Speed Testing Sparse Jacobians

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link_sparse_jacobian

$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$ This is cppad-20221105 documentation. Here is a link to its current documentation . Speed Testing Sparse Jacobians
Prototype


extern bool link_sparse_jacobian(
    const std::string&                job       ,
    size_t                            size      ,
    size_t                            repeat    ,
    size_t                            m         ,
    const CppAD::vector<size_t>&      row       ,
    const CppAD::vector<size_t>&      col       ,
          CppAD::vector<double>&      x         ,
          CppAD::vector<double>&      jacobian  ,
          size_t&                     n_color
);

Method
Given a range space dimension m the row index vector

$row$ , and column index vector

$col$ , a corresponding function

$f : \B{R}^n \rightarrow \B{R}^m$ is defined by sparse_jac_fun . The non-zero entries in the Jacobian of this function have the form

$\D{f[row[k]]}{x[col[k]]]}$ for some

$k$ between zero and K = row.size()-1 . All the other terms of the Jacobian are zero.

Sparsity Pattern
The combination of row and col determine the sparsity pattern for the Jacobian that is differentiated. The calculation of this sparsity pattern, if necessary to compute the Jacobian, is intended to be part of the timing for this test.

job
See the standard link specifications for job .

size
See the standard link specifications for size . In addition, size is referred to as

$n$ below, is the dimension of the domain space for

$f(x)$ .

repeat
See the standard link specifications for repeat .

m
Is the dimension of the range space for the function

$f(x)$ .

row
The size of the vector row defines the value

$K$ . The input value of its elements does not matter. On output, all the elements of row are between zero and

$m-1$ .

col
The argument col is a vector with size

$K$ . The input value of its elements does not matter. On output, all the elements of col are between zero and

$n-1$ .

Row Major
The indices row and col are in row major order; i.e., for each k < row.size()-2



    row[k] <= row[k+1]

and if row[k] == row[k+1] then



    col[k] < col[k+1]

x
The argument x has prototype



   CppAD::vector<double>& x

and its size is

$n$ ; i.e., x.size() == size . The input value of the elements of x does not matter. On output, it has been set to the argument value for which the function, or its derivative, is being evaluated and placed in jacobian . The value of this vector need not change with each repetition.

jacobian
The argument jacobian has prototype



   CppAD::vector<double>& jacobian

and its size is K . The input value of its elements does not matter. The output value of its elements is the Jacobian of the function

$f(x)$ . To be more specific, for

$k = 0 , \ldots , K - 1$ ,

$\D{f[ \R{row}[k] ]}{x[ \R{col}[k] ]} (x) = \R{jacobian} [k]$

n_color
The input value of n_color does not matter. On output, it has value zero or n_sweep corresponding to the evaluation of jacobian . This is also the number of colors corresponding to the coloring method , which can be set to colpack , and is otherwise cppad. If this routine returns an non-zero n_color for any job value, the non-zero value will be reported for this test.

double
In the case where package is double, only the first

$m$ elements of jacobian are used and they are set to the value of

$f(x)$ .

Input File: speed/src/link_sparse_jacobian.hpp