94 lines
2.7 KiB
Go
94 lines
2.7 KiB
Go
// LEs_Chasing
|
||
/*
|
||
------------------------------------------------------
|
||
作者 : Black Ghost
|
||
日期 : 2018-12-8
|
||
版本 : 0.0.0
|
||
------------------------------------------------------
|
||
追赶法求解严格对角占优的三对角矩阵
|
||
理论：
|
||
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 59-61.
|
||
------------------------------------------------------
|
||
输入 :
|
||
A 系数矩阵, nxn
|
||
BA 常数值向量, nx1
|
||
输出 :
|
||
sol 解向量, nx1
|
||
err 解出标志：false-未解出或达到步数上限；
|
||
true-全部解出
|
||
------------------------------------------------------
|
||
*/
|
||
|
||
package goNum
|
||
|
||
// LEs_Chasing 追赶法求解严格对角占优的三对角矩阵
|
||
func LEs_Chasing(A, BA Matrix) (Matrix, bool) {
|
||
/*
|
||
追赶法求解严格对角占优的三对角矩阵
|
||
输入 :
|
||
A 系数矩阵, nxn
|
||
BA 常数值向量, nx1
|
||
输出 :
|
||
sol 解向量, nx1
|
||
err 解出标志：false-未解出或达到步数上限；
|
||
true-全部解出
|
||
*/
|
||
//判断A是否方阵
|
||
if A.Rows != A.Columns {
|
||
panic("Error in goNum.LEs_Chasing: A is not a square matrix")
|
||
}
|
||
//判断BA是否与A行数相等
|
||
if A.Rows != BA.Rows {
|
||
panic("Error in goNum.LEs_Chasing: Rows of A and BA are not equal")
|
||
}
|
||
|
||
var err bool = false
|
||
n := A.Rows
|
||
ai := ZeroMatrix(n, 1) //第一位无效
|
||
bi := ZeroMatrix(n, 1)
|
||
ci := ZeroMatrix(n-1, 1)
|
||
gamma := ZeroMatrix(n, 1) //gammai
|
||
beta := ZeroMatrix(n, 1) //beta, 第一位无效
|
||
delta := ZeroMatrix(n-1, 1) //deltai
|
||
y := ZeroMatrix(n, 1) //yi
|
||
sol := ZeroMatrix(n, 1) //xi
|
||
|
||
//ai, bi, ci
|
||
bi.Data[0] = A.GetFromMatrix(0, 0)
|
||
ci.Data[0] = A.GetFromMatrix(0, 1)
|
||
for i := 1; i < n-1; i++ {
|
||
ai.Data[i] = A.GetFromMatrix(i, i-1)
|
||
bi.Data[i] = A.GetFromMatrix(i, i)
|
||
ci.Data[i] = A.GetFromMatrix(i, i+1)
|
||
}
|
||
ai.Data[n-1] = A.GetFromMatrix(n-1, n-2)
|
||
bi.Data[n-1] = A.GetFromMatrix(n-1, n-1)
|
||
|
||
//解gamma, beta和delta
|
||
gamma.Data[0] = bi.Data[0]
|
||
delta.Data[0] = ci.Data[0] / gamma.Data[0]
|
||
for i := 1; i < n-1; i++ {
|
||
beta.Data[i] = ai.Data[i]
|
||
gamma.Data[i] = bi.Data[i] - beta.Data[i]*delta.Data[i-1]
|
||
delta.Data[i] = ci.Data[i] / gamma.Data[i]
|
||
}
|
||
beta.Data[n-1] = ai.Data[n-1]
|
||
gamma.Data[n-1] = bi.Data[n-1] - beta.Data[n-1]*delta.Data[n-2]
|
||
|
||
//解yi
|
||
y.Data[0] = BA.Data[0] / gamma.Data[0]
|
||
for i := 1; i < BA.Rows; i++ {
|
||
y.Data[i] = (BA.Data[i] - beta.Data[i]*y.Data[i-1]) / gamma.Data[i]
|
||
}
|
||
|
||
//解xi
|
||
sol.Data[n-1] = y.Data[n-1]
|
||
for i := n - 2; i >= 0; i-- {
|
||
sol.Data[i] = y.Data[i] - delta.Data[i]*sol.Data[i+1]
|
||
}
|
||
|
||
err = true
|
||
return sol, err
|
||
}
|