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speed-> speed_main speed_utility speed_double speed_adolc speed_cppad speed_fadbad speed_sacado

speed_utility-> uniform_01 det_of_minor det_by_minor det_by_lu det_33 det_grad_33 mat_sum_sq ode_evaluate sparse_evaluate

mat_sum_sq-> mat_sum_sq.cpp mat_sum_sq.hpp

Headings-> Syntax Purpose Inclusion n x y z Vector Example Source Code

Sum Elements of a Matrix Times Itself
Syntax
# include <cppad/speed/mat_sum_sq.hpp>
mat_sum_sq(n, x, y, z)

Purpose
This routine is intended for use with the matrix multiply speed tests; to be specific, it computes $$\begin{array}{ccc}\hfill {\mathit{y}}_{\mathit{i},\mathit{j}}& \hfill =\hfill & \sum _{\mathit{k}=0}^{\mathit{n}-1}{\mathit{x}}_{\mathit{i},\mathit{k}}{\mathit{x}}_{\mathit{k},\mathit{j}}\hfill \\ \hfill {\mathit{z}}_0& \hfill =\hfill & \sum _{\mathit{i}=0}^{\mathit{n}-1}\sum _{\mathit{j}=0}^{\mathit{n}-1}{\mathit{y}}_{\mathit{i},\mathit{j}}\hfill \end{array}$$ see link_mat_mul .

Inclusion
The template function mat_sum_sq is defined in the CppAD namespace by including the file cppad/speed/mat_sum_sq.hpp (relative to the CppAD distribution directory). It is only intended for example and testing purposes, so it is not automatically included by cppad.hpp .

n
This argument has prototype
     size_t n
It specifies the size of the matrices.

x
The argument x has prototype
     const Vector &x
and x.size() == n * n . It contains the elements of $\mathit{x}$ in row major order; i.e., $${\mathit{x}}_{\mathit{i},\mathit{j}}=\mathit{x}[\mathit{i}*\mathit{n}+\mathit{j}]$$
y
The argument y has prototype
     Vector& y
and y.size() == n * n . The input value of its elements does not matter. Upon return, $$\begin{array}{ccc}\hfill {\mathit{y}}_{\mathit{i},\mathit{j}}& \hfill =\hfill & \sum _{\mathit{k}=0}^{\mathit{n}-1}{\mathit{x}}_{\mathit{i},\mathit{k}}{\mathit{x}}_{\mathit{k},\mathit{j}}\hfill \\ \hfill \mathit{y}[\mathit{i}*\mathit{n}+\mathit{j}]& \hfill =\hfill & {\mathit{y}}_{\mathit{i},\mathit{j}}\hfill \end{array}$$
z
The argument d has prototype
     Vector& z
. The input value of its element does not matter. Upon return $$\begin{array}{ccc}\hfill {\mathit{z}}_0& \hfill =\hfill & \sum _{\mathit{i}=0}^{\mathit{n}-1}\sum _{\mathit{j}=0}^{\mathit{n}}{\mathit{y}}_{\mathit{i},\mathit{j}}\hfill \\ \hfill \mathit{z}[0]& \hfill =\hfill & {\mathit{z}}_0\hfill \end{array}$$
Vector
The type Vector is any SimpleVector calls with a fixed element type. The element type must support addition, multiplication, and assignment to both its own type and to a double value.

Example
The file mat_sum_sq.cpp contains an example and test of mat_sum_sq.hpp. It returns true if it succeeds and false otherwise.

Source Code
The file mat_sum_sq.hpp contains the source for this template function.

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Input File: cppad/speed/mat_sum_sq.hpp