Cartesian3dIdentityMatrixArray

class named_arrays.Cartesian3dIdentityMatrixArray

Bases: AbstractImplicitCartesian3dMatrixArray, Cartesian2dIdentityMatrixArray

Attributes

axes	A tuple of str representing the names of each dimension of this array.
axes_flattened	Combine axes into a single str.
broadcasted	if this array has multiple components, broadcast them against each other.
cartesian_nd	Convert all cartesian vectors making up the matrix to instances of AbstractCartesianNdVectorArray
column_prototype	Return a vector representing a column of the matrix with each component zeroed.
components	The vector components of this array expressed as a dict, where the keys are the names of the component.
determinant	The determinant of this matrix
entries	The scalar entries that compose this object.
explicit	Converts this array to an instance of named_arrays.AbstractExplicitArray.
indices	Compute the index of each element of this array.
inverse	The inverse of this matrix
is_consistent	Check if all the rows of the matrix have the same abstract type.
is_square	Check if this matrix has the same number of rows and columns.
length	L2-norm of this array.
matrix	Cast this vector into its matrix representation.
matrix_transpose	Swap the rows and columns of this matrix.
ndim	Number of dimensions of the array.
normalized	Return a normalized copy of this vector, where length is unity.
prototype_vector	Return vector of same type with all components zeroed.
row_prototype	Return a vector of the same type as each row of the matrix.
rows	Rows of the matrix, same as components
shape	The number of elements along each axis of the array.
size	Total number of elements in the array.
type_abstract	The named_arrays.AbstractArray type corresponding to this array.
type_explicit	The named_arrays.AbstractExplicitArray type corresponding to this array.
type_matrix	The corresponding named_arrays.AbstractMatrixArray class
type_vector	The corresponding named_arrays.AbstractVectorArray class
value	Returns a new array with its units removed, if they exist.
x	The x row of the matrix.
xy	Only the \(x\) and \(y\) components of this vector.
y	The y row of the matrix.
z	The z row of the matrix.

Methods

__init__()
add_axes(axes)	Add new singleton axes to this array.
all([axis, where])	Return True if all of the elements along the given axes are True.
any([axis, where])	Return True if any of the elements along the given axes are True.
astype(dtype[, order, casting, subok, copy])	Copy of the array cast to a specific data type.
broadcast_to(shape[, append])	A new view of this array with the specified shape.
cell_centers([axis, random])	Convert an array from cell vertices to cell centers.
combine_axes([axes, axis_new])	Combine some of the axes of the array into a single new axis.
copy()	Create a deep copy of this array.
copy_shallow()	Create a shallow copy of this array.
cross(other)	Compute the vector product \(\mathbf{a} \times \mathbf{b}\)
index(value[, axis])
index_secant(value[, axis])
interp_linear(item)	Linearly interpolate this array to find its value at the given fractional index.
max([axis, initial, where])	The maximum value of this array along the given axes.
mean([axis, where])	The mean value of this array along the given axes.
median([axis])	The median value of this array along the given axes.
min([axis, initial, where])	The minimum value of this array along the given axes.
ndindex([axis_ignored])	An iterator that yields the index of each element of this array.
percentile(q[, axis, out, overwrite_input, ...])	The requested percentile of this array along the given axes.
power(exponent)	Compute this matrix raised to the power of a given exponent
prototype_matrix([row])
ptp([axis])	The peak-to-peak value of this array along the given axes.
replace(**changes)	A method version of dataclasses.replace() for named arrays.
reshape(shape)	Reorganize this array into a new shape.
rms([axis, where])	The root-mean-square of this array along the given axes.
solid_angle_cell([axis])	Compute the solid angle of each cell formed by interpreting this array as a logically-rectangular 2D grid of vertices.
std([axis, where])	The standard deviation of this array along the given axes.
sum([axis, where])	The sum of each element of this array along the given axes.
take_along_axis(indices, axis)	Take values from this array by matching indices along axis.
to(unit[, equivalencies, copy])	Convert this array to a new unit.
to_string([prefix, multiline])	Convert this array instance to a string representation.
to_string_array([format_value, format_unit, ...])	Convert to an array of strings where each string has an appropriately-formatted unit attached to the value.
to_value(unit[, equivalencies])	The numerical value of this array, possibly in a different unit.
transpose([axes])	Reorder the axes of this array to the given sequence.
var([axis, where])	The variance of this array along the given axes.
vmr([axis, where])	The variance-to-mean ratio of this array along the given axes.
volume_cell(axis)	Computes the n-dimensional volume of each cell formed by interpreting this array as a logically-rectangular grid of vertices.

Inheritance Diagram

add_axes(axes)

Add new singleton axes to this array.

Parameters:

• axes (str | Sequence[str]) – Either a single axis name or a sequence of axis names add to this array.

• self (Self)

Return type:

AbstractExplicitVectorArray

See also

named_arrays.add_axes()

A functional version of this method.

all(axis=None, where=<no value>)

Return True if all of the elements along the given axes are True.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

See also

numpy.all()

A functional version of this method.

any(axis=None, where=<no value>)

Return True if any of the elements along the given axes are True.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

See also

numpy.any()

A functional version of this method.

astype(dtype, order='K', casting='unsafe', subok=True, copy=True)

Copy of the array cast to a specific data type.

Equivalent to numpy.ndarray.astype().

Parameters:

• self (Self)

• dtype (str | dtype | Type | dict[str, str | dtype | Type])

• order (str)

• subok (bool)

• copy (bool)

Return type:

Self

broadcast_to(shape, append=False)

A new view of this array with the specified shape.

Parameters:

• shape (dict[str, int]) – The shape of the new array.

• append (bool) – If True, shape will be appended to the current shape of this array before broadcasting.

• self (Self)

Return type:

Self

See also

named_arrays.broadcast_to()

A functional version of this method.

cell_centers(axis=None, random=False)

Convert an array from cell vertices to cell centers.

Parameters:

• axis (None | str | Sequence[str]) – The axes of the array to average over.

• random (bool) – If true, select a random point within each cell instead of the geometric center.

Return type:

AbstractExplicitArray

combine_axes(axes=None, axis_new=None)

Combine some of the axes of the array into a single new axis.

Parameters:

• axes (Sequence[str]) – The axes to combine into a new axis

• axis_new (str) – The name of the new axis

• self (Self)

Return type:

Array with the specified axes combined

copy()

Create a deep copy of this array.

Parameters:

self (Self)

Return type:

Self

copy_shallow()

Create a shallow copy of this array.

Parameters:

self (Self)

Return type:

Self

cross(other)

Compute the vector product \(\mathbf{a} \times \mathbf{b}\)

Parameters:

other (AbstractCartesian3dVectorArray) – the right-hand operand of the cross product operation

Return type:

Cartesian3dVectorArray

index(value, axis=None)

Parameters:

• self (Self)

• value (Self)

• axis (None | str | Sequence[str])

Return type:

dict[str, Self]

index_secant(value, axis=None)

Parameters:

• self (Self)

• value (Self)

• axis (None | str | Sequence[str])

Return type:

dict[str, Self]

interp_linear(item)

Linearly interpolate this array to find its value at the given fractional index.

Parameters:

• item (dict[str, Self]) – A fractional index at which to evaluate the array.

• self (Self)

Return type:

Self

max(axis=None, initial=<no value>, where=<no value>)

The maximum value of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• initial (ArrayLike) – The initial value of the minimum, required if where provided.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

See also

numpy.max()

A functional version of this method.

mean(axis=None, where=<no value>)

The mean value of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

See also

numpy.mean()

A functional version of this method.

median(axis=None)

The median value of this array along the given axes.

Parameters:

axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

See also

numpy.median()

A functional version of this method.

min(axis=None, initial=<no value>, where=<no value>)

The minimum value of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• initial (ArrayLike) – The initial value of the minimum, required if where provided.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

See also

numpy.min()

A functional version of this method.

ndindex(axis_ignored=None)

An iterator that yields the index of each element of this array.

Parameters:

• axis_ignored (None | str | Sequence[str]) – The of the array to ignore when generating the iterator.

• self (Self)

Return type:

Iterator[dict[str, int]]

See also

named_arrays.ndindex()

A functional version of this method.

percentile(q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=False)

The requested percentile of this array along the given axes.

Parameters:

• q (int | float | Quantity | Self) – The percentile to compute.

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• out (None | Self) – An optional output array in which to place the result.

• overwrite_input (bool) – Whether to overwrite the input array.

• method (str) – How to interpolate the result.

• keepdims (bool) – A boolean flag indicating whether to keep the reduced dimensions.

• self (Self)

See also

numpy.percentile()

A functional version of this method.

power(exponent)

Compute this matrix raised to the power of a given exponent

Parameters:

exponent (float | AbstractScalar) – The power to raise this matrix to.

Return type:

AbstractCartesian2dMatrixArray

prototype_matrix(row=None)

Parameters:

row (AbstractVectorArray)

ptp(axis=None)

The peak-to-peak value of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• self (Self)

Return type:

Self

See also

numpy.ptp()

A functional version of this method.

replace(**changes)

A method version of dataclasses.replace() for named arrays.

Parameters:

changes – The fields of the dataclass to be overwritten

Return type:

Self

reshape(shape)

Reorganize this array into a new shape.

Parameters:

• shape (dict[str, int]) – The new shape of the array, must be compatible with this array.

• self (Self)

Return type:

Self

rms(axis=None, where=<no value>)

The root-mean-square of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

solid_angle_cell(axis=None)

Compute the solid angle of each cell formed by interpreting this array as a logically-rectangular 2D grid of vertices.

Note that this method is usually only used for sorted arrays

Parameters:

axis (None | tuple[str, str]) – The two axes defining the logically-rectangular 2D grid. If None (the default), axes is used and must have only two elements.

Return type:

AbstractScalar

Notes

The solid angle \(\Omega\) of a triangle formed by the vertices \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) is given by Eriksson [1990] as

\[\tan \left( \frac{1}{2} \Omega \right) = \frac{\vec{a} \cdot (\vec{b} \times \vec{c})} {a b c + (\vec{a} \cdot \vec{b}) c + (\vec{a} \cdot \vec{c}) b + (\vec{b} \cdot \vec{c}) a}.\]

Each rectangular cell is decomposed into two triangles and then the solid angle of each triangle is computed.

std(axis=None, where=<no value>)

The standard deviation of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

See also

numpy.std()

A functional version of this method.

sum(axis=None, where=<no value>)

The sum of each element of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

See also

numpy.sum()

A functional version of this method.

take_along_axis(indices, axis)

Take values from this array by matching indices along axis.

Parameters:

• indices (AbstractArray) – The integer indices to take along axis.

• axis (str) – The axis of this array along which the values are taken.

• self (Self)

Return type:

Self

See also

named_arrays.take_along_axis()

A functional version of this method.

to(unit, equivalencies=[], copy=True)

Convert this array to a new unit.

Equivalent to astropy.units.Quantity.to().

Parameters:

• unit (UnitBase | dict[str, None | UnitBase]) – New unit of the returned array

• equivalencies (None | list[tuple[Unit, Unit]]) – A list of equivalence pairs to try if the units are not directly convertible.

• copy (bool) – Boolean flag controlling whether to copy the array.

• self (Self)

Return type:

AbstractExplicitVectorArray

to_string(prefix=None, multiline=None)

Convert this array instance to a string representation.

Parameters:

• prefix (None | str) – the length of this string is used to align the output

• multiline (None | bool) – flag which controls if the output should be spread over multiple lines.

Return type:

array represented as a str

to_string_array(format_value='%.2f', format_unit='latex_inline', pad_unit='$\\,$')

Convert to an array of strings where each string has an appropriately-formatted unit attached to the value.

Parameters:

• format_value (str) – The string used to format the numeric value of each element.

• format_unit (str) – The string used to format the units of each element.

• pad_unit (str) – The string used to add horizontal space between the value and unit.

Return type:

AbstractExplicitVectorArray

to_value(unit, equivalencies=[])

The numerical value of this array, possibly in a different unit.

Equivalent to astropy.units.Quantity.to_value().

Parameters:

• unit (UnitBase | dict[str, None | UnitBase]) – New unit of the returned array

• equivalencies (None | list[tuple[Unit, Unit]]) – A list of equivalence pairs to try if the units are not directly convertible.

• self (Self)

Return type:

AbstractExplicitVectorArray

transpose(axes=None)

Reorder the axes of this array to the given sequence.

Parameters:

• axes (None | Sequence[str]) – The new axis ordering of this array.

• self (Self)

Return type:

Self

See also

numpy.transpose()

The numpy version of this method.

var(axis=None, where=<no value>)

The variance of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• where (Self) – An optional mask which selects which elements to be considered.

• self (Self)

Return type:

Self

See also

numpy.var()

A functional version of this method.

vmr(axis=None, where=<no value>)

The variance-to-mean ratio of this array along the given axes.

Parameters:

• axis (None | str | Sequence[str]) – The logical axis or axes along which the operation is computed.

• where (Self) – An optional mask which selects which elements to be considered.

volume_cell(axis)

Computes the n-dimensional volume of each cell formed by interpreting this array as a logically-rectangular grid of vertices.

Note that this method is usually only used for sorted arrays.

If self is a scalar, this method computes the length of each edge, and is equivalent to numpy.diff(). If self is a 2d vector, this method computes the area of each quadrilateral, and if self is a 3d vector, this method computes the volume of each cuboid.

Parameters:

axis (None | tuple[str, str, str]) – The axis or axes defining the logically-rectangular grid. If self is a physical scalar, there should only be one axis. If self is a physical vector, there should be one axis for each component of the vector.

Return type:

AbstractScalar

property axes: tuple[str, ...]

A tuple of str representing the names of each dimension of this array.

Must have the same length as the number of dimensions of this array.

property axes_flattened: str

Combine axes into a single str.

This is useful for functions like numpy.flatten() which returns an array with only one dimension.

property broadcasted: AbstractExplicitArray

if this array has multiple components, broadcast them against each other.

Equivalent to a.broadcast_to(a.shape).

property cartesian_nd: AbstractCartesianNdMatrixArray

Convert all cartesian vectors making up the matrix to instances of AbstractCartesianNdVectorArray

property column_prototype: AbstractMatrixArray

Return a vector representing a column of the matrix with each component zeroed.

property components: dict[str, AbstractVectorArray]

The vector components of this array expressed as a dict, where the keys are the names of the component.

property determinant: int | float | complex | ndarray | Quantity | AbstractScalar

The determinant of this matrix

property entries: dict[tuple[str, ...], int | float | complex | ndarray | Quantity | AbstractScalar]

The scalar entries that compose this object.

property explicit: Cartesian3dMatrixArray

Converts this array to an instance of named_arrays.AbstractExplicitArray.

property indices: dict[str, ScalarArrayRange]

Compute the index of each element of this array.

See also

named_arrays.indices()

A functional version of this method.

property inverse: AbstractMatrixArray

The inverse of this matrix

property is_consistent: bool

Check if all the rows of the matrix have the same abstract type.

property is_square

Check if this matrix has the same number of rows and columns.

property length: AbstractScalar

L2-norm of this array.

property matrix: AbstractMatrixArray

Cast this vector into its matrix representation.

property matrix_transpose

Swap the rows and columns of this matrix.

This is distinct from numpy.transpose() since this operates on the physical components instead of the logical ones.

property ndim: int

Number of dimensions of the array. Equivalent to numpy.ndarray.ndim.

property normalized: Self

Return a normalized copy of this vector, where length is unity.

property prototype_vector: AbstractExplicitVectorArray

Return vector of same type with all components zeroed.

property row_prototype: AbstractVectorArray

Return a vector of the same type as each row of the matrix.

property rows: dict[str, AbstractVectorArray]

Rows of the matrix, same as components

property shape: dict[str, int]

The number of elements along each axis of the array. Analogous to numpy.ndarray.shape but represented as a dict where the keys are the axis names and the values are the axis sizes.

property size: int

Total number of elements in the array. Equivalent to numpy.ndarray.size

property type_abstract: Type[AbstractCartesian3dMatrixArray]

The named_arrays.AbstractArray type corresponding to this array.

property type_explicit: Type[Cartesian3dMatrixArray]

The named_arrays.AbstractExplicitArray type corresponding to this array.

property type_matrix: Type[Cartesian3dMatrixArray]

The corresponding named_arrays.AbstractMatrixArray class

property type_vector: Type[Cartesian3dVectorArray]

The corresponding named_arrays.AbstractVectorArray class

property value: AbstractExplicitVectorArray

Returns a new array with its units removed, if they exist.

property x: int | float | complex | ndarray | Quantity | AbstractArray

The x row of the matrix.

property xy: Cartesian2dVectorArray

Only the \(x\) and \(y\) components of this vector.

property y: int | float | complex | ndarray | Quantity | AbstractArray

The y row of the matrix.

property z: int | float | complex | ndarray | Quantity | AbstractArray

The z row of the matrix.