This post is first for me, nice to meet you!
In this post, I’d like to introduceMatft library in swift to you.
Here is the source code link.
AboutMatft
Matft is easy and fast to operate vector, matrix, tensor(N dimensional array), and even complex and image data!
The nameMatft comes frommat-rix operation library in swi-ft.
If you are accustomed to usingNumpy in python,Matft will be the best option to achieve your matrix operation becauseMatft's function names are similar toNumpy's ones. (I'll show the examples later)
ManyNumpy's functions has already implemented inMatft.
You can operate complex number asNumpy can, and there is conversion function that convertsCGImage intoMfArray (Matft's object of n-dimensional array) vice versa.
Also, becauseMatft uses theAccelerate framework (link),Matft keeps high performance (some functions even achieves higher thanNumpy).
That's why I recommend to useMatft when you'd like to operate vector, matrix, tensor(N dimensional array), and even complex and image data
Basic usage
MfType
Matft's object to operate n-dimensional array is namedMfArray inMatft. AndMfArray hasmftype property topretend the n-dimensional array's type. (=Numpy's dtype)
Pretending means that the stored data type will beFloat orDouble only even if you setMfType.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 supports many types such like;
publicenumMfType:Int{caseNone// UnsupporttedcaseBoolcaseUInt8caseUInt16caseUInt32caseUInt64caseUIntcaseInt8caseInt16caseInt32caseInt64caseIntcaseFloatcaseDoublecaseObject// Unsupported}Initialization
In this section, I'll show the basic initialization ofMfArray.
From Swift Array
You can initializeMfArray from Swift's array. TheMfType will be inferred properly.
leta=MfArray([[[-8,-7,-6,-5],[-4,-3,-2,-1]],[[0,1,2,3],[4,5,6,7]]])print(a)/*mfarray = [[[ -8, -7, -6, -5],[ -4, -3, -2, -1]],[[ 0, 1, 2, 3],[ 4, 5, 6, 7]]], type=Int, shape=[2, 2, 4]*/Arrange
You can create the sequence array.
leta=Matft.arange(start:-8,to:8,by:1,shape:[2,2,4])print(a)/*mfarray = [[[ -8, -7, -6, -5],[ -4, -3, -2, -1]],[[ 0, 1, 2, 3],[ 4, 5, 6, 7]]], type=Int, shape=[2, 2, 4]*/Repeated Numbers
You can create the repeated numbers array such likenumpy.ones() * N.
leta=Matft.nums(Float(1),shape:[2,2,4])print(a)/*mfarray = [[[ 1.0, 1.0, 1.0, 1.0],[ 1.0, 1.0, 1.0, 1.0]],[[ 1.0, 1.0, 1.0, 1.0],[ 1.0, 1.0, 1.0, 1.0]]], type=Float, shape=[2, 2, 4]*/Etc.
The other functions are below;
| 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 |
MfData andMfStructure Conversion
MfArray consists of two main parts, which areMfData andMfStructure.MfData stores the pointer of raw data, the current type (=MfType), and the "stored" raw type (=StoredType, onlyFloat orDouble). On the other hand,MfStructure stores theshape andstrides property, which represents the current array's structure and are same asNumpy.
So, when we exploits theMfData andMfStructure, changing the array's structure (=MfStructure) is very efficient. For example, when you have thea array initialized below;
leta=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]*/Type conversion
You can convert the current type into many types byastype method or function.
leta=Matft.arange(start:0,to:27,by:1,shape:[3,3,3],mftype:.Int)print(a)/*mfarray = [[[ -6, -5, -4],[ -3, -2, -1],[ 0, 1, 2]],[[ 3, 4, 5],[ 6, 7, 8],[ 9, 10, 11]],[[ 12, 13, 14],[ 15, 16, 17],[ 18, 19, 20]]], type=Int, shape=[3, 3, 3]*/print(a.astype(.UInt8))/*mfarray = [[[ 250, 251, 252],[ 253, 254, 255],[ 0, 1, 2]],[[ 3, 4, 5],[ 6, 7, 8],[ 9, 10, 11]],[[ 12, 13, 14],[ 15, 16, 17],[ 18, 19, 20]]], type=UInt8, shape=[3, 3, 3]*/print(a.astype(.Float))/*mfarray = [[[ -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, 8.0],[ 9.0, 10.0, 11.0]],[[ 12.0, 13.0, 14.0],[ 15.0, 16.0, 17.0],[ 18.0, 19.0, 20.0]]], type=Float, shape=[3, 3, 3]*/Positive and Negative Indexing
You can extract the slicedMfArrray by~< efficiently.
Note that usea[0~<] instead ofa[:] to get all elements along axis (ora[Matft.all]).
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]*/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]*/Of course, you can set the value into the sliced array.
a[~<1]=Matft.arange(start:0,to:81,by:9,shape:[3,3])print(a)/*mfarray = [[[ 0, 9, 18],[ 27, 36, 45],[ 54, 63, 72]],[[ 9, 10, 11],[ 12, 13, 14],[ 15, 16, 17]],[[ 18, 19, 20],[ 21, 22, 23],[ 24, 25, 26]]], type=Int, shape=[3, 3, 3]*/Boolean Indexing
Matft supports also boolean indexing! So, you can extract the array with a specific condition you want like this. This feature will be convenient for an image processing. See thenumpy docs for more details.
letimg=Matft.arange(start:-5,to:70,by:1,shape:[5,5,3],mftype:.Float)print(img)/*mfarray = [[[ -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, 8.0, 9.0]],[[ 10.0, 11.0, 12.0],[ 13.0, 14.0, 15.0],[ 16.0, 17.0, 18.0],[ 19.0, 20.0, 21.0],[ 22.0, 23.0, 24.0]],[[ 25.0, 26.0, 27.0],[ 28.0, 29.0, 30.0],[ 31.0, 32.0, 33.0],[ 34.0, 35.0, 36.0],[ 37.0, 38.0, 39.0]],[[ 40.0, 41.0, 42.0],[ 43.0, 44.0, 45.0],[ 46.0, 47.0, 48.0],[ 49.0, 50.0, 51.0],[ 52.0, 53.0, 54.0]],[[ 55.0, 56.0, 57.0],[ 58.0, 59.0, 60.0],[ 61.0, 62.0, 63.0],[ 64.0, 65.0, 66.0],[ 67.0, 68.0, 69.0]]], type=Float, shape=[5, 5, 3]*/print(img[img<0])/*mfarray = [ -5.0, -4.0, -3.0, -2.0, -1.0], type=Float, shape=[5]*/img[img<0]=MfArray([0])print(img)/*mfarray = [[[ 0.0, 0.0, 0.0],[ 0.0, 0.0, 0.0],[ 1.0, 2.0, 3.0],[ 4.0, 5.0, 6.0],[ 7.0, 8.0, 9.0]],[[ 10.0, 11.0, 12.0],[ 13.0, 14.0, 15.0],[ 16.0, 17.0, 18.0],[ 19.0, 20.0, 21.0],[ 22.0, 23.0, 24.0]],[[ 25.0, 26.0, 27.0],[ 28.0, 29.0, 30.0],[ 31.0, 32.0, 33.0],[ 34.0, 35.0, 36.0],[ 37.0, 38.0, 39.0]],[[ 40.0, 41.0, 42.0],[ 43.0, 44.0, 45.0],[ 46.0, 47.0, 48.0],[ 49.0, 50.0, 51.0],[ 52.0, 53.0, 54.0]],[[ 55.0, 56.0, 57.0],[ 58.0, 59.0, 60.0],[ 61.0, 62.0, 63.0],[ 64.0, 65.0, 66.0],[ 67.0, 68.0, 69.0]]], type=Float, shape=[5, 5, 3]Fancy Indexing
Furthermore,Matft supports Fancy Indexing too! See thenumpy docs for more details.
leta=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]*/ Synchronizing extractedMfArray
As you can see the above examples,MfArray hasbase property (is similar to view in Numpy). Therefore, aMfArray extracted (Sliced) bypositive and negative indexing is synchronized. Seenumpy doc for more details.
Note that aMfArray extracted byBoolean Indexing andFancy Indexing isCOPY ofMfArray of the original one.
leta=Matft.arange(start:0,to:4*4*2,by:1,shape:[4,4,2])letb=a[0~<,1]b[~<<-1]=MfArray([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]*/Etc.
The other conversion functions are below;
| 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 |
Math operation
Basic mathematic operations are supported inMatft.
Arithmetic operation
print(a+a)/*mfarray = [[ 0, 2, 4],[ 6, 8, 10],[ 12, 14, 16]], type=Int, shape=[3, 3]*/print(a-a)/*mfarray = [[ 0, 0, 0],[ 0, 0, 0],[ 0, 0, 0]], type=Int, shape=[3, 3]*/print(a*a)/*mfarray = [[ 0, 1, 4],[ 9, 16, 25],[ 36, 49, 64]], type=Int, shape=[3, 3]*/print(a/a)/*mfarray = [[ -nan, 0.99999994, 0.99999994],[ 0.99999994, 0.99999994, 0.99999994],[ 0.99999994, 0.99999994, 0.99999994]], type=Float, shape=[3, 3]*/Broadcasting
The one of the main features inNumpy is broadcasting operation. Seenumpy doc for more details.
leta=Matft.arange(start:0,to:3*3,by:1,shape:[3,3])letb=MfArray([-4,10,2]).reshape([3,1])print(a+b)/*mfarray = [[ -4, -3, -2],[ 13, 14, 15],[ 8, 9, 10]], type=Int, shape=[3, 3]*/Etc.
Matft has many mathematic functions.
- 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 |
Advanced operation
Matft has complex and image processing functions too!!!!
So,Matft will be very useful for the signal and image processing!
But these functions are beta versions currently (on 22/08/08).
Complex operation
You can operate the complex values like the real ones.
letreal=Matft.arange(start:0,to:16,by:1).reshape([2,2,4])letimag=Matft.arange(start:0,to:-16,by:-1).reshape([2,2,4])leta=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]*/| Matft | Numpy |
|---|---|
| Matft.complex.angle | numpy.angle |
| Matft.complex.conjugate | numpy.conj / numpy.conjugate |
| Matft.complex.abs | numpy.abs / numpy.absolute |
Image operation
Conversion from/toCGImage
The conversion functions betweenMfArray andCGImage are ready. So, you can implement the complex image operation code
very easily! For example, if you use theMatft's indexing feature,...
importUIKitimportMatftimportAccelerateimportCoreGraphicsimportCoreGraphics.CGBitmapContextclassViewController:UIViewController{@IBOutletweakvaroriginalImageView:UIImageView!@IBOutletweakvarreverseImageView:UIImageView!@IBOutletweakvargrayreverseImageView:UIImageView!@IBOutletweakvarswapImageView:UIImageView!overridefuncviewDidLoad(){super.viewDidLoad()self.originalImageView.image=UIImage(named:"rena.jpeg")self.reverseImageView.image=UIImage(named:"rena.jpeg")self.grayreverseImageView.image=self.convertToGrayScale(image:UIImage(named:"rena.jpeg")!)self.swapImageView.image=UIImage(named:"rena.jpeg")self.reverse()self.grayreverse()self.swapchannel()self.resize()}funcreverse(){varimage=Matft.image.cgimage2mfarray(self.reverseImageView.image!.cgImage!)// reverseimage=image[Matft.reverse]// same as image[~<<-1]self.reverseImageView.image=UIImage(cgImage:Matft.image.mfarray2cgimage(image))}funcswapchannel(){varimage=Matft.image.cgimage2mfarray(self.swapImageView.image!.cgImage!)// swap channelimage=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))}funcgrayreverse(){varimage=Matft.image.cgimage2mfarray(self.grayreverseImageView.image!.cgImage!,mftype:.UInt8)// reverseimage=image[Matft.reverse]// same as image[~<<-1]self.grayreverseImageView.image=UIImage(cgImage:Matft.image.mfarray2cgimage(image))}funcconvertToGrayScale(image:UIImage)->UIImage{//let gray_mfarray = (Matft.image.color(Matft.image.cgimage2mfarray(image.cgImage!)) * Float(255)).astype(.UInt8)letgray_mfarray=Matft.image.color(Matft.image.cgimage2mfarray(image.cgImage!))returnUIImage(cgImage:Matft.image.mfarray2cgimage(gray_mfarray))}funcresize(){varimage=Matft.image.cgimage2mfarray(self.swapImageView.image!.cgImage!)// resizeimage=Matft.image.resize(image,width:300,height:300)self.swapImageView.image=UIImage(cgImage:Matft.image.mfarray2cgimage(image))//self.swapImageView.frame = CGRect(x: 0, y: 0, width: 300, height: 300)}}
Awesome!
Affine
// CGImage to MfArrayletrgb=Matft.image.cgimage2mfarray(uiimage.cgImage!)// Convert RGBA into Gray Imageletgray=Matft.image.color(rgb)// Resizeletrgb_resize=Matft.image.resize(rgb,width:150,height:150)letgray_resize=Matft.image.resize(gray,width:300,height:300)letrbg_rotated=Matft.image.warpAffine(rgb_resize,matrix:MfArray([[0,1,1],[1,0,0]]as[[Float]]),width:150,height:150)letgray_rotated=Matft.image.warpAffine(gray_resize,matrix:MfArray([[0,1,1],[1,0,0]]as[[Float]]),width:150,height:150)Matft.image.mfarray2cgimage(rbg_rotated)
| 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 |
Conclusion
I introduced theMatft in this post.Matft has many features from the basic mathematic array operations to the complicated operations such like boolean indexing, fancy indexing, complex data, image data and so on.
I hopeMatft will be useful for your project and help your project more efficient!
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