Use \ccSum.

Interpolation/doc_tex/Interpolation/interpolation.tex

@@ -7,11 +7,11 @@ re-produces linear functions exactly. The interpolation of
 $\Phi(\mathbf{x})$ is given as the linear combination of the neighbors' function
 values weighted by the coordinates:
 \begin{displaymath}
-  Z^0(\mathbf{x}) = \sum_i  \lambda_i(\mathbf{x}) z_i.
+  Z^0(\mathbf{x}) = \ccSum{i}{}{ \lambda_i(\mathbf{x}) z_i}.
 \end{displaymath}
 Indeed, if $z_i=a + \mathbf{b}^t \mathbf{p_i}$ for all natural
 neighbors of $\mathbf{x}$, we have
-\[  Z^0(\mathbf{x}) = \sum_i  \lambda_i(\mathbf{x}) (a + \mathbf{b}^t\mathbf{p_i}) = a+\mathbf{b}^t \mathbf{x}\]
+\[  Z^0(\mathbf{x}) = \ccSum{i}{}{ \lambda_i(\mathbf{x}) (a + \mathbf{b}^t\mathbf{p_i})} = a+\mathbf{b}^t \mathbf{x}\]
 by the barycentric coordinate property. The first example in
 Subsection~\ref{subsec:interpol_examples} shows how the function is
 called.
@@ -31,20 +31,20 @@ Sibson's $Z^1$ interpolant is a combination of the linear interpolant
 $Z^0$ and an interpolant $\xi$ which is the weighted sum of the first
 degree functions
 $$\xi_i(\mathbf{x}) = z_i
-+\mathbf{g_i}^t(\mathbf{x}-\mathbf{p_i}),\qquad \xi(\mathbf{x})= \frac{\sum_i \frac{\lambda_i(\mathbf{x})}
-  {\|\mathbf{x}-\mathbf{p_i}\|}\xi_i(\mathbf{x}) }{\sum_i
-  \frac{\lambda_i(\mathbf{x})}{\|\mathbf{x}-\mathbf{p_i}\|}}.$$
++\mathbf{g_i}^t(\mathbf{x}-\mathbf{p_i}),\qquad \xi(\mathbf{x})= \frac{\ccSum{i}{}{ \frac{\lambda_i(\mathbf{x})}
+  {\|\mathbf{x}-\mathbf{p_i}\|}\xi_i(\mathbf{x}) } }{\ccSum{i}{}{
+  \frac{\lambda_i(\mathbf{x})}{\|\mathbf{x}-\mathbf{p_i}\|}}}.$$
 Sibson observed that the combination of $Z^0$ and $\xi$ reconstructs exactly
 a spherical quadric if they are mixed as follows:
 $$
 Z^1(\mathbf{x}) = \frac{\alpha(\mathbf{x}) Z^0(\mathbf{x}) +
   \beta(\mathbf{x}) \xi(\mathbf{x})}{\alpha(\mathbf{x}) +
-  \beta(\mathbf{x})} \textrm{ where } \alpha(\mathbf{x}) =
-\frac{\sum_i \lambda_i(\mathbf{x}) \frac{\|\mathbf{x} -
-    \mathbf{p_i}\|^2}{f(\|\mathbf{x} - \mathbf{p_i}\|)}}{\sum_i
-  \frac{\lambda_i(\mathbf{x})} {f(\|\mathbf{x} - \mathbf{p_i}\|)}}
-\textrm{ and } \beta(\mathbf{x})= \sum_i \lambda_i(\mathbf{x})
-\|\mathbf{x} - \mathbf{p_i}\|^2,$$
+  \beta(\mathbf{x})} \mbox{ where } \alpha(\mathbf{x}) =
+\frac{\ccSum{i}{}{ \lambda_i(\mathbf{x}) \frac{\|\mathbf{x} -
+    \mathbf{p_i}\|^2}{f(\|\mathbf{x} - \mathbf{p_i}\|)}}}{\ccSum{i}{}{
+  \frac{\lambda_i(\mathbf{x})} {f(\|\mathbf{x} - \mathbf{p_i}\|)}}}
+\mbox{ and } \beta(\mathbf{x})= \ccSum{i}{}{ \lambda_i(\mathbf{x})
+\|\mathbf{x} - \mathbf{p_i}\|^2},$$
 where in Sibson's original work,
 $f(\|\mathbf{x} - \mathbf{p_i}\|) = \|\mathbf{x} - \mathbf{p_i}\|$.
 
@@ -77,8 +77,8 @@ Knowing the gradient $\mathbf{g_i}$ for all $\mathbf{p_i} \in
 exactly quadratic functions. This interpolant is not $C^1$ continuous
 in general.  It is defined as follows:
 \begin{displaymath}
-  I^1(\mathbf{x}) = \sum_i \lambda_i(\mathbf{x}) 
-  (z_i + \frac{1}{2} \mathbf{g_i}^t (\mathbf{x} - \mathbf{p_i}))  
+  I^1(\mathbf{x}) = \ccSum{i}{}{ \lambda_i(\mathbf{x}) 
+  (z_i + \frac{1}{2} \mathbf{g_i}^t (\mathbf{x} - \mathbf{p_i}))} 
 \end{displaymath} 
 
 
@@ -89,9 +89,9 @@ $f$ from the function values on the data sites. For the data point
 $\mathbf{p_i}$, we determine
 $$\mathbf{g_i} 
 = \min_{\mathbf{g}} 
-\sum_j
+\ccSum{j}{}{
 \frac{\lambda_j(\mathbf{p_i})}{\|\mathbf{p_i} - \mathbf{p_j}\|^2}
-\left( z_j - (z_i + \mathbf{g}^t (\mathbf{p_j} -\mathbf{p_i})) \right),
+\left( z_j - (z_i + \mathbf{g}^t (\mathbf{p_j} -\mathbf{p_i})) \right)},
 $$
 where $\lambda_j(\mathbf{p_i})$ is the natural neighbor coordinate
 of $\mathbf{p_i}$ with respect to $\mathbf{p_i}$ associated to

QP_solver/doc_tex/QP_solver/main.tex

@@ -514,7 +514,7 @@ the case if and only if there are real coefficients
 $\lambda_1,\ldots,\lambda_n$ such that $p$ is a convex combination of
 $p_1,\ldots,p_n$: 
 \[
-p = \sum_{j=1}^{n}~\lambda_j~p_j, \quad \sum_{j=1}^{n}~\lambda_j = 1,
+p = \ccSum{j=1}{n}{~\lambda_j~p_j}, \quad \ccSum{j=1}{n}{~\lambda_j} = 1,
 \quad \lambda_j \geq 0 \mbox{~for all $j$.}
 \]
 The problem of testing the existence of such $\lambda_j$ can 
@@ -526,11 +526,11 @@ $h_1,\ldots,h_n,h$, we have
 \[q_j = h_j \cdot (p_j \mid 1) \mbox{~for all $j$, and~} q = h \cdot
 (p\mid 1).\] Now, nonnegative $\lambda_1,\ldots,\lambda_n$ are
 suitable coefficients for a convex combination if and only if
-\[\sum_{j=1}^n~ \lambda_j(p_j \mid 1) = (p\mid 1), \]
+\[\ccSum{j=1}{n}{~ \lambda_j(p_j \mid 1)} = (p\mid 1), \]
 equivalently, if there are $\mu_1,\ldots,\mu_n$ 
 (with $\mu_j = \lambda_j \cdot h/{h_j}$ for all $j$) such that
 \[
-\sum_{j=1}^n~\mu_j~q_j = q, \quad \mu_j \geq 0\mbox{~for all $j$}.
+\ccSum{j=1}{n}{~\mu_j~q_j} = q, \quad \mu_j \geq 0\mbox{~for all $j$}.
 \]
 
 The linear program now tests for the existence of nonnegative $\mu_j$

QP_solver/doc_tex/QP_solver_ref/Quadratic_program_solution.tex

@@ -349,8 +349,8 @@ then $\lambda_i\geq 0$ ($\lambda_i\leq 0$, respectively).
 &&\leq 0 & \mbox{if $l_j=-\infty$.}
 \end{array}
 \]
-\item \[\qplambda^T\qpb \quad<\quad \sum_{j: \qplambda^TA_j <0} \qplambda^TA_j u_j 
-\quad+\quad  \sum_{j: \qplambda^TA_j >0} \qplambda^TA_j l_j.\]
+\item \[\qplambda^T\qpb \quad<\quad \ccSum{j: \qplambda^TA_j <0}{}{ \qplambda^TA_j u_j }
+\quad+\quad  \ccSum{j: \qplambda^TA_j >0}{}{ \qplambda^TA_j l_j}.\]
 \end{enumerate}
 
 {\bf Proof:} Let us assume for the purpose of obtaining a contradiction
@@ -358,10 +358,10 @@ that there is a feasible solution $\qpx$. Then we get
 \[
 \begin{array}{lcll}
 0 &\geq& \qplambda^T(A\qpx -\qpb) &  \mbox{(by $A\qpx\qprel \qpb$ and 1.)} \\
-  &=& \sum_{j: \qplambda^TA_j <0} \qplambda^TA_j x_j 
-\quad+\quad  \sum_{j: \qplambda^TA_j >0} \qplambda^TA_j x_j - \qplambda^T \qpb \\
-  &\geq& \sum_{j: \qplambda^TA_j <0} \qplambda^TA_j u_j 
-\quad+\quad  \sum_{j: \qplambda^TA_j >0} \qplambda^TA_j l_j - \qplambda^T \qpb &
+  &=& \ccSum{j: \qplambda^TA_j <0}{}{ \qplambda^TA_j x_j }
+\quad+\quad  \ccSum{j: \qplambda^TA_j >0}{}{ \qplambda^TA_j x_j} - \qplambda^T \qpb \\
+  &\geq& \ccSum{j: \qplambda^TA_j <0}{}{ \qplambda^TA_j u_j }
+\quad+\quad  \ccSum{j: \qplambda^TA_j >0}{}{ \qplambda^TA_j l_j} - \qplambda^T \qpb &
 \mbox{(by $\qpl\leq \qpx \leq \qpu$ and 2.)} \\
   &>& 0 & \mbox{(by 3.)}, 
 \end{array}