Matft

Matft is Numpy-like library in Swift. Function name and usage is similar to Numpy.

INFO: Support Complex!!

• Matft
  • Feature & Usage
  • Declaration
    • MfArray
    • MfType
  • Subscription
    • MfSlice
    • (Positive) Indexing
    • Slicing
    • Negative Indexing
    • Boolean Indexing
    • Fancy Indexing
    • View
  • Complex
  • Image
  • Function List
  • Performance
  • Installation
  • SwiftPM
  • Carthage
  • CocoaPods
  • Contact

Note: You can use Protocol version(beta version) too.

Feature & Usage

• Many types

• Pretty print

• Indexing

  • Positive
  • Negative
  • Boolean
  • Fancy
  • Complex

• Slicing

  • Start / To / By
  • New Axis

• View

  • Assignment

• Conversion

  • Broadcast
  • Transpose
  • Reshape
  • Astype

• Univarsal function reduction

• Mathematic

  • Arithmetic
  • Statistic
  • Linear Algebra

• Complex

• Image Conversion

...etc.

See Function List for all functions.

Declaration

MfArray

• The MfArray such like a numpy.ndarray

  let a = MfArray([[[ -8,  -7,  -6,  -5],
                  [ -4,  -3,  -2,  -1]],
  
                 [[ 0,  1,  2,  3],
                  [ 4,  5,  6,  7]]])
  let aa = Matft.arange(start: -8, to: 8, by: 1, shape: [2,2,4])
  print(a)
  print(aa)
  /*
  mfarray = 
  [[[   -8,     -7,     -6,     -5],
  [ -4,     -3,     -2,     -1]],
  
  [[    0,      1,      2,      3],
  [ 4,      5,      6,      7]]], type=Int, shape=[2, 2, 4]
  mfarray = 
  [[[   -8,     -7,     -6,     -5],
  [ -4,     -3,     -2,     -1]],
  
  [[    0,      1,      2,      3],
  [ 4,      5,      6,      7]]], type=Int, shape=[2, 2, 4]
  */

MfType

• You can pass MfType as MfArray's argument mftype: .Hoge. It is similar to dtype.

  ※Note that stored data type will be Float or Double only even if you set MfType.Int. So, if you input big number to MfArray, it may be cause to overflow or strange results in any calculation (+, -, *, /,... etc.). But I believe this is not problem in practical use.

• MfType's list is below

  public enum MfType: Int{
    case None // Unsupportted
    case Bool
    case UInt8
    case UInt16
    case UInt32
    case UInt64
    case UInt
    case Int8
    case Int16
    case Int32
    case Int64
    case Int
    case Float
    case Double
    case Object // Unsupported
  }

• Also, you can convert MfType easily using astype

  let a = MfArray([[[ -8,  -7,  -6,  -5],
                  [ -4,  -3,  -2,  -1]],
  
                 [[ 0,  1,  2,  3],
                  [ 4,  5,  6,  7]]])
  print(a)//See above. if mftype is not passed, MfArray infer MfType. In this example, it's MfType.Int
  
  let a = MfArray([[[ -8,  -7,  -6,  -5],
                  [ -4,  -3,  -2,  -1]],
  
                 [[ 0,  1,  2,  3],
                  [ 4,  5,  6,  7]]], mftype: .Float)
  print(a)
  /*
  mfarray = 
  [[[   -8.0,       -7.0,       -6.0,       -5.0],
  [ -4.0,       -3.0,       -2.0,       -1.0]],
  
  [[    0.0,        1.0,        2.0,        3.0],
  [ 4.0,        5.0,        6.0,        7.0]]], type=Float, shape=[2, 2, 4]
  */
  let aa = MfArray([[[ -8,  -7,  -6,  -5],
                  [ -4,  -3,  -2,  -1]],
  
                 [[ 0,  1,  2,  3],
                  [ 4,  5,  6,  7]]], mftype: .UInt)
  print(aa)
  /*
  mfarray = 
  [[[   4294967288,     4294967289,     4294967290,     4294967291],
  [ 4294967292,     4294967293,     4294967294,     4294967295]],
  
  [[    0,      1,      2,      3],
  [ 4,      5,      6,      7]]], type=UInt, shape=[2, 2, 4]
  */
  //Above output is same as numpy!
  /*
  >>> np.arange(-8, 8, dtype=np.uint32).reshape(2,2,4)
  array([[[4294967288, 4294967289, 4294967290, 4294967291],
        [4294967292, 4294967293, 4294967294, 4294967295]],
  
       [[         0,          1,          2,          3],
        [         4,          5,          6,          7]]], dtype=uint32)
  */
  
  print(aa.astype(.Float))
  /*
  mfarray = 
  [[[   -8.0,       -7.0,       -6.0,       -5.0],
  [ -4.0,       -3.0,       -2.0,       -1.0]],
  
  [[    0.0,        1.0,        2.0,        3.0],
  [ 4.0,        5.0,        6.0,        7.0]]], type=Float, shape=[2, 2, 4]
  */

Subscription

MfSlice

• You can access specific data using subscript.

You can set MfSlice (see below's list) to subscript.

• MfSlice(start: Int? = nil, to: Int? = nil, by: Int = 1)

• Matft.newaxis

• ~< //this is prefix, postfix and infix operator. same as python's slice, ":"

• Matft.all // same as python's slice :, matft's 0~<

• Matft.reverse // same as python's slice ::-1, matft's ~<<-1

(Positive) Indexing

• Normal indexing

  let a = Matft.arange(start: 0, to: 27, by: 1, shape: [3,3,3])
  print(a)
  /*
  mfarray = 
  [[[   0,      1,      2],
  [ 3,      4,      5],
  [ 6,      7,      8]],
  
  [[    9,      10,     11],
  [ 12,     13,     14],
  [ 15,     16,     17]],
  
  [[    18,     19,     20],
  [ 21,     22,     23],
  [ 24,     25,     26]]], type=Int, shape=[3, 3, 3]
  */
  print(a[2,1,0])
  // 21

  Caution

  MfArray conforms to Collection protocol, so 1D MfArray returns MfArray! Use item as workaround instead of subscription such like

  let a = Matft.arange(start: 0, to: 27, by: 1, shape: [27])
  print(a[0])
  /*
  0 // a[0] is MfArray!! Nevertheless, The scalar is printed (I don't know why...)
  */
  print(a[0] + 4)
  /*
  mfarray = 
  [    4], type=Int, shape=[1]
  */
  
  // Workaround
  print(a.item(index: 0, type: Int.self))
  /*
  0
  */
  print(a.item(index: 0, type: Int.self) + 4)
  /*
  4
  */

  Slicing

• If you replace : with ~<, you can get sliced mfarray. Note that use a[0~<] instead of a[:] to get all elements along axis.

  print(a[~<1])  //same as a[:1] for numpy
  /*
  mfarray = 
  [[[   9,      10,     11],
  [ 12,     13,     14],
  [ 15,     16,     17]]], type=Int, shape=[1, 3, 3]
  */
  print(a[1~<3]) //same as a[1:3] for numpy
  /*
  mfarray = 
  [[[   9,      10,     11],
  [ 12,     13,     14],
  [ 15,     16,     17]],
  
  [[    18,     19,     20],
  [ 21,     22,     23],
  [ 24,     25,     26]]], type=Int, shape=[2, 3, 3]
  */
  print(a[~<~<2]) //same as a[::2] for numpy
  //print(a[~<<2]) //alias
  /*
  mfarray = 
  [[[   0,      1,      2],
  [ 3,      4,      5],
  [ 6,      7,      8]],
  
  [[    18,     19,     20],
  [ 21,     22,     23],
  [ 24,     25,     26]]], type=Int, shape=[2, 3, 3]
  */
  
  print(a[Matft.all, 0]) //same as a[:, 0] for numpy
  /*
  mfarray = 
  [[    0,      1,      2],
  [ 9,      10,     11],
  [18,      19,     20]], type=Int, shape=[3, 3]
  */

Negative Indexing

• Negative indexing is also available That's implementation was hardest for me...

  print(a[~<-1])
  /*
  mfarray = 
  [[[   0,      1,      2],
  [ 3,      4,      5],
  [ 6,      7,      8]],
  
  [[    9,      10,     11],
  [ 12,     13,     14],
  [ 15,     16,     17]]], type=Int, shape=[2, 3, 3]
  */
  print(a[-1~<-3])
  /*
  mfarray = 
  [], type=Int, shape=[0, 3, 3]
  */
  print(a[Matft.reverse])
  //print(a[~<~<-1]) //alias
  //print(a[~<<-1]) //alias
  /*
  mfarray = 
  [[[   18,     19,     20],
  [ 21,     22,     23],
  [ 24,     25,     26]],
  
  [[    9,      10,     11],
  [ 12,     13,     14],
  [ 15,     16,     17]],
  
  [[    0,      1,      2],
  [ 3,      4,      5],
  [ 6,      7,      8]]], type=Int, shape=[3, 3, 3]*/

Boolean Indexing

• You can use boolean indexing.

  Caution! I don't check performance, so this boolean indexing may be slow

  Unfortunately, Matft is too slower than numpy...

  (numpy is 1ms, Matft is 7ms...)

  let img = MfArray([[1, 2, 3],
                               [4, 5, 6],
                               [7, 8, 9]], mftype: .UInt8)
  img[img > 3] = MfArray([10], mftype: .UInt8)
  print(img)
  /*
  mfarray = 
  [[    1,      2,      3],
  [ 10,     10,     10],
  [ 10,     10,     10]], type=UInt8, shape=[3, 3]
  */

Fancy Indexing

• You can use fancy indexing!!!

  let a = MfArray([[1, 2], [3, 4], [5, 6]])
  
  a[MfArray([0, 1, 2]), MfArray([0, -1, 0])] = MfArray([999,888,777])
  print(a)
  /*
  mfarray = 
  [[    999,        2],
  [ 3,      888],
  [ 777,        6]], type=Int, shape=[3, 2]
  */
  
  a.T[MfArray([0, 1, -1]), MfArray([0, 1, 0])] = MfArray([-999,-888,-777])
  print(a)
  /*
  mfarray = 
  [[    -999,       -777],
  [ 3,      -888],
  [ 777,        6]], type=Int, shape=[3, 2]
  */

View

• Note that returned subscripted mfarray will have base property (is similar to view in Numpy). See numpy doc in detail.

  let a = Matft.arange(start: 0, to: 4*4*2, by: 1, shape: [4,4,2])
  
  let b = a[0~<, 1]
  b[~<<-1] = MfArray([9999]) // cannot pass Int directly such like 9999
  
  print(a)
  /*
  mfarray = 
  [[[   0,      1],
  [ 9999,       9999],
  [ 4,      5],
  [ 6,      7]],
  
  [[    8,      9],
  [ 9999,       9999],
  [ 12,     13],
  [ 14,     15]],
  
  [[    16,     17],
  [ 9999,       9999],
  [ 20,     21],
  [ 22,     23]],
  
  [[    24,     25],
  [ 9999,       9999],
  [ 28,     29],
  [ 30,     31]]], type=Int, shape=[4, 4, 2]
  */

Complex

Matft supports Complex!!

But this is beta version. so, any bug may be ocurred.

Please report me by issue! (Progres

TODO

• [x] Arithmetic Operation
• [x] Angle, Conjugate and Absolute
• [x] Math (partial: sin,cos,tan,exp,log)
• [x] Basic Subscription Getter
• [x] Basic Subscription Setter
• [x] Boolean Indexing Getter
• [ ] Boolean Indexing Setter
• [x] Fancy Indexing Getter
• [ ] Fancy Indexing Setter

let real = Matft.arange(start: 0, to: 16, by: 1).reshape([2,2,4])
let imag = Matft.arange(start: 0, to: -16, by: -1).reshape([2,2,4])
let a = MfArray(real: real, imag: imag)
print(a)

/*
mfarray = 
[[[    0 +0j,        1 -1j,        2 -2j,        3 -3j],
[    4 -4j,        5 -5j,        6 -6j,        7 -7j]],

[[    8 -8j,        9 -9j,        10 -10j,        11 -11j],
[    12 -12j,        13 -13j,        14 -14j,        15 -15j]]], type=Int, shape=[2, 2, 4]
*/

print(a+a)
/*
mfarray = 
[[[    0 +0j,        2 -2j,        4 -4j,        6 -6j],
[    8 -8j,        10 -10j,        12 -12j,        14 -14j]],

[[    16 -16j,        18 -18j,        20 -20j,        22 -22j],
[    24 -24j,        26 -26j,        28 -28j,        30 -30j]]], type=Int, shape=[2, 2, 4]
*/

print(Matft.complex.angle(a))
/*
mfarray = 
[[[    -0.0,        -0.7853982,        -0.7853982,        -0.7853982],
[    -0.7853982,        -0.7853982,        -0.7853982,        -0.7853982]],

[[    -0.7853982,        -0.7853982,        -0.7853982,        -0.7853982],
[    -0.7853982,        -0.7853982,        -0.7853982,        -0.7853982]]], type=Float, shape=[2, 2, 4]
*/

print(Matft.complex.conjugate(a))
/*
mfarray = 
[[[    0 +0j,        1 +1j,        2 +2j,        3 +3j],
[    4 +4j,        5 +5j,        6 +6j,        7 +7j]],

[[    8 +8j,        9 +9j,        10 +10j,        11 +11j],
[    12 +12j,        13 +13j,        14 +14j,        15 +15j]]], type=Int, shape=[2, 2, 4]
*/

Image

You can acheive an image processing by Matft! (Beta version) Please refer to the example here.

@IBOutlet weak var originalImageView: UIImageView!
@IBOutlet weak var reverseImageView: UIImageView!
@IBOutlet weak var swapImageView: UIImageView!

func reverse(){
    var image = Matft.image.cgimage2mfarray(self.reverseImageView.image!.cgImage!)

    // reverse
    image = image[Matft.reverse] // same as image[~<<-1]
    self.reverseImageView.image = UIImage(cgImage: Matft.image.mfarray2cgimage(image))
}

func swapchannel(){
    var image = Matft.image.cgimage2mfarray(self.swapImageView.image!.cgImage!)

    // swap channel
    image = image[Matft.all, Matft.all, MfArray([1,0,2,3])] // same as image[0~<, 0~<, MfArray([1,0,2,3])]
    self.swapImageView.image = UIImage(cgImage: Matft.image.mfarray2cgimage(image))
}

For more complex conversion, see OpenCV code.

Function List

Below is Matft's function list. As I mentioned above, almost functions are similar to Numpy. Also, these function use Accelerate framework inside, the perfomance may keep high.

* means method function exists too. Shortly, you can use a.shallowcopy() where a is MfArray.

^ means method function only. Shortly, you can use a.tolist() not Matft.tolist where a is MfArray.

# means support complex operation

• Creation

• Conversion

• File

• Operation

  Line 2 is infix (prefix) operator.

• Universal Fucntion Reduction

• Math function

• Statistics function

• Random function

• Linear algebra

• Complex

• FFT

• Interpolation

Matft supports only natural cubic spline. I'll implement other boundary condition later.

• Image

Performance

I use Accelerate framework, so all of MfArray operation may keep high performance.

let a = Matft.arange(start: 0, to: 10*10*10*10*10*10, by: 1, shape: [10,10,10,10,10,10])
let aneg = Matft.arange(start: 0, to: -10*10*10*10*10*10, by: -1, shape: [10,10,10,10,10,10])
let aT = a.T
let b = a.transpose(axes: [0,3,4,2,1,5])
let c = a.transpose(axes: [1,2,3,4,5,0])
let posb = a > 0

import numpy as np

a = np.arange(10**6).reshape((10,10,10,10,10,10))
aneg = np.arange(0, -10**6, -1).reshape((10,10,10,10,10,10))
aT = a.T
b = a.transpose((0,3,4,2,1,5))
c = a.transpose((1,2,3,4,5,0))
posb = a > 0

• Arithmetic test

• Math test

• Bool test

• Indexing test

Matft achieved almost same performance as Numpy!!!

※Swift's performance test was conducted in release mode

However, as you can see the above table, Matft's boolean operation is toooooooo slow...(Issue #18)

So, a pull request is very welcome!!

Installation

SwiftPM

• Import
  • Project > Build Setting > +
  • Select Rules
• Update
  • File >Swift Packages >Update to Latest Package versions

Important!!! the below installation is outdated. Please install Matft via swiftPM!!!

Carthage

• Set Cartfile

  echo 'github "jjjkkkjjj/Matft"' > Cartfile
  carthage update ###or append '--platform ios'

• Import Matft.framework made by above process to your project

CocoaPods

• Create Podfile (Skip if you have already done)

  pod init

• Write pod 'Matft' in Podfile such like below

  target 'your project' do
  pod 'Matft'
  end

• Install Matft

  pod install

Contact

Feel free to ask this project or anything via junnosuke.kado.git@gmail.com