如何表示来自 2 个实值矩阵的复矩阵

Question

我试图使用 2 个实值矩阵来表示复数矩阵（在 Pytorch 中，但在这里使用 numpy 只是为了说明目的）。

目前我这样做：

import numpy as np
# represent real
X = np.random.randn(10,10)
# represent imaginary
I = np.random.randn(10,10)
# build complex matrix using the identity
real = np.concatenate([X, -I], axis=-1)
img = np.concatenate([I, X], axis=-1)
complex_W = np.concatenate([real, img,], axis=0)
# is complex_W now correctly represented?? 

我也可以这样做吗？

# represent real
X = np.random.randn(10,10)
# represent imaginary
I = np.random.randn(10,10)
complex_W = X + I

Answer 1

您可以使用 numpy 数组实现复杂的 ndarray 数据结构。您可能希望将实部存储在 datasture 的一个变量中，并将复数存储在 anthor 变量中。Python提供了一种重载一些运算符的方法，包括+、-、*、/。例如，我有以下类使用三个运算符（+，- ，*）实现复杂的数据结构

class ComplexNDArray(object):
    def __init__(self, real, imaginary):
        self.real = real
        self.imaginary = imaginary
    @property
    def real(self):
        return self.__real
    @real.setter
    def real(self, value):
        if type(value) == np.ndarray:
            self.__real = value
        elif isinstance(value, (int, float, list, tuple)):
            self.__real = np.array(value)
        else:
            raise ValueError("Unsupported type value:%s" % (str(type(value))))
    @property
    def imaginary(self):
        return self.__imaginary
    @imaginary.setter
    def imaginary(self, value):
        if type(value) == np.ndarray:
            self.__imaginary = value
        elif isinstance(value, (int, float, list, tuple)):
            self.__imaginary = np.array(value)
        else:
            raise ValueError("Unsupported type value:%s" % (str(type(value))))
    def __add__(self, other):
        real = self.real + other.real
        imaginary = self.imaginary + other.imaginary
        return ComplexNDArray(real, imaginary)
    def __sub__(self, other):
        real = self.real - other.real
        imaginary = self.imaginary - other.imaginary
        return ComplexNDArray(real, imaginary)
    def __mul__(self, other):
        real = self.real * other.real - self.imaginary * other.imaginary
        imaginary = self.real * other.imaginary + self.imaginary * other.real
        return ComplexNDArray(real, imaginary)
    def __str__(self):
        return str(self.real) + "+"+str(self.imaginary)+"i"

现在，您可以使用此数据结构执行一些操作。

a  = np.array([1, 2,3])
b = np.array([4, 5, 1])
c  = np.array([4, 7,3])
d  = np.array([5, 1,7])
cmplx = ComplexNDArray(a, b)
cmplx2 = ComplexNDArray(c, d)
print(cmplx)        # [1 2 3]+[4 5 1]i
print(cmplx2)       # [4 7 3]+[5 1 7]i
print(cmplx+cmplx2) # [5 9 6]+[9 6 8]i
print(cmplx-cmplx2) # [-3 -5  0]+[-1  4 -6]i
print(cmplx*cmplx2) # [-16   9   2]+[21 37 24]i