线性代数
trace
- 矩阵的迹，如果不是方阵，则以行和列中最小值取方阵的迹
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
var mt = MatrixBase.E<Matrix>(n: 4);
print(mt.trace());
var mt1 = MatrixBase.ELike<Matrix>(row: 3, column: 6);
print(mt1.trace());
}
output
elementaryExchange
- 矩阵的初等行变换——交换
void elementaryExchange({
required int index1, required int index2, bool horizontal = true
})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.0f";
var mt = MatrixBase.arrange<Matrix>(row: 4, column: 6);
mt.visible();
mt
..elementaryExchange(index1: 0, index2: 3, horizontal: true)
..visible()
..elementaryExchange(index1: 3, index2: 1, horizontal: false)
..visible();
}
output
[
[ 0 1 2 3 4 5]
[ 6 7 8 9 10 11]
[ 12 13 14 15 16 17]
[ 18 19 20 21 22 23]
]
[
[ 18 19 20 21 22 23]
[ 6 7 8 9 10 11]
[ 12 13 14 15 16 17]
[ 0 1 2 3 4 5]
]
[
[ 18 21 20 19 22 23]
[ 6 9 8 7 10 11]
[ 12 15 14 13 16 17]
[ 0 3 2 1 4 5]
]
elementaryMultiply
- 矩阵的初等行变换——倍乘某行，这里允许为0
void elementaryMultiply({
required int index, required double number, bool horizontal = true
})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.1f";
var mt = MatrixBase.arrange<Matrix>(row: 4, column: 6);
mt.visible();
mt
..elementaryMultiply(index: 1, number: 3.5, horizontal: true)
..visible()
..elementaryMultiply(index: 5, number: 3, horizontal: false)
..visible();
}
output
[
[ 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]
]
[
[ 0.0 1.0 2.0 3.0 4.0 5.0]
[ 21.0 24.5 28.0 31.5 35.0 38.5]
[ 12.0 13.0 14.0 15.0 16.0 17.0]
[ 18.0 19.0 20.0 21.0 22.0 23.0]
]
[
[ 0.0 1.0 2.0 3.0 4.0 15.0]
[ 21.0 24.5 28.0 31.5 35.0 115.5]
[ 12.0 13.0 14.0 15.0 16.0 51.0]
[ 18.0 19.0 20.0 21.0 22.0 69.0]
]
elementaryAdd
- 矩阵的初等变换——倍乘某行（列）index2并且加到另一行（列）index1
void elementaryAdd({
required int index1,
required int index2,
required double number,
bool horizontal = true
})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.1f";
var mt = MatrixBase.arrange<Matrix>(row: 4, column: 6);
mt
..visible()
..elementaryAdd(index1: 1, index2: 2, number: 1, horizontal: true)
..visible()
..elementaryAdd(index1: 1, index2: 5, number: 2, horizontal: false)
..visible();
}
output
[
[ 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]
]
[
[ 0.0 1.0 2.0 3.0 4.0 5.0]
[ 18.0 20.0 22.0 24.0 26.0 28.0]
[ 12.0 13.0 14.0 15.0 16.0 17.0]
[ 18.0 19.0 20.0 21.0 22.0 23.0]
]
[
[ 0.0 11.0 2.0 3.0 4.0 5.0]
[ 18.0 76.0 22.0 24.0 26.0 28.0]
[ 12.0 47.0 14.0 15.0 16.0 17.0]
[ 18.0 65.0 20.0 21.0 22.0 23.0]
]
transpose、T_
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.0f";
var mt = MatrixBase.arrange<Matrix>(row: 2, column: 3)..visible();
mt.T_.visible();
mt.transpose().visible();
}
output
[
[ 0 1 2]
[ 3 4 5]
]
[
[ 0 3]
[ 1 4]
[ 2 5]
]
[
[ 0 3]
[ 1 4]
[ 2 5]
]
det
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
var mt = Matrix.fromList([
[3, 2, 6],
[0, 8, 12],
[1, 4, 2]
]);
print(mt.det);
}
output
adjugate
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.0f";
var mt = Matrix.fromList([
[3, 2, 6],
[0, 8, 12],
[1, 4, 2]
]);
var mt1 = mt.adjugate;
print(mt1);
// A product Aadj = Adet * E;
print(mt.product(other: mt1));
}
output
[
[ -32 20 -24]
[ 12 0 -36]
[ -8 -10 24]
]
[
[-120 0 0]
[ 0 -120 0]
[ 0 0 -120]
]
inverse
- Get the inverse of a nonsingular square matrix
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList([
[3, 2, 6],
[0, 8, 12],
[1, 4, 2]
]);
var mt1 = mt.inverse;
print(mt1);
print(mt.product(other: mt1));
}
output
[
[ 0.26667 -0.16667 0.20000]
[ -0.10000 -0.00000 0.30000]
[ 0.06667 0.08333 -0.20000]
]
[
[ 1.00000 0.00000 0.00000]
[ 0.00000 1.00000 -0.00000]
[ -0.00000 0.00000 1.00000]
]
rank
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList(List.generate(3, (r) => List.generate(3, (c) => r * 3 + c + 1)))
..visible();
print(mt.rank);
}
output
[
[ 1.00000 2.00000 3.00000]
[ 4.00000 5.00000 6.00000]
[ 7.00000 8.00000 9.00000]
]
2
rref
- 通过高斯消元法化最简行阶梯型
- rank、rref、判断奇异矩阵都是通过tolerance_round容忍值控制的
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
var mt = Matrix.fromList(List.generate(3, (r) => List.generate(3, (c) => r * 3 + c + 1)))
..visible();
print(mt.rref);
print(mt.rank);
}
output
[
[ 1.00000 2.00000 3.00000]
[ 4.00000 5.00000 6.00000]
[ 7.00000 8.00000 9.00000]
]
[
[ 1.00000 0.00000 -1.00000]
[ -0.00000 1.00000 2.00000]
[ 0.00000 0.00000 0.00000]
]
2
coincidental
- 获取矩阵的去掉row和column的余子式
T coincidental({required int row, required int column})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.0f";
var mt = Matrix.fromList(List.generate(5, (r) => List.generate(6, (c) => r * 3 + c + 1)))
..visible();
mt.coincidental(row: 2, column: 4).visible();
}
output
[
[ 1 2 3 4 5 6]
[ 4 5 6 7 8 9]
[ 7 8 9 10 11 12]
[ 10 11 12 13 14 15]
[ 13 14 15 16 17 18]
]
[
[ 1 2 3 4 6]
[ 4 5 6 7 9]
[ 10 11 12 13 15]
[ 13 14 15 16 18]
]
product
- 矩阵的标准乘法
T product({required T other})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.0f";
var mt = Matrix.fromList(List.generate(3, (r) => List.generate(3, (c) => r * 3 + c + 1)))
..visible();
var mt1 = Matrix.fromList([
[2, 2, 1],
[0, 9, 2],
[2, 4, 6]
]);
print(mt.product(other: mt1));
}
output
[
[ 1 2 3]
[ 4 5 6]
[ 7 8 9]
]
[
[ 8 32 23]
[ 20 77 50]
[ 32 122 77]
]
kronecker
- 克罗内克积
T kronecker({required T other})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.0f";
var mt = Matrix.fromList(List.generate(3, (r) => List.generate(3, (c) => r * 3 + c + 1)))
..visible();
var mt1 = Matrix.fromList([
[2, 2, 1],
[0, 9, 2],
[2, 4, 6]
]);
print(mt.kronecker(other: mt1));
}
output
[
[ 1 2 3]
[ 4 5 6]
[ 7 8 9]
]
[
[ 2 2 1 4 4 2 6 6 3]
[ 0 9 2 0 18 4 0 27 6]
[ 2 4 6 4 8 12 6 12 18]
[ 8 8 4 10 10 5 12 12 6]
[ 0 36 8 0 45 10 0 54 12]
[ 8 16 24 10 20 30 12 24 36]
[ 14 14 7 16 16 8 18 18 9]
[ 0 63 14 0 72 16 0 81 18]
[ 14 28 42 16 32 48 18 36 54]
]
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