Question

在一段代码中，我发现了以下内容

M = [3,4,5]

from math import *

class matrix:

    # implements basic operations of a matrix class

    def __init__(self, value):
        self.value = value
        self.dimx = len(value)
        self.dimy = len(value[0])
        if value == [[]]:
            self.dimx = 0

    def zero(self, dimx, dimy):
        # check if valid dimensions
        if dimx < 1 or dimy < 1:
            raise ValueError, "Invalid size of matrix"
        else:
            self.dimx = dimx
            self.dimy = dimy
            self.value = [[0 for row in range(dimy)] for col in range(dimx)]

    def identity(self, dim):
        # check if valid dimension
        if dim < 1:
            raise ValueError, "Invalid size of matrix"
        else:
            self.dimx = dim
            self.dimy = dim
            self.value = [[0 for row in range(dim)] for col in range(dim)]
            for i in range(dim):
                self.value[i][i] = 1

    def show(self):
        for i in range(self.dimx):
            print self.value[i]
        print ' '

    def __add__(self, other):
        # check if correct dimensions
        if self.dimx != other.dimx or self.dimy != other.dimy:
            raise ValueError, "Matrices must be of equal dimensions to add"
        else:
            # add if correct dimensions
            res = matrix([[]])
            res.zero(self.dimx, self.dimy)
            for i in range(self.dimx):
                for j in range(self.dimy):
                    res.value[i][j] = self.value[i][j] + other.value[i][j]
            return res

    def __sub__(self, other):
        # check if correct dimensions
        if self.dimx != other.dimx or self.dimy != other.dimy:
            raise ValueError, "Matrices must be of equal dimensions to subtract"
        else:
            # subtract if correct dimensions
            res = matrix([[]])
            res.zero(self.dimx, self.dimy)
            for i in range(self.dimx):
                for j in range(self.dimy):
                    res.value[i][j] = self.value[i][j] - other.value[i][j]
            return res

    def __mul__(self, other):
        # check if correct dimensions
        if self.dimy != other.dimx:
            raise ValueError, "Matrices must be m*n and n*p to multiply"
        else:
            # subtract if correct dimensions
            res = matrix([[]])
            res.zero(self.dimx, other.dimy)
            for i in range(self.dimx):
                for j in range(other.dimy):
                    for k in range(self.dimy):
                        res.value[i][j] += self.value[i][k] * other.value[k][j]
            return res

    def transpose(self):
        # compute transpose
        res = matrix([[]])
        res.zero(self.dimy, self.dimx)
        for i in range(self.dimx):
            for j in range(self.dimy):
                res.value[j][i] = self.value[i][j]
        return res

    # Thanks to Ernesto P. Adorio for use of Cholesky and CholeskyInverse functions

    def Cholesky(self, ztol=1.0e-5):
        # Computes the upper triangular Cholesky factorization of
        # a positive definite matrix.
        res = matrix([[]])
        res.zero(self.dimx, self.dimx)

        for i in range(self.dimx):
            S = sum([(res.value[k][i])**2 for k in range(i)])
            d = self.value[i][i] - S
            if abs(d) < ztol:
                res.value[i][i] = 0.0
            else:
                if d < 0.0:
                    raise ValueError, "Matrix not positive-definite"
                res.value[i][i] = sqrt(d)
            for j in range(i+1, self.dimx):
                S = sum([res.value[k][i] * res.value[k][j] for k in range(self.dimx)])
                if abs(S) < ztol:
                    S = 0.0
                res.value[i][j] = (self.value[i][j] - S)/res.value[i][i]
        return res

    def CholeskyInverse(self):
        # Computes inverse of matrix given its Cholesky upper Triangular
        # decomposition of matrix.
        res = matrix([[]])
        res.zero(self.dimx, self.dimx)

        # Backward step for inverse.
        for j in reversed(range(self.dimx)):
            tjj = self.value[j][j]
            S = sum([self.value[j][k]*res.value[j][k] for k in range(j+1, self.dimx)])
            res.value[j][j] = 1.0/tjj**2 - S/tjj
            for i in reversed(range(j)):
                res.value[j][i] = res.value[i][j] = -sum([self.value[i][k]*res.value[k][j] for k in range(i+1, self.dimx)])/self.value[i][i]
        return res

    def inverse(self):
        aux = self.Cholesky()
        res = aux.CholeskyInverse()
        return res

    def __repr__(self):
        return repr(self.value)

for n in range(len(M)):
    Z = matrix([[M[n]]])
    Z.show()

现在如果我运行代码，我得到以下输出：

[3]
[4]
[5]

现在我不明白输出的含义以及如何解释这个。具体来说，上面的以下代码行无法理解

Z = matrix([[M[n]]])

有人可以解释一下代码的输出和上面的单行吗？

Answer 1

代码创建三个1x1矩阵，即三个矩阵，其中每个矩阵包含一个元素，并打印它们。这是你看到的[3]，[4]，[5]：三个1x1矩阵。

对于[[M[n]]]：矩阵构造函数需要矩阵的值，这是一个二维数组。这解释了[[ .. ]]。您可以通过调用

构建一个2x2单位矩阵

data = [ [1,0], [0,1] ]
matrix(data)

（这是一个包含两个其他列表的列表，每个列表都有两个元素。）

在这种情况下，矩阵初始化为每个元素，恰好是M[n]。

代码可以简化为：

for n in M:
  Z = matrix([[n]])
  Z.show()

这使得阅读更容易

Answer 2

最后一个for循环是决定输出的那个：

for n in range(len(M)):
    Z = matrix([[M[n]]])
    Z.show()

从M=[3,4,5]开始，这会将后两行调用三次：

Z = matrix([[3]])
Z.show()
Z = matrix([[4]])
Z.show()
Z = matrix([[5]])
Z.show()

每次我们将Z设置为1x1矩阵，例如[[3]]，并应用show矩阵方法，该方法基本上以很好的方式打印Z。

在python中创建矩阵

2 个答案: