Special Functions (labtoolbox.special)#

Special mathematical functions for LabToolbox.

Includes sign, pulse and waveform functions such as rectangle, triangle, Sawtooth, square and Lorentzian profiles.

labtoolbox.special.lorentz(x, x0=0.0, g=1.0)[source]#

Compute the Lorentzian (Cauchy) distribution function.

Parameters:

  • x (float or numpy.ndarray) – Input value(s), scalar or 1D array of real numbers.

  • x0 (float, optional) – Center of the Lorentzian distribution. Defaults to 0.0.

  • g (float, optional) – Width parameter. Must be positive. Defaults to 1.0.

Returns:

The Lorentzian function evaluated at x. Returns a scalar if x is scalar, otherwise a 1D array.

Return type:

float or numpy.ndarray

Raises:

  • TypeError – If x contains non-real numbers, or x0 or g are not finite real numbers.

  • ValueError – If x is not a scalar or 1D array, contains non-finite values, or g is not positive.

Examples

>>> from labtoolbox.special import lorentz
>>> lorentz(0.0, x0=0.0, g=1.0)
0.3183098861837907
>>> lorentz([0, 1, 2], x0=0.0, g=1.0)
array([0.31830989, 0.15915494, 0.06366198])
labtoolbox.special.rect(x)[source]#

Compute the rectangular function (boxcar function).

Parameters:

x (float or numpy.ndarray) – Input value(s), scalar or 1D array of real numbers.

Returns:

The rectangular function evaluated at x. Returns a scalar if x is scalar, otherwise a 1D array.

Return type:

float or numpy.ndarray

Raises:

  • TypeError – If x contains non-real numbers.

  • ValueError – If x is not a scalar or 1D array, or contains non-finite values.

Examples

>>> from labtoolbox.special import rect
>>> rect(0.4)
1.0
>>> rect([-0.6, 0.5, 0.0])
array([0. , 0.5, 1. ])
labtoolbox.special.saw(x, T=1.0)[source]#

Compute the sawtooth wave function.

Parameters:

  • x (float or numpy.ndarray) – Input value(s), scalar or 1D array of real numbers.

  • T (float, optional) – Period of the sawtooth wave. Must be positive. Defaults to 1.0.

Returns:

The sawtooth wave evaluated at x. Returns a scalar if x is scalar, otherwise a 1D array.

Return type:

float or numpy.ndarray

Raises:

  • TypeError – If x contains non-real numbers.

  • ValueError – If x is not a scalar or 1D array, contains non-finite values, or T is not positive.

Examples

>>> from labtoolbox.special import saw
>>> saw(0.25, T=1.0)
0.5
>>> saw([0, 0.5, 1.0], T=1.0)
array([ 0.,  1., -1.])
labtoolbox.special.sgn(x)[source]#

Compute the sign function of the input.

Parameters:

x (float or numpy.ndarray) – Input value(s), scalar or 1D array of real numbers.

Returns:

The sign of x. Returns a scalar if x is scalar, otherwise a 1D array.

Return type:

float or numpy.ndarray

Raises:

  • TypeError – If x contains non-real numbers.

  • ValueError – If x is not a scalar or 1D array, or contains non-finite values.

Examples

>>> from labtoolbox.special import sgn
>>> sgn(3.0)
1.0
>>> sgn([-2, 0, 1])
array([-1.,  0.,  1.])
labtoolbox.special.square(x, T=1.0)[source]#

Compute the square wave function.

The function is periodic with period T, alternating between -1 and 1 based on the sign of sin(2 * pi * x / T).

Parameters:

  • x (float or numpy.ndarray) – Input value(s), scalar or 1D array of real numbers.

  • T (float, optional) – Period of the square wave. Must be positive. Defaults to 1.0.

Returns:

The square wave evaluated at x. Returns a scalar if x is scalar, otherwise a 1D array.

Return type:

float or numpy.ndarray

Raises:

  • TypeError – If x contains non-real numbers or T is not a finite real number.

  • ValueError – If x is not a scalar or 1D array, contains non-finite values, or T is not positive.

Examples

>>> from labtoolbox.special import square
>>> square(0.25)
1.0
>>> square([0, 0.5, 1.0])
array([ 1., -1.,  1.])
labtoolbox.special.step(x)[source]#

Compute the Heaviside step function.

Returns 0 for x < 0, 1 for x >= 0.

Parameters:

x (float or numpy.ndarray) – Input value(s), scalar or 1D array of real numbers.

Returns:

The step function evaluated at x. Returns a scalar if x is scalar, otherwise a 1D array.

Return type:

float or numpy.ndarray

Raises:

  • TypeError – If x contains non-real numbers.

  • ValueError – If x is not a scalar or 1D array, or contains non-finite values.

Examples

>>> from labtoolbox.special import step
>>> step(-1.0)
0.0
>>> step([-1, 0, 1])
array([0., 1., 1.])
labtoolbox.special.tri(x)[source]#

Compute a triangle pulse. Not to be confused with labtoolbox.triangle.

Parameters:

x (float or numpy.ndarray) – Input value(s), scalar or 1D array of real numbers.

Returns:

The triangle wave evaluated at x. Returns a scalar if x is scalar, otherwise a 1D array.

Return type:

float or numpy.ndarray

Raises:

  • TypeError – If x contains non-real numbers.

  • ValueError – If x is not a scalar or 1D array, or contains non-finite values.

Examples

>>> from labtoolbox.special import tri
>>> tri(0.25)
0.75
>>> tri([0, 0.25, 0.5])
array([1, 0.75, 0.5])
labtoolbox.special.triangle(x, T=1.0)[source]#

Compute the triangle wave function.

Parameters:

  • x (float or numpy.ndarray) – Input value(s), scalar or 1D array of real numbers.

  • T (float, optional) – Period of the triangle wave. Must be positive. Defaults to 1.0.

Returns:

The triangle wave evaluated at x. Returns a scalar if x is scalar, otherwise a 1D array.

Return type:

float or numpy.ndarray

Raises:

  • TypeError – If x contains non-real numbers or T is not a finite real number.

  • ValueError – If x is not a scalar or 1D array, contains non-finite values, or T is not positive.

Examples

>>> from labtoolbox.special import triangle
>>> triangle(0.25)
1.0
>>> triangle([0, 0.25, 0.5])
array([0., 1., 0.])