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org/qmckl_sherman_morrison_woodbury.org

@@ -33,39 +33,39 @@ range(2, 22)
   
 
 * Naïve Sherman-Morrison
-    :PROPERTIES:
-    :Name:     qmckl_sherman_morrison_naive
-    :CRetType: qmckl_exit_code
-    :FRetType: qmckl_exit_code
-    :END:
+:PROPERTIES:
+:Name:     qmckl_sherman_morrison_naive
+:CRetType: qmckl_exit_code
+:FRetType: qmckl_exit_code
+:END:
 
-    This is the simplest of the available Sherman-Morrison-Woodbury kernels. It applies rank-1 updates one by one in
-    the order that is given. It only checks if the denominator in the Sherman-Morrison formula is not too close to
-    zero when an update is evaluated. It will exit with an error code of the denominator is too close to zero.
+This is the simplest of the available Sherman-Morrison-Woodbury kernels. It applies rank-1 updates one by one in
+the order that is given. It only checks if the denominator in the Sherman-Morrison formula is not too close to
+zero when an update is evaluated. It will exit with an error code of the denominator is too close to zero.
 
-    The formula for any update $u_j$ (index $j$ is suppresed for clarity) that is applied is
-    \[
-    (S + uv^T)^{-1} = S^{-1} - \frac{S^{-1} uv^T S^{-1}}{1 + v^T S^{-1} u}
-    \]
+The formula for any update $u_j$ (index $j$ is suppresed for clarity) that is applied is
+\[
+(S + uv^T)^{-1} = S^{-1} - \frac{S^{-1} uv^T S^{-1}}{1 + v^T S^{-1} u}
+\]
 
-    where
-    $S$ is the Slater-matrix,
-    $u$ and $v^T$ are the column and row vectors containing the updates,
-    $S^{-1}$ is the inverse of the Slater-matrix.
+where
+$S$ is the Slater-matrix,
+$u$ and $v^T$ are the column and row vectors containing the updates,
+$S^{-1}$ is the inverse of the Slater-matrix.
 
-    Even though the Slater-matrix $S$ with all updates applied at once is invertable, during the course of applying
-    updates to the inverse Slater-matrix $S^{-1}$ one-by-one it can happen that one of the intermediate inverse
-    matrices $S^{-1}$ becomes singular. Therefore a global threshold value $\epsilon$ is defined that is used to
-    evaluate each individual update $u_j$ when it is applied.
+Even though the Slater-matrix $S$ with all updates applied at once is invertable, during the course of applying
+updates to the inverse Slater-matrix $S^{-1}$ one-by-one it can happen that one of the intermediate inverse
+matrices $S^{-1}$ becomes singular. Therefore a global threshold value $\epsilon$ is defined that is used to
+evaluate each individual update $u_j$ when it is applied.
 
-    This value sets the lower bound for which the
-    denominator $1+v_j^TS^{-1}u_j$ is considered to be too small and will most probably result in a singular matrix
-    $S$, or at least in an inverse of $S$ of very poor numerical quality. Therefore, when $1+v_j^TS^{-1}u_j \geq \epsilon$,
-    the update is applied as usual and the kernel exits with return code \texttt{QMCKL_SUCCESS}.
-    If $1+v_j^TS^{-1}u_j \leq \epsilon$ the update is rejected and the kernel exits with return code \texttt{QMCKL_FAILURE}.
+This value sets the lower bound for which the
+denominator $1+v_j^TS^{-1}u_j$ is considered to be too small and will most probably result in a singular matrix
+$S$, or at least in an inverse of $S$ of very poor numerical quality. Therefore, when $1+v_j^TS^{-1}u_j \geq \epsilon$,
+the update is applied as usual and the kernel exits with return code \texttt{QMCKL_SUCCESS}.
+If $1+v_j^TS^{-1}u_j \leq \epsilon$ the update is rejected and the kernel exits with return code \texttt{QMCKL_FAILURE}.
 
-    If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
-    from applying the updates to the original matrix.
+If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
+from applying the updates to the original matrix.
 
 #+NAME: qmckl_sherman_morrison_naive_args
 | Variable        | Type                    | In/Out | Description                                          |
@@ -612,9 +612,9 @@ end interface
 
 * End of files
 
-   #+begin_src c :comments link :tangle (eval c_test)
-  assert (qmckl_context_destroy(context) == QMCKL_SUCCESS);
-  return 0;
+#+begin_src c :comments link :tangle (eval c_test)
+assert (qmckl_context_destroy(context) == QMCKL_SUCCESS);
+return 0;
 
 }
    #+end_src