=======================
Trigonometric functions
=======================

If trigonometric functions are needed in a certain expression, they can be easily expressed in PeP by using function calls.
The following trigonometric functions are implemented in PeP

    * sin, sind, asin, asind
    * cos, cosd, acos, acosd
    * tan, tand, atan, atand, atan2, atan2d
    * cot, cotd, acot, acotd

These functions use the same naming convention as that of Matlab/Octave where 'd' suffixed functions use degrees whereas the rest use radians.

The functions are written using the normal syntax: ``function(parameter)``. Two parameter functions, such as ``atan2`` are called using the following syntax ``function( (parameter_1) (parameter_2) )``.

Below there is an example Numerical P System that uses trigonometric functions and can also be found in ``input_files/input_trigonometric_func.pep`` ::

    num_ps = {
        # membrane names (labels)
        H = {m1, m2, m3, m4, m5, m6};

        # test trignonometric functions (Matlab/Octave names):
        #   sin, sind, asin, asind
        #   cos, cosd, acos, acosd
        #   tan, tand, atan, atand, atan2, atan2d
        #   cot, cotd, acot, acotd,
        structure = [m1 [m2 ]m2 [m3 ]m3 [m4 ]m4 [m5 ]m5 [m6 ]m6 ]m1;

        m1 = {
            var = {rez_1};
            # rez = 5
            pr = {3 + 2 * sin(3.1416 / 2) + rez_1 * 0 -> 1|rez_1};
            var0 = (0);
        };

        m2 = {
            var = {rez_2};
            # two variable functions like atan2 require variables to be defined within brackets
            # atan2 ( (y) (x) )
            # rez = -0.9272
            pr = {atan2((0 - 4) (3 * 1)) + rez_2 * 0 -> 1|rez_2};
            var0 = (0);
        };

        m3 = {
            var = {rez_3};
            # rez = 91.556 (0.52360 + 90 + 0.99749 + 0.034899)
            pr = {asin(0.5) + asind(1) + sin(1.5) + sind(2) + rez_3 * 0 -> 1|rez_3};
            var0 = (0);
        };

        m4 = {
            var = {rez_4};
            # rez = 2.1173 (1.0472 + 0 + 0.070737 + 0.99939)
            pr = {acos(0.5) + acosd(1) + cos(1.5) + cosd(2) + rez_4 * 0 -> 1|rez_4};
            var0 = (0);
        };

        m5 = {
            var = {rez_5};
            # rez = 100.05 (0.46365 + 45 + 14.101 + 0.034921 + 0.64350 + 39.806)
            pr = {atan(0.5) + atand(1) + tan(1.5) + tand(2) + atan2( (3) (4)) + atan2d((5) (6)) + rez_5 * 0 -> 1|rez_5};
            var0 = (0);
        };

        m6 = {
            var = {rez_6};
            # rez = 74.814 (1.1071 + 45 + 0.070915 + 28.636)
            pr = {acot(0.5) + acotd(1) + cot(1.5) + cotd(2) + rez_6 * 0 -> 1|rez_6};
            var0 = (0);
        };
    }

The execution of the system can be started using::

    ./pep.py input_files/input_trigonometric_func.pep -n 1

The output of this system is::

    num_ps = {
        m1:
            var = { rez_1: 0.00, }
            E = {}
            pr_0 = { 3 + 2 * sin ( 3.1416 / 2 ) + rez_1 * 0  ->  1|rez_1 }
        m2:
            var = { rez_2: 0.00, }
            E = {}
            pr_0 = { atan2 ( ( 0 - 4 ) ( 3 * 1 ) ) + rez_2 * 0  ->  1|rez_2 }
        m3:
            var = { rez_3: 0.00, }
            E = {}
            pr_0 = { asin ( 0.5 ) + asind ( 1 ) + sin ( 1.5 ) + sind ( 2 ) + rez_3 * 0  ->  1|rez_3 }
        m4:
            var = { rez_4: 0.00, }
            E = {}
            pr_0 = { acos ( 0.5 ) + acosd ( 1 ) + cos ( 1.5 ) + cosd ( 2 ) + rez_4 * 0  ->  1|rez_4 }
        m5:
            var = { rez_5: 0.00, }
            E = {}
            pr_0 = { atan ( 0.5 ) + atand ( 1 ) + tan ( 1.5 ) + tand ( 2 ) + atan2 ( ( 3 ) ( 4 ) ) + atan2d ( ( 5 ) ( 6 ) ) + rez_5 * 0  ->  1|rez_5 }
        m6:
            var = { rez_6: 0.00, }
            E = {}
            pr_0 = { acot ( 0.5 ) + acotd ( 1 ) + cot ( 1.5 ) + cotd ( 2 ) + rez_6 * 0  ->  1|rez_6 }
    }

    INFO     Starting simulation step 1 
    INFO     Simulation step finished succesfully 
    num_ps = {
      m1:
        var = { rez_1: 5.00, }
        E = {}
      m2:
        var = { rez_2: -0.93, }
        E = {}
      m3:
        var = { rez_3: 91.56, }
        E = {}
      m4:
        var = { rez_4: 2.12, }
        E = {}
      m5:
        var = { rez_5: 100.05, }
        E = {}
      m6:
        var = { rez_6: 74.81, }
        E = {}
    }

Notice that only the initial and first step states are shown. This is because the value of the six P objects does not change after the first execution step, due to the use of each P object in a production function.

Also, the P object values that are printed by the simulator are not always precisely equal to those obtained in other mathematical software. The reason is that during the printing of each value, these are rounded to the nearest 2 digit value. The internal calculations are always done using *double* precision floating point values.