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Commit 2cce156d authored by Davis King's avatar Davis King
Browse files

Clarified the sparse vector spec and formally introduced the concept 

of unsorted sparse vectors.
parent 14dbd96b
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Showing with 44 additions and 22 deletions
dlib/svm/sparse_vector_abstract.h
View file @ 2cce156d
......@@ -13,20 +13,40 @@ namespace dlib
// ----------------------------------------------------------------------------------------
/*!A sparse_vectors
In dlib, sparse vectors are represented using the container objects
in the C++ STL. In particular, a sparse vector is any container that
contains a sorted range of std::pair<key, scalar_value> objects where:
contains a range of std::pair<key, scalar_value> objects where:
- key is an unsigned integral type
- scalar_value is float, double, or long double
- the std::pair objects have unique key values
- the std::pair objects are sorted such that small keys come first
Therefore, if an object satisfies the above requirements we call it a
"sparse vector". Additionally, we define the concept of an "unsorted sparse vector"
to be a sparse vector that doesn't necessarily have sorted or unique key values.
Therefore, all sparse vectors are valid unsorted sparse vectors but not the other
way around.
An unsorted sparse vector with duplicate keys is always interpreted as
a vector where each dimension contains the sum of all corresponding elements
of the unsorted sparse vector. For example, an unsorted sparse vector
with the elements { (3,1), (0, 4), (3,5) } represents the 4D vector:
[4, 0, 0, 1+5]
So examples of valid sparse vectors are:
Examples of valid sparse vectors are:
- std::map<unsigned long, double>
- std::vector<std::pair<unsigned long, float> > where the vector is sorted.
(you could make sure it was sorted by applying std::sort to it)
This file defines a number of helper functions for doing normal vector
arithmetic things with sparse vectors.
Finally, by "dense vector" we mean a dlib::matrix object which represents
either a row or column vector.
The rest of this file defines a number of helper functions for doing normal
vector arithmetic things with sparse vectors.
!*/
// ----------------------------------------------------------------------------------------
......@@ -54,8 +74,7 @@ namespace dlib
);
/*!
requires
- a is a sorted range of std::pair objects
- b is a sorted range of std::pair objects
- a and b are sparse vectors
ensures
- returns the squared distance between the vectors
a and b
......@@ -72,8 +91,7 @@ namespace dlib
);
/*!
requires
- a is a sorted range of std::pair objects
- b is a sorted range of std::pair objects
- a and b are sparse vectors
ensures
- returns the squared distance between the vectors
a_scale*a and b_scale*b
......@@ -88,8 +106,7 @@ namespace dlib
);
/*!
requires
- a is a sorted range of std::pair objects
- b is a sorted range of std::pair objects
- a and b are sparse vectors
ensures
- returns the distance between the vectors
a and b. (i.e. std::sqrt(distance_squared(a,b)))
......@@ -106,8 +123,7 @@ namespace dlib
);
/*!
requires
- a is a sorted range of std::pair objects
- b is a sorted range of std::pair objects
- a and b are sparse vectors
ensures
- returns the distance between the vectors
a_scale*a and b_scale*b. (i.e. std::sqrt(distance_squared(a_scale,a,b_scale,b)))
......@@ -143,7 +159,7 @@ namespace dlib
);
/*!
requires
- a and b are valid sparse vectors (as defined at the top of this file).
- a and b are sparse vectors
ensures
- returns the dot product between the vectors a and b
!*/
......@@ -157,7 +173,7 @@ namespace dlib
);
/*!
requires
- a is a valid sparse vector (as defined at the top of this file).
- a is an unsorted sparse vector
- is_vector(b) == true
ensures
- returns the dot product between the vectors a and b
......@@ -172,7 +188,7 @@ namespace dlib
);
/*!
requires
- b is a valid sparse vector (as defined at the top of this file).
- b is an unsorted sparse vector
- is_vector(a) == true
ensures
- returns the dot product between the vectors a and b
......@@ -186,7 +202,7 @@ namespace dlib
);
/*!
requires
- a is a sorted range of std::pair objects
- a is a sparse vector
ensures
- returns dot(a,a)
!*/
......@@ -199,7 +215,7 @@ namespace dlib
);
/*!
requires
- a is a sorted range of std::pair objects
- a is a sparse vector
ensures
- returns std::sqrt(length_squared(a,a))
!*/
......@@ -213,7 +229,7 @@ namespace dlib
);
/*!
requires
- a is a sorted range of std::pair objects
- a is an unsorted sparse vector
ensures
- #a == a*value
(i.e. multiplies every element of the vector a by value)
......@@ -260,9 +276,12 @@ namespace dlib
);
/*!
requires
- SRC == a matrix expression or a sparse vector
- SRC == a matrix expression or an unsorted sparse vector
- is_vector(dest) == true
- max_index_plus_one(src) <= dest.size()
- Let MAX denote the largest element index in src.
Then we require that:
- MAX < dest.size()
- (i.e. dest needs to be big enough to contain all the elements of src)
ensures
- #dest == dest + C*src
!*/
......@@ -277,9 +296,12 @@ namespace dlib
);
/*!
requires
- SRC == a matrix expression or a sparse vector
- SRC == a matrix expression or an unsorted sparse vector
- is_vector(dest) == true
- max_index_plus_one(src) <= dest.size()
- Let MAX denote the largest element index in src.
Then we require that:
- MAX < dest.size()
- (i.e. dest needs to be big enough to contain all the elements of src)
ensures
- #dest == dest - C*src
!*/
......
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