Matft

Numpy-like library in swift. (Multi-dimensional Array, ndarray, matrix and vector library)

Programming language: Swift

License: BSD 3-clause "New" or "Revised" License

Tags: Math    

README

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](#-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.

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

• swift Matft.newaxis

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

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

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

(Positive) Indexing

• Normal indexing ```swift
  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

  #### Slicing

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

  ```swift
  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!

TODO

• [x] Arithmetic Operation
• [x] Angle, Conjugate and Absolute
• [x] Math (partial: sin,cos,tan,exp,log)
• [x] Basic Subscription Getter
• [ ] 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](./MatftDemo/MatftDemo/ViewController.swift).

@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

Matft	Numpy
*#Matft.shallowcopy	*numpy.copy
*#Matft.deepcopy	copy.deepcopy
Matft.nums	numpy.ones * N
Matft.nums_like	numpy.ones_like * N
Matft.arange	numpy.arange
Matft.eye	numpy.eye
Matft.diag	numpy.diag
Matft.vstack	numpy.vstack
Matft.hstack	numpy.hstack
Matft.concatenate	numpy.concatenate
*Matft.append	numpy.append
*Matft.insert	numpy.insert
*Matft.take	numpy.take

• Conversion

Matft	Numpy
*#Matft.astype	*numpy.astype
*#Matft.transpose	*numpy.transpose
*#Matft.expand_dims	*numpy.expand_dims
*#Matft.squeeze	*numpy.squeeze
*#Matft.broadcast_to	*numpy.broadcast_to
*#Matft.to_contiguous	*numpy.ascontiguousarray
*#Matft.flatten	*numpy.flatten
*#Matft.flip	*numpy.flip
*#Matft.clip	*numpy.clip
*#Matft.swapaxes	*numpy.swapaxes
*#Matft.moveaxis	*numpy.moveaxis
*Matft.roll	numpy.roll
*Matft.sort	*numpy.sort
*Matft.argsort	*numpy.argsort
MfArray.toArray	numpy.ndarray.tolist
MfArray.toFlattenArray	n/a
*Matft.orderedUnique	numpy.unique

• File

Matft	Numpy
Matft.file.loadtxt	numpy.loadtxt
Matft.file.genfromtxt	numpy.genfromtxt
Matft.file.savetxt	numpy.savetxt

• Operation

Line 2 is infix (prefix) operator.

Matft	Numpy
#Matft.add+	numpy.add+
#Matft.sub-	numpy.sub-
#Matft.div/	numpy.div.
#Matft.mul*	numpy.multiply*
Matft.inner*+	numpy.innern/a
Matft.cross*^	numpy.crossn/a
Matft.matmul*&	numpy.matmul@
Matft.dot	numpy.dot
Matft.equal===	numpy.equal==
Matft.not_equal!==	numpy.not_equal!=
Matft.less<	numpy.less<
Matft.less_equal<=	numpy.less_equal<=
Matft.greater>	numpy.greater>
Matft.greater_equal>=	numpy.greater_equal>=
#Matft.allEqual==	numpy.array_equaln/a
#Matft.neg-	numpy.negative-

• Universal Fucntion Reduction

Matft	Numpy
*#Matft.ufuncReducee.g.) Matft.ufuncReduce(a, Matft.add)	numpy.add.reducee.g.) numpy.add.reduce(a)
*#Matft.ufuncAccumulatee.g.) Matft.ufuncAccumulate(a, Matft.add)	numpy.add.accumulatee.g.) numpy.add.accumulate(a)

• Math function

Matft	Numpy
#Matft.math.sin	numpy.sin
Matft.math.asin	numpy.asin
Matft.math.sinh	numpy.sinh
Matft.math.asinh	numpy.asinh
#Matft.math.cos	numpy.cos
Matft.math.acos	numpy.acos
Matft.math.cosh	numpy.cosh
Matft.math.acosh	numpy.acosh
#Matft.math.tan	numpy.tan
Matft.math.atan	numpy.atan
Matft.math.tanh	numpy.tanh
Matft.math.atanh	numpy.atanh
Matft.math.sqrt	numpy.sqrt
Matft.math.rsqrt	numpy.rsqrt
#Matft.math.exp	numpy.exp
#Matft.math.log	numpy.log
Matft.math.log2	numpy.log2
Matft.math.log10	numpy.log10
*Matft.math.ceil	numpy.ceil
*Matft.math.floor	numpy.floor
*Matft.math.trunc	numpy.trunc
*Matft.math.nearest	numpy.nearest
*Matft.math.round	numpy.round
#Matft.math.abs	numpy.abs
Matft.math.reciprocal	numpy.reciprocal
#Matft.math.power	numpy.power
Matft.math.arctan2	numpy.arctan2
Matft.math.square	numpy.square
Matft.math.sign	numpy.sign

• Statistics function

Matft	Numpy
*Matft.stats.mean	*numpy.mean
*Matft.stats.max	*numpy.max
*Matft.stats.argmax	*numpy.argmax
*Matft.stats.min	*numpy.min
*Matft.stats.argmin	*numpy.argmin
*Matft.stats.sum	*numpy.sum
Matft.stats.maximum	numpy.maximum
Matft.stats.minimum	numpy.minimum
*Matft.stats.sumsqrt	n/a
*Matft.stats.squaresum	n/a
*Matft.stats.cumsum	*numpy.cumsum

• Random function

Matft	Numpy
Matft.random.rand	numpy.random.rand
Matft.random.randint	numpy.random.randint

• Linear algebra

Matft	Numpy
Matft.linalg.solve	numpy.linalg.solve
Matft.linalg.inv	numpy.linalg.inv
Matft.linalg.det	numpy.linalg.det
Matft.linalg.eigen	numpy.linalg.eig
Matft.linalg.svd	numpy.linalg.svd
Matft.linalg.pinv	numpy.linalg.pinv
Matft.linalg.polar_left	scipy.linalg.polar
Matft.linalg.polar_right	scipy.linalg.polar
Matft.linalg.normlp_vec	scipy.linalg.norm
Matft.linalg.normfro_mat	scipy.linalg.norm
Matft.linalg.normnuc_mat	scipy.linalg.norm

• Complex

Matft	Numpy
Matft.complex.angle	numpy.angle
Matft.complex.conjugate	numpy.conj / numpy.conjugate
Matft.complex.abs	numpy.abs / numpy.absolute

• Interpolation

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

Matft	Numpy
Matft.interp1d.cubicSpline	scipy.interpolation.CubicSpline

• Image

Matft	Numpy
Matft.image.cgimage2mfarray	N/A
Matft.image.mfarray2cgimage	N/A

Matft	OpenCV
Matft.image.color	cv2.cvtColor
Matft.image.resize	cv2.resize
Matft.image.warpAffine	cv2.warpAffine

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

Matft	time	Numpy	time
let _ = a+aneg	596μs	a+aneg	1.04ms
let _ = b+aT	4.46ms	b+aT	4.31ms
let _ = c+aT	5.31ms	c+aT	2.92ms

• Math test

Matft	time	Numpy	time
let _ = Matft.math.sin(a)	2.14ms	np.sin(a)	14.7ms
let _ = Matft.math.sin(b)	7.02ms	np.sin(b)	15.8ms
let _ = Matft.math.sign(a)	3.09ms	np.sign(a)	1.37ms
let _ = Matft.math.sign(b)	8.33ms	np.sign(b)	1.42ms

• Bool test

Matft	time	Numpy	time
let _ = a > 0	4.63ms	a > 0	855μs
let _ = a > b	17.8ms	a > b	1.83ms
let _ = a === 0	4.65ms	a == 0	603μs
let _ = a === b	19.7ms	a == b	1.78ms

• Indexing test

Matft	time	Numpy	time
let _ = a[posb]	1.21ms	a[posb]	1.29ms

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 [email protected]