// Copyright (C) 2008  Davis E. King (davis@dlib.net)
// License: Boost Software License   See LICENSE.txt for the full license.
#undef DLIB_STATISTICs_ABSTRACT_
#ifdef DLIB_STATISTICs_ABSTRACT_

#include <limits>
#include <cmath>
#include "../matrix/matrix_abstract.h"

namespace dlib
{

// ----------------------------------------------------------------------------------------

    template <
        typename T, 
        typename alloc
        >
    double mean_sign_agreement (
        const std::vector<T,alloc>& a,
        const std::vector<T,alloc>& b
    );
    /*!
        requires
            - a.size() == b.size()
        ensures
            - returns the number of times a[i] has the same sign as b[i] divided by
              a.size().  So we return the probability that elements of a and b have
              the same sign.
    !*/

// ----------------------------------------------------------------------------------------

    template <
        typename T, 
        typename alloc
        >
    double correlation (
        const std::vector<T,alloc>& a,
        const std::vector<T,alloc>& b
    );
    /*!
        requires
            - a.size() == b.size()
            - a.size() > 1
        ensures
            - returns the correlation coefficient between all the elements of a and b.
              (i.e. how correlated is a(i) with b(i))
    !*/

// ----------------------------------------------------------------------------------------

    template <
        typename T, 
        typename alloc
        >
    double covariance (
        const std::vector<T,alloc>& a,
        const std::vector<T,alloc>& b
    );
    /*!
        requires
            - a.size() == b.size()
            - a.size() > 1
        ensures
            - returns the covariance between all the elements of a and b.
              (i.e. how does a(i) vary with b(i))
    !*/

// ----------------------------------------------------------------------------------------

    template <
        typename T, 
        typename alloc
        >
    double r_squared (
        const std::vector<T,alloc>& a,
        const std::vector<T,alloc>& b
    );
    /*!
        requires
            - a.size() == b.size()
            - a.size() > 1
        ensures
            - returns the R^2 coefficient of determination between all the elements of a and b.
              This value is just the square of correlation(a,b).
    !*/

// ----------------------------------------------------------------------------------------

    template <
        typename T, 
        typename alloc
        >
    double mean_squared_error (
        const std::vector<T,alloc>& a,
        const std::vector<T,alloc>& b
    );
    /*!
        requires
            - a.size() == b.size()
        ensures
            - returns the mean squared error between all the elements of a and b.
              (i.e. mean(squared(mat(a)-mat(b))))
    !*/

// ----------------------------------------------------------------------------------------

    template <
        typename T
        >
    class running_stats
    {
        /*!
            REQUIREMENTS ON T
                - T must be a float, double, or long double type

            INITIAL VALUE
                - max_n() == std::numeric_limits<T>::max()
                - mean() == 0
                - current_n() == 0

            WHAT THIS OBJECT REPRESENTS
                This object represents something that can compute the running mean and
                variance of a stream of real numbers.  

                As this object accumulates more and more numbers it will be the case
                that each new number impacts the current mean and variance estimate
                less and less.  This may be what you want.  But it might not be. 

                For example, your stream of numbers might be non-stationary, that is,
                the mean and variance might change over time.  To enable you to use
                this object on such a stream of numbers this object provides the 
                ability to set a "max_n."  The meaning of the max_n() parameter
                is that after max_n() samples have been seen each new sample will
                have the same impact on the mean and variance estimates from then on.

                So if you have a highly non-stationary stream of data you might
                set the max_n to a small value while if you have a very stationary
                stream you might set it to a very large value.
        !*/
    public:

        running_stats(
        );
        /*!
            ensures
                - this object is properly initialized
        !*/

        void clear(
        );
        /*!
            ensures
                - this object has its initial value
                - clears all memory of any previous data points
        !*/

        void set_max_n (
            const T& val
        );
        /*!
            ensures
                - #max_n() == val
        !*/

        T max_n (
        ) const;
        /*!
            ensures
                - returns the max value that current_n() is allowed to take on
        !*/

        T current_n (
        ) const;
        /*!
            ensures
                - returns the number of points given to this object so far or
                  max_n(), whichever is smallest.
        !*/

        void add (
            const T& val
        );
        /*!
            ensures
                - updates the mean and variance stored in this object so that
                  the new value is factored into them
                - #mean() == mean()*current_n()/(current_n()+1) + val/(current_n()+1)
                - #variance() == the updated variance that takes this new value into account
                - if (current_n() < max_n()) then
                    - #current_n() == current_n() + 1
                - else
                    - #current_n() == current_n()
        !*/

        T mean (
        ) const;
        /*!
            ensures
                - returns the mean of all the values presented to this object 
                  so far.
        !*/

        T variance (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the unbiased sample variance of all the values presented to this
                  object so far.
        !*/

        T stddev (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the unbiased sampled standard deviation of all the values
                  presented to this object so far.
        !*/

        T max (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the largest value presented to this object so far.
        !*/

        T min (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the smallest value presented to this object so far.
        !*/

        T scale (
            const T& val
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - return (val-mean())/stddev();
        !*/

        running_stats operator+ (
            const running_stats& rhs
        ) const;
        /*!
            requires
                - max_n() == rhs.max_n()
            ensures
                - returns a new running_stats object that represents the combination of all
                  the values given to *this and rhs.  That is, this function returns a
                  running_stats object, R, that is equivalent to what you would obtain if
                  all calls to this->add() and rhs.add() had instead been done to R.
        !*/
    };

    template <typename T>
    void serialize (
        const running_stats<T>& item, 
        std::ostream& out 
    );
    /*!
        provides serialization support 
    !*/

    template <typename T>
    void deserialize (
        running_stats<T>& item, 
        std::istream& in
    );
    /*!
        provides serialization support 
    !*/

// ----------------------------------------------------------------------------------------

    template <
        typename T
        >
    class running_scalar_covariance
    {
        /*!
            REQUIREMENTS ON T
                - T must be a float, double, or long double type

            INITIAL VALUE
                - mean_x() == 0
                - mean_y() == 0
                - current_n() == 0

            WHAT THIS OBJECT REPRESENTS
                This object represents something that can compute the running covariance 
                of a stream of real number pairs.
        !*/

    public:

        running_scalar_covariance(
        );
        /*!
            ensures
                - this object is properly initialized
        !*/

        void clear(
        );
        /*!
            ensures
                - this object has its initial value
                - clears all memory of any previous data points
        !*/

        void add (
            const T& x,
            const T& y
        );
        /*!
            ensures
                - updates the statistics stored in this object so that
                  the new pair (x,y) is factored into them.
                - #current_n() == current_n() + 1
        !*/

        T current_n (
        ) const;
        /*!
            ensures
                - returns the number of points given to this object so far. 
        !*/

        T mean_x (
        ) const;
        /*!
            ensures
                - returns the mean value of all x samples presented to this object
                  via add().
        !*/

        T mean_y (
        ) const;
        /*!
            ensures
                - returns the mean value of all y samples presented to this object
                  via add().
        !*/

        T covariance (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the covariance between all the x and y samples presented
                  to this object via add()
        !*/

        T correlation (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the correlation coefficient between all the x and y samples 
                  presented to this object via add()
        !*/

        T variance_x (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the unbiased sample variance value of all x samples presented 
                  to this object via add().
        !*/

        T variance_y (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the unbiased sample variance value of all y samples presented 
                  to this object via add().
        !*/

        T stddev_x (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the unbiased sample standard deviation of all x samples
                  presented to this object via add().
        !*/

        T stddev_y (
        ) const;
        /*!
            requires
                - current_n() > 1
            ensures
                - returns the unbiased sample standard deviation of all y samples
                  presented to this object via add().
        !*/

        running_scalar_covariance operator+ (
            const running_covariance& rhs
        ) const;
        /*!
            ensures
                - returns a new running_scalar_covariance object that represents the
                  combination of all the values given to *this and rhs.  That is, this
                  function returns a running_scalar_covariance object, R, that is
                  equivalent to what you would obtain if all calls to this->add() and
                  rhs.add() had instead been done to R.
        !*/
    };

// ----------------------------------------------------------------------------------------

    template <
        typename matrix_type
        >
    class running_covariance
    {
        /*!
            REQUIREMENTS ON matrix_type
                Must be some type of dlib::matrix.

            INITIAL VALUE
                - in_vector_size() == 0
                - current_n() == 0

            WHAT THIS OBJECT REPRESENTS
                This object is a simple tool for computing the mean and
                covariance of a sequence of vectors.  
        !*/
    public:

        typedef typename matrix_type::mem_manager_type mem_manager_type;
        typedef typename matrix_type::type scalar_type;
        typedef typename matrix_type::layout_type layout_type;
        typedef matrix<scalar_type,0,0,mem_manager_type,layout_type> general_matrix;
        typedef matrix<scalar_type,0,1,mem_manager_type,layout_type> column_matrix;

        running_covariance(
        );
        /*!
            ensures
                - this object is properly initialized
        !*/

        void clear(
        );
        /*!
            ensures
                - this object has its initial value
                - clears all memory of any previous data points
        !*/

        long current_n (
        ) const;
        /*!
            ensures
                - returns the number of samples that have been presented to this object
        !*/

        long in_vector_size (
        ) const;
        /*!
            ensures
                - if (this object has been presented with any input vectors) then
                    - returns the dimension of the column vectors used with this object
                - else
                    - returns 0
        !*/

        void add (
            const matrix_exp& val
        );
        /*!
            requires
                - is_col_vector(val) == true
                - if (in_vector_size() != 0) then
                    - val.size() == in_vector_size()
            ensures
                - updates the mean and covariance stored in this object so that
                  the new value is factored into them.
                - #in_vector_size() == val.size()
        !*/

        const column_matrix mean (
        ) const;
        /*!
            requires
                - in_vector_size() != 0 
            ensures
                - returns the mean of all the vectors presented to this object 
                  so far.
        !*/

        const general_matrix covariance (
        ) const;
        /*!
            requires
                - in_vector_size() != 0 
                - current_n() > 1
            ensures
                - returns the unbiased sample covariance matrix for all the vectors 
                  presented to this object so far.
        !*/

        const running_covariance operator+ (
            const running_covariance& item
        ) const;
        /*!
            requires
                - in_vector_size() == 0 || item.in_vector_size() == 0 || in_vector_size() == item.in_vector_size()
                  (i.e. the in_vector_size() of *this and item must match or one must be zero)
            ensures
                - returns a new running_covariance object that represents the combination of all 
                  the vectors given to *this and item.  That is, this function returns a
                  running_covariance object, R, that is equivalent to what you would obtain if all
                  calls to this->add() and item.add() had instead been done to R.
        !*/
    };

// ----------------------------------------------------------------------------------------

    template <
        typename matrix_type
        >
    class vector_normalizer
    {
        /*!
            REQUIREMENTS ON matrix_type
                - must be a dlib::matrix object capable of representing column 
                  vectors

            INITIAL VALUE
                - in_vector_size() == 0
                - out_vector_size() == 0
                - means().size() == 0
                - std_devs().size() == 0

            WHAT THIS OBJECT REPRESENTS
                This object represents something that can learn to normalize a set 
                of column vectors.  In particular, normalized column vectors should 
                have zero mean and a variance of one.  

                Also, if desired, this object can use principal component 
                analysis for the purposes of reducing the number of elements in a 
                vector.  

            THREAD SAFETY
                Note that this object contains a cached matrix object it uses 
                to store intermediate results for normalization.  This avoids
                needing to reallocate it every time this object performs normalization
                but also makes it non-thread safe.  So make sure you don't share
                instances of this object between threads. 
        !*/

    public:
        typedef typename matrix_type::mem_manager_type mem_manager_type;
        typedef typename matrix_type::type scalar_type;
        typedef matrix_type result_type;

        template <typename vector_type>
        void train (
            const vector_type& samples
        );
        /*!
            requires
                - samples.size() > 0
                - samples == a column matrix or something convertible to a column 
                  matrix via mat().  Also, x should contain 
                  matrix_type objects that represent nonempty column vectors.
            ensures
                - #in_vector_size() == samples(0).nr()
                - #out_vector_size() == samples(0).nr()
                - This object has learned how to normalize vectors that look like
                  vectors in the given set of samples.  
                - #means() == mean(samples)
                - #std_devs() == reciprocal(sqrt(variance(samples)));
        !*/

        long in_vector_size (
        ) const;
        /*!
            ensures
                - returns the number of rows that input vectors are
                  required to contain if they are to be normalized by
                  this object.
        !*/

        long out_vector_size (
        ) const;
        /*!
            ensures
                - returns the number of rows in the normalized vectors
                  that come out of this object.
        !*/

        const matrix_type& means (
        ) const;
        /*!
            ensures               
                - returns a matrix M such that:
                    - M.nc() == 1
                    - M.nr() == in_vector_size()
                    - M(i) == the mean of the ith input feature shown to train()
        !*/

        const matrix_type& std_devs (
        ) const;
        /*!
            ensures               
                - returns a matrix SD such that:
                    - SD.nc() == 1
                    - SD.nr() == in_vector_size()
                    - SD(i) == the reciprocal of the standard deviation of the ith 
                      input feature shown to train() 
        !*/
 
        const result_type& operator() (
            const matrix_type& x
        ) const;
        /*!
            requires
                - x.nr() == in_vector_size()
                - x.nc() == 1
            ensures
                - returns a normalized version of x, call it Z, that has the 
                  following properties: 
                    - Z.nr() == out_vector_size()
                    - Z.nc() == 1
                    - the mean of each element of Z is 0 
                    - the variance of each element of Z is 1
                    - Z == pointwise_multiply(x-means(), std_devs());
        !*/

        void swap (
            vector_normalizer& item
        );
        /*!
            ensures
                - swaps *this and item
        !*/
    };

    template <
        typename matrix_type
        >
    inline void swap (
        vector_normalizer<matrix_type>& a, 
        vector_normalizer<matrix_type>& b 
    ) { a.swap(b); }   
    /*!
        provides a global swap function
    !*/

    template <
        typename matrix_type,
        >
    void deserialize (
        vector_normalizer<matrix_type>& item, 
        std::istream& in
    );   
    /*!
        provides deserialization support 
    !*/

    template <
        typename matrix_type,
        >
    void serialize (
        const vector_normalizer<matrix_type>& item, 
        std::ostream& out 
    );   
    /*!
        provides serialization support 
    !*/

// ----------------------------------------------------------------------------------------

    template <
        typename matrix_type
        >
    class vector_normalizer_pca
    {
        /*!
            REQUIREMENTS ON matrix_type
                - must be a dlib::matrix object capable of representing column 
                  vectors

            INITIAL VALUE
                - in_vector_size() == 0
                - out_vector_size() == 0
                - means().size() == 0
                - std_devs().size() == 0
                - pca_matrix().size() == 0

            WHAT THIS OBJECT REPRESENTS
                This object represents something that can learn to normalize a set 
                of column vectors.  In particular, normalized column vectors should 
                have zero mean and a variance of one.  

                Also, this object uses principal component analysis for the purposes 
                of reducing the number of elements in a vector.  

            THREAD SAFETY
                Note that this object contains a cached matrix object it uses 
                to store intermediate results for normalization.  This avoids
                needing to reallocate it every time this object performs normalization
                but also makes it non-thread safe.  So make sure you don't share
                instances of this object between threads. 
        !*/

    public:
        typedef typename matrix_type::mem_manager_type mem_manager_type;
        typedef typename matrix_type::type scalar_type;
        typedef matrix<scalar_type,0,1,mem_manager_type> result_type;

        template <typename vector_type>
        void train (
            const vector_type& samples,
            const double eps = 0.99
        );
        /*!
            requires
                - 0 < eps <= 1
                - samples.size() > 0
                - samples == a column matrix or something convertible to a column 
                  matrix via mat().  Also, x should contain 
                  matrix_type objects that represent nonempty column vectors.
            ensures
                - This object has learned how to normalize vectors that look like
                  vectors in the given set of samples.  
                - Principal component analysis is performed to find a transform 
                  that might reduce the number of output features. 
                - #in_vector_size() == samples(0).nr()
                - 0 < #out_vector_size() <= samples(0).nr()
                - eps is a number that controls how "lossy" the pca transform will be.
                  Large values of eps result in #out_vector_size() being larger and
                  smaller values of eps result in #out_vector_size() being smaller. 
                - #means() == mean(samples)
                - #std_devs() == reciprocal(sqrt(variance(samples)));
                - #pca_matrix() == the PCA transform matrix that is out_vector_size()
                  rows by in_vector_size() columns.
        !*/

        long in_vector_size (
        ) const;
        /*!
            ensures
                - returns the number of rows that input vectors are
                  required to contain if they are to be normalized by
                  this object.
        !*/

        long out_vector_size (
        ) const;
        /*!
            ensures
                - returns the number of rows in the normalized vectors
                  that come out of this object.
        !*/

        const matrix<scalar_type,0,1,mem_manager_type>& means (
        ) const;
        /*!
            ensures               
                - returns a matrix M such that:
                    - M.nc() == 1
                    - M.nr() == in_vector_size()
                    - M(i) == the mean of the ith input feature shown to train()
        !*/

        const matrix<scalar_type,0,1,mem_manager_type>& std_devs (
        ) const;
        /*!
            ensures               
                - returns a matrix SD such that:
                    - SD.nc() == 1
                    - SD.nr() == in_vector_size()
                    - SD(i) == the reciprocal of the standard deviation of the ith 
                      input feature shown to train() 
        !*/
 
        const matrix<scalar_type,0,0,mem_manager_type>& pca_matrix (
        ) const;
        /*!
            ensures
                - returns a matrix PCA such that:
                    - PCA.nr() == out_vector_size()
                    - PCA.nc() == in_vector_size()
                    - PCA == the principal component analysis transformation 
                      matrix 
        !*/

        const result_type& operator() (
            const matrix_type& x
        ) const;
        /*!
            requires
                - x.nr() == in_vector_size()
                - x.nc() == 1
            ensures
                - returns a normalized version of x, call it Z, that has the 
                  following properties: 
                    - Z.nr() == out_vector_size()
                    - Z.nc() == 1
                    - the mean of each element of Z is 0 
                    - the variance of each element of Z is 1
                    - Z == pca_matrix()*pointwise_multiply(x-means(), std_devs());
        !*/

        void swap (
            vector_normalizer_pca& item
        );
        /*!
            ensures
                - swaps *this and item
        !*/
    };

    template <
        typename matrix_type
        >
    inline void swap (
        vector_normalizer_pca<matrix_type>& a, 
        vector_normalizer_pca<matrix_type>& b 
    ) { a.swap(b); }   
    /*!
        provides a global swap function
    !*/

    template <
        typename matrix_type,
        >
    void deserialize (
        vector_normalizer_pca<matrix_type>& item, 
        std::istream& in
    );   
    /*!
        provides deserialization support 
    !*/

    template <
        typename matrix_type,
        >
    void serialize (
        const vector_normalizer_pca<matrix_type>& item, 
        std::ostream& out 
    );   
    /*!
        provides serialization support 
    !*/

// ----------------------------------------------------------------------------------------

}

#endif // DLIB_STATISTICs_ABSTRACT_

