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- <a name="Additional-kinsol-notes"></a>
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- <a name="Additional-kinsol-notes-1"></a>
- <h3 class="subsection">D.9.4 Additional <code>kinsol</code> notes</h3>
- <p>When a user supplied Jacobian function <var>j</var> is specified, the
- <a name="index-Jacobian-1"></a>
- solution is likely to be found faster and more accurately. The
- Jacobian should be given if an analytical form for <var>f</var> is known,
- from which the Jacobian can be obtained easily by partial
- differentiation. If the Jacobian is unavailable, a finite difference
- method implemented internally by <code>kinsol</code> is used as a substitute
- and will usually yield acceptable results.
- </p>
- <p>Tolerances are not explicitly specified on the virtual side of the
- interface although the native <code>kinsol</code> API requires them. A range
- of tolerances over ten orders of magnitude is automatically tried
- before giving up.
- </p>
- <p>Similarly to the <code>glpk</code> and <code>lpsolve</code> library interfaces
- (<a href="glpk.html#glpk"><code>glpk</code></a> and <a href="lpsolve.html#lpsolve"><code>lpsolve</code></a>), the only expressible constraint through
- <a name="index-constraints-1"></a>
- the virtual code interface is that all variables are
- non-negative. Arbitrary upper and lower bounds can be simulated by
- appropriate variable substitutions in the formulation of the problem.
- </p>
- <p>The <code>kinsol</code> library natively requires a system function <var>f</var>
- with equally many inputs as outputs, and will search only for the
- input associated with an output vector of all zeros, but the virtual
- code interface relaxes these requirements by allowing a function that
- transforms between lists of unequal lengths, and will search for the
- input of <var>f</var> causing it to match any given “optimal” output
- <var>o</var>. These effects are achieved by padding the shorter of the two
- vectors transparently and subtracting the specified optimum from the
- result.
- </p>
- <p>The <code>kinsol</code> library can be configured to use single precision,
- double precision, or extended precision arithmetic, but only a double
- precision configuration is compatible with <code>avram</code>. This
- condition is checked when <code>avram</code> is configured and it will not
- interface with alternative <code>kinsol</code> configurations.
- </p>
- <p>The <code>kinsol</code> library has some more advanced features to which
- this interface doesn’t do justice, such as preconditioning, scaling,
- solution of systems with band limited Jacobians, and concurrent
- computation.
- </p>
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