Complex Algebra¶
- qucumber.utils.cplx.absolute_value(x)[source]¶
Returns the complex absolute value elementwise.
- Parameters
x (torch.Tensor) – A complex tensor.
- Returns
A real tensor.
- Return type
- qucumber.utils.cplx.conj(x)[source]¶
Returns the element-wise complex conjugate of the argument.
- Parameters
x (torch.Tensor) – A complex tensor.
- Returns
The complex conjugate of x.
- Return type
- qucumber.utils.cplx.conjugate(x)[source]¶
Returns the conjugate transpose of the argument.
In the case of a scalar or vector, only the complex conjugate is taken. In the case of a rank-2 or higher tensor, the complex conjugate is taken, then the first two indices of the tensor are swapped.
- Parameters
x (torch.Tensor) – A complex tensor.
- Returns
The conjugate of x.
- Return type
- qucumber.utils.cplx.einsum(equation, a, b, real_part=True, imag_part=True)[source]¶
Complex-aware version of einsum. See the torch documentation for more details.
- Parameters
equation (str) – The index equation. Passed directly to torch.einsum.
a (torch.Tensor) – A complex tensor.
b (torch.Tensor) – A complex tensor.
real_part (bool) – Whether to compute and return the real part of the result.
imag_part (bool) – Whether to compute and return the imaginary part of the result.
- Returns
The Einstein summation of the input tensors performed according to the given equation. If both real_part and imag_part are true, the result will be a complex tensor, otherwise a real tensor.
- Return type
- qucumber.utils.cplx.elementwise_division(x, y)[source]¶
Element-wise 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()
.
- 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.inverse(z)[source]¶
Returns the multiplicative inverse of z. Acts elementwise.
- Parameters
z (torch.Tensor) – The complex tensor.
- Returns
1 / z
- Return type
- qucumber.utils.cplx.kronecker_prod(x, y)[source]¶
Returns the tensor / Kronecker product of 2 complex matrices, 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 Kronecker product of x and y, .
- Return type
- qucumber.utils.cplx.make_complex(x, y=None)[source]¶
A function that creates a torch compatible complex tensor.
Note
x and y must have the same shape.
- Parameters
x (torch.Tensor or numpy.ndarray) – The real part or a complex numpy array. If a numpy array, will ignore y.
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 .
- 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]¶
Returns the norm of the argument.
- Parameters
x (torch.Tensor) – A complex scalar.
- Returns
.
- Return type
- qucumber.utils.cplx.norm_sqr(x)[source]¶
Returns the squared norm of the argument.
- Parameters
x (torch.Tensor) – A complex scalar.
- Returns
.
- Return type
- qucumber.utils.cplx.numpy(x)[source]¶
Converts a complex torch tensor into a numpy array
- Parameters
x (torch.Tensor) – The tensor to convert.
- Returns
A complex numpy array containing the data from x.
- 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 an error will be raised.
- 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]¶
Divides x by y. If x and y have the same shape, then acts elementwise. If y is a complex scalar, then performs a scalar division.
- Parameters
x (torch.Tensor) – The numerator (a complex tensor).
y (torch.Tensor) – The denominator (a complex tensor).
- 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.
- Returns
The product between x and y. Either overwrites out, or returns a new tensor.
- Return type
- qucumber.utils.cplx.sigmoid(x, y)[source]¶
Returns the sigmoid function of a complex number. Acts elementwise.
- Parameters
x (torch.Tensor) – The real part of the complex number
y (torch.Tensor) – The imaginary part of the complex number
- Returns
The complex sigmoid of
- Return type