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67 lines
1.8 KiB
67 lines
1.8 KiB
2 years ago
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/*
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* Copyright(C) 1999-2020 National Technology & Engineering Solutions
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* of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with
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* NTESS, the U.S. Government retains certain rights in this software.
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*
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* See packages/seacas/LICENSE for details
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*/
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#include <math.h>
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static double s, c; /* sign and cosine of angle */
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static double s2, cos2; /* squares of sign and cosine of angle */
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double func2d(double coeffs[5], /* five different 4-way products */
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double theta /* angular parameter */
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)
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/* Returns value of penalty function at given angle. */
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{
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double val; /* functional value */
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s = sin(theta);
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c = cos(theta);
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cos2 = c * c;
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s2 = s * s;
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val = (cos2 * cos2 + s2 * s2) * (coeffs[0] + coeffs[4]);
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val += 12 * cos2 * s2 * coeffs[2];
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val += 4 * (s2 * s * c - cos2 * c * s) * (coeffs[3] - coeffs[1]);
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return (val);
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}
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double grad2d(double coeffs[5], /* five different 4-way products */
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double theta /* angular parameter */
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)
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/* Returns 1st derivative of penalty function at given angle. */
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{
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double val; /* functional value */
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s = sin(theta);
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c = cos(theta);
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cos2 = c * c;
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s2 = s * s;
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val = 4 * (cos2 * cos2 + s2 * s2) * (coeffs[1] - coeffs[3]);
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val += 24 * cos2 * s2 * (coeffs[3] - coeffs[1]);
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val += 4 * (s2 * s * c - cos2 * c * s) * (coeffs[0] + coeffs[4] - 6 * coeffs[2]);
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return (val);
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}
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double hess2d(double coeffs[5] /* five different 4-way products */
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)
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/* Returns 2nd derivative of penalty function at given angle. */
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{
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double val; /* functional value */
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val = -4 * (cos2 * cos2 + s2 * s2) * (coeffs[0] + coeffs[4] - 6 * coeffs[2]);
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val += 24 * s2 * cos2 * (coeffs[0] + coeffs[4] - 6 * coeffs[2]);
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val += 64 * (s2 * s * c - cos2 * c * s) * (coeffs[1] - coeffs[3]);
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return (val);
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}
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