2017-02-27 22:31:21 +00:00
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/*-
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2018-08-04 18:44:35 +00:00
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* Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
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2015-03-08 22:14:50 +00:00
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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2017-02-27 22:31:21 +00:00
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* Project homepage:
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2017-07-14 09:30:24 +00:00
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* https://amath.innolan.net
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2017-02-27 22:31:21 +00:00
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*
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2015-03-08 22:14:50 +00:00
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*/
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2015-04-01 12:43:50 +00:00
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#include "prim.h"
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2015-03-08 22:14:50 +00:00
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/**
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2017-04-12 22:50:51 +00:00
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* @brief Hyperbolic secant of a complex number
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2015-04-01 12:43:50 +00:00
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* @details
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* Calculated as in Open Office:<BR>
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* https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMSECH_function
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* <pre>
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* a+bi
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* 2.0 * cosh(a) * cos(b)
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* real = ------------------------------
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* cosh(2.0 * a) + cos(2.0 * b)
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2015-03-08 22:14:50 +00:00
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*
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2015-04-01 12:43:50 +00:00
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* -2.0 * sinh(2.0 * a) * sin(b)
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* imag = ------------------------------
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* cosh(2.0 * a) + cos(2.0 * b)
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* </pre>
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2015-03-08 22:14:50 +00:00
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*/
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2015-04-01 12:43:50 +00:00
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complex csech(complex z)
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{
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complex w;
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double a, b;
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double d;
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a = creal(z);
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b = cimag(z);
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d = cosh(2.0 * a) + cos(2.0 * b);
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w = cpack((2.0 * cosh(a) * cos(b) / d), (-2.0 * sinh(a) * sin(b) / d));
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return w;
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}
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