principia_materia.mathematics.fourier_transform module

principia_materia.mathematics.fourier_transform.backward_fourier_transform(tensors, p, q)

Backward Fourier Transform for arbitrary orders

Parameters:

• tensors (array of complex/float of shape(N, n_1, ..., n_n)) – Tensors to be Fourier Transformed.

• p (array of numbers of shape(N, m_1, ..., m_m)) – The corresponding T/Q points of the tensors.

• q (array of numbers of shape(M, m_1, ..., m_m) or shape(m_1, ..., m_m)) – The Q/T points for the tensors to be transformed into.

Returns:

restult – The result of Fourier Transform. (If input q has shape of (m_1, …, m_m), returns shape (n_1, …, n_n).)

Return type:

length M array of complex/float of shape(M, n_1, …, n_n)

principia_materia.mathematics.fourier_transform.forward_fourier_transform(tensors, p, q)

Forward Fourier Transform for arbitrary orders

Parameters:

• tensors (array of complex/float of shape(N, n_1, ..., n_n)) – Tensors to be Fourier Transformed.

• p (array of numbers of shape(N, m_1, ..., m_m)) – The corresponding T/Q points of the tensors.

• q (array of numbers of shape(M, m_1, ..., m_m) or shape(m_1, ..., m_m)) – The Q/T points for the tensors to be transformed into.

Returns:

restult – The result of Fourier Transform. (If input q has shape of (m_1, …, m_m), returns shape (n_1, …, n_n).)

Return type:

length M array of complex/float of shape(M, n_1, …, n_n)