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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>exp_2: Verify First Order Reverse Sweep</title>
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<meta name="description" id="description" content="exp_2: Verify First Order Reverse Sweep"/>
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body { color : black }
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<center><b><big><big>exp_2: Verify First Order Reverse Sweep</big></big></b></center>
<code><font color='blue'><pre style='display:inline'> # include &lt;cstddef&gt;                 // define size_t
# include &lt;cmath&gt;                   // prototype for fabs
extern bool exp_2_for0(double *v0); // computes zero order forward sweep
bool exp_2_rev1(void)
{	bool ok = true;

	// set the value of v0[j] for j = 1 , ... , 5
	double v0[6];
	ok &amp;= exp_2_for0(v0);

	// initial all partial derivatives as zero
	double f_v[6];
	size_t j;
	for(j = 0; j &lt; 6; j++)
		f_v[j] = 0.;

	// set partial derivative for f5
	f_v[5] = 1.;
	ok &amp;= std::fabs( f_v[5] - 1. ) &lt;= 1e-10; // f5_v5

	// f4 = f5( v1 , v2 , v3 , v4 , v2 + v4 )
	f_v[2] += f_v[5] * 1.;
	f_v[4] += f_v[5] * 1.;
	ok &amp;= std::fabs( f_v[2] - 1. ) &lt;= 1e-10; // f4_v2
	ok &amp;= std::fabs( f_v[4] - 1. ) &lt;= 1e-10; // f4_v4

	// f3 = f4( v1 , v2 , v3 , v3 / 2 )
	f_v[3] += f_v[4] / 2.;
	ok &amp;= std::fabs( f_v[3] - 0.5) &lt;= 1e-10; // f3_v3

	// f2 = f3( v1 , v2 , v1 * v1 )
	f_v[1] += f_v[3] * 2. * v0[1];
	ok &amp;= std::fabs( f_v[1] - 0.5) &lt;= 1e-10; // f2_v1

	// f1 = f2( v1 , 1 + v1 )
	f_v[1] += f_v[2] * 1.;
	ok &amp;= std::fabs( f_v[1] - 1.5) &lt;= 1e-10; // f1_v1

	return ok;
}
</pre></font></code>


<hr/>Input File: introduction/exp_apx/exp_2_rev1.cpp

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