qics.vectorize.mat_to_vec

qics.vectorize.mat_to_vec(mat, compact=False)

Reshapes a symmetric or Hermitian matrix into a column vector.

If mat is of type float64 and compact=False, then this performs the vectorization

\[\begin{split}\begin{bmatrix}a & b & d \\ b & c & e \\ d & e & f\end{bmatrix} \mapsto \begin{bmatrix}a & b & d & b & c & e & d & e & f\end{bmatrix}^\top.\end{split}\]

If mat is of type float64 and compact=True, then this performs the vectorization

\[\begin{split}\begin{bmatrix}a & b & d \\ b & c & e \\ d & e & f\end{bmatrix} \mapsto\begin{bmatrix} a & \sqrt{2} b & c & \sqrt{2} d & \sqrt{2}e & f \end{bmatrix}^{\top}.\end{split}\]

If mat is of type complex128 and compact=False, then this performs the vectorization

\[\begin{split}\begin{bmatrix} a & b+ci & e+fi \\ b-ci & d & g+hi \\ e-fi & g-hi & k \end{bmatrix}\mapsto \begin{bmatrix} a & 0 & b & c & e & f & b & -c & d & 0 & g & h & e & -f & g & -h & k & 0 \end{bmatrix}^{\top}.\end{split}\]

If mat is of type complex128 and compact=True, then this performs the vectorization

\[\begin{split}\begin{bmatrix} a & b+ci & e+fi \\ b-ci & d & g+hi \\ e-fi & g-hi & k \end{bmatrix}\mapsto \begin{bmatrix} a & \sqrt{2} b & \sqrt{2} c & d & \sqrt{2} e & \sqrt{2} f & \sqrt{2} g & \sqrt{2} h & k \end{bmatrix}^{\top}.\end{split}\]

Parameters:

matndarray

Input matrix to vectorize, either of type float64 or complex128.

compactbool, optional

Whether to convert to a compact vector representation or not. The default is False.

Returns:

ndarray

The resulting vectorized matrix.