Working on building the prototype matrix AIJpq #143.

src/determinants/configurations.org

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+# -*- 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_PROIDER[ integer, NSOMOMax]
+  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
+  BEGIN_PROIDER[ double precision, AIJpqMatrixList, (NSOMOMax,NSOMOMax,4,NSOMOMax,NSOMOMax,NCSFMax,NCSFMax)]
+  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
+  do i = 1,NSOMOMax
+     do j = i-1,i+1
+        if(j > NSOMOMax || j ==0) then
+           continue
+        end if
+     end do
+  end do
+  END_PROVIDER
+
+  #+end_src
+
+- [ ] Perform the conversion by matrix-vector BLAS level 2 call

src/determinants/configurations_sigma_vector.irp.f

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+  BEGIN_PROIDER[ integer, NSOMOMax]
+  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