# SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
# SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
# SPDX-FileContributor: 2003-23 Bradley M. Bell
# ----------------------------------------------------------------------------
/*
{xrst_begin VecAD}
{xrst_spell
   grep
   ld
   ldp
   ldv
   st
   vp
   wc
}

AD Vectors that Record Index Operations
#######################################

Syntax
******
``VecAD`` < *Base* > *vec* ( *n* )

*vec* . ``size`` ()

*base* = *vec* [ *i* ]

| *abase* = *vec* [ *ind* ]
| *vec* [ *ind* ]   = *right*
| *left* = *vec* [ *ind* ]

Purpose
*******
If either *vec* or *ind* is a
:ref:`glossary@Variable` or
:ref:`dynamic parameter<glossary@Parameter@Dynamic>` ,
the indexing operation

   *vec* [ *ind* ]

is recorded in the corresponding ``AD`` < *Base* >
:ref:`operation sequence<glossary@Operation@Sequence>` and
included in the corresponding :ref:`ADFun-name` object *f* .
Such an index can change each time
zero order :ref:`f.Forward<Forward-name>` is used; i.e.,
each time *f* is evaluated with new value for the
:ref:`independent variables<glossary@Tape@Independent Variable>` .
Note that the value of *vec* [ *ind* ]
depends on the value of *ind*
in a discrete fashion and CppAD computes its partial derivative with
respect to *ind* as zero.

Alternatives
************
If only the values in *vec* ,
and not the indices *ind* ,
depend on the independent variables,
a :ref:`SimpleVector-name` with elements of type ``AD`` < *Base* >
would be more efficient than using ``VecAD`` < *Base* > .
If only the indices, and not the values in the vector,
depend on the independent variables,
a :ref:`Discrete-name` functions would be a much more efficient.

Efficiency
**********
If one uses ``VecAD`` vector where one could use a simple vector,
the :ref:`sparsity_pattern-name` will be less efficient
because the dependence on different elements cannot be separated.
In addition, ``VecAD`` objects that only depend on dynamic parameters
are treated as if they were variables making sparsity patterns
even less efficient (have more possibly non-zero values than necessary);
see :ref:`wish_list@Dynamic Parameters@VecAD Vectors`
under dynamic parameters in the wish list.

VecAD<Base>::reference
**********************
The expression *vec* [ *ind* ] has prototype

   ``VecAD`` < *Base* >:: ``reference`` *vec* [ *ind* ]

which is like the ``AD`` < *Base* > type
with some notable exceptions:

Exceptions
==========

#. This object cannot be used with the
   :ref:`Value-name` function to compute the corresponding *Base* value.
   In some cases, the syntax

      *vec* [ *i* ]

   can be used to obtain the corresponding *Base* value; see below.

#. This object cannot be used as the left hand side in a
   with a :ref:`compound assignment<compound_assign-name>` ; i.e.,
   ``+=`` ,
   ``-=`` ,
   ``*=`` , or
   ``/=`` .
   For example, the following syntax is not valid:

      *vec* [ *ind* ] += *z* ;

   no matter what the types of *z* .

#. Assignment to ``vec`` [ ``ind`` ] returns a ``void`` .
   For example, the following syntax is not valid:

      *z* = *vec* [ *ind* ] = *u* ;

   no matter what the types of *z* , and *u* .

#. A *vec* [ *ind* ] object cannot appear in a :ref:`CondExp-name` ;
   For example, the following syntax is not valid:

      ``CondExpGt`` ( *vec* [ *ind* ], *u* , *v* , *w* )

   no matter what the types of *u* , *v* , and *w* .

#. A *vec* [ *ind* ] object should not be used with the
   ``Constant`` , ``Dynamic`` , ``Parameter`` , and ``Variable``
   functions (see :ref:`con_dyn_var-name` ).
   The entire vector *vec* should be used instead.

#. A ``VecAD`` vector
   cannot be passed to ``Independent`` function.

Constructor
***********

vec
===
The syntax

   ``VecAD`` < *Base* > *vec* ( *n* )

creates an ``VecAD`` object *vec* with
*n* elements.
The initial value of the elements of *vec* is unspecified.

n
=
The argument *n* has prototype

   ``size_t`` *n*

size
****
The syntax

   *vec* . ``size`` ()

returns the number of elements in the vector *vec* ;
i.e., the value of *n* when it was constructed.

Base Indexing
*************
We refer to the syntax

   *base* = *vec* [ *i* ]

as base indexing of a ``VecAD`` object.
This indexing is only valid if the vector *vec* is a
:ref:`con_dyn_var@Constant` ; i.e.,
it does not depend on the independent variables.

i
=
The operand *i* has prototype

   ``size_t`` *i*

and must be less than *n* ; i.e., less than
the number of elements in *vec* .

base
====
The result *base* has prototype

   *Base* & *base*

i.e., it is a reference to the *i*-th element in the vector *vec* .
It can be used to change the element value;
for example,

   *vec* [ *i* ] = *b*

is valid where *b* is a *Base* object.
The reference *base* is no longer valid once the
*vec* changes in any way; i.e., has another assignment.

AD Indexing
***********
We refer to the syntax

   *vec* [ *ind* ]

as AD indexing of a ``VecAD`` object.

ind
===
The argument *ind* has prototype

   ``const AD`` < *Base* >& *ind*

The value of *ind* must be greater than or equal zero
and less than *n* ; i.e., less than
the number of elements in *vec* .

result
======
The resulting expression has prototype

   ``VecAD`` < *Base* >:: ``reference`` *vec* [ *ind* ]

This objects operations are recorded as part of the ``AD`` < *Base* >
:ref:`operation sequence<glossary@Operation@Sequence>` .
It acts like a reference to the
element with index ``floor`` ( *ind* ) in the vector *vec* ;
( ``floor`` ( *ind* ) is
the greatest integer less than or equal *ind* ).

right
=====
Is the right hand side of the assignment statement
and specifies the new value for the corresponding element of *vec* .
It has one of the following prototypes:

| |tab| ``int`` *right*
| |tab| ``const`` *Base* & *right*
| |tab| ``const AD`` < *Base* >& *right*
| |tab| ``const VecAD_reverence`` < *Base* >& *right*

left
====
Is the left hand side of the assignment statement
is the current value for the corresponding element of *vec* .
It has the following prototype:

   ``const AD`` < *Base* >& *left*

Example
*******
{xrst_toc_hidden
   example/general/vec_ad.cpp
}
The file
:ref:`vec_ad.cpp-name`
contains an example and test using ``VecAD`` vectors.

base2ad
*******
Forward mode on a ``base2ad`` function does not preserve
:ref:`VecAD-name` operations (which might be expected); see the
:ref:`base2vec_ad.cpp-name` example.

Speed and Memory
****************
The :ref:`VecAD-name` vector type is inefficient because every
time an element of a vector is accessed, a new CppAD
:ref:`glossary@Variable` is created on the tape
using either the ``Ldp`` or ``Ldv`` operation
(unless all of the elements of the vector are
:ref:`parameters<glossary@Parameter>` ).
The effect of this can be seen by executing the following steps:

#. In the file ``cppad/local/forward1sweep.h`` ,
   change the definition of ``CPPAD_FORWARD1SWEEP_TRACE`` to
   ::

      # define CPPAD_FORWARD1SWEEP_TRACE 1

#. In the ``Example`` directory, execute the command
   ::

      ./test_one.sh lu_vec_ad_ok.cpp lu_vec_ad.cpp -DNDEBUG > lu_vec_ad_ok.log

   This will write a trace of all the forward tape operations,
   for the test case :ref:`lu_vec_ad_ok.cpp-name` ,
   to the file ``lu_vec_ad_ok.log`` .
#. In the ``Example`` directory execute the commands
   ::

      grep "op="           lu_vec_ad_ok.log | wc -l
      grep "op=Ld[vp]"     lu_vec_ad_ok.log | wc -l
      grep "op=St[vp][vp]" lu_vec_ad_ok.log | wc -l

   The first command counts the number of operators in the tracing,
   the second counts the number of VecAD load operations,
   and the third counts the number of VecAD store operations.
   (For CppAD version 05-11-20 these counts were 956, 348, and 118
   respectively.)

{xrst_end VecAD}
------------------------------------------------------------------------
*/
