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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 Second Order Reverse Sweep</title>
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<meta name="description" id="description" content="exp_2: Verify Second Order Reverse Sweep"/>
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<center><b><big><big>exp_2: Verify Second 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
extern bool exp_2_for1(double *v1); // computes first order forward sweep
bool exp_2_rev2(void)
{	bool ok = true;

	// set the value of v0[j], v1[j] for j = 1 , ... , 5
	double v0[6], v1[6];
	ok &amp;= exp_2_for0(v0);
	ok &amp;= exp_2_for1(v1);

	// initial all partial derivatives as zero
	double f_v0[6], f_v1[6];
	size_t j;
	for(j = 0; j &lt; 6; j++)
	{	f_v0[j] = 0.;
		f_v1[j] = 0.;
	}

	// set partial derivative for f_5
	f_v1[5] = 1.;
	ok &amp;= std::fabs( f_v1[5] - 1. ) &lt;= 1e-10; // partial f_5 w.r.t v_5^1

	// f_4 = f_5( v_1^0 , ... , v_4^1 , v_2^0 + v_4^0 , v_2^1 + v_4^1 )
	f_v0[2] += f_v0[5] * 1.;
	f_v0[4] += f_v0[5] * 1.;
	f_v1[2] += f_v1[5] * 1.;
	f_v1[4] += f_v1[5] * 1.;
	ok &amp;= std::fabs( f_v0[2] - 0. ) &lt;= 1e-10; // partial f_4 w.r.t. v_2^0
	ok &amp;= std::fabs( f_v0[4] - 0. ) &lt;= 1e-10; // partial f_4 w.r.t. v_4^0
	ok &amp;= std::fabs( f_v1[2] - 1. ) &lt;= 1e-10; // partial f_4 w.r.t. v_2^1
	ok &amp;= std::fabs( f_v1[4] - 1. ) &lt;= 1e-10; // partial f_4 w.r.t. v_4^1

	// f_3 = f_4( v_1^0 , ... , v_3^1, v_3^0 / 2 , v_3^1 / 2 )
	f_v0[3] += f_v0[4] / 2.;
	f_v1[3] += f_v1[4] / 2.;
	ok &amp;= std::fabs( f_v0[3] - 0.  ) &lt;= 1e-10; // partial f_3 w.r.t. v_3^0
	ok &amp;= std::fabs( f_v1[3] - 0.5 ) &lt;= 1e-10; // partial f_3 w.r.t. v_3^1

	// f_2 = f_3(  v_1^0 , ... , v_2^1, v_1^0 * v_1^0 , 2 * v_1^0 * v_1^1 )
	f_v0[1] += f_v0[3] * 2. * v0[1];
	f_v0[1] += f_v1[3] * 2. * v1[1];
	f_v1[1] += f_v1[3] * 2. * v0[1];
	ok &amp;= std::fabs( f_v0[1] - 1.  ) &lt;= 1e-10; // partial f_2 w.r.t. v_1^0
	ok &amp;= std::fabs( f_v1[1] - 0.5 ) &lt;= 1e-10; // partial f_2 w.r.t. v_1^1

	// f_1 = f_2( v_1^0 , v_1^1 , 1 + v_1^0 , v_1^1 )
	f_v0[1] += f_v0[2] * 1.;
	f_v1[1] += f_v1[2] * 1.;
	ok &amp;= std::fabs( f_v0[1] - 1. ) &lt;= 1e-10; // partial f_1 w.r.t. v_1^0
	ok &amp;= std::fabs( f_v1[1] - 1.5) &lt;= 1e-10; // partial f_1 w.r.t. v_1^1

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


<hr/>Input File: introduction/exp_apx/exp_2_rev2.cpp

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