Matft

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

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

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

Feature & Usage

• Many types

• Pretty print

• Indexing

  • Positive
  • Negative
  • Boolean
  • Fancy

• Slicing

  • Start / To / By
  • New Axis

• View

  • Assignment

• Conversion

  • Broadcast
  • Transpose
  • Reshape
  • Astype

• Univarsal function reduction

• Mathematic

  • Arithmetic
  • Statistic
  • Linear Algebra

...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, ":"

(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

  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]
  */

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[~<~<-1])
  //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]
  */

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.

• Creation

• Conversion

• File

  save function has not developed yet.

• Operation

  Line 2 is infix (prefix) operator.

• Universal Fucntion Reduction

• Math function

• Statistics function

• Linear algebra

• Interpolation

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

Performance

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

func testPefAdd1() {
        do{
            let a = Matft.arange(start: 0, to: 10*10*10*10*10*10, by: 1, shape: [10,10,10,10,10,10])
            let b = Matft.arange(start: 0, to: -10*10*10*10*10*10, by: -1, shape: [10,10,10,10,10,10])
            
            self.measure {
                let _ = a+b
            }
            /*
             '-[MatftTests.ArithmeticPefTests testPefAdd1]' measured [Time, seconds] average: 0.001, relative standard deviation: 23.418%, values: [0.001707, 0.001141, 0.000999, 0.000969, 0.001029, 0.000979, 0.001031, 0.000986, 0.000963, 0.001631]
            1.14ms
             */
        }
    }
    
    func testPefAdd2(){
        do{
            let a = Matft.arange(start: 0, to: 10*10*10*10*10*10, by: 1, shape: [10,10,10,10,10,10])
            let b = a.transpose(axes: [0,3,4,2,1,5])
            let c = a.T
            
            self.measure {
                let _ = b+c
            }
            /*
             '-[MatftTests.ArithmeticPefTests testPefAdd2]' measured [Time, seconds] average: 0.004, relative standard deviation: 5.842%, values: [0.004680, 0.003993, 0.004159, 0.004564, 0.003955, 0.004200, 0.003998, 0.004317, 0.003919, 0.004248]
            4.20ms
             */
        }
    }

    func testPefAdd3(){
        do{
            let a = Matft.arange(start: 0, to: 10*10*10*10*10*10, by: 1, shape: [10,10,10,10,10,10])
            let b = a.transpose(axes: [1,2,3,4,5,0])
            let c = a.T
            
            self.measure {
                let _ = b+c
            }
            /*
             '-[MatftTests.ArithmeticPefTests testPefAdd3]' measured [Time, seconds] average: 0.004, relative standard deviation: 16.815%, values: [0.004906, 0.003785, 0.003702, 0.005981, 0.004261, 0.003665, 0.004083, 0.003654, 0.003836, 0.003874]
            4.17ms
             */
        }

Matft achieved almost same performance as Numpy!!!

※Swift's performance test was conducted in release mode

My codes have several overhead and redundant part so this performance could be better than now.

import numpy as np
#import timeit

a = np.arange(10**6).reshape((10,10,10,10,10,10))
b = np.arange(0, -10**6, -1).reshape((10,10,10,10,10,10))

#timeit.timeit("b+c", repeat=10, globals=globals())
%timeit -n 10 a+b
"""
962 µs ± 273 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
"""

a = np.arange(10**6).reshape((10,10,10,10,10,10))
b = a.transpose((0,3,4,2,1,5))
c = a.T
#timeit.timeit("b+c", repeat=10, globals=globals())
%timeit -n 10 b+c
"""
5.68 ms ± 1.45 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
"""

a = np.arange(10**6).reshape((10,10,10,10,10,10))
b = a.transpose((1,2,3,4,5,0))
c = a.T
#timeit.timeit("b+c", repeat=10, globals=globals())
%timeit -n 10 b+c
"""
3.92 ms ± 897 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
"""

Installation

SwiftPM

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

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