matrix

dup_matrix(m, M, n1, n2)

Copy the contents of matrix M to matrix m.

Parameters:

Name	Type	Description	Default
m	ndarray	The destination matrix.	required
M	ndarray	The source matrix.	required
n1	int	The number of rows in the matrices.	required
n2	int	The number of columns in the matrices.	required

Returns:

Name	Type	Description
ndarray	ndarray	The updated destination matrix m.

Examples:

>>> M = np.array([[1, 2], [3, 4], [5, 6]])
>>> m = np.zeros((3, 2))
>>> dup_matrix(m, M, 3, 2)
>>> print(m)
[[1. 2.]
 [3. 4.]
 [5. 6.]]

Source code in spotpython/gp/matrix.py

def dup_matrix(m, M, n1, n2) -> np.ndarray:
    """
    Copy the contents of matrix M to matrix m.

    Args:
        m (ndarray): The destination matrix.
        M (ndarray): The source matrix.
        n1 (int): The number of rows in the matrices.
        n2 (int): The number of columns in the matrices.

    Returns:
        ndarray: The updated destination matrix m.

    Examples:
        >>> M = np.array([[1, 2], [3, 4], [5, 6]])
        >>> m = np.zeros((3, 2))
        >>> dup_matrix(m, M, 3, 2)
        >>> print(m)
        [[1. 2.]
         [3. 4.]
         [5. 6.]]
    """
    for i in range(n1):
        for j in range(n2):
            m[i, j] = M[i, j]
    return m

dupv(v, vold, n)

Copies vold to v (assumes v has already been allocated).

Parameters:

Name	Type	Description	Default
v	ndarray	The array to copy to.	required
vold	ndarray	The original array to copy from.	required
n	int	The size of the arrays.	required

Returns:

Name	Type	Description
ndarray	ndarray	The updated array v.

Examples:

>>> v = np.empty(3)
>>> vold = np.array([1.0, 2.0, 3.0])
>>> n = 3
>>> dupv(v, vold, n)
>>> print(v)
[1. 2. 3.]

Source code in spotpython/gp/matrix.py

def dupv(v, vold, n) -> np.ndarray:
    """
    Copies vold to v (assumes v has already been allocated).

    Args:
        v (ndarray): The array to copy to.
        vold (ndarray): The original array to copy from.
        n (int): The size of the arrays.

    Returns:
        ndarray: The updated array v.

    Examples:
        >>> v = np.empty(3)
        >>> vold = np.array([1.0, 2.0, 3.0])
        >>> n = 3
        >>> dupv(v, vold, n)
        >>> print(v)
        [1. 2. 3.]
    """
    for i in range(n):
        v[i] = vold[i]
    return v

new_dup_matrix(M, n1, n2)

Create a new n1 x n2 matrix which is allocated like an n1*n2 array, and copy the contents of n1 x n2 matrix M into it.

Parameters:

Name	Type	Description	Default
M	ndarray	The source matrix.	required
n1	int	The number of rows in the matrix.	required
n2	int	The number of columns in the matrix.	required

Returns:

Name	Type	Description
ndarray	ndarray	The new n1 x n2 matrix with copied contents.

Examples:

>>> M = np.array([[1, 2], [3, 4], [5, 6]])
>>> n1 = 3
>>> n2 = 2
>>> m = new_dup_matrix(M, n1, n2)
>>> print(m)
[[1. 2.]
 [3. 4.]
 [5. 6.]]

Source code in spotpython/gp/matrix.py

def new_dup_matrix(M, n1, n2) -> np.ndarray:
    """
    Create a new n1 x n2 matrix which is allocated like an n1*n2 array,
    and copy the contents of n1 x n2 matrix M into it.

    Args:
        M (ndarray): The source matrix.
        n1 (int): The number of rows in the matrix.
        n2 (int): The number of columns in the matrix.

    Returns:
        ndarray: The new n1 x n2 matrix with copied contents.

    Examples:
        >>> M = np.array([[1, 2], [3, 4], [5, 6]])
        >>> n1 = 3
        >>> n2 = 2
        >>> m = new_dup_matrix(M, n1, n2)
        >>> print(m)
        [[1. 2.]
         [3. 4.]
         [5. 6.]]
    """
    if n1 <= 0 or n2 <= 0:
        return None

    m = new_matrix(n1, n2)
    dup_matrix(m, M, n1, n2)
    return m

new_dup_vector(vold, n)

Allocates a new numpy array of size n and fills it with the contents of vold.

Parameters:

Name	Type	Description	Default
vold	ndarray	The original array to duplicate.	required
n	int	The size of the new array.	required

Returns:

Name	Type	Description
ndarray	ndarray	The new array filled with the contents of vold.

Examples:

>>> vold = np.array([1.0, 2.0, 3.0])
>>> n = 3
>>> v = new_dup_vector(vold, n)
>>> print(v)
[1. 2. 3.]

Source code in spotpython/gp/matrix.py

def new_dup_vector(vold, n) -> np.ndarray:
    """
    Allocates a new numpy array of size n and fills it with the contents of vold.

    Args:
        vold (ndarray): The original array to duplicate.
        n (int): The size of the new array.

    Returns:
        ndarray: The new array filled with the contents of vold.

    Examples:
        >>> vold = np.array([1.0, 2.0, 3.0])
        >>> n = 3
        >>> v = new_dup_vector(vold, n)
        >>> print(v)
        [1. 2. 3.]
    """
    v = np.empty(n)
    v = dupv(v, vold, n)
    return v

new_id_matrix(n)

Create a new n x n identity matrix.

Parameters:

Name	Type	Description	Default
n	int	The size of the identity matrix.	required

Returns:

Name	Type	Description
ndarray	ndarray	The new n x n identity matrix.

Examples:

>>> n = 3
>>> m = new_id_matrix(n)
>>> print(m)
[[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

Source code in spotpython/gp/matrix.py

def new_id_matrix(n) -> np.ndarray:
    """
    Create a new n x n identity matrix.

    Args:
        n (int): The size of the identity matrix.

    Returns:
        ndarray: The new n x n identity matrix.

    Examples:
        >>> n = 3
        >>> m = new_id_matrix(n)
        >>> print(m)
        [[1. 0. 0.]
         [0. 1. 0.]
         [0. 0. 1.]]
    """
    return np.eye(n)

new_matrix(n1, n2)

Create a new n1 x n2 matrix which is allocated like an n1*n2 array, but can be referenced as a 2-d array.

Parameters:

Name	Type	Description	Default
n1	int	The number of rows in the matrix.	required
n2	int	The number of columns in the matrix.	required

Returns:

Name	Type	Description
ndarray	ndarray	The new n1 x n2 matrix.

Examples:

>>> n1 = 3
>>> n2 = 2
>>> m = new_matrix(n1, n2)
>>> print(m)
[[0. 0.]
 [0. 0.]
 [0. 0.]]

Source code in spotpython/gp/matrix.py

def new_matrix(n1, n2) -> np.ndarray:
    """
    Create a new n1 x n2 matrix which is allocated like an n1*n2 array,
    but can be referenced as a 2-d array.

    Args:
        n1 (int): The number of rows in the matrix.
        n2 (int): The number of columns in the matrix.

    Returns:
        ndarray: The new n1 x n2 matrix.

    Examples:
        >>> n1 = 3
        >>> n2 = 2
        >>> m = new_matrix(n1, n2)
        >>> print(m)
        [[0. 0.]
         [0. 0.]
         [0. 0.]]
    """
    if n1 == 0 or n2 == 0:
        return None

    m = np.zeros((n1, n2))
    return m

new_matrix_bones(v, n1, n2)

Create a 2D numpy array (matrix) from a 1D numpy array (vector). The resulting matrix shares the same memory as the input vector.

Parameters:

Name	Type	Description	Default
v	ndarray	The input 1D numpy array (vector).	required
n1	int	The number of rows in the resulting matrix.	required
n2	int	The number of columns in the resulting matrix.	required

Returns:

Name	Type	Description
ndarray	ndarray	The resulting 2D numpy array (matrix).

Examples:

>>> v = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
>>> n1 = 2
>>> n2 = 3
>>> M = new_matrix_bones(v, n1, n2)
>>> print(M)
[[1. 2. 3.]
 [4. 5. 6.]]

Source code in spotpython/gp/matrix.py

def new_matrix_bones(v, n1, n2) -> np.ndarray:
    """
    Create a 2D numpy array (matrix) from a 1D numpy array (vector).
    The resulting matrix shares the same memory as the input vector.

    Args:
        v (ndarray): The input 1D numpy array (vector).
        n1 (int): The number of rows in the resulting matrix.
        n2 (int): The number of columns in the resulting matrix.

    Returns:
        ndarray: The resulting 2D numpy array (matrix).

    Examples:
        >>> v = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
        >>> n1 = 2
        >>> n2 = 3
        >>> M = new_matrix_bones(v, n1, n2)
        >>> print(M)
        [[1. 2. 3.]
         [4. 5. 6.]]
    """
    M = np.empty((n1, n2), dtype=v.dtype)
    M[0] = v[:n2]
    for i in range(1, n1):
        M[i] = v[i * n2 : (i + 1) * n2]
    return M

new_p_submatrix_rows(p, v, nrows, ncols, row_offset)

Create a new matrix from the rows of v, specified by p. Must have ncol(v) == ncol(V) and nrow(V) >= nrows and nrow(v) >= max(p).

Parameters:

Name	Type	Description	Default
p	ndarray	The array of row indices to copy.	required
v	ndarray	The source matrix.	required
nrows	int	The number of rows in the new matrix.	required
ncols	int	The number of columns in the new matrix.	required
row_offset	int	The row offset in the new matrix.	required

Returns:

Name	Type	Description
ndarray	ndarray	The new matrix with specified rows copied from v.

Examples:

>>> p = np.array([0, 2])
>>> v = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> nrows = 2
>>> ncols = 3
>>> row_offset = 1
>>> V = new_p_submatrix_rows(p, v, nrows, ncols, row_offset)
>>> print(V)
[[0. 0. 0.]
 [1. 2. 3.]
 [0. 0. 0.]
 [7. 8. 9.]
 [0. 0. 0.]]

Source code in spotpython/gp/matrix.py

def new_p_submatrix_rows(p, v, nrows, ncols, row_offset) -> np.ndarray:
    """
    Create a new matrix from the rows of v, specified by p.
    Must have ncol(v) == ncol(V) and nrow(V) >= nrows and nrow(v) >= max(p).

    Args:
        p (ndarray): The array of row indices to copy.
        v (ndarray): The source matrix.
        nrows (int): The number of rows in the new matrix.
        ncols (int): The number of columns in the new matrix.
        row_offset (int): The row offset in the new matrix.

    Returns:
        ndarray: The new matrix with specified rows copied from v.

    Examples:
        >>> p = np.array([0, 2])
        >>> v = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
        >>> nrows = 2
        >>> ncols = 3
        >>> row_offset = 1
        >>> V = new_p_submatrix_rows(p, v, nrows, ncols, row_offset)
        >>> print(V)
        [[0. 0. 0.]
         [1. 2. 3.]
         [0. 0. 0.]
         [7. 8. 9.]
         [0. 0. 0.]]
    """
    if nrows + row_offset == 0 or ncols == 0:
        return None

    V = np.zeros((nrows + row_offset, ncols))
    if nrows > 0:
        V = sub_p_matrix_rows(V, p, v, ncols, nrows, row_offset)
    return V

new_vector(n)

Allocates a new numpy array of size n.

Parameters:

Name	Type	Description	Default
n	int	The size of the new array.	required

Returns:

Name	Type	Description
ndarray	ndarray	The new array of size n.

Examples:

>>> n = 3
>>> v = new_vector(n)
>>> print(v)
[0. 0. 0.]

Source code in spotpython/gp/matrix.py

def new_vector(n) -> np.ndarray:
    """
    Allocates a new numpy array of size n.

    Args:
        n (int): The size of the new array.

    Returns:
        ndarray: The new array of size n.

    Examples:
        >>> n = 3
        >>> v = new_vector(n)
        >>> print(v)
        [0. 0. 0.]
    """
    if n == 0:
        return None
    v = np.empty(n)
    return v

sub_p_matrix(V, p, v, nrows, lenp, col_offset)

Copy the columns v[1:n1][p[n2]] to V. Must have nrow(v) == nrow(V) and ncol(V) >= lenp and ncol(v) >= max(p).

Parameters:

Name	Type	Description	Default
V	ndarray	The destination matrix.	required
p	ndarray	The array of column indices to copy.	required
v	ndarray	The source matrix.	required
nrows	int	The number of rows in the matrices.	required
lenp	int	The length of the array p.	required
col_offset	int	The column offset in the destination matrix.	required

Returns:

Name	Type	Description
ndarray	ndarray	The updated destination matrix V.

Examples:

>>> V = np.zeros((3, 5))
>>> p = np.array([0, 2])
>>> v = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> nrows = 3
>>> lenp = 2
>>> col_offset = 1
>>> V = sub_p_matrix(V, p, v, nrows, lenp, col_offset)
>>> print(V)
[[0. 1. 3. 0. 0.]
 [0. 4. 6. 0. 0.]
 [0. 7. 9. 0. 0.]]

Source code in spotpython/gp/matrix.py

def sub_p_matrix(V, p, v, nrows, lenp, col_offset) -> np.ndarray:
    """
    Copy the columns `v[1:n1][p[n2]]` to V.
    Must have nrow(v) == nrow(V) and ncol(V) >= lenp and ncol(v) >= max(p).

    Args:
        V (ndarray): The destination matrix.
        p (ndarray): The array of column indices to copy.
        v (ndarray): The source matrix.
        nrows (int): The number of rows in the matrices.
        lenp (int): The length of the array p.
        col_offset (int): The column offset in the destination matrix.

    Returns:
        ndarray: The updated destination matrix V.

    Examples:
        >>> V = np.zeros((3, 5))
        >>> p = np.array([0, 2])
        >>> v = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
        >>> nrows = 3
        >>> lenp = 2
        >>> col_offset = 1
        >>> V = sub_p_matrix(V, p, v, nrows, lenp, col_offset)
        >>> print(V)
        [[0. 1. 3. 0. 0.]
         [0. 4. 6. 0. 0.]
         [0. 7. 9. 0. 0.]]
    """
    assert V is not None and p is not None and v is not None
    assert nrows > 0 and lenp > 0

    for i in range(nrows):
        for j in range(lenp):
            V[i, j + col_offset] = v[i, p[j]]
    return V

sub_p_matrix_rows(V, p, v, ncols, lenp, row_offset)

Copy the rows v[1:n1][p[n2]] to V. Must have ncol(v) == ncol(V) and nrow(V) >= lenp and nrow(v) >= max(p).

Parameters:

Name	Type	Description	Default
V	ndarray	The destination matrix.	required
p	ndarray	The array of row indices to copy.	required
v	ndarray	The source matrix.	required
ncols	int	The number of columns in the matrices.	required
lenp	int	The length of the array p.	required
row_offset	int	The row offset in the destination matrix.	required

Returns:

Name	Type	Description
ndarray	ndarray	The updated destination matrix V.

Examples:

>>> V = np.zeros((5, 3))
>>> p = np.array([0, 2])
>>> v = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> ncols = 3
>>> lenp = 2
>>> row_offset = 1
>>> sub_p_matrix_rows(V, p, v, ncols, lenp, row_offset)
>>> print(V)
[[0. 0. 0.]
 [1. 2. 3.]
 [0. 0. 0.]
 [7. 8. 9.]
 [0. 0. 0.]]

Source code in spotpython/gp/matrix.py

def sub_p_matrix_rows(V, p, v, ncols, lenp, row_offset) -> np.ndarray:
    """
    Copy the rows `v[1:n1][p[n2]]` to V.
    Must have ncol(v) == ncol(V) and nrow(V) >= lenp and nrow(v) >= max(p).

    Args:
        V (ndarray): The destination matrix.
        p (ndarray): The array of row indices to copy.
        v (ndarray): The source matrix.
        ncols (int): The number of columns in the matrices.
        lenp (int): The length of the array p.
        row_offset (int): The row offset in the destination matrix.

    Returns:
        ndarray: The updated destination matrix V.

    Examples:
        >>> V = np.zeros((5, 3))
        >>> p = np.array([0, 2])
        >>> v = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
        >>> ncols = 3
        >>> lenp = 2
        >>> row_offset = 1
        >>> sub_p_matrix_rows(V, p, v, ncols, lenp, row_offset)
        >>> print(V)
        [[0. 0. 0.]
         [1. 2. 3.]
         [0. 0. 0.]
         [7. 8. 9.]
         [0. 0. 0.]]
    """
    assert V is not None and p is not None and v is not None
    assert ncols > 0 and lenp > 0

    for i in range(lenp):
        V[i + row_offset, :ncols] = v[p[i], :ncols]
    return V