## Feature & Usage

• Many types

• Pretty print

• Indexing

• Positive
• Negative
• Boolean
• Fancy
• Slicing

• Start / To / By
• New Axis
• View

• Assignment
• Conversion

• 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
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.conv_order *numpy.ascontiguousarray
*Matft.flatten *numpy.flatten
*Matft.flip *numpy.flip
*Matft.clip *numpy.clip
*Matft.swapaxes *numpy.swapaxes
*Matft.moveaxis *numpy.moveaxis
*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.genfromtxt numpy.genfromtxt
Matft.file.savetxt numpy.savetxt
• Operation

Line 2 is infix (prefix) operator.

Matft Numpy
+
+
Matft.sub
-
numpy.sub
-
Matft.div
/
numpy.div
.
Matft.mul
*
numpy.multiply
*
Matft.inner
*+
numpy.inner
n/a
Matft.cross
*^
numpy.cross
n/a
Matft.matmul
*&
numpy.matmul
@
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_equal
n/a
Matft.neg
-
numpy.negative
-
• Universal Fucntion Reduction
Matft Numpy
*Matft.ufuncReduce
*Matft.ufuncAccumulate
• 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.sin 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.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
• Interpolation

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

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

## 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 863μs a+aneg 1.04ms
let _ = b+aT 4.47ms b+aT 4.31ms
let _ = c+aT 5.30ms c+aT 2.92ms
• Math test
Matft time Numpy time
let _ = Matft.math.sin(a) 1.80ms np.sin(a) 14.7ms
let _ = Matft.math.sin(b) 8.24ms np.sin(b) 15.8ms
let _ = Matft.math.sign(a) 30.4ms np.sign(a) 1.37ms
let _ = Matft.math.sign(b) 35.6ms np.sign(b) 1.42ms
• Bool test
Matft time Numpy time
let _ = a > 0 7.27ms a > 0 855μs
let _ = a > b 13.3ms a > b 1.83ms
let _ = a === 0 9.91ms a == 0 603μs
let _ = a === b 22.3ms a == b 1.78ms
• Indexing test
Matft time Numpy time
let _ = a[posb] 1.07ms 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

Caution: I strongly recommend to use SwiftPM!!

### 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'

### CocoaPods

• Create Podfile (Skip if you have already done)

pod init

• Write pod 'Matft' in Podfile such like below

pod 'Matft'
end

• Install Matft

pod install

## Contact

Feel free to ask this project or anything via [email protected]

## GitHub

https://github.com/jjjkkkjjj/Matft