.. index:: single: numberlistp
.. _numberlistp/0:

.. rst-class:: right

**protocol**

``numberlistp``
===============

List of numbers protocol.

| **Availability:** 
|    ``logtalk_load(types(loader))``

| **Author:** Paulo Moura
| **Version:** 1:10:0
| **Date:** 2025-03-13

| **Compilation flags:**
|    ``static``


| **Dependencies:**
|   (none)


| **Remarks:**
|    (none)

| **Inherited public predicates:**
|    (none)

.. contents::
   :local:
   :backlinks: top

Public predicates
-----------------

.. index:: min/2
.. _numberlistp/0::min/2:

``min/2``
^^^^^^^^^

Determines the minimum value in a list using arithmetic order. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``min(List,Minimum)``
| **Mode and number of proofs:**
|    ``min(+list(number),-number)`` - ``zero_or_one``


------------

.. index:: max/2
.. _numberlistp/0::max/2:

``max/2``
^^^^^^^^^

Determines the list maximum value using arithmetic order. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``max(List,Maximum)``
| **Mode and number of proofs:**
|    ``max(+list(number),-number)`` - ``zero_or_one``


------------

.. index:: min_max/3
.. _numberlistp/0::min_max/3:

``min_max/3``
^^^^^^^^^^^^^

Determines the minimum and maximum values in a list using arithmetic order. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``min_max(List,Minimum,Maximum)``
| **Mode and number of proofs:**
|    ``min_max(+list(number),-number,-number)`` - ``zero_or_one``


------------

.. index:: product/2
.. _numberlistp/0::product/2:

``product/2``
^^^^^^^^^^^^^

Calculates the product of all list numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``product(List,Product)``
| **Mode and number of proofs:**
|    ``product(+list(number),-number)`` - ``zero_or_one``


------------

.. index:: sum/2
.. _numberlistp/0::sum/2:

``sum/2``
^^^^^^^^^

Calculates the sum of all list numbers. Returns the integer zero if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``sum(List,Sum)``
| **Mode and number of proofs:**
|    ``sum(+list(number),-number)`` - ``one``


------------

.. index:: average/2
.. _numberlistp/0::average/2:

``average/2``
^^^^^^^^^^^^^

Calculates the average (i.e., arithmetic mean) of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``average(List,Average)``
| **Mode and number of proofs:**
|    ``average(+list(number),-float)`` - ``zero_or_one``


------------

.. index:: median/2
.. _numberlistp/0::median/2:

``median/2``
^^^^^^^^^^^^

Calculates the median of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``median(List,Median)``
| **Mode and number of proofs:**
|    ``median(+list(number),-float)`` - ``zero_or_one``


------------

.. index:: modes/2
.. _numberlistp/0::modes/2:

``modes/2``
^^^^^^^^^^^

Returns the list of modes of a list of numbers in ascending order. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``modes(List,Modes)``
| **Mode and number of proofs:**
|    ``modes(+list(number),-list(number))`` - ``zero_or_one``


------------

.. index:: euclidean_norm/2
.. _numberlistp/0::euclidean_norm/2:

``euclidean_norm/2``
^^^^^^^^^^^^^^^^^^^^

Calculates the Euclidean norm of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``euclidean_norm(List,Norm)``
| **Mode and number of proofs:**
|    ``euclidean_norm(+list(number),-float)`` - ``zero_or_one``


------------

.. index:: chebyshev_norm/2
.. _numberlistp/0::chebyshev_norm/2:

``chebyshev_norm/2``
^^^^^^^^^^^^^^^^^^^^

Calculates the Chebyshev norm of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``chebyshev_norm(List,Norm)``
| **Mode and number of proofs:**
|    ``chebyshev_norm(+list(integer),-integer)`` - ``zero_or_one``
|    ``chebyshev_norm(+list(float),-float)`` - ``zero_or_one``


------------

.. index:: manhattan_norm/2
.. _numberlistp/0::manhattan_norm/2:

``manhattan_norm/2``
^^^^^^^^^^^^^^^^^^^^

Calculates the Manhattan norm of a list of numbers. Fails if the list is empty.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``manhattan_norm(List,Norm)``
| **Mode and number of proofs:**
|    ``manhattan_norm(+list(integer),-integer)`` - ``zero_or_one``
|    ``manhattan_norm(+list(float),-float)`` - ``zero_or_one``


------------

.. index:: euclidean_distance/3
.. _numberlistp/0::euclidean_distance/3:

``euclidean_distance/3``
^^^^^^^^^^^^^^^^^^^^^^^^

Calculates the Euclidean distance between two lists of numbers. Fails if the two lists are empty or not of the same length.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``euclidean_distance(List1,List2,Distance)``
| **Mode and number of proofs:**
|    ``euclidean_distance(+list(number),+list(number),-float)`` - ``zero_or_one``


------------

.. index:: chebyshev_distance/3
.. _numberlistp/0::chebyshev_distance/3:

``chebyshev_distance/3``
^^^^^^^^^^^^^^^^^^^^^^^^

Calculates the Chebyshev distance between two lists of numbers. Fails if the two lists are empty or not of the same length.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``chebyshev_distance(List1,List2,Distance)``
| **Mode and number of proofs:**
|    ``chebyshev_distance(+list(integer),+list(integer),-integer)`` - ``zero_or_one``
|    ``chebyshev_distance(+list(float),+list(float),-float)`` - ``zero_or_one``


------------

.. index:: manhattan_distance/3
.. _numberlistp/0::manhattan_distance/3:

``manhattan_distance/3``
^^^^^^^^^^^^^^^^^^^^^^^^

Calculates the Manhattan distance between two lists of numbers. Fails if the two lists are empty or not of the same length.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``manhattan_distance(List1,List2,Distance)``
| **Mode and number of proofs:**
|    ``manhattan_distance(+list(integer),+list(integer),-integer)`` - ``zero_or_one``
|    ``manhattan_distance(+list(float),+list(float),-float)`` - ``zero_or_one``


------------

.. index:: scalar_product/3
.. _numberlistp/0::scalar_product/3:

``scalar_product/3``
^^^^^^^^^^^^^^^^^^^^

Calculates the scalar product of two lists of numbers. Fails if the two lists are empty or not of the same length.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``scalar_product(List1,List2,Product)``
| **Mode and number of proofs:**
|    ``scalar_product(+list(integer),+list(integer),-integer)`` - ``zero_or_one``
|    ``scalar_product(+list(float),+list(float),-float)`` - ``zero_or_one``


------------

.. index:: normalize_range/2
.. _numberlistp/0::normalize_range/2:

``normalize_range/2``
^^^^^^^^^^^^^^^^^^^^^

Normalizes a list of numbers into the ``[0.0,1.0]`` range. Caller must handle arithmetic exceptions if the input list if not normalizable.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``normalize_range(List,NormalizedList)``
| **Mode and number of proofs:**
|    ``normalize_range(+list(number),-list(float))`` - ``one``


------------

.. index:: normalize_range/4
.. _numberlistp/0::normalize_range/4:

``normalize_range/4``
^^^^^^^^^^^^^^^^^^^^^

Normalizes a list of numbers into the given range. Caller must handle arithmetic exceptions if the input list if not normalizable.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``normalize_range(List,Minimum,Maximum,NormalizedList)``
| **Mode and number of proofs:**
|    ``normalize_range(+list(number),+number,+number,-list(float))`` - ``one``


------------

.. index:: normalize_unit/2
.. _numberlistp/0::normalize_unit/2:

``normalize_unit/2``
^^^^^^^^^^^^^^^^^^^^

Normalizes a list of numbers returning its unit vector (i.e., a list with Euclidean norm equal to one). Caller must handle arithmetic exceptions if the input list if not normalizable.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``normalize_unit(List,NormalizedList)``
| **Mode and number of proofs:**
|    ``normalize_unit(+list(number),-list(float))`` - ``one``


------------

.. index:: normalize_scalar/2
.. _numberlistp/0::normalize_scalar/2:

``normalize_scalar/2``
^^^^^^^^^^^^^^^^^^^^^^

Normalizes a list of numbers such that the sum of all numbers is equal to one. Caller must handle arithmetic exceptions if the input list if not normalizable.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``normalize_scalar(List,NormalizedList)``
| **Mode and number of proofs:**
|    ``normalize_scalar(+list(number),-list(float))`` - ``one``


------------

.. index:: rescale/3
.. _numberlistp/0::rescale/3:

``rescale/3``
^^^^^^^^^^^^^

Rescales all numbers in a list by the given factor.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``rescale(List,Factor,RescaledList)``
| **Mode and number of proofs:**
|    ``rescale(+list(integer),+integer,-list(integer))`` - ``one``
|    ``rescale(+list(number),+float,-list(float))`` - ``one``


------------

.. index:: least_common_multiple/2
.. _numberlistp/0::least_common_multiple/2:

``least_common_multiple/2``
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Computes the least common multiple of a list of two or more positive integers. Fails if the list is empty or contains a single element. Fails also if any of the elements is zero. May require backend support for unbound integer arithmetic.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``least_common_multiple(Integers,LeastCommonMultiple)``
| **Mode and number of proofs:**
|    ``least_common_multiple(+list(positive_integer),-positive_integer)`` - ``zero_or_one``


------------

.. index:: softmax/2
.. _numberlistp/0::softmax/2:

``softmax/2``
^^^^^^^^^^^^^

Computes the softmax of a list of floats, returning a probability distribution.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``softmax(Floats,Softmax)``
| **Mode and number of proofs:**
|    ``softmax(+list(float),-list(float))`` - ``one``


------------

.. index:: softmax/3
.. _numberlistp/0::softmax/3:

``softmax/3``
^^^^^^^^^^^^^

Computes the softmax of a list of floats with the given temperature, returning a probability distribution.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``softmax(Floats,Temperature,Softmax)``
| **Mode and number of proofs:**
|    ``softmax(+list(float),+positive_float,-list(float))`` - ``one``

| **Remarks:**

    - ``Temperature > 1.0``: Makes the distribution more uniform.
    - ``Temperature < 1.0``: Makes the distribution more concentrated on the largest values.
    - ``Temperature = 1.0``: Standard softmax behavior.


------------

Protected predicates
--------------------

(none)

Private predicates
------------------

(none)

Operators
---------

(none)

.. seealso::

   :ref:`numberlist <numberlist/0>`, :ref:`listp <listp/0>`, :ref:`varlistp <varlistp/0>`

