Converting Tensors to Complex Numbers with High Precision in PyTorch

Understanding PyTorch Tensors

• PyTorch offers various data types for tensors, including floating-point numbers (like float32 and float64), integers, and complex numbers.
• A torch.Tensor in PyTorch is a multi-dimensional array that stores elements of a single data type. It's the fundamental data structure for numerical computations.

Complex Numbers in PyTorch

• There are two main complex number data types:
  • torch.complex64 (or torch.cfloat): Represents complex numbers with 64-bit floating-point precision for both the real and imaginary parts.
  • torch.complex128 (or torch.cdouble): Represents complex numbers with 128-bit floating-point precision for both parts, offering higher accuracy.
• PyTorch supports complex numbers, which represent values with both a real and an imaginary part. These are useful for representing signals, wave functions, and other applications in scientific computing.

torch.Tensor.cdouble Method

• In essence, it creates a new tensor with the same dimensions and values as the original tensor, but with each element now represented as a complex number with 128-bit precision.
• It's used to cast (convert) a tensor's data type to torch.complex128 (or torch.cdouble).
• torch.Tensor.cdouble is a method associated with a torch.Tensor object.

Example

import torch

# Create a tensor with real numbers
real_tensor = torch.tensor([1.0, 2.0, 3.0])

# Cast the tensor to complex128 (cdouble)
complex_tensor = real_tensor.cdouble()

print(complex_tensor.dtype)  # Output: torch.complex128

# Access real and imaginary components (both will be 0 initially)
print(complex_tensor.real)
print(complex_tensor.imag)

Key Points

• If you need to create a new complex tensor from scratch, you can use functions like torch.complex(real, imag), where real and imag are tensors or scalars representing the real and imaginary parts.
• torch.Tensor.cdouble is primarily for converting existing tensors to complex numbers with higher precision.

• Consider factors like memory usage and computational efficiency when choosing between complex64 and complex128. If accuracy is not a major concern, complex64 might be sufficient.
• Use cdouble when you need higher precision for complex number calculations compared to torch.complex64.

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Creating a Complex Tensor from Scratch

import torch

# Create real and imaginary tensors (or scalars)
real_part = torch.tensor([1.0, 2.0, 3.0])
imag_part = torch.tensor([0.5, 1.0, 1.5])

# Combine them into a complex tensor
complex_tensor = torch.complex(real_part, imag_part)

print(complex_tensor)

Complex Arithmetic with cdouble

import torch

# Create real and imaginary tensors
real1 = torch.tensor([2.0, 3.0])
imag1 = torch.tensor([1.0, 2.0])
real2 = torch.tensor([1.0, -2.0])
imag2 = torch.tensor([0.5, 1.5])

# Convert to complex128 (cdouble)
complex1 = torch.complex(real1, imag1).cdouble()
complex2 = torch.complex(real2, imag2).cdouble()

# Addition and subtraction
sum_result = complex1 + complex2
difference_result = complex1 - complex2

print("Sum:", sum_result)
print("Difference:", difference_result)

import torch

# Create a complex tensor (or use previous examples)
complex_tensor = torch.complex(torch.tensor([1.0]), torch.tensor([2.0]))

# Magnitude (absolute value)
magnitude = complex_tensor.abs()

# Angle (phase)
angle = complex_tensor.angle()

print("Magnitude:", magnitude)
print("Angle:", angle)

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1. Using torch.complex64 (or cfloat):

   • If you don't require the higher precision of torch.complex128 (cdouble), you can use torch.complex64 (or cfloat). It offers 64-bit floating-point precision for both real and imaginary parts, which might be sufficient for many applications while reducing memory usage compared to cdouble.

2. Creating a Complex Tensor from Scratch:

   • If you're building a complex tensor from scratch, consider using torch.complex(real, imag). This function allows you to directly create a complex tensor with the desired data type (e.g., torch.complex64 or torch.complex128).

Example (Using torch.complex64)

import torch

# Create a real tensor
real_tensor = torch.tensor([1.0, 2.0, 3.0])

# Cast to complex64 (cfloat)
complex_tensor = real_tensor.to(torch.complex64)  # Or use torch.complex(real_tensor)

print(complex_tensor.dtype)  # Output: torch.complex64

Choosing the Right Approach

• If you're creating a complex tensor from scratch, both torch.complex and cdouble are applicable, depending on the desired data type.
• If memory usage is a concern and you can tolerate slightly lower precision, consider using torch.complex64.
• If you already have a real tensor and need to convert it to a complex type with high precision, cdouble remains the best choice.
• The best alternative depends on your specific use case.