Made LinearOperator independent of spLinearOperator (#482)

* Made LinearOperator independent of spLinearOperator

* Added Docstrings

* Updated _matvec and _rmatvec

* Added and Updated _AdjointLinearOperator, _TransposeLinearOperator, _ProductLinearOperator

* minor: fix some issues as documented in PR review
This commit cleans up the linearoperator module, reducing
the use of LinearOperator and aslinearoperator only to
those cases where it is stricly needed - mostly to allow mix
pylops and scipy operators as much as possible.

* Added docs

* bug: fix issue introduced in describe with new private classes in linearoperator

* Removed docstrings

* minor: small changes to doc"

* minor: small change to LinearOperator docstring

* minor: small change to LinearOperator docstring

---------

Co-authored-by: mrava87 <[email protected]>

Author: rohanbabbar04

docs/source/adding.rst

@@ -23,10 +23,11 @@ which will be used as *parent* class for any of our operators:
 
    from pylops import LinearOperator
 
-This class is a child of the
-:py:class:`scipy.sparse.linalg.LinearOperator` class itself which implements the same methods of its parent class
-as well as an additional method for quick inversion: such method can be easily accessed by using ``\`` between the
-operator and the data (e.g., ``A \ y``).
+This class was originally defined as a child of the :py:class:`scipy.sparse.linalg.LinearOperator`, implementing
+the same methods of its parent class as well as additional methods for quick inversion (e.g., ``A \ y``),
+eigenvalues computation, conversion to dense matrices, etc. From version ``v2.1`` onwards, our linear operator
+class has become stand-alone; however, by keeping the same naming structure of the original scipy class, we still
+allow inter-operability with scipy-native linear operators and solvers.
 
 After that we define our new object:
 

docs/source/index.rst

@@ -14,7 +14,6 @@ PyLops offers such solvers for many different types of problems, in particular l
 Get started by :ref:`installing PyLops <Installation>` and following our quick tour.
 
 
-
 Terminology
 -----------
 A common *terminology* is used within the entire documentation of PyLops. Every linear operator and its application to
@@ -48,19 +47,22 @@ such as `Basic Earth Imaging <http://sepwww.stanford.edu/sep/prof/bei11.2010.pdf
 
 Implementation
 --------------
-PyLops is build on top of the `scipy <http://www.scipy.org/scipylib/index.html>`_ class :py:class:`scipy.sparse.linalg.LinearOperator`.
+PyLops was originally build on top of the `scipy <http://www.scipy.org/scipylib/index.html>`_ class
+:py:class:`scipy.sparse.linalg.LinearOperator`.  From version ``v2.1`` onwards, whilst still being heavily inspired
+by its scipy counterpart, PyLops's :py:class:`pylops.linearoperator.LinearOperator` has become a stand-alone class.
 
-This class allows in fact for the creation of objects (or interfaces) for matrix-vector and matrix-matrix products
+This class allows for the creation of objects (or interfaces) for matrix-vector and matrix-matrix products
 that can ultimately be used to solve any inverse problem of the form :math:`\mathbf{y}=\mathbf{A}\mathbf{x}`.
 
-As explained in the `scipy LinearOperator <https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html>`_
-official documentation, to construct a :py:class:`scipy.sparse.linalg.LinearOperator`, a user is required to pass appropriate callables
+To construct a :py:class:`pylops.linearoperator.LinearOperator`, a user is required to pass appropriate arguments
 to the constructor of this class, or subclass it. More specifically one of the methods ``_matvec`` and ``_matmat`` must be implemented for
 the *forward operator* and one of the methods ``_rmatvec`` or ``_adjoint`` may be implemented to apply the *Hermitian adjoint*.
-The attributes/properties ``shape`` (pair of integers) and ``dtype`` (may be None) must also be provided during ``__init__`` of this class.
+The attributes/properties ``dtype`` (may be None) and ``shape`` (pair of integers) -- or alternatively ``dims`` and ``dimsd`` --
+must also be provided during ``__init__`` of this class.
 
 Any linear operator developed within the PyLops library follows this philosophy. As explained more in details in :ref:`addingoperator` section,
-a linear operator is created by subclassing the :py:class:`scipy.sparse.linalg.LinearOperator` class and ``_matvec`` and ``_rmatvec`` are implemented.
+a linear operator is created by subclassing the :py:class:`pylops.linearoperator.LinearOperator` class and implementing the
+``_matvec`` and ``_rmatvec``.
 
 
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