97 lines
2.5 KiB
Go
97 lines
2.5 KiB
Go
// LEs_ECPE
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// linear equations - elemination of column principle
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// element
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/*
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------------------------------------------------------
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作者 : Black Ghost
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日期 : 2018-11-19
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版本 : 0.0.0
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------------------------------------------------------
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线性代数方程组的列主元消去法
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理论：
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参考 李信真, 车刚明, 欧阳洁, 等. 计算方法. 西北工业大学
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出版社, 2000, pp 47-49.
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乘除运算的次数 n^3/3+n^2-n/3
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------------------------------------------------------
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输入 :
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a a x = b线性代数方程组的系数矩阵
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b a x = b线性代数方程组的右侧常数列向量
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输出 :
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sol 解值
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err 解出标志：false-未解出或达到步数上限；
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true-全部解出
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------------------------------------------------------
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*/
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package goNum
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// LEs_ECPE 线性代数方程组的列主元消去法
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func LEs_ECPE(a [][]float64, b []float64) ([]float64, bool) {
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/*
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线性代数方程组的列主元消去法
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输入 :
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a a x = b线性代数方程组的系数矩阵
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b a x = b线性代数方程组的右侧常数列向量
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输出 :
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sol 解值
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err 解出标志：false-未解出或达到步数上限；
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true-全部解出
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*/
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//方程个数为n
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var err bool = false
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atemp := a
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btemp := b
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n := len(btemp)
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sol := make([]float64, n)
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temp0 := make([]float64, n)
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var temp1 float64
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// 输入判断
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if len(atemp) != n {
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return sol, err
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}
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//求解
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//消去，求得上三角矩阵
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for i := 0; i < n-1; i++ {
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//求第i列的主元素并调整顺序
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acol := make([]float64, n-i)
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for icol := i; icol < n; icol++ {
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acol[icol-i] = atemp[icol][i]
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}
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_, ii, _ := MaxAbs(acol)
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if ii+i != i {
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temp0 = atemp[ii+i]
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atemp[ii+i] = atemp[i]
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atemp[i] = temp0
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temp1 = btemp[ii+i]
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btemp[ii+i] = btemp[i]
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btemp[i] = temp1
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}
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//列消去
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for j := i + 1; j < n; j++ {
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mul := atemp[j][i] / atemp[i][i]
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for k := i; k < n; k++ {
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atemp[j][k] = atemp[j][k] - atemp[i][k]*mul
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}
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btemp[j] = btemp[j] - btemp[i]*mul
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}
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}
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//回代
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sol[n-1] = btemp[n-1] / atemp[n-1][n-1]
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for i := n - 2; i >= 0; i-- {
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temp1 = 0.0
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for j := i + 1; j < n; j++ {
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temp1 = temp1 + atemp[i][j]*sol[j]
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}
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sol[i] = (btemp[i] - temp1) / atemp[i][i]
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}
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//返回结果
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err = true
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return sol, err
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}
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