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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_eps: Verify First Order Reverse Sweep</title>
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<meta name="description" id="description" content="exp_eps: Verify First Order Reverse Sweep"/>
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<center><b><big><big>exp_eps: 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;                       // for fabs function
extern bool exp_eps_for0(double *v0);   // computes zero order forward sweep
bool exp_eps_rev1(void)
{	bool ok = true;

	// set the value of v0[j] for j = 1 , ... , 7
	double v0[8];
	ok &amp;= exp_eps_for0(v0);

	// initial all partial derivatives as zero
	double f_v[8];
	size_t j;
	for(j = 0; j &lt; 8; j++)
		f_v[j] = 0.;

	// set partial derivative for f7
	f_v[7] = 1.;
	ok    &amp;= std::fabs( f_v[7] - 1. ) &lt;= 1e-10;     // f7_v7

	// f6( v1 , v2 , v3 , v4 , v5 , v6 )
	f_v[4] += f_v[7] * 1.;
	f_v[6] += f_v[7] * 1.;
	ok     &amp;= std::fabs( f_v[4] - 1.  ) &lt;= 1e-10;   // f6_v4
	ok     &amp;= std::fabs( f_v[6] - 1.  ) &lt;= 1e-10;   // f6_v6

	// f5( v1 , v2 , v3 , v4 , v5 )
	f_v[5] += f_v[6] / 2.;
	ok     &amp;= std::fabs( f_v[5] - 0.5 ) &lt;= 1e-10;   // f5_v5

	// f4( v1 , v2 , v3 , v4 )
	f_v[1] += f_v[5] * v0[3];
	f_v[3] += f_v[5] * v0[1];
	ok     &amp;= std::fabs( f_v[1] - 0.25) &lt;= 1e-10;   // f4_v1
	ok     &amp;= std::fabs( f_v[3] - 0.25) &lt;= 1e-10;   // f4_v3

	// f3( v1 , v2 , v3 )
	f_v[3] += f_v[4] * 1.;
	ok     &amp;= std::fabs( f_v[3] - 1.25) &lt;= 1e-10;   // f3_v3

	// f2( v1 , v2 )
	f_v[2] += f_v[3] / 1.;
	ok     &amp;= std::fabs( f_v[2] - 1.25) &lt;= 1e-10;   // f2_v2

	// f1( v1 )
	f_v[1] += f_v[2] * 1.;
	ok     &amp;= std::fabs( f_v[1] - 1.5 ) &lt;= 1e-10;   // f1_v2

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


<hr/>Input File: introduction/exp_apx/exp_eps_rev1.cpp

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