$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Speed Testing Derivative of Matrix Multiply

Prototype
extern bool link_mat_mul(      size_t                         size    ,      size_t                         repeat  ,      CppAD::vector<double>&         x       ,      CppAD::vector<double>&         z       ,      CppAD::vector<double>&         dz ); 
Purpose
Each package must define a version of this routine as specified below. This is used by the speed_main program to run the corresponding speed and correctness tests.

Return Value
If this speed test is not yet supported by a particular package , the corresponding return value for link_mat_mul should be false.

n
The argument n is the number of rows and columns in the square matrix x .

repeat
The argument repeat is the number of different argument values that the derivative of z (or just the value of z ) will be computed.

x
The argument x is a vector with x.size() = size * size elements. The input value of its elements does not matter. The output value of its elements is the last random matrix that is multiplied and then summed to form z ; $$x_{i,j} = x[ i * s + j ]$$ where s = size .

z
The argument z is a vector with one element. The input value of the element does not matter. The output of its element the sum of the elements of y = x * x ; i.e., $$\begin{array}{rcl} y_{i,j} & = & \sum_{k=0}^{s-1} x_{i,k} x_{k, j} \\ z & = & \sum_{i=0}^{s-1} \sum_{j=0}^{s-1} y_{i,j} \end{array}$$

dz
The argument dz is a vector with dz.size() = size * size . The input values of its elements do not matter. The output value of its elements form the derivative of z with respect to x .