# Complex numbers

Source: https://www.tensorplay.cn/docs/complex_numbers.html

TensorPlay supports complex tensors — elements stored as a real and an imaginary part. Complex
dtypes are tensorplay.complex64 and tensorplay.complex128.

```
import tensorplay as tp

x = tp.tensor([1 + 2j, 3 - 4j])
print(x.dtype)          # tensorplay.complex64
print(x.real)           # the real part
print(x.imag)           # the imaginary part
```

## Creating complex tensors

tensorplay.complex builds a complex tensor from separate real and imaginary tensors, and
tensorplay.polar builds one from magnitude and angle:

```
re = tp.tensor([1.0, 3.0])
im = tp.tensor([2.0, -4.0])
z = tp.complex(re, im)             # tensor([1.+2.j, 3.-4.j])

mag = tp.tensor([2.0, 1.0])
ang = tp.tensor([0.0, 1.5708])
p = tp.polar(mag, ang)             # magnitude, angle
```

## Reading and converting

tensorplay.real and tensorplay.imag extract the real and imaginary parts. conj returns
the complex conjugate and resolve_conj produces a tensor whose conjugation is applied;
view_as_real reinterprets a complex tensor as a float tensor with an extra trailing
dimension of size 2, while view_as_complex removes that pairing:

```
z = tp.tensor([1 + 2j, 3 + 4j])
print(tp.conj(z))                   # [1.-2.j, 3.-4.j]
print(tp.view_as_real(z).shape)     # (2, 2) — the trailing 2 is (real, imag)
```

tensorplay.is_complex reports whether a tensor has a complex dtype.

| tensorplay.complex |Constructs a complex tensor with its real part equal to real and its imaginary part equal to imag. |
| --- | --- |
| tensorplay.polar | Constructs a complex tensor whose elements are Cartesian coordinates corresponding to the polar coordinates with absolute value abs and angle angle. |
| tensorplay.view_as_complex | Returns a view of input as a complex tensor. |
| tensorplay.view_as_real | Returns a view of input as a real tensor. |
| tensorplay.is_complex | Returns True if the data type of input is a complex data type i.e., one of tensorplay.complex64, and tensorplay.complex128. |
| tensorplay.conj | Returns a view of input with a flipped conjugate bit. |
| tensorplay.resolve_conj | Returns a new tensor with materialized conjugation if input's conjugate bit is set to True, else returns input. |
| tensorplay.real | Returns a new tensor containing real values of the self tensor. |
| tensorplay.imag | Returns a new tensor containing imaginary values of the self tensor. |

## Where to go next

- [Tensors](/docs/tensorplay.html) — the full tensor API.

- [Type information](/docs/type_info.html) — the limits of a complex dtype.