作业1 图表完成

numerical_analysis/1/README.md

@@ -56,5 +56,8 @@ end
 作业提交有效时间是今天到10月23日（两周后）之前的任意时间。提交作业请将代码和报告打包，以“课后作业1-名字-学号”命名提交。
 
 
+![image-20210116232529898](https://public.veypi.com/img/screenshot/20210116232529.png)
 
+![image-20210116235118221](https://public.veypi.com/img/screenshot/20210116235118.png)
 
+![image-20210116235324496](https://public.veypi.com/img/screenshot/20210116235324.png)

numerical_analysis/1/main.py

@@ -28,7 +28,7 @@ def LU_decomposition(A):
     return L, U
 
 
-# 生成范围在 [-100, 100]之前的方阵A 和 b
+# 生成随机矩阵 A, b, 范围[-10, 10]
 def randomAb(m):
     A = np.random.random([m, m]) * 20 - 10
     dia = np.random.random(m) * 10
@@ -37,6 +37,29 @@ def randomAb(m):
     return A, np.random.randint(0, 10, [m, 1])
 
 
+# 生成稀疏矩阵A, b
+def sparseMatrix(m):
+    A, b = randomAb(m)
+    for i in range(m):
+        for j in range(m):
+            if i != j:
+                a = A[i][j]
+                if abs(a) < 9:
+                    A[i][j] = 0
+                elif a > 0:
+                    A[i][j] = 10 * (a - 9)
+                else:
+                    A[i][j] = 10 * (9 + a)
+
+    return A, b
+
+
+# 生成病态矩阵A, b
+def illMatrix(m):
+    A, b = randomAb(m)
+    return A, b
+
+
 class Question1:
     """
     求解 Ax=b
@@ -104,60 +127,58 @@ class Question1:
         """
         return np.linalg.solve(A, b)
 
-    def RMSE(self, solver, n=8):
+    def RMSE(self, solver, n=8, randFunc=randomAb):
         ## 计算方差
         s = time.time()
-        A, b = randomAb(n)
+        A, b = randFunc(n)
         X = (A.dot(solver(A, b)) - b) ** 2
         for i in range(1000):
-            A, b = randomAb(n)
+            A, b = randFunc(n)
             X = X + (A.dot(solver(A, b)) - b) ** 2
         return np.max(X), time.time() - s
 
     def show(self):
-        N = [2 ** i for i in range(12)]
+        n = 12
-        Y = [[0 for i in range(12)] for _ in range(4)]
+        N = [2 ** i for i in range(n)]
-        Z = [[0 for i in range(12)] for _ in range(4)]
+        Y = [[0 for i in range(n)] for _ in range(4)]
+        Z = [[0 for i in range(n)] for _ in range(4)]
 
-        plt.subplot(1, 2, 1)
+        randomFuns = [randomAb, sparseMatrix, illMatrix]
-        for i in range(len(N)):
+        for r in range(3):
-            print("size: %s" % N[i])
+            plt.subplot(3, 2, 2*r + 1)
-            print("LU")
+            for i in range(n):
-            Y[0][i], Z[0][i] = self.RMSE(self.solver1, N[i])
+                print("size: %s" % N[i])
-            print("jacobi")
+                print("LU")
-            Y[1][i], Z[1][i] = self.RMSE(self.solver3, N[i])
+                Y[0][i], Z[0][i] = self.RMSE(self.solver1, N[i])
-            print("inverse")
+                print("jacobi")
-            Y[2][i], Z[2][i] = self.RMSE(self.solver3, N[i])
+                Y[1][i], Z[1][i] = self.RMSE(self.solver3, N[i])
-            print("default\n")
+                print("inverse")
-            Y[3][i], Z[3][i] = self.RMSE(self.solver4, N[i])
+                Y[2][i], Z[2][i] = self.RMSE(self.solver3, N[i])
+                print("default\n")
+                Y[3][i], Z[3][i] = self.RMSE(self.solver4, N[i])
 
-        # N = range(12)
+            # N = range(12)
-        plt.plot(N, Y[0], label="LU")
+            plt.plot(N, Y[0], label="LU")
-        plt.plot(N, Y[1], label="Jacobi")
+            plt.plot(N, Y[1], label="Jacobi")
-        plt.plot(N, Y[2], label="inverse")
+            plt.plot(N, Y[2], label="inverse")
-        plt.plot(N, Y[3], label="default solver")
+            plt.plot(N, Y[3], label="default solver")
-        # plt.xticks([0, 10, 100, 1000], [0, 10, 100, 1000])
+            # plt.xticks([0, 10, 100, 1000], [0, 10, 100, 1000])
-        plt.title('Accuracy')
+            plt.title('Accuracy')
-        plt.yscale('symlog')
+            plt.yscale('symlog')
-        plt.xscale('symlog')
+            plt.xscale('symlog')
-        plt.legend(loc='lower right')
+            # plt.legend(loc='lower right')
-        plt.subplot(1, 2, 2)
+            plt.subplot(3, 2, 2 * r + 2)
-        plt.plot(N, Z[0], label="LU")
+            plt.plot(N, Z[0], label="LU")
-        plt.plot(N, Z[1], label="Jacobi")
+            plt.plot(N, Z[1], label="Jacobi")
-        plt.plot(N, Z[2], label="inverse")
+            plt.plot(N, Z[2], label="inverse")
-        plt.plot(N, Z[3], label="default solver")
+            plt.plot(N, Z[3], label="default solver")
-        plt.xscale('symlog')
+            plt.xscale('symlog')
-        plt.yscale('symlog')
+            plt.yscale('symlog')
-        plt.title('time cost')
+            plt.title('time cost')
-        plt.legend(loc='lower right')
+            # plt.legend(loc='lower right')
         plt.show()
 
 
 if __name__ == "__main__":
     q = Question1()
-    A, b = randomAb(3)
-    print(A)
-    print(np.linalg.det(A))
-    # print(q.solver2(A, b))
-    # print(q.solver4(A, b))
     q.show()