# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Compute the total of a list of numbers all taken to some power

Contributed by:
Seth J. Chandler

ResourceFunction["PowerTotal"][ takes | |

ResourceFunction["PowerTotal"][ represents an operator form of ResourceFunction["PowerTotal"] that can be applied to an expression | |

ResourceFunction["PowerTotal"][ represents an operator form of ResourceFunction["PowerTotal"] that, when applied to | |

ResourceFunction["PowerTotal"][] represents an operator form of ResourceFunction["PowerTotal"] that, when applied to |

Both *x* and *y* can be real, complex or symbolic.

The level specification *n* may take the form of:

an integer *n*, meaning the summation is performed at all levels down to level *n*;

a List of two integers {*n*_{1},*n*_{2}}, meaning the summation is performed at all levels *n*_{1} through *n*_{2}.

See the documentation for Total for a more complete explanation of how the level specification works there.

Compute the sum of the squares of a list:

In[1]:= |

Out[1]= |

Compute the sum of the cubes of a list with symbolic parts:

In[2]:= |

Out[2]= |

Compute the sum of the cubes of a symbolic array:

In[3]:= |

Out[3]= |

Create an operator which when confronted with an expression computes the sum of its square roots:

In[4]:= |

Out[4]= |

The power may be complex, as may the list:

In[5]:= |

Out[5]= |

The level specification can affect the results when the data has more than one dimension:

In[6]:= |

Out[6]= |

The default behavior is to apply at level 1:

In[7]:= |

Out[7]= |

Apply the total down to level 2:

In[8]:= |

Out[8]= |

Apply the total in the last two dimensions:

In[9]:= |

Out[9]= |

Use PowerTotal to conduct ordinary least squares linear regression by finding the values of two parameters *a* and *b* that minimize the sum of the squared distances between the actual value of the independent variable and a value that depends on *a* and *b*:

In[10]:= |

Out[10]= |

Use PowerTotal to perform "Tikhonov" (ridge) regression:

In[11]:= |

Out[11]= |

Use PowerTotal to perform "LASSO" regression:

In[12]:= |

Out[12]= |

PowerTotal[] is the same as the square of the results from the Norm function if the arguments it confronts are real-valued, but is not necessarily the same if the values it confronts are complex:

In[13]:= |

Out[13]= |

In[14]:= |

Out[14]= |

PowerTotal is the same as Total if the power argument is 1:

In[15]:= |

Out[15]= |

- 1.0.0 – 30 December 2019

This work is licensed under a Creative Commons Attribution 4.0 International License