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<?xml version='1.0'?>
<html xmlns='http://www.w3.org/1999/xhtml'
      xmlns:math='http://www.w3.org/1998/Math/MathML'
>
<head>
<title>Gradient of Determinant Using Expansion by Minors: Example and Test</title>
<meta http-equiv='Content-Type' content='text/html' charset='utf-8'/>
<meta name="description" id="description" content="Gradient of Determinant Using Expansion by Minors: Example and Test"/>
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body { color : black }
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<center><b><big><big>Gradient of Determinant Using Expansion by Minors: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 

# include &lt;cppad/cppad.hpp&gt;
# include &lt;cppad/speed/det_by_minor.hpp&gt;
# include &lt;complex&gt;

typedef std::complex&lt;double&gt;     Complex;
typedef CppAD::<a href="ad.xml" target="_top">AD</a>&lt;Complex&gt;       ADComplex;
typedef <a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(ADComplex)   ADVector;

// ----------------------------------------------------------------------------

bool HesMinorDet(void)
{	bool ok = true;

	using namespace CppAD;

	size_t n = 2;

	// object for computing determinants
	det_by_minor&lt;ADComplex&gt; Det(n);

	// independent and dependent variable vectors
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(ADComplex)  X(n * n);
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(ADComplex)  D(1);

	// value of the independent variable
	size_t i;
	for(i = 0; i &lt; n * n; i++)
		X[i] = Complex(int(i), -int(i));

	// set the independent variables
	<a href="independent.xml" target="_top">Independent</a>(X);

	// comupute the determinant
	D[0] = Det(X); 

	// create the function object
	<a href="funconstruct.xml" target="_top">ADFun</a>&lt;Complex&gt; f(X, D);

	// argument value
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(Complex)     x( n * n );
	for(i = 0; i &lt; n * n; i++)
		x[i] = Complex(2 * i, i);

	// first derivative of the determinant
	<a href="testvector.xml" target="_top">CPPAD_TESTVECTOR</a>(Complex) H( n * n * n * n);
	H = f.Hessian(x, 0);

	/*
	f(x)     = x[0] * x[3] - x[1] * x[2]
	f'(x)    = ( x[3], -x[2], -x[1], x[0] )
	*/
	Complex zero(0., 0.);
	Complex one(1., 0.);
	Complex Htrue[]  = { 
		zero, zero, zero,  one,
		zero, zero, -one, zero,
		zero, -one, zero, zero,
		 one, zero, zero, zero
	};
	for( i = 0; i &lt; n*n*n*n; i++)
		ok &amp;= Htrue[i] == H[i];

	return ok;

}

</pre>

</font></code>


<hr/>Input File: example/hes_minor_det.cpp

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