Julia Base, except that it returns an aview instance with more efficient representation:

a = rand(4, 5, 6)

aview(a, :)
aview(a, :, 2)
aview(a, 1:2, 1:2:5, 4)
aview(a, 2, :, 3:6)

The aview function returns an array view of type ArrayView. Here, ArrayView is an abstract type with two derived types (ContiguousView and StridedView), defined as:

abstract type ArrayView{T,N,M} <: DenseArray{T,N} end

We can see that each view type has three static properties: element type T, the number of dimensions N, and the contiguous rank M.

Contiguous Rank

The contiguous rank plays an important role in determining (statically) the contiguousness of a subview. Below are illustrations of 2D views respective with contiguous rank 0, 1, and 2.

2D View with contiguous rank 0

* * * * * *
. . . . . .
* * * * * *
. . . . . .
* * * * * *
. . . . . .

Here, * indicates a position covered by the array view, and . otherwise. We can see that the columns are not contiguous.

2D View with contiguous rank 1

* * * * * *
* * * * * *
* * * * * *
* * * * * *
. . . . . .
. . . . . .

We can see that each column is contiguous, while the entire array view is not.

2D View with contiguous rank 2

* * * * * *
* * * * * *
* * * * * *
* * * * * *
* * * * * *
* * * * * *

The entire 2D array view is contiguous.

Formally, when v is an array view with contiguous rank M, then aview(v, :, :, ..., :, 1) must be contiguous when the number of colons is less than or equal to M.

View Types

The package provide a hierarchy of array view types (defined as follows):

# T: the element type
# N: the number of dimensions
# M: the contiguous rank

abstract StridedArrayView{T,N,M} <: DenseArray{T,N}
abstract ArrayView{T,N,M} <: StridedArrayView{T,N,M}
abstract UnsafeArrayView{T,N,M} <: StridedArrayView{T,N,M}

immutable ContiguousView{T,N,Arr<:Array} <: ArrayView{T,N,N}
immutable StridedView{T,N,M,Arr<:Array} <: ArrayView{T,N,M}

immutable UnsafeContiguousView{T,N} <: UnsafeArrayView{T,N,N}
immutable UnsafeStridedView{T,N,M} <: UnsafeArrayView{T,N,M}

Here, an instance of ArrayView maintains a reference to the underlying array, and is generally safe to use in most cases. An instance of UnsafeArrayView maintains a raw pointer, and should only be used within a local scope (as it does not guarantee that the source array remains valid if it is passed out of a function).

View Types in Action

The following example illustrates how contiguous rank is used to determine aview types in practice.

a = rand(m, n)

# safe views

v0 = aview(a, :)         # of type ContiguousView{Float64, 1}

u1 = aview(a, a:b, :)    # of type StridedView{Float64, 2, 1}
u2 = aview(u1, :, i)     # of type ContiguousView{Float64, 1}

v1 = aview(a, a:2:b, :)  # of type StridedView{Float64, 2, 0}
v2 = aview(v1, :, i)     # of type StridedView{Float64, 1, 0}

# unsafe views

v0 = unsafe_aview(a, :)         # of type UnsafeContiguousView{Float64, 1}

u1 = unsafe_aview(a, a:b, :)    # of type UnsafeStridedView{Float64, 2, 1}
u2 = unsafe_aview(u1, :, i)     # of type UnsafeContiguousView{Float64, 1}

v1 = unsafe_aview(a, a:2:b, :)  # of type UnsafeStridedView{Float64, 2, 0}
v2 = unsafe_aview(v1, :, i)     # of type UnsafeStridedView{Float64, 1, 0}

Four kinds of indexers are supported, integer, range (e.g. a:b), stepped range (e.g. a:b:c), and colon (i.e., :).

View Construction

The procedure of constructing a aview consists of several steps:

Compute the shape of an array view. This is done by an internal function vshape.

Compute the offset of an array view. This is done by an internal function aoffset. The computation is based on the following formula:

offset(v(I1, I2, ..., Im)) = (first(I1) - 1) * stride(v, 1)
                           + (first(I2) - 1) * stride(v, 2)
                           + ...
                           + (first(Im) - 1) * stride(v, m)

Compute the contiguous rank, based on both view shape and the combination of indexer types. A type ContRank{M} is introduced for static computation of contiguous rank (please refer to src/contrank.jl for details).

Construct a aview, where the array view type is determined by both the number of dimensions and the value of contiguous rank (which is determined statically).

For runtime efficiency, specialized methods of these functions are implemented for views of 1D, 2D, and 3D. These methods are extensively tested.

Convenience Functions

The ArrayViews package provides several functions to make it more convenient to constructing certain views:


diagview(a)   # make a strided view of the diagonal elements, the length is `min(size(a)...)`
              # `a` needs to be a matrix here (contiguous or strided)

flatten_view(a)   # make a contiguous view of `a` as a vector
                  # `a` needs to be contiguous here

reshape_view(a, shp)   # make a contiguous view of `a` of shape `shp`
                       # `a` needs to be contiguous here.

rowvec_view(a, i)   # make a view of `a[i,:]` as a strided vector.
                    # `a` needs to be a matrix here (contiguous or strided)

ellipview(a, i)     # make a view of the i-th slice of a
                    # e.g. `a` is a matrix => this is equiv. to `aview(a, :, i)`
                    #      `a` is a cube => this is equiv. to `aview(a, :, :, i)`, etc.

Download Details:

Author: JuliaArrays
Source Code: https://github.com/JuliaArrays/ArrayViews.jl 
License: MIT license

#julia #arrays #view 

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ArrayViews.jl: A Julia Package to Explore A New System Of Array Views

How to Create Arrays in Python

In this tutorial, you'll know the basics of how to create arrays in Python using the array module. Learn how to use Python arrays. You'll see how to define them and the different methods commonly used for performing operations on them.

This tutorialvideo on 'Arrays in Python' will help you establish a strong hold on all the fundamentals in python programming language. Below are the topics covered in this video:  
1:15 What is an array?
2:53 Is python list same as an array?
3:48  How to create arrays in python?
7:19 Accessing array elements
9:59 Basic array operations
        - 10:33  Finding the length of an array
        - 11:44  Adding Elements
        - 15:06  Removing elements
        - 18:32  Array concatenation
       - 20:59  Slicing
       - 23:26  Looping  


Python Array Tutorial – Define, Index, Methods

In this article, you'll learn how to use Python arrays. You'll see how to define them and the different methods commonly used for performing operations on them.

The artcile covers arrays that you create by importing the array module. We won't cover NumPy arrays here.

Table of Contents

  1. Introduction to Arrays
    1. The differences between Lists and Arrays
    2. When to use arrays
  2. How to use arrays
    1. Define arrays
    2. Find the length of arrays
    3. Array indexing
    4. Search through arrays
    5. Loop through arrays
    6. Slice an array
  3. Array methods for performing operations
    1. Change an existing value
    2. Add a new value
    3. Remove a value
  4. Conclusion

Let's get started!

What are Python Arrays?

Arrays are a fundamental data structure, and an important part of most programming languages. In Python, they are containers which are able to store more than one item at the same time.

Specifically, they are an ordered collection of elements with every value being of the same data type. That is the most important thing to remember about Python arrays - the fact that they can only hold a sequence of multiple items that are of the same type.

What's the Difference between Python Lists and Python Arrays?

Lists are one of the most common data structures in Python, and a core part of the language.

Lists and arrays behave similarly.

Just like arrays, lists are an ordered sequence of elements.

They are also mutable and not fixed in size, which means they can grow and shrink throughout the life of the program. Items can be added and removed, making them very flexible to work with.

However, lists and arrays are not the same thing.

Lists store items that are of various data types. This means that a list can contain integers, floating point numbers, strings, or any other Python data type, at the same time. That is not the case with arrays.

As mentioned in the section above, arrays store only items that are of the same single data type. There are arrays that contain only integers, or only floating point numbers, or only any other Python data type you want to use.

When to Use Python Arrays

Lists are built into the Python programming language, whereas arrays aren't. Arrays are not a built-in data structure, and therefore need to be imported via the array module in order to be used.

Arrays of the array module are a thin wrapper over C arrays, and are useful when you want to work with homogeneous data.

They are also more compact and take up less memory and space which makes them more size efficient compared to lists.

If you want to perform mathematical calculations, then you should use NumPy arrays by importing the NumPy package. Besides that, you should just use Python arrays when you really need to, as lists work in a similar way and are more flexible to work with.

How to Use Arrays in Python

In order to create Python arrays, you'll first have to import the array module which contains all the necassary functions.

There are three ways you can import the array module:

  • By using import array at the top of the file. This includes the module array. You would then go on to create an array using array.array().
import array

#how you would create an array
array.array()
  • Instead of having to type array.array() all the time, you could use import array as arr at the top of the file, instead of import array alone. You would then create an array by typing arr.array(). The arr acts as an alias name, with the array constructor then immediately following it.
import array as arr

#how you would create an array
arr.array()
  • Lastly, you could also use from array import *, with * importing all the functionalities available. You would then create an array by writing the array() constructor alone.
from array import *

#how you would create an array
array()

How to Define Arrays in Python

Once you've imported the array module, you can then go on to define a Python array.

The general syntax for creating an array looks like this:

variable_name = array(typecode,[elements])

Let's break it down:

  • variable_name would be the name of the array.
  • The typecode specifies what kind of elements would be stored in the array. Whether it would be an array of integers, an array of floats or an array of any other Python data type. Remember that all elements should be of the same data type.
  • Inside square brackets you mention the elements that would be stored in the array, with each element being separated by a comma. You can also create an empty array by just writing variable_name = array(typecode) alone, without any elements.

Below is a typecode table, with the different typecodes that can be used with the different data types when defining Python arrays:

TYPECODEC TYPEPYTHON TYPESIZE
'b'signed charint1
'B'unsigned charint1
'u'wchar_tUnicode character2
'h'signed shortint2
'H'unsigned shortint2
'i'signed intint2
'I'unsigned intint2
'l'signed longint4
'L'unsigned longint4
'q'signed long longint8
'Q'unsigned long longint8
'f'floatfloat4
'd'doublefloat8

Tying everything together, here is an example of how you would define an array in Python:

import array as arr 

numbers = arr.array('i',[10,20,30])


print(numbers)

#output

#array('i', [10, 20, 30])

Let's break it down:

  • First we included the array module, in this case with import array as arr .
  • Then, we created a numbers array.
  • We used arr.array() because of import array as arr .
  • Inside the array() constructor, we first included i, for signed integer. Signed integer means that the array can include positive and negative values. Unsigned integer, with H for example, would mean that no negative values are allowed.
  • Lastly, we included the values to be stored in the array in square brackets.

Keep in mind that if you tried to include values that were not of i typecode, meaning they were not integer values, you would get an error:

import array as arr 

numbers = arr.array('i',[10.0,20,30])


print(numbers)

#output

#Traceback (most recent call last):
# File "/Users/dionysialemonaki/python_articles/demo.py", line 14, in <module>
#   numbers = arr.array('i',[10.0,20,30])
#TypeError: 'float' object cannot be interpreted as an integer

In the example above, I tried to include a floating point number in the array. I got an error because this is meant to be an integer array only.

Another way to create an array is the following:

from array import *

#an array of floating point values
numbers = array('d',[10.0,20.0,30.0])

print(numbers)

#output

#array('d', [10.0, 20.0, 30.0])

The example above imported the array module via from array import * and created an array numbers of float data type. This means that it holds only floating point numbers, which is specified with the 'd' typecode.

How to Find the Length of an Array in Python

To find out the exact number of elements contained in an array, use the built-in len() method.

It will return the integer number that is equal to the total number of elements in the array you specify.

import array as arr 

numbers = arr.array('i',[10,20,30])


print(len(numbers))

#output
# 3

In the example above, the array contained three elements – 10, 20, 30 – so the length of numbers is 3.

Array Indexing and How to Access Individual Items in an Array in Python

Each item in an array has a specific address. Individual items are accessed by referencing their index number.

Indexing in Python, and in all programming languages and computing in general, starts at 0. It is important to remember that counting starts at 0 and not at 1.

To access an element, you first write the name of the array followed by square brackets. Inside the square brackets you include the item's index number.

The general syntax would look something like this:

array_name[index_value_of_item]

Here is how you would access each individual element in an array:

import array as arr 

numbers = arr.array('i',[10,20,30])

print(numbers[0]) # gets the 1st element
print(numbers[1]) # gets the 2nd element
print(numbers[2]) # gets the 3rd element

#output

#10
#20
#30

Remember that the index value of the last element of an array is always one less than the length of the array. Where n is the length of the array, n - 1 will be the index value of the last item.

Note that you can also access each individual element using negative indexing.

With negative indexing, the last element would have an index of -1, the second to last element would have an index of -2, and so on.

Here is how you would get each item in an array using that method:

import array as arr 

numbers = arr.array('i',[10,20,30])

print(numbers[-1]) #gets last item
print(numbers[-2]) #gets second to last item
print(numbers[-3]) #gets first item
 
#output

#30
#20
#10

How to Search Through an Array in Python

You can find out an element's index number by using the index() method.

You pass the value of the element being searched as the argument to the method, and the element's index number is returned.

import array as arr 

numbers = arr.array('i',[10,20,30])

#search for the index of the value 10
print(numbers.index(10))

#output

#0

If there is more than one element with the same value, the index of the first instance of the value will be returned:

import array as arr 


numbers = arr.array('i',[10,20,30,10,20,30])

#search for the index of the value 10
#will return the index number of the first instance of the value 10
print(numbers.index(10))

#output

#0

How to Loop through an Array in Python

You've seen how to access each individual element in an array and print it out on its own.

You've also seen how to print the array, using the print() method. That method gives the following result:

import array as arr 

numbers = arr.array('i',[10,20,30])

print(numbers)

#output

#array('i', [10, 20, 30])

What if you want to print each value one by one?

This is where a loop comes in handy. You can loop through the array and print out each value, one-by-one, with each loop iteration.

For this you can use a simple for loop:

import array as arr 

numbers = arr.array('i',[10,20,30])

for number in numbers:
    print(number)
    
#output
#10
#20
#30

You could also use the range() function, and pass the len() method as its parameter. This would give the same result as above:

import array as arr  

values = arr.array('i',[10,20,30])

#prints each individual value in the array
for value in range(len(values)):
    print(values[value])

#output

#10
#20
#30

How to Slice an Array in Python

To access a specific range of values inside the array, use the slicing operator, which is a colon :.

When using the slicing operator and you only include one value, the counting starts from 0 by default. It gets the first item, and goes up to but not including the index number you specify.

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#get the values 10 and 20 only
print(numbers[:2])  #first to second position

#output

#array('i', [10, 20])

When you pass two numbers as arguments, you specify a range of numbers. In this case, the counting starts at the position of the first number in the range, and up to but not including the second one:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])


#get the values 20 and 30 only
print(numbers[1:3]) #second to third position

#output

#rray('i', [20, 30])

Methods For Performing Operations on Arrays in Python

Arrays are mutable, which means they are changeable. You can change the value of the different items, add new ones, or remove any you don't want in your program anymore.

Let's see some of the most commonly used methods which are used for performing operations on arrays.

How to Change the Value of an Item in an Array

You can change the value of a specific element by speficying its position and assigning it a new value:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#change the first element
#change it from having a value of 10 to having a value of 40
numbers[0] = 40

print(numbers)

#output

#array('i', [40, 20, 30])

How to Add a New Value to an Array

To add one single value at the end of an array, use the append() method:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#add the integer 40 to the end of numbers
numbers.append(40)

print(numbers)

#output

#array('i', [10, 20, 30, 40])

Be aware that the new item you add needs to be the same data type as the rest of the items in the array.

Look what happens when I try to add a float to an array of integers:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#add the integer 40 to the end of numbers
numbers.append(40.0)

print(numbers)

#output

#Traceback (most recent call last):
#  File "/Users/dionysialemonaki/python_articles/demo.py", line 19, in <module>
#   numbers.append(40.0)
#TypeError: 'float' object cannot be interpreted as an integer

But what if you want to add more than one value to the end an array?

Use the extend() method, which takes an iterable (such as a list of items) as an argument. Again, make sure that the new items are all the same data type.

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#add the integers 40,50,60 to the end of numbers
#The numbers need to be enclosed in square brackets

numbers.extend([40,50,60])

print(numbers)

#output

#array('i', [10, 20, 30, 40, 50, 60])

And what if you don't want to add an item to the end of an array? Use the insert() method, to add an item at a specific position.

The insert() function takes two arguments: the index number of the position the new element will be inserted, and the value of the new element.

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#add the integer 40 in the first position
#remember indexing starts at 0

numbers.insert(0,40)

print(numbers)

#output

#array('i', [40, 10, 20, 30])

How to Remove a Value from an Array

To remove an element from an array, use the remove() method and include the value as an argument to the method.

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

numbers.remove(10)

print(numbers)

#output

#array('i', [20, 30])

With remove(), only the first instance of the value you pass as an argument will be removed.

See what happens when there are more than one identical values:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30,10,20])

numbers.remove(10)

print(numbers)

#output

#array('i', [20, 30, 10, 20])

Only the first occurence of 10 is removed.

You can also use the pop() method, and specify the position of the element to be removed:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30,10,20])

#remove the first instance of 10
numbers.pop(0)

print(numbers)

#output

#array('i', [20, 30, 10, 20])

Conclusion

And there you have it - you now know the basics of how to create arrays in Python using the array module. Hopefully you found this guide helpful.

Thanks for reading and happy coding!

#python #programming 

Connor Mills

Connor Mills

1670560264

Understanding Arrays in Python

Learn how to use Python arrays. Create arrays in Python using the array module. You'll see how to define them and the different methods commonly used for performing operations on them.
 

The artcile covers arrays that you create by importing the array module. We won't cover NumPy arrays here.

Table of Contents

  1. Introduction to Arrays
    1. The differences between Lists and Arrays
    2. When to use arrays
  2. How to use arrays
    1. Define arrays
    2. Find the length of arrays
    3. Array indexing
    4. Search through arrays
    5. Loop through arrays
    6. Slice an array
  3. Array methods for performing operations
    1. Change an existing value
    2. Add a new value
    3. Remove a value
  4. Conclusion

Let's get started!


What are Python Arrays?

Arrays are a fundamental data structure, and an important part of most programming languages. In Python, they are containers which are able to store more than one item at the same time.

Specifically, they are an ordered collection of elements with every value being of the same data type. That is the most important thing to remember about Python arrays - the fact that they can only hold a sequence of multiple items that are of the same type.

What's the Difference between Python Lists and Python Arrays?

Lists are one of the most common data structures in Python, and a core part of the language.

Lists and arrays behave similarly.

Just like arrays, lists are an ordered sequence of elements.

They are also mutable and not fixed in size, which means they can grow and shrink throughout the life of the program. Items can be added and removed, making them very flexible to work with.

However, lists and arrays are not the same thing.

Lists store items that are of various data types. This means that a list can contain integers, floating point numbers, strings, or any other Python data type, at the same time. That is not the case with arrays.

As mentioned in the section above, arrays store only items that are of the same single data type. There are arrays that contain only integers, or only floating point numbers, or only any other Python data type you want to use.

When to Use Python Arrays

Lists are built into the Python programming language, whereas arrays aren't. Arrays are not a built-in data structure, and therefore need to be imported via the array module in order to be used.

Arrays of the array module are a thin wrapper over C arrays, and are useful when you want to work with homogeneous data.

They are also more compact and take up less memory and space which makes them more size efficient compared to lists.

If you want to perform mathematical calculations, then you should use NumPy arrays by importing the NumPy package. Besides that, you should just use Python arrays when you really need to, as lists work in a similar way and are more flexible to work with.

How to Use Arrays in Python

In order to create Python arrays, you'll first have to import the array module which contains all the necassary functions.

There are three ways you can import the array module:

  1. By using import array at the top of the file. This includes the module array. You would then go on to create an array using array.array().
import array

#how you would create an array
array.array()
  1. Instead of having to type array.array() all the time, you could use import array as arr at the top of the file, instead of import array alone. You would then create an array by typing arr.array(). The arr acts as an alias name, with the array constructor then immediately following it.
import array as arr

#how you would create an array
arr.array()
  1. Lastly, you could also use from array import *, with * importing all the functionalities available. You would then create an array by writing the array() constructor alone.
from array import *

#how you would create an array
array()

How to Define Arrays in Python

Once you've imported the array module, you can then go on to define a Python array.

The general syntax for creating an array looks like this:

variable_name = array(typecode,[elements])

Let's break it down:

  • variable_name would be the name of the array.
  • The typecode specifies what kind of elements would be stored in the array. Whether it would be an array of integers, an array of floats or an array of any other Python data type. Remember that all elements should be of the same data type.
  • Inside square brackets you mention the elements that would be stored in the array, with each element being separated by a comma. You can also create an empty array by just writing variable_name = array(typecode) alone, without any elements.

Below is a typecode table, with the different typecodes that can be used with the different data types when defining Python arrays:

TYPECODEC TYPEPYTHON TYPESIZE
'b'signed charint1
'B'unsigned charint1
'u'wchar_tUnicode character2
'h'signed shortint2
'H'unsigned shortint2
'i'signed intint2
'I'unsigned intint2
'l'signed longint4
'L'unsigned longint4
'q'signed long longint8
'Q'unsigned long longint8
'f'floatfloat4
'd'doublefloat8

Tying everything together, here is an example of how you would define an array in Python:

import array as arr 

numbers = arr.array('i',[10,20,30])


print(numbers)

#output

#array('i', [10, 20, 30])

Let's break it down:

  • First we included the array module, in this case with import array as arr .
  • Then, we created a numbers array.
  • We used arr.array() because of import array as arr .
  • Inside the array() constructor, we first included i, for signed integer. Signed integer means that the array can include positive and negative values. Unsigned integer, with H for example, would mean that no negative values are allowed.
  • Lastly, we included the values to be stored in the array in square brackets.

Keep in mind that if you tried to include values that were not of i typecode, meaning they were not integer values, you would get an error:

import array as arr 

numbers = arr.array('i',[10.0,20,30])


print(numbers)

#output

#Traceback (most recent call last):
# File "/Users/dionysialemonaki/python_articles/demo.py", line 14, in <module>
#   numbers = arr.array('i',[10.0,20,30])
#TypeError: 'float' object cannot be interpreted as an integer

In the example above, I tried to include a floating point number in the array. I got an error because this is meant to be an integer array only.

Another way to create an array is the following:

from array import *

#an array of floating point values
numbers = array('d',[10.0,20.0,30.0])

print(numbers)

#output

#array('d', [10.0, 20.0, 30.0])

The example above imported the array module via from array import * and created an array numbers of float data type. This means that it holds only floating point numbers, which is specified with the 'd' typecode.

How to Find the Length of an Array in Python

To find out the exact number of elements contained in an array, use the built-in len() method.

It will return the integer number that is equal to the total number of elements in the array you specify.

import array as arr 

numbers = arr.array('i',[10,20,30])


print(len(numbers))

#output
# 3

In the example above, the array contained three elements – 10, 20, 30 – so the length of numbers is 3.

Array Indexing and How to Access Individual Items in an Array in Python

Each item in an array has a specific address. Individual items are accessed by referencing their index number.

Indexing in Python, and in all programming languages and computing in general, starts at 0. It is important to remember that counting starts at 0 and not at 1.

To access an element, you first write the name of the array followed by square brackets. Inside the square brackets you include the item's index number.

The general syntax would look something like this:

array_name[index_value_of_item]

Here is how you would access each individual element in an array:

import array as arr 

numbers = arr.array('i',[10,20,30])

print(numbers[0]) # gets the 1st element
print(numbers[1]) # gets the 2nd element
print(numbers[2]) # gets the 3rd element

#output

#10
#20
#30

Remember that the index value of the last element of an array is always one less than the length of the array. Where n is the length of the array, n - 1 will be the index value of the last item.

Note that you can also access each individual element using negative indexing.

With negative indexing, the last element would have an index of -1, the second to last element would have an index of -2, and so on.

Here is how you would get each item in an array using that method:

import array as arr 

numbers = arr.array('i',[10,20,30])

print(numbers[-1]) #gets last item
print(numbers[-2]) #gets second to last item
print(numbers[-3]) #gets first item
 
#output

#30
#20
#10

How to Search Through an Array in Python

You can find out an element's index number by using the index() method.

You pass the value of the element being searched as the argument to the method, and the element's index number is returned.

import array as arr 

numbers = arr.array('i',[10,20,30])

#search for the index of the value 10
print(numbers.index(10))

#output

#0

If there is more than one element with the same value, the index of the first instance of the value will be returned:

import array as arr 


numbers = arr.array('i',[10,20,30,10,20,30])

#search for the index of the value 10
#will return the index number of the first instance of the value 10
print(numbers.index(10))

#output

#0

How to Loop through an Array in Python

You've seen how to access each individual element in an array and print it out on its own.

You've also seen how to print the array, using the print() method. That method gives the following result:

import array as arr 

numbers = arr.array('i',[10,20,30])

print(numbers)

#output

#array('i', [10, 20, 30])

What if you want to print each value one by one?

This is where a loop comes in handy. You can loop through the array and print out each value, one-by-one, with each loop iteration.

For this you can use a simple for loop:

import array as arr 

numbers = arr.array('i',[10,20,30])

for number in numbers:
    print(number)
    
#output
#10
#20
#30

You could also use the range() function, and pass the len() method as its parameter. This would give the same result as above:

import array as arr  

values = arr.array('i',[10,20,30])

#prints each individual value in the array
for value in range(len(values)):
    print(values[value])

#output

#10
#20
#30

How to Slice an Array in Python

To access a specific range of values inside the array, use the slicing operator, which is a colon :.

When using the slicing operator and you only include one value, the counting starts from 0 by default. It gets the first item, and goes up to but not including the index number you specify.


import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#get the values 10 and 20 only
print(numbers[:2])  #first to second position

#output

#array('i', [10, 20])

When you pass two numbers as arguments, you specify a range of numbers. In this case, the counting starts at the position of the first number in the range, and up to but not including the second one:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])


#get the values 20 and 30 only
print(numbers[1:3]) #second to third position

#output

#rray('i', [20, 30])

Methods For Performing Operations on Arrays in Python

Arrays are mutable, which means they are changeable. You can change the value of the different items, add new ones, or remove any you don't want in your program anymore.

Let's see some of the most commonly used methods which are used for performing operations on arrays.

How to Change the Value of an Item in an Array

You can change the value of a specific element by speficying its position and assigning it a new value:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#change the first element
#change it from having a value of 10 to having a value of 40
numbers[0] = 40

print(numbers)

#output

#array('i', [40, 20, 30])

How to Add a New Value to an Array

To add one single value at the end of an array, use the append() method:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#add the integer 40 to the end of numbers
numbers.append(40)

print(numbers)

#output

#array('i', [10, 20, 30, 40])

Be aware that the new item you add needs to be the same data type as the rest of the items in the array.

Look what happens when I try to add a float to an array of integers:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#add the integer 40 to the end of numbers
numbers.append(40.0)

print(numbers)

#output

#Traceback (most recent call last):
#  File "/Users/dionysialemonaki/python_articles/demo.py", line 19, in <module>
#   numbers.append(40.0)
#TypeError: 'float' object cannot be interpreted as an integer

But what if you want to add more than one value to the end an array?

Use the extend() method, which takes an iterable (such as a list of items) as an argument. Again, make sure that the new items are all the same data type.

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#add the integers 40,50,60 to the end of numbers
#The numbers need to be enclosed in square brackets

numbers.extend([40,50,60])

print(numbers)

#output

#array('i', [10, 20, 30, 40, 50, 60])

And what if you don't want to add an item to the end of an array? Use the insert() method, to add an item at a specific position.

The insert() function takes two arguments: the index number of the position the new element will be inserted, and the value of the new element.

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

#add the integer 40 in the first position
#remember indexing starts at 0

numbers.insert(0,40)

print(numbers)

#output

#array('i', [40, 10, 20, 30])

How to Remove a Value from an Array

To remove an element from an array, use the remove() method and include the value as an argument to the method.

import array as arr 

#original array
numbers = arr.array('i',[10,20,30])

numbers.remove(10)

print(numbers)

#output

#array('i', [20, 30])

With remove(), only the first instance of the value you pass as an argument will be removed.

See what happens when there are more than one identical values:


import array as arr 

#original array
numbers = arr.array('i',[10,20,30,10,20])

numbers.remove(10)

print(numbers)

#output

#array('i', [20, 30, 10, 20])

Only the first occurence of 10 is removed.

You can also use the pop() method, and specify the position of the element to be removed:

import array as arr 

#original array
numbers = arr.array('i',[10,20,30,10,20])

#remove the first instance of 10
numbers.pop(0)

print(numbers)

#output

#array('i', [20, 30, 10, 20])

Conclusion

And there you have it - you now know the basics of how to create arrays in Python using the array module. Hopefully you found this guide helpful.

You'll start from the basics and learn in an interacitve and beginner-friendly way. You'll also build five projects at the end to put into practice and help reinforce what you learned.

Thanks for reading and happy coding!

Original article source at https://www.freecodecamp.org

#python 

ArrayViews.jl: A Julia Package to Explore A New System Of Array Views

ArrayViews.jl

A Julia package to explore a new system of array views.


For users of julia 0.4 or higher

By and large, this package is no longer necessary: base julia now has efficient SubArrays (i.e., sub and slice). In choosing whether to use SubArrays or the ArrayViews package, here are some considerations:

Reasons to prefer SubArrays:

ArrayViews can only make a view of an Array, whereas SubArrays can create a view of any AbstractArray.

The views created by ArrayViews are most efficient for ContiguousViews such as column slices. In contrast, the views created by SubArrays are efficient for any type of view (e.g., also row slices), in some cases resulting in a 3- to 10-fold advantage. In either case, it's generally recommended to write functions using cartesian indexing rather than linear indexing (e.g., for I in eachindex(S) rather than for i = 1:length(S)), although in both cases there are some view types that are also efficient under linear indexing.

SubArrays allow more general slicing behavior, e.g., you can make a view with S = sub(A, [1,3,17], :).

By default, SubArrays check bounds upon construction whereas ArrayViews do not: V = view(A, -5:10, :) does not generate an error, and if V is used in a function with an @inbounds declaration you are likely to get a segfault. (You can bypass bounds checking with Base._sub and Base._slice, in cases where you want out-of-bounds construction for SubArrays.)

Reasons to prefer ArrayViews:

  • Construction of SubArrays is frequently (but not always) 2-4 times slower than construction of views. If you are constructing many column views, ArrayViews may still be the better choice.

Main Features

  • An efficient aview function that implements array views
  • Support of arrays of arbitrary dimension and arbitrary combinations of indexers
  • Support aview composition (i.e. construct views over views)
  • Special attention to ensure type stability in most cases
  • Efficient indexing (both cartesian and linear)
  • Light weight array view construction
  • A systematic approach to detect contiguous views (statically)
  • Views work with linear algebra functions

Overview

The key function in this package is aview. This function is similar to sub in Julia Base, except that it returns an aview instance with more efficient representation:

a = rand(4, 5, 6)

aview(a, :)
aview(a, :, 2)
aview(a, 1:2, 1:2:5, 4)
aview(a, 2, :, 3:6)

The aview function returns an array view of type ArrayView. Here, ArrayView is an abstract type with two derived types (ContiguousView and StridedView), defined as:

abstract type ArrayView{T,N,M} <: DenseArray{T,N} end

We can see that each view type has three static properties: element type T, the number of dimensions N, and the contiguous rank M.

Contiguous Rank

The contiguous rank plays an important role in determining (statically) the contiguousness of a subview. Below are illustrations of 2D views respective with contiguous rank 0, 1, and 2.

2D View with contiguous rank 0

* * * * * *
. . . . . .
* * * * * *
. . . . . .
* * * * * *
. . . . . .

Here, * indicates a position covered by the array view, and . otherwise. We can see that the columns are not contiguous.

2D View with contiguous rank 1

* * * * * *
* * * * * *
* * * * * *
* * * * * *
. . . . . .
. . . . . .

We can see that each column is contiguous, while the entire array view is not.

2D View with contiguous rank 2

* * * * * *
* * * * * *
* * * * * *
* * * * * *
* * * * * *
* * * * * *

The entire 2D array view is contiguous.

Formally, when v is an array view with contiguous rank M, then aview(v, :, :, ..., :, 1) must be contiguous when the number of colons is less than or equal to M.

View Types

The package provide a hierarchy of array view types (defined as follows):

# T: the element type
# N: the number of dimensions
# M: the contiguous rank

abstract StridedArrayView{T,N,M} <: DenseArray{T,N}
abstract ArrayView{T,N,M} <: StridedArrayView{T,N,M}
abstract UnsafeArrayView{T,N,M} <: StridedArrayView{T,N,M}

immutable ContiguousView{T,N,Arr<:Array} <: ArrayView{T,N,N}
immutable StridedView{T,N,M,Arr<:Array} <: ArrayView{T,N,M}

immutable UnsafeContiguousView{T,N} <: UnsafeArrayView{T,N,N}
immutable UnsafeStridedView{T,N,M} <: UnsafeArrayView{T,N,M}

Here, an instance of ArrayView maintains a reference to the underlying array, and is generally safe to use in most cases. An instance of UnsafeArrayView maintains a raw pointer, and should only be used within a local scope (as it does not guarantee that the source array remains valid if it is passed out of a function).

View Types in Action

The following example illustrates how contiguous rank is used to determine aview types in practice.

a = rand(m, n)

# safe views

v0 = aview(a, :)         # of type ContiguousView{Float64, 1}

u1 = aview(a, a:b, :)    # of type StridedView{Float64, 2, 1}
u2 = aview(u1, :, i)     # of type ContiguousView{Float64, 1}

v1 = aview(a, a:2:b, :)  # of type StridedView{Float64, 2, 0}
v2 = aview(v1, :, i)     # of type StridedView{Float64, 1, 0}

# unsafe views

v0 = unsafe_aview(a, :)         # of type UnsafeContiguousView{Float64, 1}

u1 = unsafe_aview(a, a:b, :)    # of type UnsafeStridedView{Float64, 2, 1}
u2 = unsafe_aview(u1, :, i)     # of type UnsafeContiguousView{Float64, 1}

v1 = unsafe_aview(a, a:2:b, :)  # of type UnsafeStridedView{Float64, 2, 0}
v2 = unsafe_aview(v1, :, i)     # of type UnsafeStridedView{Float64, 1, 0}

Four kinds of indexers are supported, integer, range (e.g. a:b), stepped range (e.g. a:b:c), and colon (i.e., :).

View Construction

The procedure of constructing a aview consists of several steps:

Compute the shape of an array view. This is done by an internal function vshape.

Compute the offset of an array view. This is done by an internal function aoffset. The computation is based on the following formula:

offset(v(I1, I2, ..., Im)) = (first(I1) - 1) * stride(v, 1)
                           + (first(I2) - 1) * stride(v, 2)
                           + ...
                           + (first(Im) - 1) * stride(v, m)

Compute the contiguous rank, based on both view shape and the combination of indexer types. A type ContRank{M} is introduced for static computation of contiguous rank (please refer to src/contrank.jl for details).

Construct a aview, where the array view type is determined by both the number of dimensions and the value of contiguous rank (which is determined statically).

For runtime efficiency, specialized methods of these functions are implemented for views of 1D, 2D, and 3D. These methods are extensively tested.

Convenience Functions

The ArrayViews package provides several functions to make it more convenient to constructing certain views:


diagview(a)   # make a strided view of the diagonal elements, the length is `min(size(a)...)`
              # `a` needs to be a matrix here (contiguous or strided)

flatten_view(a)   # make a contiguous view of `a` as a vector
                  # `a` needs to be contiguous here

reshape_view(a, shp)   # make a contiguous view of `a` of shape `shp`
                       # `a` needs to be contiguous here.

rowvec_view(a, i)   # make a view of `a[i,:]` as a strided vector.
                    # `a` needs to be a matrix here (contiguous or strided)

ellipview(a, i)     # make a view of the i-th slice of a
                    # e.g. `a` is a matrix => this is equiv. to `aview(a, :, i)`
                    #      `a` is a cube => this is equiv. to `aview(a, :, :, i)`, etc.

Download Details:

Author: JuliaArrays
Source Code: https://github.com/JuliaArrays/ArrayViews.jl 
License: MIT license

#julia #arrays #view 

Strided.jl: A Julia Package for Strided Array Views

Strided.jl

Strided array views with efficient (cache-friendly and multithreaded) manipulations

A Julia package for working more efficiently with strided arrays, i.e. dense arrays whose memory layout has a fixed stride along every dimension. Strided.jl does not make any assumptions about the strides (such as stride 1 along first dimension, or monotonically increasing strides) and provides multithreaded and cache friendly implementations for mapping, reducing, broadcasting such arrays, as well as taking views, reshaping and permuting dimensions. Most of these are simply accessible by annotating a block of standard Julia code involving broadcasting and other array operations with the macro @strided.

What's new

Strided.jl v1 uses the new @spawn threading infrastructure of Julia 1.3 and higher. Futhermore, the use of multithreading is now more customizable, via the function Strided.set_num_threads(n), where n can be any integer between 1 (no threading) and Base.Threads.nthreads(). This allows to spend only a part of the Julia threads on multithreading, i.e. Strided will never spawn more than n-1 additional tasks. By default, n = Base.Threads.nthreads(), i.e. threading is enabled by default. There are also convenience functions Strided.enable_threads() = Strided.set_num_threads(Threads.nthreads()) and Strided.disable_threads() = Strided.set_num_threads(1).

Furthermore, there is an experimental feature (disabled by default) to apply multithreading for matrix multiplication using a divide-and-conquer strategy. It can be enabled via Strided.enable_threaded_mul() (and similarly Strided.disable_threaded_mul() to revert to the default setting). For matrices with a LinearAlgebra.BlasFloat element type (i.e. any of Float32, Float64, ComplexF32 or ComplexF64), this is typically not necessary as BLAS is multithreaded by default. However, it can be beneficial to implement the multithreading using Julia Tasks, which then run on Julia's threads as distributed by Julia's scheduler. Hence, this feature should likely be used in combination with LinearAlgebra.BLAS.set_num_threads(1). Performance seems to be on par (within a few percent margin) with the threading strategies of OpenBLAS and MKL. However, note that the latter call also disables any multithreading used in LAPACK (e.g. eigen, svd, qr, ...) and Strided.jl does not help with that.

Examples

Running Julia with a single thread

julia> using Strided

julia> using BenchmarkTools

julia> A = randn(4000,4000);

julia> B = similar(A);

julia> @btime $B .= ($A .+ $A') ./ 2;
  145.214 ms (0 allocations: 0 bytes)

julia> @btime @strided $B .= ($A .+ $A') ./ 2;
  56.189 ms (6 allocations: 352 bytes)

julia> A = randn(1000,1000);

julia> B = similar(A);

julia> @btime $B .= 3 .* $A';
  2.449 ms (0 allocations: 0 bytes)

julia> @btime @strided $B .= 3 .* $A';
  1.459 ms (5 allocations: 288 bytes)

julia> @btime $B .= $A .* exp.( -2 .* $A) .+ sin.( $A .* $A);
  22.493 ms (0 allocations: 0 bytes)

julia> @btime @strided $B .= $A .* exp.( -2 .* $A) .+ sin.( $A .* $A);
  22.240 ms (10 allocations: 480 bytes)

julia> A = randn(32,32,32,32);

julia> B = similar(A);

julia> @btime permutedims!($B, $A, (4,3,2,1));
  5.203 ms (2 allocations: 128 bytes)

julia> @btime @strided permutedims!($B, $A, (4,3,2,1));
  2.201 ms (4 allocations: 320 bytes)

julia> @btime $B .= permutedims($A, (1,2,3,4)) .+ permutedims($A, (2,3,4,1)) .+ permutedims($A, (3,4,1,2)) .+ permutedims($A, (4,1,2,3));
  21.863 ms (32 allocations: 32.00 MiB)

julia> @btime @strided $B .= permutedims($A, (1,2,3,4)) .+ permutedims($A, (2,3,4,1)) .+ permutedims($A, (3,4,1,2)) .+ permutedims($A, (4,1,2,3));
  8.495 ms (9 allocations: 640 bytes)

And now with export JULIA_NUM_THREADS = 4

julia> using Strided

julia> using BenchmarkTools

julia> A = randn(4000,4000);

julia> B = similar(A);

julia> @btime $B .= ($A .+ $A') ./ 2;
  146.618 ms (0 allocations: 0 bytes)

julia> @btime @strided $B .= ($A .+ $A') ./ 2;
  30.355 ms (12 allocations: 912 bytes)

julia> A = randn(1000,1000);

julia> B = similar(A);

julia> @btime $B .= 3 .* $A';
  2.030 ms (0 allocations: 0 bytes)

julia> @btime @strided $B .= 3 .* $A';
  808.874 μs (11 allocations: 784 bytes)

julia> @btime $B .= $A .* exp.( -2 .* $A) .+ sin.( $A .* $A);
  21.971 ms (0 allocations: 0 bytes)

julia> @btime @strided $B .= $A .* exp.( -2 .* $A) .+ sin.( $A .* $A);
  5.811 ms (16 allocations: 1.05 KiB)

julia> A = randn(32,32,32,32);

julia> B = similar(A);

julia> @btime permutedims!($B, $A, (4,3,2,1));
  5.334 ms (2 allocations: 128 bytes)

julia> @btime @strided permutedims!($B, $A, (4,3,2,1));
  1.192 ms (10 allocations: 928 bytes)

julia> @btime $B .= permutedims($A, (1,2,3,4)) .+ permutedims($A, (2,3,4,1)) .+ permutedims($A, (3,4,1,2)) .+ permutedims($A, (4,1,2,3));
  22.465 ms (32 allocations: 32.00 MiB)

julia> @btime @strided $B .= permutedims($A, (1,2,3,4)) .+ permutedims($A, (2,3,4,1)) .+ permutedims($A, (3,4,1,2)) .+ permutedims($A, (4,1,2,3));
  2.796 ms (15 allocations: 1.44 KiB)

Design principles

StridedView

Strided.jl is centered around the type StridedView, which provides a view into a parent array of type DenseArray such that the resulting view is strided, i.e. any dimension has an associated stride, such that e.g.

getindex(A, i₁, i₂, i₃, ...) = A.op(A.parent[offset + 1 + (i₁-1)*s₁ + (i₂-1)*s₂ + (i₃-1)*s₃ + ...])

with sⱼ = stride(A, iⱼ). There are no further assumptions on the strides, e.g. they are not assumed to be monotonously increasing or have s₁ == 1. Furthermore, A.op can be any of the operations identity, conj, transpose or adjoint (the latter two are equivalent to the former two if eltype(A) <: Number). Since these operations are their own inverse, they are also used in the corresponding setindex!.

This definition enables a StridedView to be lazy (i.e. returns just another StridedView over the same parent data) under application of conj, transpose, adjoint, permutedims and indexing (getindex) with Union{Integer, Colon, AbstractRange{<:Integer}} (a.k.a slicing).

Furthermore, the strided structure can be retained under certain reshape operations, but not all of them. Any dimension can always be split into smaller dimensions, but two subsequent dimensions i and i+1 can only be joined if stride(A,i+1) == size(A,i)*stride(A,i). Instead of overloading reshape, Strided.jl provides a separate function sreshape which returns a StridedView over the same parent data, or throws a runtime error if this is impossible.

Broadcasting and map(reduce)

Whenever an expression only contains StridedViews and non-array objects (scalars), overloaded methods for broadcasting and functions as map(!) and mapreduce are used that exploit the known strided structure in order to evaluate the result in a more efficient way, at least for sufficiently large arrays where the overhead of the extra preparatory work is negligible. In particular, this involves choosing a blocking strategy and loop order that aims to avoid cache misses. This matters in particular if some of the StridedViews involved have strides which are not monotonously increasing, e.g. if transpose, adjoint or permutedims has been applied. The fact that the latter also acts lazily (whereas it creates a copy of the data in Julia base) can potentially provide a further speedup.

Furthermore, these optimized methods are implemented with support for multithreading. Thus, if Threads.nthreads() > 1 and the arrays involved are sufficiently large, performance can be boosted even for plain arrays with a strictly sequential memory layout, provided that the broadcast operation is compute bound and not memory bound (i.e. the broadcast function is sufficienlty complex).

The @strided macro annotation

Rather than manually wrapping every array in a StridedView, there is the macro annotation @strided some_expression, which will wrap all DenseArrays appearing in some_expression in a StridedView. Note that, because StridedViews behave lazily under indexing with ranges, this acts similar to the @views macro in Julia Base, i.e. there is no need to use a view.

The macro @strided acts as a contract, i.e. the user ensures that all array manipulations in the following expressions will preserve the strided structure. Therefore, reshape and view are are replaced by sreshape and sview respectively. As mentioned above, sreshape will throw an error if the requested new shape is incompatible with preserving the strided structure. The function sview is only defined for index arguments which are ranges, Ints or Colon (:), and will thus also throw an error if indexed by anything else.

StridedView versus StridedArray and BLAS/LAPACK compatibility

StridedArray is a union type to denote arrays with a strided structure in Julia Base. Because of its definition as a type union rather than an abstract type, it is impossible to have user types be recognized as StridedArray. This is rather unfortunate, since dispatching to BLAS and LAPACK routines is based on StridedArray. As a consequence, StridedView will not fall back to BLAS or LAPACK by default. Currently, only matrix multiplication is overloaded so as to fall back to BLAS (i.e. gemm!) if possible. In general, one should not attempt use e.g. matrix factorizations or other lapack operations within the @strided context. Support for this is on the TODO list. Some BLAS inspired methods (axpy!, axpby!, scalar multiplication via mul!, rmul! or lmul!) are however overloaded by relying on the optimized yet generic map! implementation.

StridedViews can currently only be created with certainty from DenseArray (typically just Array in Julia Base). For Base.SubArray or Base.ReshapedArray instances, the StridedView constructor will first act on the underlying parent array, and then try to mimic the corresponding view or reshape operation using sview and sreshape. These, however, are more limited then their Base counterparts (because they need to guarantee that the result still has a strided memory layout with respect to the new dimensions), so an error can result. However, this approach can also succeed in creating StridedView wrappers around combinations of view and reshape that are not recognised as Base.StridedArray. For example, reshape(view(randn(40,40), 1:36, 1:20), (6,6,5,4)) is not a Base.StridedArrray, and indeed, it cannot statically be inferred to be strided, from only knowing the argument types provided to view and reshape. For example, the similarly looking reshape(view(randn(40,40), 1:36, 1:20), (6,3,10,4)) is not strided. The StridedView constructor will try to act on both, and yield a runtime error in the second case. Note that Base.ReinterpretArray is currently not supported.

Note again that, unlike StridedArrays, StridedViews behave lazily (i.e. still produce a view on the same parent array) under permutedims and regular indexing with ranges.

UnsafeStridedView and @unsafe_strided

Based on the work of UnsafeArrays.jl there is also an UnsafeStridedView, which references the parent array via a pointer, and therefore is itself a stack allocated struct (i.e. isbitstype(UnsafeStridedView{...}) is true).

It behaves in all respects the same as StridedView (they are both subtypes of AbstractStridedView), except that by itself it does not keep a reference to the parent array in a way that is visible to Julia's garbage collector. It can therefore not be the return value of an operation (in particular similar(::UnsafeStridedView, ...) -> ::StridedView) and an explicit reference to the parent array needs to be kept alive. Furthermore, UnsafeStridedView wrappers can only be created of AbstractArray{T} instances with isbitstype(T).

There is a corresponding @unsafe_strided macro annotation. However, in this case the arrays in the expression need to be identified explicitly as

@unsafe_strided A₁ A₂ ... some_expression

because this will be translated into the expression

GC.@preserve A₁ A₂ ...
let A₁ = UnsafeStridedView(A₁), A₂ = ...
    some_expression
end

Planned features / wish list

  • Support for GPUArrays with dedicated GPU kernels?

Download Details:

Author: Jutho
Source Code: https://github.com/Jutho/Strided.jl 
License: View license

#julia #array #views 

Ruth  Nabimanya

Ruth Nabimanya

1620633584

System Databases in SQL Server

Introduction

In SSMS, we many of may noticed System Databases under the Database Folder. But how many of us knows its purpose?. In this article lets discuss about the System Databases in SQL Server.

System Database

Fig. 1 System Databases

There are five system databases, these databases are created while installing SQL Server.

  • Master
  • Model
  • MSDB
  • Tempdb
  • Resource
Master
  • This database contains all the System level Information in SQL Server. The Information in form of Meta data.
  • Because of this master database, we are able to access the SQL Server (On premise SQL Server)
Model
  • This database is used as a template for new databases.
  • Whenever a new database is created, initially a copy of model database is what created as new database.
MSDB
  • This database is where a service called SQL Server Agent stores its data.
  • SQL server Agent is in charge of automation, which includes entities such as jobs, schedules, and alerts.
TempDB
  • The Tempdb is where SQL Server stores temporary data such as work tables, sort space, row versioning information and etc.
  • User can create their own version of temporary tables and those are stored in Tempdb.
  • But this database is destroyed and recreated every time when we restart the instance of SQL Server.
Resource
  • The resource database is a hidden, read only database that holds the definitions of all system objects.
  • When we query system object in a database, they appear to reside in the sys schema of the local database, but in actually their definitions reside in the resource db.

#sql server #master system database #model system database #msdb system database #sql server system databases #ssms #system database #system databases in sql server #tempdb system database