day9_2

# Credit for the solution goes to "pmtatar" on the hackerrank forums

# multiple linear regression implementation in python from scratch

from copy import deepcopy

def transpose(x):
  x_dash = []
  for col in range(len(x[0])):
    x_dash.append([x_row[col] for x_row in x])
  return x_dash

def determinant(x):
  if len(x) == 2:
    return x[0][0] * x[1][1] - x[0][1] * x[1][0]
  
  sign = 1
  answer    = []
  for col in range(len(x[0])):
    new_matrix = []
    for row in x[1:]:
      n_row = row.copy()
      n_row.pop(col)
      new_matrix.append(n_row)
    answer.append(sign * x[0][col] * determinant(new_matrix))
    sign *= -1
  return sum(answer)

def matrix_inverse(x):
  answer = [[0 for _ in range(len(x[0]))] for _ in range(len(x))]

  # matrix of minors
  for row in range(len(x)):
    for col in range(len(x[0])):
      new_matrix = deepcopy(x)
      new_matrix.pop(row)
      for n_row in range(len(new_matrix)):
        new_matrix[n_row].pop(col)
      answer[row][col] = determinant(new_matrix)
       
  # matrix of cofactor
  for row in range(len(answer)):
    for col in range(len(answer[0])):
      answer[row][col] *= (-1) ** (row + col)
      
  # adjoint matrix
  answer = transpose(answer)

  # final inverse
  inv_det = 1 / determinant(x)
  for row in range(len(answer)):
    for col in range(len(answer[0])):
      answer[row][col] *= inv_det

  return answer
  

def matrix_mult(A, B):
  row_a = len(A)
  col_b = len(B[0])
  new_mat = [[0 for _ in range(col_b)] for _ in range(row_a)]
  m_sum   = 0  
  for row_a in range(len(A)):
    for col_b in range(len(B[0])):
      m_sum = 0
      for k in range(len(A[0])):
        m_sum += A[row_a][k] * B[k][col_b]
      new_mat[row_a][col_b] = m_sum
  return new_mat


def solve(y, x, x_pred):
  x_dash  = transpose(x)
  X       = matrix_mult(x_dash, x)
  X_inv   = matrix_inverse(X)
  X_final = matrix_mult(X_inv, x_dash)
  # reshape 1D y into 2d matrix
  y       = [[yi] for yi in y]
  B       = matrix_mult(X_final, y)
  y_pred  = matrix_mult(x_pred,B)
  # reshape 2d y_pred matrix into 1d matrix
  y_output  = []
  for yi in y_pred:
    y_output.append(*yi)
  return y_output

def main():
  m, n = map(int, input().strip().split())
  x = []; y = []; x_pred = []
  for _ in range(n):
    *features, y_val = map(float, input().strip().split())
    x.append([1] + features)
    y.append(y_val)

  for _ in range(int(input())):
    features = list(map(float, input().strip().split()))
    x_pred.append([1] + features)
  
  answer = solve(y, x, x_pred)
  for num in answer:
    print(round(num, 2))

if __name__ == "__main__":
  main()