underworld.function.math module¶

This module provides math functions. All functions take functions (or convertibles) as arguments. These functions effectively wrap to the c++ standard template library equivalent. For example, the ‘exp’ class generates a function with uses std::exp(double).

All functions operate on and return ‘double’ type data (or ‘float’ from python).

Classes¶

`underworld.function.math.abs`	Computes the absolute value of its argument function.
`underworld.function.math.acos`	Computes the principal value of the arc cosine of x, expressed in radians.
`underworld.function.math.acosh`	Computes the inverse hyperbolic cosine of its argument function.
`underworld.function.math.asin`	Computes the principal value of the arc sine of x, expressed in radians.
`underworld.function.math.asinh`	Computes the inverse hyperbolic sine of its argument function.
`underworld.function.math.atan`	Computes the principal value of the arc tangent of x, expressed in radians.
`underworld.function.math.atanh`	Computes the inverse hyperbolic tangent of its argument function.
`underworld.function.math.cos`	Computes the cosine of its argument function (measured in radians).
`underworld.function.math.cosh`	Computes the hyperbolic cosine of its argument function.
`underworld.function.math.dot`	Dot product function.
`underworld.function.math.erf`	Computes the error function of its argument function.
`underworld.function.math.erfc`	Computes the complementary error function of its argument function.
`underworld.function.math.exp`	Computes the exponent of its argument function.
`underworld.function.math.log`	Computes the natural logarithm of its argument function.
`underworld.function.math.log10`	Computes the base 10 logarithm of its argument function.
`underworld.function.math.log2`	Computes the base 2 logarithm of its argument function.
`underworld.function.math.pow`	Power function.
`underworld.function.math.sin`	Computes the sine of its argument function (measured in radians).
`underworld.function.math.sinh`	Computes the hyperbolic sine of its argument function.
`underworld.function.math.sqrt`	Computes the square root of its argument function.
`underworld.function.math.tan`	Computes the tangent of its argument function (measured in radians).
`underworld.function.math.tanh`	Computes the hyperbolic tangent of its argument function.

class underworld.function.math.abs(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the absolute value of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = abs()
>>> np.allclose( func.evaluate(-0.1234), sysmath.fabs(0.1234) )
True

class underworld.function.math.acos(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the principal value of the arc cosine of x, expressed in radians.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = acos()
>>> np.allclose( func.evaluate(0.1234), sysmath.acos(0.1234) )
True

class underworld.function.math.acosh(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the inverse hyperbolic cosine of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = acosh()
>>> np.allclose( func.evaluate(5.1234), sysmath.acosh(5.1234) )
True

class underworld.function.math.asin(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the principal value of the arc sine of x, expressed in radians.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = asin()
>>> np.allclose( func.evaluate(0.1234), sysmath.asin(0.1234) )
True

class underworld.function.math.asinh(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the inverse hyperbolic sine of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = asinh()
>>> np.allclose( func.evaluate(5.1234), sysmath.asinh(5.1234) )
True

class underworld.function.math.atan(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the principal value of the arc tangent of x, expressed in radians.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = atan()
>>> np.allclose( func.evaluate(0.1234), sysmath.atan(0.1234) )
True

class underworld.function.math.atanh(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the inverse hyperbolic tangent of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = atanh()
>>> np.allclose( func.evaluate(0.1234), sysmath.atanh(0.1234) )
True

class underworld.function.math.cos(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the cosine of its argument function (measured in radians).

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = cos()
>>> np.allclose( func.evaluate(0.1234), sysmath.cos(0.1234) )
True

class underworld.function.math.cosh(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the hyperbolic cosine of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = cosh()
>>> np.allclose( func.evaluate(0.1234), sysmath.cosh(0.1234) )
True

class underworld.function.math.dot(fn1, fn2, **kwargs)[source]¶

Bases: underworld.function._function.Function

Dot product function. Returns fn1.fn2. Argument functions must return values of identical size.

Parameters:	fn1 (underworld.function.Function (or convertible)) – Argument function 1. fn2 (underworld.function.Function (or convertible)) – Argument function 2.

Example

>>> import math as sysmath
>>> import numpy as np
>>> input1 = (2.,3.,4.)
>>> input2 = (5.,6.,7.)
>>> func = dot( input1, input2 )

The function is constant, so evaluate anywhere:

>>> np.allclose( func.evaluate(0.), np.dot(input1,input2) )
True

class underworld.function.math.erf(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the error function of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = erf()
>>> np.allclose( func.evaluate(0.1234), sysmath.erf(0.1234) )
True

class underworld.function.math.erfc(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the complementary error function of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = erfc()
>>> np.allclose( func.evaluate(0.1234), sysmath.erfc(0.1234) )
True

class underworld.function.math.exp(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the exponent of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = exp()
>>> np.allclose( func.evaluate(0.1234), sysmath.exp(0.1234) )
True

class underworld.function.math.log(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the natural logarithm of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = log()
>>> np.allclose( func.evaluate(0.1234), sysmath.log(0.1234) )
True

class underworld.function.math.log10(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the base 10 logarithm of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = log10()
>>> np.allclose( func.evaluate(0.1234), sysmath.log10(0.1234) )
True

class underworld.function.math.log2(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the base 2 logarithm of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = log2()
>>> np.allclose( func.evaluate(0.1234), sysmath.log(0.1234,2) )
True

class underworld.function.math.pow(fn1, fn2, **kwargs)[source]¶

Bases: underworld.function._function.Function

Power function. Raises fn1 to the power of fn2.

Parameters:	fn1 (underworld.function.Function (or convertible)) – The base function. fn2 (underworld.function.Function (or convertible)) – The power function.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = pow(_uw.function.input(),3.)
>>> np.allclose( func.evaluate(2.), sysmath.pow(2.,3.) )
True

class underworld.function.math.sin(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the sine of its argument function (measured in radians).

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = sin()
>>> np.allclose( func.evaluate(0.1234), sysmath.sin(0.1234) )
True

class underworld.function.math.sinh(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the hyperbolic sine of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = sinh()
>>> np.allclose( func.evaluate(0.1234), sysmath.sinh(0.1234) )
True

class underworld.function.math.sqrt(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the square root of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = sqrt()
>>> np.allclose( func.evaluate(0.1234), sysmath.sqrt(0.1234) )
True

class underworld.function.math.tan(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the tangent of its argument function (measured in radians).

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = tan()
>>> np.allclose( func.evaluate(0.1234), sysmath.tan(0.1234) )
True

class underworld.function.math.tanh(fn=None, *args, **kwargs)[source]¶

Bases: underworld.function._function.Function

Computes the hyperbolic tangent of its argument function.

Parameters:	fn (underworld.function.Function (or convertible)) – Optionally provided for function composition.

Example

>>> import math as sysmath
>>> import numpy as np
>>> func = tanh()
>>> np.allclose( func.evaluate(0.1234), sysmath.tanh(0.1234) )
True