Complex Algebra¶
-
qucumber.utils.cplx.
absolute_value
(x)[source]¶ Computes the complex absolute value elementwise.
- Parameters
x (torch.Tensor) – A complex tensor.
- Returns
A real tensor.
- Return type
-
qucumber.utils.cplx.
conjugate
(x)[source]¶ A function that takes the conjugate transpose of the argument.
- Parameters
x (torch.Tensor) – A complex vector or matrix.
- Returns
The conjugate of x.
- Return type
-
qucumber.utils.cplx.
elementwise_division
(x, y)[source]¶ Elementwise division of x by y.
- Parameters
x (torch.Tensor) – A complex tensor.
y (torch.Tensor) – A complex tensor.
- Return type
-
qucumber.utils.cplx.
elementwise_mult
(x, y)[source]¶ Alias for
scalar_mult()
.
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qucumber.utils.cplx.
imag
(x)[source]¶ Returns the imaginary part of a complex tensor.
- Parameters
x (torch.Tensor) – The complex tensor
- Returns
The imaginary part of x; will have one less dimension than x.
- Return type
-
qucumber.utils.cplx.
inner_prod
(x, y)[source]¶ A function that returns the inner product of two complex vectors, x and y (<x|y>).
- Parameters
x (torch.Tensor) – A complex vector.
y (torch.Tensor) – A complex vector.
- Raises
ValueError – If x and y are not complex vectors with their first dimensions being 2, then the function will not execute.
- Returns
The inner product, .
- Return type
-
qucumber.utils.cplx.
kronecker_prod
(x, y)[source]¶ A function that returns the tensor / kronecker product of 2 complex tensors, x and y.
- Parameters
x (torch.Tensor) – A complex matrix.
y (torch.Tensor) – A complex matrix.
- Raises
ValueError – If x and y do not have 3 dimensions or their first dimension is not 2, the function cannot execute.
- Returns
The tensorproduct of x and y, .
- Return type
-
qucumber.utils.cplx.
make_complex
(x, y=None)[source]¶ A function that combines the real (x) and imaginary (y) parts of a vector or a matrix.
Note
x and y must have the same shape. Also, this will not work for rank zero tensors.
- Parameters
x (torch.Tensor) – The real part
y (torch.Tensor) – The imaginary part. Can be None, in which case, the resulting complex tensor will have imaginary part equal to zero.
- Returns
The tensor [x,y] = x + yi.
- Return type
-
qucumber.utils.cplx.
matmul
(x, y)[source]¶ A function that computes complex matrix-matrix and matrix-vector products.
Note
If one wishes to do matrix-vector products, the vector must be the second argument (y).
- Parameters
x (torch.Tensor) – A complex matrix.
y (torch.Tensor) – A complex vector or matrix.
- Returns
The product between x and y.
- Return type
-
qucumber.utils.cplx.
norm
(x)[source]¶ A function that returns the norm of the argument.
- Parameters
x (torch.Tensor) – A complex scalar.
- Returns
.
- Return type
-
qucumber.utils.cplx.
norm_sqr
(x)[source]¶ A function that returns the squared norm of the argument.
- Parameters
x (torch.Tensor) – A complex scalar.
- Returns
.
- Return type
-
qucumber.utils.cplx.
outer_prod
(x, y)[source]¶ A function that returns the outer product of two complex vectors, x and y.
- Parameters
x (torch.Tensor) – A complex vector.
y (torch.Tensor) – A complex vector.
- Raises
ValueError – If x and y are not complex vectors with their first dimensions being 2, then the function will not execute.
- Returns
The outer product between x and y, .
- Return type
-
qucumber.utils.cplx.
real
(x)[source]¶ Returns the real part of a complex tensor.
- Parameters
x (torch.Tensor) – The complex tensor
- Returns
The real part of x; will have one less dimension than x.
- Return type
-
qucumber.utils.cplx.
scalar_divide
(x, y)[source]¶ A function that computes the division of x by y.
- Parameters
x (torch.Tensor) – The numerator (a complex scalar, vector or matrix).
y (torch.Tensor) – The denominator (a complex scalar).
- Returns
x / y
- Return type
-
qucumber.utils.cplx.
scalar_mult
(x, y, out=None)[source]¶ A function that computes the product between complex matrices and scalars, complex vectors and scalars or two complex scalars.
- Parameters
x (torch.Tensor) – A complex scalar, vector or matrix.
y (torch.Tensor) – A complex scalar, vector or matrix.
z (torch.Tensor) – The complex tensor to write the output to.
z – A complex scalar, vector or matrix. Can be None, in which case, a new tensor is created and returned. Otherwise, the method overwrites z.
- Returns
The product between x and y. Either overwrites z, or returns a new tensor.
- Return type