all

227-4.py

@@ -0,0 +1,45 @@
+# 储存下三角矩阵 a11, a21, a22, a31, a32, a33 ...
+A = [4,2,2,-2,-3,14]
+
+
+b = [10,5,4]
+
+#列 行
+def getIndexFromDownMatrix(col, row):
+    if row > col:
+        row, col = col, row
+    return (1+col)*col//2+row
+
+
+# 平方根法求解
+def SqrtSolve(A,b):
+    n = len(b)
+    L = [0]*(n*(n+1)//2)
+    for j in range(n):
+        for i in range(j,n):
+            if i == j:
+                L[getIndexFromDownMatrix(i,j)] = A[getIndexFromDownMatrix(i,j)]
+                for k in range(j):
+                    L[getIndexFromDownMatrix(i,j)] -= L[getIndexFromDownMatrix(j,k)]**2
+                L[getIndexFromDownMatrix(i,j)] = L[getIndexFromDownMatrix(i,j)]**0.5
+            else:
+                L[getIndexFromDownMatrix(i,j)] = A[getIndexFromDownMatrix(i,j)]
+                for k in range(j):
+                    L[getIndexFromDownMatrix(i,j)] -= L[getIndexFromDownMatrix(i,k)]*L[getIndexFromDownMatrix(j,k)]
+                L[getIndexFromDownMatrix(i,j)] /= L[getIndexFromDownMatrix(j,j)]
+
+    for i in range(n):
+        for k in range(i):
+            b[i] -= L[getIndexFromDownMatrix(i,k)]*b[k]
+        b[i] /= L[getIndexFromDownMatrix(i,i)]
+
+    for i in range(n-1,-1,-1):
+        for k in range(i+1,n):
+            b[i] -= L[getIndexFromDownMatrix(k,i)]*b[k]
+        b[i] /= L[getIndexFromDownMatrix(i,i)]
+    return b
+
+
+if __name__ == "__main__":
+    print("x:")
+    print(SqrtSolve(A,b))