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.. _hoc_math:
Common Math Functions (HOC)
---------------------------
These math functions return a double precision value and take a double
precision argument. The exception is :hoc: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.
----
.. hoc:function:: abs
absolute value
see :hoc:meth:`Vector.abs` for the :hoc:class:`Vector` class.
----
.. hoc:function:: int
returns the integer part of its argument (truncates toward 0).
----
.. hoc:function:: sqrt
square root
see :hoc:meth:`Vector.sqrt` for the :hoc:class:`Vector` class.
----
.. hoc: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::
none
for i=690, 710 print i, exp(i)
----
.. hoc:function:: log
logarithm to the base e
see :hoc:meth:`Vector.log` for the :hoc:class:`Vector` class.
----
.. hoc:function:: log10
logarithm to the base 10
see :hoc:meth:`Vector.log10` for the :hoc:class:`Vector` class.
----
.. hoc:function:: cos
trigonometric function of radian argument.
see :hoc:meth:`Vector.sin`
----
.. hoc:function:: sin
trigonometric function of radian argument.
see :hoc:meth:`Vector.sin` for the :hoc:class:`Vector` class.
----
.. hoc:function:: tanh
hyperbolic tangent.
see :hoc:meth:`Vector.tanh` for the :hoc:class:`Vector` class.
----
.. hoc:function:: atan
returns the arc-tangent of y/x in the range -PI/2 to PI/2. (x > 0)
----
.. hoc:function:: atan2
Syntax:
``radians = atan2(y, x)``
Description:
returns the arc-tangent of y/x in the range -PI < radians <= 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::
none
atan2(0,0)
for i=-1,1 { print atan2(i*1e-6, 10) }
for i=-1,1 { print atan2(i*1e-6, -10) }
for i=-1,1 { print atan2(10, i*1e-6) }
for i=-1,1 { print atan2(-10, i*1e-6) }
atan2(10,10)
atan2(10,-10)
atan2(-10,10)
atan2(-10,-10)
----
.. hoc:function:: erf
normalized error function
.. math::
{\rm erf}(z) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2} dt
----
.. hoc:function:: erfc
returns ``1.0 - erf(z)`` but on sun machines computed by other methods
that avoid cancellation for large z.
|
