From 0f6572bde1d752b9141baa76e48d5f0da24a4808 Mon Sep 17 00:00:00 2001
From: ydamour <yann.damour@hotmail.fr>
Date: Tue, 8 Nov 2022 15:34:10 +0100
Subject: [PATCH] mat to vec index

---
 src/bitmask/core_inact_act_virt.irp.f         |  6 +-
 src/utils_trust_region/mat_to_vec_index.irp.f | 61 +++++++++++++++++++
 2 files changed, 62 insertions(+), 5 deletions(-)
 create mode 100644 src/utils_trust_region/mat_to_vec_index.irp.f

diff --git a/src/bitmask/core_inact_act_virt.irp.f b/src/bitmask/core_inact_act_virt.irp.f
index d83d69e9..f3eaff32 100644
--- a/src/bitmask/core_inact_act_virt.irp.f
+++ b/src/bitmask/core_inact_act_virt.irp.f
@@ -173,10 +173,7 @@ BEGIN_PROVIDER [integer, n_core_inact_act_orb ]
   END_DOC
   n_core_inact_act_orb = (n_core_orb + n_inact_orb + n_act_orb)
 END_PROVIDER
- 
 
-
- 
  BEGIN_PROVIDER [ integer(bit_kind), core_bitmask , (N_int,2) ]
    implicit none
    BEGIN_DOC
@@ -443,5 +440,4 @@ BEGIN_PROVIDER [integer, list_all_but_del_orb, (n_all_but_del_orb)]
   endif
  enddo
 
-END_PROVIDER 
-
+END_PROVIDER
diff --git a/src/utils_trust_region/mat_to_vec_index.irp.f b/src/utils_trust_region/mat_to_vec_index.irp.f
new file mode 100644
index 00000000..35e12232
--- /dev/null
+++ b/src/utils_trust_region/mat_to_vec_index.irp.f
@@ -0,0 +1,61 @@
+! Matrix to vector index
+
+! *Compute the index i of a vector element from the indexes p,q of a
+! matrix element*
+
+! Lower diagonal matrix (p,q), p > q -> vector (i)
+
+! If a matrix is antisymmetric it can be reshaped as a vector. And the
+! vector can be reshaped as an antisymmetric matrix
+
+! \begin{align*}
+! \begin{pmatrix}
+! 0 & -1 & -2 & -4 \\
+! 1 & 0  & -3 & -5 \\
+! 2 & 3 & 0  & -6  \\
+! 4 & 5 & 6 & 0
+! \end{pmatrix}
+! \Leftrightarrow
+! \begin{pmatrix}
+! 1 & 2 & 3 & 4 & 5 & 6
+! \end{pmatrix}
+! \end{align*}
+
+! !!! Here the algorithm only work for the lower diagonal !!!
+
+! Input:
+! | p,q | integer | indexes of a matrix element in the lower diagonal |
+! |     |         | p > q, q -> column                                |
+! |     |         | p -> row,                                         |
+! |     |         | q -> column                                       |
+
+! Input:
+! | i | integer | corresponding index in the vector |
+
+
+subroutine mat_to_vec_index(p,q,i)
+
+  include 'pi.h'
+
+  implicit none
+  
+  ! Variables
+  
+  ! in
+  integer, intent(in) :: p,q
+  
+  ! out
+  integer, intent(out) :: i 
+
+  ! internal
+  integer :: a,b
+  double precision :: da
+
+  ! Calculation
+ 
+  a = p-1
+  b = a*(a-1)/2
+  
+  i = q+b
+
+end subroutine