# -*- mode:org -*-
#+TITLE: CFG-CI
#+AUTHOR: Vijay Gopal Chilkuri
#+FILE: configurations.org
#+EMAIL: vijay.gopal.c@gmail.com
#+OPTIONS: toc:t
#+LATEX_CLASS: article
#+LATEX_HEADER: \usepackage{tabularx}
#+LATEX_HEADER: \usepackage{braket}
#+LATEX_HEADER: \usepackage{minted}

* Configuration based CI

Here we write the main functions that perform the functions necessary for
the Configuration based CI.

There are three main functions required for doing the CI

- Convert wavefunction from determinant basis to configuration state function (CSF) basis

- Apply the Hamiltonian to the wavefunction in CSF basis

- Convert the converged wavefunction back to determinant basis

** TODO[0/3] Convert basis from DET to CSF

The conversion of basis is done by going via bonded functions (BFs).
Importantly, all the CSFs of a chosen configuration (CFG) are kept.

The advantage is that the sigma-vector can be performed efficiently
via BLAS level 3 operations.


- [ ] Write a function to calculate the maximum dimensions required

  Prototype array contains the \( <I|\hat{E}_{pq}|J> \) for all possible
  CFGs \( I, J\) and all \(4\) types of excitations for all possible model
  orbitals \(p,q\). Note that the orbital ids \(p,q\) here do not refer to
  the actual MO ids, they simply refer to the orbitals involved in that spefcific
  SOMO, for e.g. an excitation of the type [2 2 2 1 1 1 1 0] -> [ 2 2 1 1 1 1 1]
  implies an excitation from orbital \(3\) to orbital \(8\) which are the real MO ids.
  However, the prototype only concerns the SOMOs like so [2 1 1 1 1 0] -> [ 1 1 1 1 1 1]
  therefore \(p,q\) are model space ids \(1,6\).

  #+begin_src f90 :main no :tangle configurations_sigma_vector.irp.f

  BEGIN_PROVIDER [ integer, NSOMOMax]
 &BEGIN_PROVIDER [ integer, NCSFMax]
  implicit none
  BEGIN_DOC
  ! Documentation for NSOMOMax
  ! The maximum number of SOMOs for the current calculation.
  ! required for the calculation of prototype arrays.
  END_DOC
  NSOMOMax = 8
  NCSFMax = 14 ! TODO: NCSFs for MS=0
  END_PROVIDER
  #+end_src

  The prototype matrix AIJpqMatrixList has the following dimensions
  \(\left(NSOMOMax, NSOMOMax, 4, NSOMOMax, NSOMOMax,NCSFMAx,NCSFMax\right)\) where the first two
  indices represent the somos in \(I,J\) followed by the type of excitation and
  finally the two model space orbitals \(p,q\).

- [ ] Read the transformation matrix based on the number of SOMOs

  #+begin_src f90 :main no :tangle configurations_sigma_vector.irp.f
  BEGIN_PROVIDER [ double precision, AIJpqMatrixDimsList, (NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,2)]
  use cfunctions
  implicit none
  BEGIN_DOC
  ! Documentation for AIJpqMatrixList
  ! The prototype matrix containing the <I|E_{pq}|J>
  ! matrices for each I,J somo pair and orb ids.
  END_DOC
  integer i,j,k,l
  integer*8 Isomo, Jsomo
  Isomo = 0
  Jsomo = 0
  integer*8 rows, cols
  rows = -1
  cols = -1
  integer*8 MS
  MS = 0
  print *,"NSOMOMax = ",NSOMOMax
  !allocate(AIJpqMatrixDimsList(NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,2))
  do i = 2, NSOMOMax, 2
     Isomo = ISHFT(1,i)-1
     do j = i-2,i+2, 2
        Jsomo = ISHFT(1,j)-1
        if(j .GT. NSOMOMax .OR. j .LE. 0) then
           cycle
        end if
        do k = 1,NSOMOMax
           do l = k,NSOMOMax
              call getApqIJMatrixDims(Isomo,           &
                   Jsomo, &
                   MS,                       &
                   rows,                     &
                   cols)
              print *, i,j,k,l,">",Isomo,Jsomo,">",rows, cols
              ! i -> j
              AIJpqMatrixDimsList(i,j,1,k,l,1) = rows
              AIJpqMatrixDimsList(i,j,1,k,l,2) = cols
              AIJpqMatrixDimsList(i,j,1,l,k,1) = rows
              AIJpqMatrixDimsList(i,j,1,l,k,2) = cols
              ! j -> i
              AIJpqMatrixDimsList(j,i,1,k,l,1) = rows
              AIJpqMatrixDimsList(j,i,1,k,l,2) = cols
              AIJpqMatrixDimsList(j,i,1,l,k,1) = rows
              AIJpqMatrixDimsList(j,i,1,l,k,2) = cols
           end do
        end do
     end do
  end do
  END_PROVIDER

  #+end_src

- [ ] Perform the conversion by matrix-vector BLAS level 2 call