f_lin_mahalanobis_core Function

public pure function f_lin_mahalanobis_core(x, y, cov) result(dist)

Compute Mahalanobis distance between vectors x and y using covariance matrix cov if provided; otherwise estimate covariance from the two-sample dataset formed by x and y. NOTE: check if cov matrix is positive definite.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: x(:)

input vector 1 (features)
real(kind=wp), intent(in) :: y(:)

input vector 2 (features)
real(kind=wp), intent(in), optional :: cov(:,:)

covariance matrix (m,m)

Return Value real(kind=wp)

Mahalanobis distance


Calls

proc~~f_lin_mahalanobis_core~~CallsGraph proc~f_lin_mahalanobis_core f_lin_mahalanobis_core proc~f_sts_cov_core f_sts_cov_core proc~f_lin_mahalanobis_core->proc~f_sts_cov_core proc~s_utl_cholesky_solve s_utl_cholesky_solve proc~f_lin_mahalanobis_core->proc~s_utl_cholesky_solve proc~f_sts_mean_core f_sts_mean_core proc~f_sts_cov_core->proc~f_sts_mean_core chol chol proc~s_utl_cholesky_solve->chol

Called by

proc~~f_lin_mahalanobis_core~~CalledByGraph proc~f_lin_mahalanobis_core f_lin_mahalanobis_core proc~f_lin_mahalanobis f_lin_mahalanobis proc~f_lin_mahalanobis->proc~f_lin_mahalanobis_core proc~s_nlp_hclust_core s_nlp_hclust_core proc~s_nlp_hclust_core->proc~f_lin_mahalanobis_core proc~s_nlp_kmeans_core s_nlp_kmeans_core proc~s_nlp_kmeans_core->proc~f_lin_mahalanobis_core interface~fsml_mahalanobis fsml_mahalanobis interface~fsml_mahalanobis->proc~f_lin_mahalanobis proc~s_nlp_hclust s_nlp_hclust proc~s_nlp_hclust->proc~s_nlp_hclust_core proc~s_nlp_hkmeans_core s_nlp_hkmeans_core proc~s_nlp_hkmeans_core->proc~s_nlp_hclust_core proc~s_nlp_hkmeans_core->proc~s_nlp_kmeans_core proc~s_nlp_kmeans s_nlp_kmeans proc~s_nlp_kmeans->proc~s_nlp_kmeans_core interface~fsml_hclust fsml_hclust interface~fsml_hclust->proc~s_nlp_hclust interface~fsml_kmeans fsml_kmeans interface~fsml_kmeans->proc~s_nlp_kmeans proc~s_nlp_hkmeans s_nlp_hkmeans proc~s_nlp_hkmeans->proc~s_nlp_hkmeans_core interface~fsml_hkmeans fsml_hkmeans interface~fsml_hkmeans->proc~s_nlp_hkmeans

Source Code

pure function f_lin_mahalanobis_core(x, y, cov) result(dist)

! ==== Description
!! Compute Mahalanobis distance between vectors x and y
!! using covariance matrix cov if provided; otherwise
!! estimate covariance from the two-sample dataset formed by x and y.
!! NOTE: check if cov matrix is positive definite.

! ==== Declarations
  real(wp), intent(in)           :: x(:)       !! input vector 1 (features)
  real(wp), intent(in)           :: y(:)       !! input vector 2 (features)
  real(wp), intent(in), optional :: cov(:,:)   !! covariance matrix (m,m)
  real(wp)                       :: dist       !! Mahalanobis distance
  real(wp), allocatable          :: cov_w(:,:) !! covariance matrix
  real(wp), allocatable          :: diff(:)    !! difference vector
  real(wp), allocatable          :: z(:)       !! solution vector
  real(wp), allocatable          :: xy(:,:)    !! 2-sample data matrix
  integer(i4)                    :: m          !! number of features
  integer(i4)                    :: i, j

! ==== Instructions

! ---- prepare data

  ! get dims and allocate
  m = size(x)
  allocate(diff(m))
  allocate(z(m))
  allocate(xy(2,m))

  ! create 2-sample dataset with x and y as rows
  xy(1,:) = x
  xy(2,:) = y

  ! compute difference vector
  diff = x - y

! ---- use cholesky-based solver and calculate distance

  ! get final cov matrix and use solver
  if (present(cov)) then
     ! use passed covariance matrix directly (m x m)
     z = s_utl_cholesky_solve(cov, diff, m)
  else
     ! estimate covariance matrix (m x m) from xy rows (samples)
     allocate(cov_w(m,m))
     do i = 1, m
        do j = 1, m
           cov_w(i,j) = f_sts_cov_core(xy(:,i), xy(:,j), ddf=1.0_wp)
        enddo
     enddo
     z = s_utl_cholesky_solve(cov_w, diff, m)
  endif

  ! get distance
  dist = sqrt( max(0.0_wp, dot_product(diff, z)) )

! ---- finish

  ! deallocate where needed
  deallocate(diff)
  deallocate(z)
  deallocate(xy)
  if (.not. present(cov)) deallocate(cov_w)

end function f_lin_mahalanobis_core