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<h4 class="subsection">D.9.1 <code>kinsol</code> input parameters</h4>

<p>Functions whose names are of the form <var>x</var><code>d_</code><var>zzzzz</var>
take an argument of the form
<code>(</code><var>f</var><code>,(</code><var>i</var><code>,</code><var>o</var><code>))</code>,
and functions whose names are of the form <var>x</var><code>j_</code><var>zzzzz</var>
take an argument of the form
<code>((</code><var>f</var><code>,</code><var>j</var><code>),(</code><var>i</var><code>,</code><var>o</var><code>))</code>. 
The parameters have these interpretations.

     <ul>
<li><var>f</var> is a function to be optimized, expressed in virtual machine
code. It takes a list of real numbers as input and returns a list of
real numbers as output. The numbers must be in floating point format
as described in <a href="math.html#math">math</a>. 
<li><var>j</var> is a function in virtual machine code that computes the
Jacobian or partial derivatives of <var>f</var> for a given list of input
<a name="index-Jacobian-741"></a>numbers. The exact calling convention for <var>j</var> depends on the
optimization algorithm selected, as explained below. 
<li><var>i</var> is a list of real numbers suitable as an input for <var>f</var>. 
The exact values of the numbers in <var>i</var> are not crucial but the
length of <var>i</var> is taken as an indication of the required length for
any input list to <var>f</var>. In the case of constrained optimization
problems (i.e., functions with names beginning with <code>c</code>), <var>i</var> must
consist entirely of non-negative numbers. 
<li><var>o</var> is a list numbers indicating the &ldquo;optimal&rdquo; output from
<var>f</var> in the sense described below (<a href="kinsol-output.html#kinsol-output">kinsol output</a>). Its length
is taken to indicate the usual length of an output returned by
<var>f</var>. 
</ul>

   <p>If the optimization problem is being solved by either the
<code>cj_dense</code> or the <code>uj_dense</code> method, the Jacobian parameter
<var>j</var> is expected to take a list <var>v</var> of real numbers the length
of <var>i</var> as input and return a list of lists of reals as output. The
numbers are represented as described in <a href="math.html#math">math</a>. The outer list in
the output from <var>j</var> is required to be the length of <var>o</var>, while
each inner list is required to be the length of <var>i</var>.

   <p>The output from <var>j</var> is interpreted as a matrix of the form
described in <a href="Two-dimensional-arrays.html#Two-dimensional-arrays">Two dimensional arrays</a>. The entry in row <var>m</var>
and column <var>n</var> is the partial derivative (evaluated at <var>v</var>) of
the <var>m</var>-th component of the output of <var>f</var> with respect to the
<var>n</var>-th item of the input list.

   <p>For optimization problems being solved by the methods of
<var>x</var><code>j_gmres</code>, <var>x</var><code>j_bicgs</code>, or
<var>x</var><code>j_tfqmr</code>, (i.e., where <var>x</var> is either <code>c</code> or
<code>u</code>) the Jacobian function <var>j</var> follows a different convention
that is meant to be more memory efficient. Given an argument of the
form <code>(</code><var>m</var><code>,</code><var>v</var><code>)</code>, it returns only the <var>m</var>-th row of
the matrix described above instead of the whole thing. The parameter
<var>m</var> is a natural number less than the length of <var>o</var>, and
<var>v</var> is a list of real numbers the length of <var>i</var> the same as
above. The number <var>m</var> is encoded as described in
<a href="Representation-of-Numeric-and-Textual-Data.html#Representation-of-Numeric-and-Textual-Data">Representation of Numeric and Textual Data</a>.

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