纯数学工具
min
- 获取矩阵的最小值
Object min({int dim = -1})
test
import 'dart:math';
import 'package:flutter_matrix/matrix_type.dart';
main(){
var mt = Matrix.fromList([
[double.nan, 3, -5, 0.5],
[5, 9, 10, double.negativeInfinity],
[-5, 3, 0, double.infinity],
]);
print(mt.min(dim: 0));
print(mt.min(dim: 1));
print(mt.min(dim: 2));
print(min(double.nan, double.negativeInfinity));
}
output
[NaN, -Infinity, -5.0]
[NaN, 3.0, -5.0, -Infinity]
NaN
NaN
max
- 获取矩阵的最大值
Object max({int dim = -1})
test
import 'dart:math';
import 'package:flutter_matrix/matrix_type.dart';
main(){
var mt = Matrix.fromList([
[double.nan, 3, -5, 0.5],
[5, 9, 10, double.negativeInfinity],
[-5, 3, 0, double.infinity],
]);
print(mt.max(dim: 0));
print(mt.max(dim: 1));
print(mt.max(dim: 2));
print(max(double.nan, double.infinity));
}
output
[NaN, 10.0, Infinity]
[NaN, 9.0, 10.0, Infinity]
NaN
NaN
argmin
- 获取矩阵的最小值的索引
Object argmin({int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
var mt = Matrix.fromList([
[double.nan, 3, -5, 0.5],
[5, 9, 10, double.negativeInfinity],
[-5, 3, 0, double.infinity],
]);
print(mt.argmin(dim: 0));
print(mt.argmin(dim: 1));
print(mt.argmin(dim: 2));
print(double.nan == double.nan); // always false
var mt2 = Matrix.fromList([
[4.3, 3, -5, 0.5],
[5, 9, 10, double.negativeInfinity],
[-5, 3, 0, double.infinity],
]);
print(mt2.argmin(dim: 0));
print(mt2.argmin(dim: 1));
print(mt2.argmin(dim: 2));
}
output
[-1, 3, 0]
[-1, 0, 0, 1]
-1
false
[2, 3, 0]
[2, 0, 0, 1]
7
argmax
- 获取矩阵的最大值的索引
Object argmax({int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
var mt = Matrix.fromList([
[double.nan, 3, -5, 0.5],
[5, 9, 10, double.negativeInfinity],
[-5, 3, 0, double.infinity],
]);
print(mt.argmax(dim: 0));
print(mt.argmax(dim: 1));
print(mt.argmax(dim: 2));
print(double.nan == double.nan); // always false
var mt2 = Matrix.fromList([
[4.3, 3, -5, 0.5],
[5, 9, 10, double.negativeInfinity],
[-5, 3, 0, double.infinity],
]);
print(mt2.argmax(dim: 0));
print(mt2.argmax(dim: 1));
print(mt2.argmax(dim: 2));
}
output
[-1, 2, 3]
[-1, 1, 1, 2]
-1
false
[0, 2, 3]
[1, 1, 1, 2]
11
getRange
- 获取矩阵的值域，返回值为与Range相关的类型
Object getRange({int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
var mt2 = Matrix.fromList([
[4.3, 3, -5, 0.5],
[5, 9, 10, double.negativeInfinity],
[-5, 3, 0, double.infinity],
]);
print(mt2.getRange(dim: 0));
print(mt2.getRange(dim: 1));
print(mt2.getRange(dim: 2));
}
output
[Range: [-5.0, 4.3], count: 0, Range: (-Infinity, 10.0], count: 0, Range: [-5.0, Infinity), count: 0]
[Range: [-5.0, 5.0], count: 0, Range: [3.0, 9.0], count: 0, Range: [-5.0, 10.0], count: 0, Range: (-Infinity, Infinity), count: 0]
Range: (-Infinity, Infinity), count: 0
sum
- 求和
Object sum({int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
var mt = Matrix.fromList([
[4.3, 3, -5, 0.5],
[5, 9, 10, 6],
[-5, 3, 0, double.infinity],
]);
print(mt.sum(dim: 0));
print(mt.sum(dim: 1));
print(mt.sum(dim: 2));
}
output
[2.8, 30.0, Infinity]
[4.300000000000001, 15.0, 5.0, Infinity]
Infinity
power
- 矩阵的数据的number幂次方，reverse为true则表示矩阵数据为幂
T power({required double number, bool reverse = false})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList([
[4.3, 3, -5, 0.5],
[5, 9, 10, double.negativeInfinity],
[-5, 3, 0, double.infinity],
]);
mt.power(number: 2, reverse: true).visible();
mt.power(number: 2, reverse: false).visible();
(mt ^ 2).visible();
}
output
[
[ 19.69831 8.00000 0.03125 1.41421]
[ 32.00000 512.00000 1024.00000 0.00000]
[ 0.03125 8.00000 1.00000 Infinity]
]
[
[ 18.49000 9.00000 25.00000 0.25000]
[ 25.00000 81.00000 100.00000 Infinity]
[ 25.00000 9.00000 0.00000 Infinity]
]
[
[ 18.49000 9.00000 25.00000 0.25000]
[ 25.00000 81.00000 100.00000 Infinity]
[ 25.00000 9.00000 0.00000 Infinity]
]
atan2
- 方位角公式，reverse为true表示number为分母，反之为分子
T atan2({required double number, bool reverse = false})
test
import 'dart:math';
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList([
[1, sqrt(3), sqrt(3) / 3]
]);
mt.atan2(number: 1, reverse: true).visible();
mt.atan2(number: 1, reverse: false).visible();
}
output
[
[ 0.78540 0.52360 1.04720]
]
[
[ 0.78540 1.04720 0.52360]
]
一些单变量通用数学方法
T get sin => _fromList(self.sinExtension);
T get cos => _fromList(self.cosExtension);
T get tan => _fromList(self.tanExtension);
T get asin => _fromList(self.asinExtension);
T get acos => _fromList(self.acosExtension);
T get atan => _fromList(self.atanExtension);
T get sinh => _fromList(self.sinhExtension);
T get cosh => _fromList(self.coshExtension);
T get tanh => _fromList(self.tanhExtension);
T get asinh => _fromList(self.asinhExtension);
T get acosh => _fromList(self.acoshExtension);
T get atanh => _fromList(self.atanhExtension);
T get exp => _fromList(self.expExtension);
T get log => _fromList(self.logExtension);
T get sqrt => _fromList(self.sqrtExtension);
T get log10 => _fromList(self.log10Extension);
T get square => _fromList(self.squareExtension);
T get cube => _fromList(self.cubeExtension);
T get abs => _fromList(self.absExtension);
T get ceil => _fromList(self.ceilExtension);
T get floor => _fromList(self.floorExtension);
T get round => _fromList(self.roundExtension);
T get degree => _fromList(self.degreeExtension);
T get radian => _fromList(self.radianExtension);
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList([List.generate(9, (_) => _ + 0.0)].reshape(row: 3, column: 3));
mt.visible();
mt.sin.visible(start_point: '-----sin-----');
mt.cos.visible(start_point: '-----cos-----');
mt.tan.visible(start_point: '-----tan-----');
mt.asin.visible(start_point: '-----asin-----');
mt.acos.visible(start_point: '-----acos-----');
mt.atan.visible(start_point: '-----atan-----');
mt.sinh.visible(start_point: '-----sinh-----');
mt.cosh.visible(start_point: '-----cosh-----');
mt.tanh.visible(start_point: '-----tanh-----');
mt.asinh.visible(start_point: '-----asinh-----');
mt.acosh.visible(start_point: '-----acosh-----');
mt.atanh.visible(start_point: '-----atanh-----');
mt.exp.visible(start_point: '-----exp-----');
mt.log.visible(start_point: '-----log-----');
mt.sqrt.visible(start_point: '-----sqrt-----');
mt.log10.visible(start_point: '-----log10-----');
mt.square.visible(start_point: '-----square-----');
mt.cube.visible(start_point: '-----cube-----');
mt.abs.visible(start_point: '-----abs-----');
mt.ceil.visible(start_point: '-----ceil-----');
mt.floor.visible(start_point: '-----floor-----');
mt.round.visible(start_point: '-----round-----');
mt.degree.visible(start_point: '-----degree-----');
mt.radian.visible(start_point: '-----radian-----');
}
output
[
[ 0.00000 1.00000 2.00000]
[ 3.00000 4.00000 5.00000]
[ 6.00000 7.00000 8.00000]
]
-----sin-----
[
[ 0.00000 0.84147 0.90930]
[ 0.14112 -0.75680 -0.95892]
[ -0.27942 0.65699 0.98936]
]
-----cos-----
[
[ 1.00000 0.54030 -0.41615]
[ -0.98999 -0.65364 0.28366]
[ 0.96017 0.75390 -0.14550]
]
-----tan-----
[
[ 0.00000 1.55741 -2.18504]
[ -0.14255 1.15782 -3.38052]
[ -0.29101 0.87145 -6.79971]
]
-----asin-----
[
[ 0.00000 1.57080 NaN]
[ NaN NaN NaN]
[ NaN NaN NaN]
]
-----acos-----
[
[ 1.57080 0.00000 NaN]
[ NaN NaN NaN]
[ NaN NaN NaN]
]
-----atan-----
[
[ 0.00000 0.78540 1.10715]
[ 1.24905 1.32582 1.37340]
[ 1.40565 1.42890 1.44644]
]
-----sinh-----
[
[ 0.00000 1.17520 3.62686]
[ 10.01787 27.28992 74.20321]
[201.71316 548.31612 1490.47883]
]
-----cosh-----
[
[ 1.00000 1.54308 3.76220]
[ 10.06766 27.30823 74.20995]
[201.71564 548.31704 1490.47916]
]
-----tanh-----
[
[ 0.00000 0.76159 0.96403]
[ 0.99505 0.99933 0.99991]
[ 0.99999 1.00000 1.00000]
]
-----asinh-----
[
[ 0.00000 0.88137 1.44364]
[ 1.81845 2.09471 2.31244]
[ 2.49178 2.64412 2.77647]
]
-----acosh-----
[
[ NaN 0.00000 1.31696]
[ 1.76275 2.06344 2.29243]
[ 2.47789 2.63392 2.76866]
]
-----atanh-----
[
[ 0.00000 Infinity NaN]
[ NaN NaN NaN]
[ NaN NaN NaN]
]
-----exp-----
[
[ 1.00000 2.71828 7.38906]
[ 20.08554 54.59815 148.41316]
[403.42879 1096.63316 2980.95799]
]
-----log-----
[
[-Infinity 0.00000 0.69315]
[ 1.09861 1.38629 1.60944]
[ 1.79176 1.94591 2.07944]
]
-----sqrt-----
[
[ 0.00000 1.00000 1.41421]
[ 1.73205 2.00000 2.23607]
[ 2.44949 2.64575 2.82843]
]
-----log10-----
[
[-Infinity 0.00000 0.30103]
[ 0.47712 0.60206 0.69897]
[ 0.77815 0.84510 0.90309]
]
-----square-----
[
[ 0.00000 1.00000 4.00000]
[ 9.00000 16.00000 25.00000]
[ 36.00000 49.00000 64.00000]
]
-----cube-----
[
[ 0.00000 1.00000 8.00000]
[ 27.00000 64.00000 125.00000]
[216.00000 343.00000 512.00000]
]
-----abs-----
[
[ 0.00000 1.00000 2.00000]
[ 3.00000 4.00000 5.00000]
[ 6.00000 7.00000 8.00000]
]
-----ceil-----
[
[ 0.00000 1.00000 2.00000]
[ 3.00000 4.00000 5.00000]
[ 6.00000 7.00000 8.00000]
]
-----floor-----
[
[ 0.00000 1.00000 2.00000]
[ 3.00000 4.00000 5.00000]
[ 6.00000 7.00000 8.00000]
]
-----round-----
[
[ 0.00000 1.00000 2.00000]
[ 3.00000 4.00000 5.00000]
[ 6.00000 7.00000 8.00000]
]
-----degree-----
[
[ 0.00000 57.29578 114.59156]
[171.88734 229.18312 286.47890]
[343.77468 401.07046 458.36624]
]
-----radian-----
[
[ 0.00000 0.01745 0.03491]
[ 0.05236 0.06981 0.08727]
[ 0.10472 0.12217 0.13963]
]
add
- 两个矩阵同位置数据或者矩阵与数的加法
- 该方法支持广播，dim为0则按照行方向，dim为1则按照列方向，其他则和两个同形状矩阵加法一样的效果
T add({required Object other, int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList([List.generate(12, (_) => _ + 0.0)].reshape(row: 3, column: 4));
mt.visible();
mt.add(other: mt).visible();
mt.add(other: 2).visible();
mt.add(other: Matrix([[4, 2, 1, 3]]), dim: 0).visible();
mt.add(other: Matrix([[4, 2, 1]]).T_, dim: 1).visible();
}
output
[
[ 0.00000 1.00000 2.00000 3.00000]
[ 4.00000 5.00000 6.00000 7.00000]
[ 8.00000 9.00000 10.00000 11.00000]
]
[
[ 0.00000 2.00000 4.00000 6.00000]
[ 8.00000 10.00000 12.00000 14.00000]
[ 16.00000 18.00000 20.00000 22.00000]
]
[
[ 2.00000 3.00000 4.00000 5.00000]
[ 6.00000 7.00000 8.00000 9.00000]
[ 10.00000 11.00000 12.00000 13.00000]
]
[
[ 4.00000 3.00000 3.00000 6.00000]
[ 8.00000 7.00000 7.00000 10.00000]
[ 12.00000 11.00000 11.00000 14.00000]
]
[
[ 4.00000 5.00000 6.00000 7.00000]
[ 6.00000 7.00000 8.00000 9.00000]
[ 9.00000 10.00000 11.00000 12.00000]
]
- 两个矩阵同位置数据或者矩阵与数的减法
- 该方法支持广播，dim为0则按照行方向，dim为1则按照列方向，其他则和两个同形状矩阵减法一样的效果
T minus({required Object other, int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList([List.generate(12, (_) => _ + 0.0)].reshape(row: 3, column: 4));
mt.visible();
mt.minus(other: mt).visible();
mt.minus(other: 2).visible();
mt.minus(other: Matrix([[4, 2, 1, 3]]), dim: 0).visible();
mt.minus(other: Matrix([[4, 2, 1]]).T_, dim: 1).visible();
}
output
[
[ 0.00000 1.00000 2.00000 3.00000]
[ 4.00000 5.00000 6.00000 7.00000]
[ 8.00000 9.00000 10.00000 11.00000]
]
[
[ 0.00000 0.00000 0.00000 0.00000]
[ 0.00000 0.00000 0.00000 0.00000]
[ 0.00000 0.00000 0.00000 0.00000]
]
[
[ -2.00000 -1.00000 0.00000 1.00000]
[ 2.00000 3.00000 4.00000 5.00000]
[ 6.00000 7.00000 8.00000 9.00000]
]
[
[ -4.00000 -1.00000 1.00000 0.00000]
[ 0.00000 3.00000 5.00000 4.00000]
[ 4.00000 7.00000 9.00000 8.00000]
]
[
[ -4.00000 -3.00000 -2.00000 -1.00000]
[ 2.00000 3.00000 4.00000 5.00000]
[ 7.00000 8.00000 9.00000 10.00000]
]
multiply
- 两个矩阵同位置数据或者矩阵与数的乘法
- 该方法支持广播，dim为0则按照行方向，dim为1则按照列方向，其他则和两个同形状矩阵乘法一样的效果
T multiply({required Object other, int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList([List.generate(12, (_) => _ + 0.0)].reshape(row: 3, column: 4));
mt.visible();
mt.multiply(other: mt).visible();
mt.multiply(other: 2).visible();
mt.multiply(other: Matrix([[4, 2, 1, 3]]), dim: 0).visible();
mt.multiply(other: Matrix([[4, 2, 1]]).T_, dim: 1).visible();
}
output
[
[ 0.00000 1.00000 2.00000 3.00000]
[ 4.00000 5.00000 6.00000 7.00000]
[ 8.00000 9.00000 10.00000 11.00000]
]
[
[ 0.00000 1.00000 4.00000 9.00000]
[ 16.00000 25.00000 36.00000 49.00000]
[ 64.00000 81.00000 100.00000 121.00000]
]
[
[ 0.00000 2.00000 4.00000 6.00000]
[ 8.00000 10.00000 12.00000 14.00000]
[ 16.00000 18.00000 20.00000 22.00000]
]
[
[ 0.00000 2.00000 2.00000 9.00000]
[ 16.00000 10.00000 6.00000 21.00000]
[ 32.00000 18.00000 10.00000 33.00000]
]
[
[ 0.00000 4.00000 8.00000 12.00000]
[ 8.00000 10.00000 12.00000 14.00000]
[ 8.00000 9.00000 10.00000 11.00000]
]
T divide({required Object other, int dim = -1})
- 两个矩阵同位置数据或者矩阵与数的除法
- 该方法支持广播，dim为0则按照行方向，dim为1则按照列方向，其他则和两个同形状矩阵除法一样的效果
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList([List.generate(12, (_) => _ + 0.0)].reshape(row: 3, column: 4));
mt.visible();
mt.divide(other: mt).visible();
mt.divide(other: 2).visible();
mt.divide(other: Matrix([[4, 2, 1, 3]]), dim: 0).visible();
mt.divide(other: Matrix([[4, 2, 1]]).T_, dim: 1).visible();
}
output
[
[ 0.00000 1.00000 2.00000 3.00000]
[ 4.00000 5.00000 6.00000 7.00000]
[ 8.00000 9.00000 10.00000 11.00000]
]
[
[ NaN 1.00000 1.00000 1.00000]
[ 1.00000 1.00000 1.00000 1.00000]
[ 1.00000 1.00000 1.00000 1.00000]
]
[
[ 0.00000 0.50000 1.00000 1.50000]
[ 2.00000 2.50000 3.00000 3.50000]
[ 4.00000 4.50000 5.00000 5.50000]
]
[
[ 0.00000 0.50000 2.00000 1.00000]
[ 1.00000 2.50000 6.00000 2.33333]
[ 2.00000 4.50000 10.00000 3.66667]
]
[
[ 0.00000 0.25000 0.50000 0.75000]
[ 2.00000 2.50000 3.00000 3.50000]
[ 8.00000 9.00000 10.00000 11.00000]
]
fftComplex
- 快速傅里叶变换，基于Cooley–Tukey FFT algorithm
- 默认每行都是复数的实部和虚部，复数个数必须是2的幂
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%8.5f";
var t1 = Matrix.fromList([
[3, 6],
[0, 2],
[9, -0.2],
[5, 2]
]);
print(t1.fftComplex());
}
output
[
[ 17.00000 9.80000]
[ -6.00000 11.20000]
[ 7.00000 1.80000]
[ -6.00000 1.20000]
]
toComplexLike
- 把一个row * column的矩阵转换为size个复数模样的矩阵，isReal为true表示矩阵的元素作为复数实部，反之为虚部
##T toComplexLike({bool isReal = true})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.2f";
var t1 = Matrix.fromList([
[3, 6],
[0, 2],
[9, -0.2],
[5, 2]
]);
print(t1.toComplexLike(isReal: true));
print(t1.toComplexLike(isReal: false));
}
output
[
[ 3.00 0.00]
[ 6.00 0.00]
[ 0.00 0.00]
[ 2.00 0.00]
[ 9.00 0.00]
[-0.20 0.00]
[ 5.00 0.00]
[ 2.00 0.00]
]
[
[ 0.00 3.00]
[ 0.00 6.00]
[ 0.00 0.00]
[ 0.00 2.00]
[ 0.00 9.00]
[ 0.00 -0.20]
[ 0.00 5.00]
[ 0.00 2.00]
]
dftComplex
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.4f";
var t1 = Matrix.fromList([
[3, 6],
[0, 2],
[9, -0.2],
[5, 2],
[4, 7]
]);
print(t1.dftComplex());
}
output
[
[21.0000 16.8000]
[-13.1386 8.7780]
[ 3.2436 5.4304]
[ 4.9368 -6.8803]
[-1.0418 5.8718]
]
dft
- 傅里叶变换
List<List<Complex>> dft()
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.4f";
var t1 = Matrix.fromList(List.generate(3, (r) => List.generate(4, (c) => r * 3.0 + c)))..visible();
t1.dft().forEach((list) => list.forEach((c) => print(c)));
}
output
[
[ 0.0000 1.0000 2.0000 3.0000]
[ 3.0000 4.0000 5.0000 6.0000]
[ 6.0000 7.0000 8.0000 9.0000]
]
Complex(54.0, 0.0)
Complex(-6.000000000000002, 5.999999999999998)
Complex(-6.0, -4.408728476930472e-15)
Complex(-5.999999999999992, -6.000000000000005)
Complex(-18.000000000000007, 10.39230484541326)
Complex(8.881784197001252e-15, 0.0)
Complex(6.217248937900877e-15, 6.217248937900877e-15)
Complex(8.881784197001252e-15, -4.440892098500626e-15)
Complex(-17.999999999999986, -10.392304845413282)
Complex(1.4210854715202004e-14, 1.509903313490213e-14)
Complex(0.0, 5.329070518200751e-15)
Complex(-3.552713678800501e-15, 1.3322676295501878e-14)
diff
- 基于中心差分进行函数求导
T diff(double Function(double) func)
test
import 'dart:math';
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%10.5f";
var t1 = Matrix.fromList(List.generate(3, (r) => List.generate(4, (c) => r * 3.0 + c)))..visible();
f(double x) => x * 2 + 5 * sin(x) - exp(x * 2) + pow(5, 1 / (x + 1));
f1(double x) => 2 + 5 * cos(x) - exp(x * 2) * 2 + pow(5, 1 / (x + 1)) * log(5) * (-1 / pow(x + 1, 2));
var get1 = t1.diff(f)..visible();
var get2 = t1.customize(f1)..visible();
(get1 - get2).visible(format: "%3.8f");
}
output
[
[ 0.00000 1.00000 2.00000 3.00000]
[ 3.00000 4.00000 5.00000 6.00000]
[ 6.00000 7.00000 8.00000 9.00000]
]
[
[ -3.04719 -10.97630 -109.58282 -809.95797]
[ -809.95797 -5963.27302 -44049.57174 -325502.82332]
[ -325502.82332 -2405202.82653 -17772219.69551 -131319936.34594]
]
[
[ -3.04719 -10.97630 -109.58282 -809.95797]
[ -809.95797 -5963.27302 -44049.57174 -325502.82332]
[ -325502.82332 -2405202.82957 -17772219.79228 -131319940.84922]
]
[
[ -0.00000000 -0.00000000 0.00000000 0.00000000]
[ 0.00000000 -0.00000036 0.00000059 0.00000185]
[ 0.00000185 0.00304389 0.09676288 4.50327742]
]
sgn
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.0f";
var t1 = Matrix.fromList(
List.generate(3, (r) => List.generate(4, (c) => r * 3.0 + c))
)..[0][2] = -5
..[1][1] = double.nan
..visible();
t1.sgn.visible();
}
output
[
[ 0 1 -5 3]
[ 3 NaN 5 6]
[ 6 7 8 9]
]
[
[ 0 1 -1 1]
[ 1 NaN 1 1]
[ 1 1 1 1]
]
下一篇：一些机器学习工具的简单实现