multivariate_normal_distribution Derived Type

type, public, extends(multivariate_distribution) :: multivariate_normal_distribution

Defines a multivariate normal (Gaussian) distribution.


Type-Bound Procedures

procedure, public :: get_cholesky_factored_matrix => mvnd_get_cholesky

  • private pure function mvnd_get_cholesky(this) result(rst)

    Gets the lower triangular form of the Cholesky factorization of the covariance matrix of the distribution.

    Arguments

    Type IntentOptional Attributes Name
    class(multivariate_normal_distribution), intent(in) :: this

    The multivariate_normal_distribution object.

    Return Value real(kind=real64), allocatable, dimension(:,:)

    The Cholesky factored matrix.

procedure, public :: get_covariance => mvnd_get_covariance

  • private pure function mvnd_get_covariance(this) result(rst)

    Gets the covariance matrix of the distribution.

    Arguments

    Type IntentOptional Attributes Name
    class(multivariate_normal_distribution), intent(in) :: this

    The multivariate_normal_distribution object.

    Return Value real(kind=real64), allocatable, dimension(:,:)

    The covariance matrix.

procedure, public :: get_means => mvnd_get_means

  • private pure function mvnd_get_means(this) result(rst)

    Gets the mean values of the distribution.

    Arguments

    Type IntentOptional Attributes Name
    class(multivariate_normal_distribution), intent(in) :: this

    The multivariate_normal_distribution object.

    Return Value real(kind=real64), allocatable, dimension(:)

    The mean values.

procedure, public :: initialize => mvnd_init

  • private pure subroutine mvnd_init(this, mu, sigma)

    Initializes the multivariate normal distribution by defining the mean values and covariance matrix.

    Arguments

    Type IntentOptional Attributes Name
    class(multivariate_normal_distribution), intent(inout) :: this

    The multivariate_normal_distribution object.
    real(kind=real64), intent(in), dimension(:) :: mu

    An N-element array containing the mean values.
    real(kind=real64), intent(in), dimension(:,:) :: sigma

    The N-by-N covariance matrix. The PDF exists only if this matrix is positive-definite; therefore, the positive-definite constraint is checked within this routine and enforced. An error is thrown if the supplied matrix is not positive-definite.

procedure, public :: log_pdf => mvnd_log_pdf

  • private pure function mvnd_log_pdf(this, x) result(rst)

    Computes the multivariate-normal log density without an explicit inverse. A triangular solve whitens the residual; normalization uses a log determinant.

    Arguments

    Type IntentOptional Attributes Name
    class(multivariate_normal_distribution), intent(in) :: this

    Initialized distribution with a symmetric positive-definite covariance.
    real(kind=real64), intent(in), dimension(:) :: x

    Evaluation point, the same length as the stored mean vector.

    Return Value real(kind=real64)

    Log density; uninitialized objects or nonfinite points give NaN. An unrepresentably large squared residual gives negative infinity.

procedure, public :: pdf => mvnd_pdf

  • private pure function mvnd_pdf(this, x) result(rst)

    Evaluates the PDF for the multivariate normal distribution.

    Arguments

    Type IntentOptional Attributes Name
    class(multivariate_normal_distribution), intent(in) :: this

    The multivariate_normal_distribution object.
    real(kind=real64), intent(in), dimension(:) :: x

    The values at which to evaluate the function.

    Return Value real(kind=real64)

    The value of the function.

procedure, public :: set_means => mvnd_update_mean

  • private pure subroutine mvnd_update_mean(this, x)

    Updates the mean value array.

    Arguments

    Type IntentOptional Attributes Name
    class(multivariate_normal_distribution), intent(inout) :: this

    The multivariate_normal_distribution object.
    real(kind=real64), intent(in), dimension(:) :: x

    The N-element array of new mean values.