distances

covar_anisotropic(X1=None, X2=None, d=None, g=None)

Calculate the separable covariance matrix between the rows of X1 and X2 with lengthscale d and nugget g.

Parameters:

Name	Type	Description	Default
X1	ndarray	First input matrix.	None
X2	ndarray	Second input matrix (optional).	None
d	ndarray	Array of lengthscale parameters.	None
g	float	Nugget parameter.	None

Returns:

Type	Description
ndarray	np.ndarray: Covariance matrix K.

Examples:

>>> import numpy as np
>>> from spotpython.gp.distances import covar_anisotropic
>>> X1 = np.array([[1.0, 2.0], [3.0, 4.0]])
>>> X2 = np.array([[5.0, 6.0], [7.0, 8.0]])
>>> d = np.array([1.0, 1.0])
>>> g = 0.1
>>> K_symm = covar_anisotropic(X1=X1, d=d, g=g)
>>> print(K_symm)
[[1.1        0.36787944]
 [0.36787944 1.1       ]]
>>> K = covar_anisotropic(X1=X1, X2=X2, d=d, g=g)
>>> print(K)
[[0.00012341 0.00033546]
 [0.00033546 0.000911

Source code in spotpython/gp/distances.py

def covar_anisotropic(X1=None, X2=None, d=None, g=None) -> np.ndarray:
    """
    Calculate the separable covariance matrix between the rows of X1 and X2 with lengthscale d and nugget g.

    Args:
        X1 (np.ndarray): First input matrix.
        X2 (np.ndarray): Second input matrix (optional).
        d (np.ndarray): Array of lengthscale parameters.
        g (float): Nugget parameter.

    Returns:
        np.ndarray: Covariance matrix K.

    Examples:
        >>> import numpy as np
        >>> from spotpython.gp.distances import covar_anisotropic
        >>> X1 = np.array([[1.0, 2.0], [3.0, 4.0]])
        >>> X2 = np.array([[5.0, 6.0], [7.0, 8.0]])
        >>> d = np.array([1.0, 1.0])
        >>> g = 0.1
        >>> K_symm = covar_anisotropic(X1=X1, d=d, g=g)
        >>> print(K_symm)
        [[1.1        0.36787944]
         [0.36787944 1.1       ]]
        >>> K = covar_anisotropic(X1=X1, X2=X2, d=d, g=g)
        >>> print(K)
        [[0.00012341 0.00033546]
         [0.00033546 0.000911
    """
    # Convert pandas dataframes to numpy arrays
    X1 = np.asarray(X1)
    if X2 is not None:
        X2 = np.asarray(X2)
    if X1 is None:
        raise ValueError("X1 cannot be None")

    if not isinstance(X1, np.ndarray):
        if X2 is None:
            raise ValueError("X2 cannot be None in this context")
        m = X2.shape[1]
        X1 = np.reshape(X1, (-1, m))
    else:
        m = X1.shape[1]
    n1 = X1.shape[0]

    if len(d) != m:
        raise ValueError("bad d argument")
    if not isinstance(g, float):
        raise ValueError("bad g argument")

    if X2 is None:
        # Calculate K using covar_sep_symm_R
        # K = covar_sep_symm_R(m, X1.flatten(), n1, d, g)
        K = covar_sep_symm(m, X1, n1, d, g)
        return K
    else:
        if X1.shape[1] != X2.shape[1]:
            raise ValueError("col dim mismatch for X1 & X2")

        X2 = np.asarray(X2)
        n2 = X2.shape[0]

        # Calculate K using covar_sep_R
        # K = covar_sep_R(m, X1.flatten(), n1, X2.flatten(), n2, d, g)
        K = covar_sep(m, X1, n1, X2, n2, d, g)
        return K

dist(X1, X2=None)

Calculate the distance matrix between the rows of X1 and X2, or between X1 and itself when X2 is None.

Parameters:

Name	Type	Description	Default
X1	ndarray	First input matrix.	required
X2	ndarray	Second input matrix.	None

Returns:

Type	Description
ndarray	np.ndarray: Distance matrix D.

Examples:

>>> import numpy as np
>>> from spotpython.gp.distances import dist
>>> X1 = np.array([[1.0, 2.0], [3.0, 4.0]])
>>> X2 = np.array([[5.0, 6.0], [7.0, 8.0]])
>>> D_symm = dist(X1)
>>> print(D_symm)
[[ 0.  8.]
 [ 8.  0.]]
>>> D = dist(X1, X2)
>>> print(D)
    [[32.  8.]
    [18.  2.]]

Source code in spotpython/gp/distances.py

def dist(X1, X2=None) -> np.ndarray:
    """
    Calculate the distance matrix between the rows of X1 and X2, or between X1 and itself when X2 is None.

    Args:
        X1 (np.ndarray): First input matrix.
        X2 (np.ndarray, optional): Second input matrix.

    Returns:
        np.ndarray: Distance matrix D.

    Examples:
        >>> import numpy as np
        >>> from spotpython.gp.distances import dist
        >>> X1 = np.array([[1.0, 2.0], [3.0, 4.0]])
        >>> X2 = np.array([[5.0, 6.0], [7.0, 8.0]])
        >>> D_symm = dist(X1)
        >>> print(D_symm)
        [[ 0.  8.]
         [ 8.  0.]]
        >>> D = dist(X1, X2)
        >>> print(D)
            [[32.  8.]
            [18.  2.]]
    """
    # Coerce arguments and extract dimensions
    X1 = np.asarray(X1)
    n1, m = X1.shape

    if X2 is None:
        # Calculate D using distance_symm_R
        D = distance_symm_R(X1.flatten(), n1, m)
        return D
    else:
        # Coerce arguments and extract dimensions
        X2 = np.asarray(X2)
        n2 = X2.shape[0]

        # Check inputs
        if X1.shape[1] != X2.shape[1]:
            raise ValueError("col dim mismatch for X1 & X2")

        # Calculate D using distance_R
        D = distance_R(X1.flatten(), n1, X2.flatten(), n2, m)
        return D

distance(X1, n1, X2, n2, m)

Calculate the distance matrix (D) between X1 and X2.

Parameters:

Name	Type	Description	Default
X1	ndarray	First input matrix of shape (n1, m).	required
n1	int	Number of rows in X1.	required
X2	ndarray	Second input matrix of shape (n2, m).	required
n2	int	Number of rows in X2.	required
m	int	Number of columns (features).	required

Returns:

Type	Description
ndarray	np.ndarray: Distance matrix D of shape (n1, n2).

Examples:

>>> import numpy as np
>>> from spotpython.gp.distances import distance
>>> X1 = np.array([[1.0, 2.0], [3.0, 4.0]])
>>> n1 = 2
>>> X2 = np.array([[5.0, 6.0], [7.0, 8.0]])
>>> n2 = 2
>>> m = 2
>>> D_out = distance(X1, n1, X2, n2, m)
>>> print(D_out)
[[32.  8.]
 [18.  2.]]

Source code in spotpython/gp/distances.py

def distance(X1, n1, X2, n2, m) -> np.ndarray:
    """
    Calculate the distance matrix (D) between X1 and X2.

    Args:
        X1 (np.ndarray): First input matrix of shape (n1, m).
        n1 (int): Number of rows in X1.
        X2 (np.ndarray): Second input matrix of shape (n2, m).
        n2 (int): Number of rows in X2.
        m (int): Number of columns (features).

    Returns:
        np.ndarray: Distance matrix D of shape (n1, n2).

    Examples:
        >>> import numpy as np
        >>> from spotpython.gp.distances import distance
        >>> X1 = np.array([[1.0, 2.0], [3.0, 4.0]])
        >>> n1 = 2
        >>> X2 = np.array([[5.0, 6.0], [7.0, 8.0]])
        >>> n2 = 2
        >>> m = 2
        >>> D_out = distance(X1, n1, X2, n2, m)
        >>> print(D_out)
        [[32.  8.]
         [18.  2.]]
    """
    D = np.zeros((n1, n2))

    for i in range(n1):
        for j in range(n2):
            D[i, j] = 0.0
            for k in range(m):
                D[i, j] += (X1[i, k] - X2[j, k]) ** 2

    return D

distance_R(X1_in, n1_in, X2_in, n2_in, m_in)

Calculate the distance matrix between the rows of X1 and X2.

Parameters:

Name	Type	Description	Default
X1_in	ndarray	First input matrix of shape (n1, m).	required
n1_in	int	Number of rows in X1.	required
X2_in	ndarray	Second input matrix of shape (n2, m).	required
n2_in	int	Number of rows in X2.	required
m_in	int	Number of columns (features).	required

Returns:

Type	Description
ndarray	np.ndarray: Distance matrix D of shape (n1, n2).

Examples:

>>> import numpy as np
>>> from spotpython.gp.distances import distance_R
>>> X1_in = np.array([1.0, 2.0, 3.0, 4.0])
>>> n1_in = 2
>>> X2_in = np.array([5.0, 6.0, 7.0, 8.0])
>>> n2_in = 2
>>> m_in = 2
>>> D_out = distance_R(X1_in, n1_in, X2_in, n2_in, m_in)
>>> print(D_out)
[[32.  8.]
 [18.  2.]]

Source code in spotpython/gp/distances.py

def distance_R(X1_in, n1_in, X2_in, n2_in, m_in) -> np.ndarray:
    """
    Calculate the distance matrix between the rows of X1 and X2.

    Args:
        X1_in (np.ndarray): First input matrix of shape (n1, m).
        n1_in (int): Number of rows in X1.
        X2_in (np.ndarray): Second input matrix of shape (n2, m).
        n2_in (int): Number of rows in X2.
        m_in (int): Number of columns (features).

    Returns:
        np.ndarray: Distance matrix D of shape (n1, n2).

    Examples:
        >>> import numpy as np
        >>> from spotpython.gp.distances import distance_R
        >>> X1_in = np.array([1.0, 2.0, 3.0, 4.0])
        >>> n1_in = 2
        >>> X2_in = np.array([5.0, 6.0, 7.0, 8.0])
        >>> n2_in = 2
        >>> m_in = 2
        >>> D_out = distance_R(X1_in, n1_in, X2_in, n2_in, m_in)
        >>> print(D_out)
        [[32.  8.]
         [18.  2.]]
    """
    # Make matrix bones
    X1 = np.reshape(X1_in, (n1_in, m_in))
    X2 = np.reshape(X2_in, (n2_in, m_in))
    D = distance(X1, n1_in, X2, n2_in, m_in)
    return D

distance_symm_R(X_in, n_in, m_in)

Calculate the distance matrix between the rows of X and itself, with output in the symmetric D_out matrix.

Parameters:

Name	Type	Description	Default
X_in	ndarray	Input matrix of shape (n, m).	required
n_in	int	Number of rows in X.	required
m_in	int	Number of columns (features).	required

Returns:

Type	Description
ndarray	np.ndarray: Symmetric distance matrix D of shape (n, n).

Examples:

>>> import numpy as np
>>> from spotpython.gp.distances import distance_symm_R
>>> X_in = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
>>> n_in = 3
>>> m_in = 2
>>> D_out = distance_symm_R(X_in, n_in, m_in)
>>> print(D_out)
[[ 0.  8. 32.]
 [ 8.  0.  8.]
 [32.  8.  0.]]

Source code in spotpython/gp/distances.py

def distance_symm_R(X_in, n_in, m_in) -> np.ndarray:
    """
    Calculate the distance matrix between the rows of X and itself, with output in the symmetric D_out matrix.

    Args:
        X_in (np.ndarray): Input matrix of shape (n, m).
        n_in (int): Number of rows in X.
        m_in (int): Number of columns (features).

    Returns:
        np.ndarray: Symmetric distance matrix D of shape (n, n).

    Examples:
        >>> import numpy as np
        >>> from spotpython.gp.distances import distance_symm_R
        >>> X_in = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
        >>> n_in = 3
        >>> m_in = 2
        >>> D_out = distance_symm_R(X_in, n_in, m_in)
        >>> print(D_out)
        [[ 0.  8. 32.]
         [ 8.  0.  8.]
         [32.  8.  0.]]
    """
    n = n_in
    m = m_in

    # Make matrix bones
    X = new_matrix_bones(X_in, n, m)
    D = np.zeros((n, n))

    # For each row of X and itself
    for i in range(n):
        D[i][i] = 0.0
        for j in range(i + 1, n):
            D[i][j] = 0.0
            for k in range(m):
                D[i][j] += (X[i][k] - X[j][k]) ** 2
            D[j][i] = D[i][j]

    return D

new_matrix_bones(data, rows, cols)

Create a matrix view of the given data.

Parameters:

Name	Type	Description	Default
data	ndarray	Input data.	required
rows	int	Number of rows.	required
cols	int	Number of columns.	required

Returns:

Type	Description
ndarray	np.ndarray: Matrix view of the input data.

Source code in spotpython/gp/distances.py

def new_matrix_bones(data, rows, cols) -> np.ndarray:
    """
    Create a matrix view of the given data.

    Args:
        data (np.ndarray): Input data.
        rows (int): Number of rows.
        cols (int): Number of columns.

    Returns:
        np.ndarray: Matrix view of the input data.
    """
    return np.reshape(data, (rows, cols))