Photo Credit: Michael Rose

# Science with objects

An object in computer science is a collection of labeled data together with actions or methods you can perform on that data. The methods are collected together and defined in one place called a class or module.

Sometimes methods are also called messages i.e. you pass messages to the object to ask it to perform an action. These methods or messages may involving other objects of different type which may also change. An object may also be called an abstract data type.

## Dot notation

Any number may be regarded as an object.

That’s because a particular number is a datum, and we can perform actions on it e.g adding or multiplying it by another number. If collect together these routines we have defined a class.

The example code snippets below demonstrate a near universal notation, called “dot notation”, which I illustrate on numbers:

a,b :: INT

a = 1
a.plus(1)

b = 2
b.times(3)

Here the variable a is set to 1. a and b are integer variables as seen by the declaration a,b :: INT. Then a message is sent to it via a dot followed by plus(1). The intention of the message is that the value of a is incremented by the number 1. Presumably the value of a is 2 after this method is applied. Likewise, the number b is set to 2 and then the operations times(3) is performed on it, resulting in a value of 6. For those of you who like quantum mechanics, this is nothing other than the application an operator, except the operator comes after the entity on which the action is performed.

All of this might seem rather trivial. But consider this example:

m :: MAT{REAL}(3,3)
eigenvalues  :: VEC{REAL}(3)
eigenvectors :: MAT{REAL}(3,3)
i,j :: INT

do i = 1,3
do j = 1,3
m(i,j) = i + j
end
end

m.solve_eigenproblem(eigenvalues,eigenvectors)

Look closely.

It does not require much imagination to guess that m is a $$3\times3$$ matrix of REAL numbers, as is eigenvectors. eigenvectors is a 3-dimensional real vector.

Next come a couple of do statements. These are a loops. Meaning that the integer variables i and j independently cycle from 1 to 3 and the matrix m is set so its $$i,j$$-th element is i+j.

The next part is more interesting: a message is sent to to the matrix m to please solve_eigenproblem(eigenectors,eigenvalues). Again it does not take much to guess that eigenvalues are the list of eigenvalues, while eigenvectors holds the matrix of eigenvector coefficients.

All this is cute, but has anything really been achieved? Isn’t this just a familiar subroutine call? Well yes. But notice how the object-message makes it clear what the entity actually being “acted on” is, and what the inputs or output are.

## A leap

Let me now give a final example which quantum chemists will recognize. It is slightly changed from the Tonto code base. It is written in the Foo language, as are all the above examples. This is a big leap from the previous examples, but you know enough to unravel it.

usual_scf ::: recursive
! Do an SCF calculation. The .molecular_orbitals,
! .orbital_energies, and .density_matrix are produced as results.
self :: MOLECULE

ENSURE(self.atom.created,   "no atom list")
ENSURE(self.scfdata.created,"no scfdata")

self.initialize_scf

self.put_scf_banner_and_options

do

self.update_molecular_orbitals
self.make_scf_density_matrix
self.make_fock_matrix
self.update_scfdata
self.update_scfdata_error
self.put_scf_table_body

if (self.scfdata.scf_done) exit

end

self.put_scf_results
self.cleanup_scf

end

Look carefully.

It is clearly an SCF subroutine called usual_scf (for those who are not familiar with quantum chemistry, the SCF procedure is the one which yeilds the molecular orbitals for a molecule, from which the Hartree-Fock or density functional theory energy may be calculated). The declaration indicates that usual_scf is recursive i.e. it calles itself.

There are descriptive comments following the routine name, following the exclamation marks, describing the results. They seem reasonable except for the do in front of soke of the terms.

Next, a variable called self is declared. It is not an integer, or a real, or matrix as we have seen before, but a MOLECULE. We don’t know exactly what this MOLECULE is, but working by analogy it wpuld seem reasnable that is is comprised of data — probably quite a lot of data since a molecule is a compicated object. One might speculate that, stored in this variable of type MOLECULE are the types of atoms in it, and perhaps their positions. Notice that you can work all this out by intuition and by the naming of the entity. I don’t want to rub it in, but I did stress the importance of naming things properly in a previous post.

What is the actual data that comprises the self variable of type MOLECULE? Where is it defined? We don’t get that information here, obviously.

Let me inform you that the type MOLECULE is defined in the types.foo file along with all the other types in the Tonto system.

Let me also tell you that self is in fact a hidden argument to this routine. In other words, to the routine called usual_scf requires self as an argument. In Fortran it might be called like this in another part of the library:

usual_scf(self)

In actual fact is called like this

self.usual_scf

or even more succinctly like this

.usual_scf

Pause on this a moment. I am saying that self is the object to which the message usual_scf is passed to. That is, the SCF calculation is performed on self itself. Perhaps this helps to explain the initially rather cryptic name. In any case, the appearance of a single dot after an empty space signifies the presence of a hidden self variable. Apart from anything this leads to less typing.

## Removing your self

Let’s rewrite the above SCF routine without the unnecessary self. prefix.

usual_scf ::: recursive
! Do an SCF calculation. The .molecular_orbitals,
! .orbital_energies, and .density_matrix are produced as results.
self :: MOLECULE

ENSURE(.atom.created,   "no atom list")
ENSURE(.scfdata.created,"no scfdata")

.initialize_scf

.put_scf_banner_and_options

do

.update_molecular_orbitals
.make_scf_density_matrix
.make_fock_matrix
.update_scfdata
.update_scfdata_error
.put_scf_table_body

if (.scfdata.scf_done) exit

end

.put_scf_results
.cleanup_scf

end

Now the routine reads like a dot-point list of things to do. It is really extremely readable. Indeed, It may seem hard to believe that this is a working program — perhaps even more unbelievable that this is essentially just syntactically modified Fortran. (Much of the bad reputation has come from the style of coding that scientists use: it is not the language itself these days).

Furthermore, if we revisit the comments at the start of the routine it finally becomes clear why the dots appear before .molecular_orbitals, .orbital_energies and .density_matrix. These are messages passed to te self variable to return certain entities. You can guess what they are. These are in fact part of the data components which comprise the definition of a MOLECULE

## Complex numbers as objects

If you have understood all of this, test yourself with the following example.

We are going to define a complex number type, as follows, in the types.foo file. (We don’t actually need to do thisbecause complex numbers are built-in, but this is an exercise)

begin type COMPLEX_NUMBER

a :: REAL
! The real part

b :: REAL
! The complex part

end type

Now you know how to define a derived type comprised of built-in types, in this case two REAL number types. A derived type may be comparised of any previously defined derived type or built-in type.

What is the purpose of the following method? I will tell you that the rouine is not correct. Can you find the bug?

module COMPLEX_NUMBER

contains

to_product_with(z2) result (res)
! What do I do?

self :: IN
z2 :: COMPLEX_NUMBER, IN
res :: COMPLEX_NUMBER

z_1 :: COMPLEX_NUMBER

z_1   = self
res.a = z1.a z2.a + z1.b z2.b
res.b = z1.a z2.b + z1.b z2.a

end

end

## What all the fuss is about

This has been a long post but the key idea is just this:

The power of objects is in their organizing ability

In particular

1. All methods pertaining to an object are found in the corresponding module. This is helpful because duplication of code is eliminated. Consider the case of a program written by many contributors not written in object oriented way. The chances are that the different authors write many duplicated routines. In particular domains, much hard work has been expended to make libraries of, for example, linear algebra and array routines. However, in other fields this effort is almost non-existent. Consider the case of quantum chemistry, for example, with it’s plethora of programs. Consider the wasted and duplicated efforts of so many smart people!

2. Organizing programs in an object oriented way facilitates program evolution. Let’s illustrate this again with examples from quantum chemistry.

• How easy would it be to make use of the integrals in this program in another one? Perhaps it isn’t hard if they have been written to a file … perhaps.

• What if now you wanted to use some of the integrals and not others? Perhaps you want to calculate the energy contributions from a particular region to gain some physical insight?

• What if now you have a new and better way of calculating the integrals. Perhaps you have discovered that gaussian basis functions with complex exponents work much better. How easy would it be to slot those integras into the code? After all, it would not be desirable to rewrite *everything in the original program.

In general all of these tasks would be difficult to do unless the data used was well separated from the other parts of the program, and all actions on those data are encapulated in one place. But this is precisely the idea behind the object oriented approach. Indeed, as we saw, not only are all the methods which act on the same data collected in the same module — the data object on which the methods are applied are always the first argument in any routine.

3. It is easier to maintain an object oriented program. If you have understood the above argument you should be able to provide reasons for this. As a matter of fact, it is well documented that during the life cycle of a program much more effort goes into maintenance and bug fixing that into the original writing! If this is accepted then it follows that much is gained by using objects.

## Proof of the pudding

The arguments given above may well seem like preaching. Some others may think that the idea behind object oriented methods is just the concept of a library — organizing routines acting on the same data in one place. This is correct: object orientation is just the library concept on steroids. In a later post I hope to illustrate how easy it is to write code in a well-designed quantum chemistry package.