mirror of
https://gitee.com/chfenger/goNum.git
synced 2025-12-06 16:49:24 +08:00
96fccdb6ef
update comments in all of files in convenient to generate package information using `godoc` command or give tips in LiteIDE editor when the cursor keeps resting on a function or method.
94 lines
2.7 KiB
Go
94 lines
2.7 KiB
Go
// InconsistentLSQ_test
|
||
/*
|
||
------------------------------------------------------
|
||
作者 : Black Ghost
|
||
日期 : 2018-12-11
|
||
版本 : 0.0.0
|
||
------------------------------------------------------
|
||
求解矛盾方程组的最小二乘法（Least Square Method）
|
||
理论：
|
||
对于矛盾方程组Ax=b，即
|
||
|
||
n
|
||
Sum aij*xj = bi (i=1, 2, ..., N)
|
||
j=1
|
||
|
||
rank(A) = n (N > n)
|
||
|
||
则A'Ax=A'b的唯一解为原矛盾方程组的最小二乘解
|
||
|
||
参考 李信真, 车刚明, 欧阳洁, 等. 计算方法. 西北工业大学
|
||
出版社, 2000, pp 130-135.
|
||
------------------------------------------------------
|
||
输入 :
|
||
A 原方程组系数矩阵，Nxn
|
||
b 原方程组值向量，Nx1
|
||
输出 :
|
||
sol 解向量
|
||
err 解出标志：false-未解出或达到步数上限；
|
||
true-全部解出
|
||
------------------------------------------------------
|
||
*/
|
||
|
||
package goNum_test
|
||
|
||
import (
|
||
"testing"
|
||
|
||
"github.com/chfenger/goNum"
|
||
)
|
||
|
||
// InconsistentLSQ 求解矛盾方程组的最小二乘法（Least Square Method）
|
||
func InconsistentLSQ(A, b goNum.Matrix) (goNum.Matrix, bool) {
|
||
/*
|
||
求解矛盾方程组的最小二乘法（Least Square Method）
|
||
输入 :
|
||
A 原方程组系数矩阵，Nxn
|
||
b 原方程组值向量，Nx1
|
||
输出 :
|
||
sol 解向量
|
||
err 解出标志：false-未解出或达到步数上限；
|
||
true-全部解出
|
||
*/
|
||
//判断A和b的行数是否对应
|
||
if A.Rows != b.Rows {
|
||
panic("Error in goNum.InconsistentLSQ: Rows of A and b are not equal")
|
||
}
|
||
|
||
//求解A'A和A'b
|
||
AA := goNum.DotPruduct(A.Transpose(), A)
|
||
Ab := goNum.DotPruduct(A.Transpose(), b)
|
||
|
||
//转换矩阵为切片
|
||
Atemp := goNum.Matrix2ToSlices(AA)
|
||
btemp := goNum.Matrix1ToSlices(Ab)
|
||
if (len(Atemp) != A.Columns) || (len(Atemp[0]) != A.Columns) || (len(btemp) != A.Columns) {
|
||
panic("Error in goNum.InconsistentLSQ: Matrix to slices error")
|
||
}
|
||
//求解x向量，采用列主元消去法（LEs_ECPE）
|
||
soltemp, err := goNum.LEs_ECPE(Atemp, btemp)
|
||
if err != true {
|
||
panic("Error in goNum.InconsistentLSQ: Solve error")
|
||
}
|
||
//转换切片为矩阵
|
||
sol := goNum.Slices1ToMatrix(soltemp)
|
||
if sol.Rows != A.Columns {
|
||
panic("Error in goNum.InconsistentLSQ: Slice to matrix error")
|
||
}
|
||
|
||
return sol, true
|
||
}
|
||
|
||
func BenchmarkInconsistentLSQ(b *testing.B) {
|
||
A32 := goNum.NewMatrix(6, 3, []float64{1.0, 0.0, 0.0,
|
||
0.0, 1.0, 0.0,
|
||
0.0, 0.0, 1.0,
|
||
-1.0, 1.0, 0.0,
|
||
0.0, -1.0, 1.0,
|
||
-1.0, 0.0, 1.0})
|
||
b32 := goNum.NewMatrix(6, 1, []float64{1.0, 2.0, 3.0, 1.0, 2.0, 1.0})
|
||
for i := 0; i < b.N; i++ {
|
||
goNum.InconsistentLSQ(A32, b32)
|
||
}
|
||
}
|