anaflow.tools.mean¶

Anaflow subpackage providing several mean calculating routines.

The following functions are provided

 annular_fmean(func, val_arr, f_def, f_inv[, …]) Calculating the annular generalized f-mean. annular_amean(func, val_arr[, ann_dim, arg_dict]) Calculating the annular arithmetic mean. annular_gmean(func, val_arr[, ann_dim, arg_dict]) Calculating the annular geometric mean. annular_hmean(func, val_arr[, ann_dim, arg_dict]) Calculating the annular harmonic mean. annular_pmean(func, val_arr[, p, ann_dim, …]) Calculating the annular p-mean.
annular_amean(func, val_arr, ann_dim=2, arg_dict=None, **kwargs)[source]

Calculating the annular arithmetic mean.

Calculating the annular arithmetic mean of a radial symmetric function for given consecutive radii defining annuli by the following formula

Parameters
• func (callable) – Function that should be used ( in the formula). The first argument needs to be the radial variable: func(r, **kwargs)

• val_arr (numpy.ndarray) – Radii defining the annuli.

• ann_dim (float, optional) – The dimension of the annuli. Default: 2.0

• arg_dict (dict or None, optional) – Keyword-arguments given as a dictionary that are forwarded to the function given in func. Will be merged with **kwargs. This is designed for overlapping keywords in annular_amean and func. Default: None

• **kwargs – Keyword-arguments that are forwarded to the function given in func. Will be merged with arg_dict

Returns

Array with all calculated arithmetic means

Return type

numpy.ndarray

Raises
• ValueError – If func is not callable.

• ValueError – If val_arr has less than 2 values.

• ValueError – If val_arr is not sorted in incresing order.

Notes

If the last value in val_arr is “inf”, the given function should provide a value for “inf” as input: func(float("inf"))

annular_fmean(func, val_arr, f_def, f_inv, ann_dim=2, arg_dict=None, **kwargs)[source]

Calculating the annular generalized f-mean.

Calculating the annular generalized f-mean of a radial symmetric function for given consecutive radii defining annuli by the following formula

Parameters
• func (callable) – Function that should be used ( in the formula). The first argument needs to be the radial variable: func(r, **kwargs)

• val_arr (numpy.ndarray) – Radii defining the annuli.

• ann_dim (float, optional) – The dimension of the annuli. Default: 2.0

• f_def (callable) – Function defining the f-mean.

• f_inv (callable) – Inverse of the function defining the f-mean.

• arg_dict (dict or None, optional) – Keyword-arguments given as a dictionary that are forwarded to the function given in func. Will be merged with **kwargs. This is designed for overlapping keywords in annular_fmean and func. Default: None

• **kwargs – Keyword-arguments that are forwarded to the function given in func. Will be merged with arg_dict

Returns

Array with all calculated arithmetic means

Return type

numpy.ndarray

Raises
• ValueError – If func is not callable.

• ValueError – If f_def is not callable.

• ValueError – If f_inv is not callable.

• ValueError – If val_arr has less than 2 values.

• ValueError – If val_arr is not sorted in incresing order.

Notes

If the last value in val_arr is “inf”, the given function should provide a value for “inf” as input: func(float("inf"))

annular_gmean(func, val_arr, ann_dim=2, arg_dict=None, **kwargs)[source]

Calculating the annular geometric mean.

Calculating the annular geometric mean of a radial symmetric function for given consecutive radii defining annuli by the following formula

Parameters
• func (callable) – Function that should be used ( in the formula). The first argument needs to be the radial variable: func(r, **kwargs)

• val_arr (numpy.ndarray) – Radii defining the annuli.

• ann_dim (float, optional) – The dimension of the annuli. Default: 2.0

• arg_dict (dict or None, optional) – Keyword-arguments given as a dictionary that are forwarded to the function given in func. Will be merged with **kwargs. This is designed for overlapping keywords in annular_gmean and func. Default: None

• **kwargs – Keyword-arguments that are forwarded to the function given in func. Will be merged with arg_dict

Returns

Array with all calculated geometric means

Return type

numpy.ndarray

Raises
• ValueError – If func is not callable.

• ValueError – If val_arr has less than 2 values.

• ValueError – If val_arr is not sorted in incresing order.

Notes

If the last value in val_arr is “inf”, the given function should provide a value for “inf” as input: func(float("inf"))

Examples

>>> f = lambda x: x**2
>>> annular_gmean(f, [1,2,3])
array([ 2.33588885,  6.33423311])

annular_hmean(func, val_arr, ann_dim=2, arg_dict=None, **kwargs)[source]

Calculating the annular harmonic mean.

Calculating the annular harmonic mean of a radial symmetric function for given consecutive radii defining annuli by the following formula

Parameters
• func (callable) – Function that should be used ( in the formula). The first argument needs to be the radial variable: func(r, **kwargs)

• val_arr (numpy.ndarray) – Radii defining the annuli.

• ann_dim (float, optional) – The dimension of the annuli. Default: 2.0

• arg_dict (dict or None, optional) – Keyword-arguments given as a dictionary that are forwarded to the function given in func. Will be merged with **kwargs. This is designed for overlapping keywords in annular_hmean and func. Default: None

• **kwargs – Keyword-arguments that are forwarded to the function given in func. Will be merged with arg_dict

Returns

Array with all calculated geometric means

Return type

numpy.ndarray

Raises
• ValueError – If func is not callable.

• ValueError – If val_arr has less than 2 values.

• ValueError – If val_arr is not sorted in incresing order.

Notes

If the last value in val_arr is “inf”, the given function should provide a value for “inf” as input: func(float("inf"))

annular_pmean(func, val_arr, p=2.0, ann_dim=2, arg_dict=None, **kwargs)[source]

Calculating the annular p-mean.

Calculating the annular p-mean of a radial symmetric function for given consecutive radii defining annuli by the following formula

Parameters
• func (callable) – Function that should be used ( in the formula). The first argument needs to be the radial variable: func(r, **kwargs)

• val_arr (numpy.ndarray) – Radii defining the annuli.

• p (float, optional) – The potency defining the p-mean. Default: 2.0

• ann_dim (float, optional) – The dimension of the annuli. Default: 2.0

• arg_dict (dict or None, optional) – Keyword-arguments given as a dictionary that are forwarded to the function given in func. Will be merged with **kwargs. This is designed for overlapping keywords in annular_pmean and func. Default: None

• **kwargs – Keyword-arguments that are forwarded to the function given in func. Will be merged with arg_dict

Returns

Array with all calculated p-means

Return type

numpy.ndarray

Raises
• ValueError – If func is not callable.

• ValueError – If val_arr has less than 2 values.

• ValueError – If val_arr is not sorted in incresing order.

Notes

If the last value in val_arr is “inf”, the given function should provide a value for “inf” as input: func(float("inf"))