Performance

Matft uses Apple's Accelerate framework, so MfArray operations keep high performance. The tables below compare Matft with Numpy on the same inputs, prepared as follows.

let a = Matft.arange(start: 0, to: 10*10*10*10*10*10, by: 1, shape: [10,10,10,10,10,10])
let ad = a.astype(.Double)
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
let idx = MfArray([1, 3, 5, 7, 9])
let values = a[posb]
let signal = Matft.arange(start: 0, to: 1024*1024, by: 1, shape: [1024, 1024], mftype: .Float)
let v = Matft.arange(start: 0, to: 10000, by: 1)
let nested: [[Float]] = (0..<1000).map{ i in (0..<100).map{ Float(i*100 + $0) } }
let m = MfArray((0..<256).map{ (i: Int) -> [Double] in (0..<256).map{ (j: Int) -> Double in i == j ? 256 : Double((i*256 + j) % 7) } })

import numpy as np

a = np.arange(10**6).reshape((10,10,10,10,10,10))
ad = a.astype(np.float64)
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
idx = np.array([1, 3, 5, 7, 9])
values = a[posb]
signal = np.arange(1024*1024, dtype=np.float32).reshape((1024,1024))
v = np.arange(10000)
nested = np.arange(100000, dtype=np.float32).reshape(1000, 100).tolist()
m = np.fromfunction(lambda i, j: np.where(i == j, 256, (i*256 + j) % 7), (256, 256))

• Arithmetic

Matft	time	Numpy	time	Matft / Numpy
let _ = a+aneg	52.1μs	a+aneg	197μs	0.26x
let _ = b+aT	689μs	b+aT	959μs	0.72x
let _ = c+aT	864μs	c+aT	735μs	1.18x
let _ = a + Float(0.5)	30.3μs	a + np.float32(0.5)	319μs	0.10x

• Math

Matft	time	Numpy	time	Matft / Numpy
let _ = Matft.math.sin(a)	290μs	np.sin(a)	2.80ms	0.10x
let _ = Matft.math.sin(b)	289μs	np.sin(b)	2.81ms	0.10x
let _ = Matft.math.sign(a)	265μs	np.sign(a)	128μs	2.08x
let _ = Matft.math.sign(b)	266μs	np.sign(b)	128μs	2.09x
let _ = Matft.math.power(bases: ad, exponents: 2)	125μs	np.power(ad, 2)	4.06ms	0.03x
let _ = Matft.math.arctan2(x1: ad, x2: ad)	1.93ms	np.arctan2(ad, ad)	1.09ms	1.76x

• Stats

Matft	time	Numpy	time	Matft / Numpy
let _ = a.mean()	34.0μs	a.mean()	347μs	0.10x
let _ = Matft.stats.cumsum(a, axis: 0)	31.3μs	np.cumsum(a, axis=0)	645μs	0.05x
let _ = Matft.stats.cumsum(a, axis: 5)	371μs	np.cumsum(a, axis=5)	686μs	0.54x
let _ = Matft.stats.cumsum(v)	16.1μs	np.cumsum(v)	15.0μs	1.07x
let _ = a.argmax(axis: 5)	961μs	np.argmax(a, axis=5)	211μs	4.56x
let _ = a.argmax(axis: 0)	916μs	np.argmax(a, axis=0)	562μs	1.63x

• Conversion

Matft	time	Numpy	time	Matft / Numpy
let _ = aneg.argsort(axis: -1)	7.02ms	np.argsort(aneg, axis=-1)	2.41ms	2.91x
let _ = a.astype(.Double)	122μs	a.astype(np.float64)	236μs	0.52x
let _ = Matft.deepcopy(a)	49.2μs	a.copy()	128μs	0.38x
let _ = a.reshape([1000, 1000])	49.4μs	a.reshape((1000, 1000)).copy()	132μs	0.37x

• Creation

Matft	time	Numpy	time	Matft / Numpy
let _ = MfArray(nested)	3.95ms	np.array(nested, dtype=np.float32)	1.19ms	3.31x
let _ = Matft.nums(Float(1), shape: [1000, 1000])	47.7μs	np.full((1000, 1000), 1, dtype=np.float32)	48.6μs	0.98x

• LinAlg

Matft	time	Numpy	time	Matft / Numpy
let _ = try! Matft.linalg.inv(m)	490μs	np.linalg.inv(m)	506μs	0.97x

• Bool

Matft	time	Numpy	time	Matft / Numpy
let _ = a > 0	122μs	a > 0	75.9μs	1.60x
let _ = ad > 0	248μs	ad > 0	156μs	1.59x
let _ = a > b	474μs	a > b	394μs	1.20x
let _ = a === 0	184μs	a == 0	75.6μs	2.43x
let _ = a === b	551μs	a == b	407μs	1.36x
let _ = a === 5	232μs	a == 5	76.6μs	3.03x
let _ = a !== 0	187μs	a != 0	87.6μs	2.13x
let _ = Matft.logical_not(posb)	28.7μs	np.logical_not(posb)	17.8μs	1.62x
let _ = a == a	114μs	np.array_equal(a, a)	110μs	1.03x

• FFT

Matft	time	Numpy	time	Matft / Numpy
let _ = Matft.fft.rfft(signal)	1.98ms	np.fft.rfft(signal)	1.43ms	1.39x
let _ = Matft.fft.rfft(signal, vDSP: true)	629μs	np.fft.rfft(signal)	1.45ms	0.43x

• Indexing

Matft	time	Numpy	time	Matft / Numpy
let _ = a[posb]	319μs	a[posb]	391μs	0.82x
let _ = a[a > 0]	443μs	a[a > 0]	448μs	0.99x
let _ = aT[aT > 0]	3.47ms	aT[aT > 0]	1.55ms	2.24x
let _ = a[idx]	11.3μs	a[idx]	50.0μs	0.23x
let x = Matft.deepcopy(a); x[x > 0] = MfArray([0])	360μs	x = a.copy(); x[x > 0] = 0	556μs	0.65x
let x = Matft.deepcopy(a); x[posb] = values	667μs	x = a.copy(); x[posb] = values	529μs	1.26x
let x = Matft.deepcopy(a).T; x[x > 0] = MfArray([0])	3.88ms	x = a.copy().T; x[x > 0] = 0	1.73ms	2.24x

Measured on Apple M5, macOS 26.5.1, Swift version 6.2.3, Python 3.9.6, numpy 2.0.2 (Matft 1.0.0, 2026-09-27).

Matft: median of XCTest measure {} in release build (swift test -c release), after a warm-up and with several calls per sample (like timeit). Numpy: median of timeit. Ratios > 1 (Matft slower) are shown in bold.

Regenerate with python3 scripts/benchmark.py --update-docs.

Performance improvements are always welcome (Issue #18)!!