.. _math: Common Math Functions (HOC) --------------------------- These math functions return a double precision value and take a double precision argument. The exception is :func:atan2 which has two double precision arguments. Diagnostics: Arguments that are out of range give an argument domain diagnostic. These functions call the library routines supplied by the compiler. ---- .. function:: abs absolute value .. code-block:: none >>> h.abs(-42.2) 42.2 See :meth:Vector.abs for the :class:Vector class. .. note:: In Python code, use Python's abs function, which works on both numbers and numpy arrays: .. code-block:: python >>> abs(-42.2) 42.2 >>> abs(-3 + 4j) 5.0 >>> v = h.Vector([1, 6, -2, -65]) >>> abs(v.as_numpy()) array([ 1., 6., 2., 65.]) ---- .. function:: int returns the integer part of its argument (truncates toward 0). .. code-block:: none >>> h.int(3.14) 3.0 >>> h.int(-3.14) -3.0 .. note:: In Python code, use Python's int function instead. The behavior is slightly different in that the Python function returns an int type instead of a double: .. code-block:: python >>> int(-3.14) -3 >>> int(3.14) 3 ---- .. function:: sqrt square root see :meth:Vector.sqrt for the :class:Vector class. .. note:: Consider using Python's built in math.sqrt instead. ---- .. function:: exp Description: returns the exponential function to the base e When exp is used in model descriptions, it is often the case that the cvode variable step integrator extrapolates voltages to values which return out of range values for the exp (often used in rate functions). There were so many of these false warnings that it was deemed better to turn off the warning message when Cvode is active. In any case the return value is exp(700). This message is not turned off at the interpreter level or when cvode is not active. .. code-block:: python from neuron import h for i in range(6,12): print('%g %g' % (i, h.exp(i))) .. note:: Consider using Python's built in math.exp instead. ---- .. function:: log logarithm to the base e see :meth:Vector.log for the :class:Vector class. .. note:: Consider using Python's built in math.log instead. ---- .. function:: log10 logarithm to the base 10 see :meth:Vector.log10 for the :class:Vector class. .. note:: Consider using Python's built in math.log10 instead. ---- .. function:: cos trigonometric function of radian argument. see :meth:Vector.sin .. note:: Consider using Python's built in math.cos instead. ---- .. function:: sin trigonometric function of radian argument. see :meth:Vector.sin for the :class:Vector class. .. note:: Consider using Python's built in math.sin instead. ---- .. function:: tanh hyperbolic tangent. see :meth:Vector.tanh for the :class:Vector class. .. note:: Consider using Python's built in math.tanh instead. ---- .. function:: atan returns the arc-tangent of y/x in the range :math:-\pi/2 to :math:\pi/2. (x > 0) .. note:: Consider using Python's built in math.atan instead. ---- .. function:: atan2 Syntax: radians = atan2(y, x) Description: returns the arc-tangent of y/x in the range :math:-\pi < radians <= :math:\pi. y and x can be any double precision value, including 0. If both are 0 the value returned is 0. Imagine a right triangle with base x and height y. The result is the angle in radians between the base and hypotenuse. Example: .. code-block:: python from neuron import h h.atan2(0,0) for i in range(-1,2): print(h.atan2(i*1e-6, 10)) for i in range(-1,2): print(h.atan2(i*1e-6, -10)) for i in range(-1,2): print(h.atan2(10, i*1e-6)) for i in range(-1,2): print(h.atan2(-10, i*1e-6)) h.atan2(10,10) h.atan2(10,-10) h.atan2(-10,10) h.atan2(-10,-10) .. note:: Consider using Python's built in math.atan2 instead. ---- .. function:: erf normalized error function .. math:: {\rm erf}(z) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2} dt .. note:: In Python 3.2+, use math.erf instead. ---- .. function:: erfc returns 1.0 - erf(z) but on sun machines computed by other methods that avoid cancellation for large z. .. note:: In Python 3.2+, use math.erfc instead.