abs · atan · atan2 · cos · erf · erfc · exp · int · log · log10 · sin · sqrt · tanh

Common Math Functions (HOC)

These math functions return a double precision value and take a double precision argument. The exception is 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.

Note

Every function on this page has a pure-Python alternative. When working with Vector objects, to create a new Vector with the function applied to each element of the original, use either list comprehensions or numpy. When working with rxd objects (e.g., a rxd.Rate), use the rxd.rxdmath module.

abs()

Python

Absolute value

>>> n.abs(-42.2)
42.2

See Vector.abs() for the Vector class.

Note

In Python code, use Python’s abs function, which works on both numbers and numpy arrays, as well as Vectors (Vectors do not print their contents) :

>>> abs(-42.2)
42.2
>>> abs(-3 + 4j)
5.0
>>> v = n.Vector([1, 6, -2, -65])
>>> abs(v).printf()
1       6       2       65
4

HOC

absolute value

see Vector.abs() for the Vector class.

int()

Python

Returns the integer part of its argument (truncates toward 0).

>>> n.int(3.14)
3.0
>>> n.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:

>>> int(-3.14)
-3
>>> int(3.14)
3

HOC

returns the integer part of its argument (truncates toward 0).

sqrt(): Python

Square root

see Vector.sqrt() for the Vector class.

Note

Consider using Python’s built in math.sqrt instead.

HOC

square root

see Vector.sqrt() for the Vector class.

exp()

Python

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.

from neuron import n

for i in range(6, 12):
    print(i, n.exp(i))

Note

Consider using Python’s built in math.exp instead.

HOC

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.

for i=690, 710 print i, exp(i)

log(): Python

Logarithm to the base e

see Vector.log() for the Vector class.

Note

Consider using Python’s built in math.log instead.

HOC

logarithm to the base e see Vector.log() for the Vector class.

log10(): Python

Logarithm to the base 10

see Vector.log10() for the Vector class.

Note

Consider using Python’s built in math.log10 instead.

HOC

logarithm to the base 10

see Vector.log10() for the Vector class.

cos()

Python

Returns the trigonometric function of radian argument (a number).

If you need to take the cosine of a Vector, use numpy; e.g.,

import numpy as np
from neuron import n

v = n.Vector([0, n.PI/6, n.PI/4, n.PI/2])
v2 = n.Vector(np.cos(v))
print(list(v2))

# [1.0, 0.8660254037844387, 0.7071067811865476, 6.123233995736766e-17]

To create a vector filled with a cosine/sine wave, see Vector.sin() or use numpy.

Note

Consider using Python’s built in math.cos instead.

HOC

trigonometric function of radian argument.

see Vector.sin()

sin()

Python

Returns the trigonometric function of radian argument (a number).

If you need to take the sine of a Vector, use numpy; e.g.,

import numpy as np
from neuron import n

v = n.Vector([0, n.PI/6, n.PI/4, n.PI/2])
v2 = n.Vector(np.sin(v))
print(list(v2))

# [0.0, 0.49999999999999994, 0.7071067811865475, 1.0]

To create a vector filled with a sine wave, see Vector.sin() or use numpy.

Note

Consider using Python’s built in math.sin instead.

HOC

trigonometric function of radian argument.

see Vector.sin() for the Vector class.

tanh()

Python

Hyperbolic tangent.

For Vector objects, use Vector.tanh() to store the values in-place, or use numpy to create a new Vector; e.g.,

import numpy as np
from neuron import n

v = n.Vector([0, 1, 2, 3])
v2 = n.Vector(np.tanh(v))
print(list(v2))

# [0.0, 0.7615941559557649, 0.9640275800758169, 0.9950547536867305]

Note

Consider using Python’s built in math.tanh instead.

HOC

hyperbolic tangent. see Vector.tanh() for the Vector class.

atan(): Python

Returns the arc-tangent of y/x in the range \(-\pi/2\) to \(\pi/2\). (x > 0)

Note

Consider using Python’s built in math.atan instead.

HOC

returns the arc-tangent of y/x in the range -PI/2 to PI/2. (x > 0)

atan2()

Python

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:

from neuron import n

print(n.atan2(0, 0))
for i in range(-1, 2):
    print(n.atan2(i*1e-6, 10))
for i in range(-1, 2):
    print(n.atan2(i*1e-6, -10))
for i in range(-1, 2):
    print(n.atan2(10, i*1e-6))
for i in range(-1, 2):
    print(n.atan2(-10, i*1e-6))
print(n.atan2(10, 10))
print(n.atan2(10, -10))
print(n.atan2(-10, 10))
print(n.atan2(-10, -10))

Note

Consider using Python’s built in math.atan2 instead.

HOC

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:

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)

erf(): Python

Normalized error function

\[{\rm erf}(z) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2} dt\]

Note

In Python 3.2+, use math.erf instead.

HOC

normalized error function

\[{\rm erf}(z) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2} dt\]

erfc(): Python

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.

HOC

returns 1.0 - erf(z) but on sun machines computed by other methods that avoid cancellation for large z.