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<a name="minpack-calling-conventions"></a>
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<a name="minpack-calling-conventions-1"></a>
<h3 class="subsection">D.13.1 <code>minpack</code> calling conventions</h3>

<p>The <code>minpack</code> library solves a similar problem to that of the
<code>kinsol</code> library (<a href="kinsol.html#kinsol"><code>kinsol</code></a>), and the two libraries have
identical calling conventions at the level of the virtual code
interface.
</p>
<p>The <code>hybrd</code> and <code>lmdif</code> functions take input arguments of
the form <code>(<var>f</var>,(<var>i</var>,<var>o</var>))</code>, whereas <code>hybrj</code>,
<code>lmder</code>, and <code>lmstr</code> take arguments of the form
<code>((<var>f</var>,<var>j</var>),(<var>i</var>,<var>o</var>))</code>.  The interpretations of
these parameters are explained in <a href="kinsol-input-parameters.html#kinsol-input-parameters"><code>kinsol</code> input parameters</a>.
</p>
<p>For the <code>lmstr</code> function, the Jacobian function <var>j</var> takes
<a name="index-Jacobian-2"></a>
an argument <code>(<var>m</var>,<var>v</var>)</code> and returns only the <var>m</var>-th
row of the Jacobian matrix. For <code>lmder</code> and <code>hybrj</code>, the
Jacobian function takes only an input vector <var>v</var> and returns the
whole matrix. These specifications are also explained further in
relation to the <code>kinsol</code> library.
</p>
<p>The output from any minpack function is a vector <var>v</var> satisfying
<code><var>f</var>(<var>v</var>) = <var>o</var></code> to the best possible tolerance if a
<a name="index-tolerance-2"></a>
solution is found. A range of tolerances over ten orders of magnitude
is sampled starting from <code>1e-15</code>. If no solution is found, an
empty list is returned.
</p>
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