numpy庫中的dot函數來計算矩陣和向量的點積
def matrix_vector_dot_product(a, b):import numpy as npif (len(a[0]) != len(b)):return -1# 使用tolist()將結果轉換為列表return np.dot(a, b).tolist()原始方法
def matrix_vector_dot_product(matrix, vector):if len(matrix[0]) != len(vector):return -1l = []for i in matrix:num = 0for j in range(len(i)):num += (i[j]*vector[j])l.append(num)return l# 主程序
if __name__ == "__main__":# 輸入矩陣和向量matrix_input = input()vector_input = input()# 處理輸入import astmatrix = ast.literal_eval(matrix_input)vector = ast.literal_eval(vector_input)# 調用函數計算點積output = matrix_vector_dot_product(matrix, vector)# 輸出結果print(output)numpy庫中給定的矩陣 A，其轉置矩陣表示為 A^T
def transpose_matrix(a: List[List[Union[int, float]]]) -> List[List[Union[int, float]]]:import numpy as npreturn np.array(a).T.tolist()使用numpy庫的reshape方法矩陣重塑
矩陣重塑是將一個矩陣轉換為另一個形狀的過程，前提是新形狀的元素總數與原矩陣相同
def reshape_matrix(a: List[List[Union[int, float]]], new_shape: Tuple[int, int]) -> List[List[Union[int, float]]]:import numpy as npif len(a) * len(a[0]) != new_shape[0] * new_shape[1]:return -1return np.array(a).reshape(new_shape).tolist()
使用numpy庫的mean方法按行或列計算平均值
def calculate_matrix_mean(matrix: List[List[Union[int, float]]], mode: str) -> List[float]:import numpy as npif mode == 'column':return np.mean(matrix, axis=0).tolist()elif mode == 'row':return np.mean(matrix, axis=1).tolist()else:raise ValueError("Mode must be 'row' or 'column'")
使用python的廣播機制進行標量的矩陣乘法
def scalar_multiply(matrix: List[List[Union[int, float]]], scalar: Union[int, float]) -> List[List[Union[int, float]]]:import numpy as npreturn (np.array(matrix) * scalar).tolist()
使用numpy庫的cov方法計算協方差矩陣
協方差矩陣是一種描述兩個隨機變量之間關系的矩陣，其計算公式為：
import numpy as npdef jia(vectors, a):return [i + a for i in vectors]def dianji(a,b):if len(a) != len(b):return -1s = 0for j in range(len(a)):s += a[j] * b[j]return sdef cov(x,y):return dianji(jia(x, -sum(x)/len(x)),jia(y, -sum(y)/len(y))) / (len(x)-1)def calculate_covariance_matrix(vectors):# 補全代碼return [[cov(x,y) for x in vectors] for y in vectors]# 主程序
if __name__ == "__main__":# 輸入ndarrayA = input()# 處理輸入import astA = ast.literal_eval(ndarrayA)# 調用函數計算output = calculate_covariance_matrix(A)# 輸出結果print(output)原始方法
import numpy as npdef calculate_covariance_matrix(vectors):n_features = len(vectors)n_observations = len(vectors[0])covariance_matrix = np.zeros([n_features, n_features])means = [sum(feature) / n_observations for feature in vectors]for i in range(n_features):for j in range(i, n_features):covariance = sum((vectors[i][k] - means[i]) * (vectors[j][k] - means[j])for k in range(n_observations)) / (n_observations - 1)covariance_matrix[i][j] = covariance_matrix[j][i] = covariancereturn covariance_matrix.tolist()
# 主程序
if __name__ == "__main__":# 輸入ndarrayA = input()# 處理輸入import astA = ast.literal_eval(ndarrayA)# 調用函數計算output = calculate_covariance_matrix(A)# 輸出結果print(output)基向量變換矩陣
基向量變換矩陣（Basis Vector Transformation?Matrix）是一種常用的矩陣，用于將基向量變換為另一個基向量。
import numpy as npdef transform_basis(B, C):B = np.array(B)C = np.array(C)C = np.linalg.inv(C)P = B@Creturn P.tolist()if __name__ == "__main__":B = np.array(eval(input()))C = np.array(eval(input()))print(transform_basis(B, C))?將向量轉換為對角矩陣
def make_diagonal(x):identity_matrix = np.identity(np.size(x))return (identity_matrix*x)
原始方法
def make_diagonal(x):x = np.array(x)zeros = np.zeros((len(x),len(x)),dtype=np.float16)for i in range(len(x)):zeros[i,i]=x[i]return zerosif __name__ == "__main__":x = np.array(eval(input()))print(make_diagonal(x))實現壓縮行稀疏矩陣（CSR）格式轉換
壓縮行稀疏矩陣（CSR）格式是一種特殊的矩陣存儲格式，其特點是只存儲非零元素的值、行號和列指針。本質上是一種三元組表示法。
輸入
[[1, 0, 0], [2, 3, 0], [0, 4, 5]]
輸出
[1, 2, 3, 4, 5]
[0, 0, 1, 1, 2]
[0, 1, 3, 5]
def compressed_row_sparse_matrix(dense_matrix):vals = []col_idx = []row_ptr=[0]for x in dense_matrix:for i,y in enumerate(x):if y!=0:vals.append(y)col_idx.append(i)row_ptr.append(len(vals))return vals, col_idx, row_ptrif __name__ == "__main__":dense_matrix = eval(input())vals, col_idx, row_ptr = compressed_row_sparse_matrix(dense_matrix)print(vals)print(col_idx)print(row_ptr)實現向量到直線的正交投影
def orthogonal_projection(v, L):import numpy as npv = np.array(v)L = np.array(L)a = (((v@L)/np.dot(L,L))*L)a = a.tolist()return aif __name__ == "__main__":v = eval(input())L = eval(input())print(orthogonal_projection(v, L))實現壓縮列稀疏矩陣
def compressed_col_sparse_matrix(dense_matrix):from scipy.sparse import csc_matrixsparse = csc_matrix(dense_matrix)return sparse.data.tolist(), sparse.indices.tolist(), sparse.indptr.tolist()
原始方法
def compressed_col_sparse_matrix(dense_matrix):vals, row_idx, col_ptr = [],[],[0]import numpy as npdense_matrix = np.array(dense_matrix)dense_matrix = dense_matrix.Tfor i in dense_matrix:for j,x in enumerate(i):if x!=0:vals.append(x)row_idx.append(j)col_ptr.append(len(vals))return vals, row_idx, col_ptrif __name__ == "__main__":dense_matrix = eval(input())vals, row_idx, col_ptr = compressed_col_sparse_matrix(dense_matrix)print(vals)print(row_idx)print(col_ptr)計算向量之間的余弦相似度
import numpy as npdef cosine_similarity(v1, v2):# Implement your code hereif v1.shape != v2.shape:raise ValueError("Arrays must have the same shape")if v1.size == 0:raise ValueError("Arrays cannot be empty")v1 = v1.flatten()v2 = v2.flatten()val= (v1@v2)/(np.sqrt(np.dot(v1,v1))*np.sqrt(np.dot(v2,v2)))return round(val, 3)if __name__ == "__main__":v1 = np.array(eval(input()))v2 = np.array(eval(input()))print(cosine_similarity(v1, v2))泊松分布概率計算器
泊松分布是一種描述隨機事件發生次數的概率分布，其計算公式為：
import mathdef poisson_probability(k, lam):# Your code hereo=(math.exp(-lam))*(lam**k)u=math.factorial(k)val=o/ureturn round(val, 5)if __name__ == "__main__":k, lam = map(int, input().split())print(poisson_probability(k, lam))
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