Module org.apache.sis.referencing
Package org.apache.sis.parameter

# Class TensorParameters<E>

Object
TensorParameters<E>

Type Parameters:
  `E` - the type of tensor element values.

All Implemented Interfaces:
  `Serializable`

public class TensorParameters<E> extends Object implements Serializable
Creates parameter groups for tensors (usually matrices). Matrices are handled as a special case of tensors (second-order tensors).

Each group of parameters contains the following elements:

- Parameters (usually mandatory) for the tensor dimensions:
  - number of rows (named `"num_row"` in WKT1 conventions),
  - number of columns (named `"num_col"` in WKT1 conventions),
  - etc. for third-order or higher-order tensors.
- A maximum of `num_row` × `num_col` × … optional parameters for the matrix or tensor element values. Parameter names depend on the formatting convention.

For all matrix or tensor elements, the default value is 1 for elements on the diagonal (where all indices have the same value) and 0 for all other elements. Those default values defines an identity matrix, or (more generally) Kroenecker delta tensor.

Parameters are not an efficient storage format for large tensors. Parameters are used only for small matrices/tensors to be specified in coordinate operations or processing libraries. In particular, those parameters integrate well in Well Known Text (WKT) format. For a more efficient matrix storage, see the matrix package.

## Formatting

In the particular case of a tensor of rank 2 (i.e. a matrix), the parameters are typically formatted as below. Note that in the EPSG convention, the matrix is implicitly affine and of dimension 3×3.

Well Known Text (WKT) formats for matrix parameters
Using EPSG:9624 names and identifiers | Using OGC names
--- | ---
      Parameter["A0", <value>, Id["EPSG", 8623]],
      Parameter["A1", <value>, Id["EPSG", 8624]],
      Parameter["A2", <value>, Id["EPSG", 8625]],
      Parameter["B0", <value>, Id["EPSG", 8639]],
      Parameter["B1", <value>, Id["EPSG", 8640]],
      Parameter["B2", <value>, Id["EPSG", 8641]]
Note: the EPSG database also contains A3, A4, A5, A6, A7, A8 and B3 parameters, but they are for polynomial transformations, not for affine transformations. |
      Parameter["num_row", 3],
      Parameter["num_col", 3],
      Parameter["elt_0_0", <value>],
      Parameter["elt_0_1", <value>],
      ...
      Parameter["elt_0_<num_col-1>", <value>],
      Parameter["elt_1_0", <value>],
      Parameter["elt_1_1", <value>],
      ...
      Parameter["elt_<num_row-1>_<num_col-1>", <value>]

Those groups are extensible, i.e. the number of `"elt_row_col"` parameters depends on the `"num_row"` and `"num_col"` parameter values. For this reason, the descriptor of matrix or tensor parameters is not immutable.

## Usage examples

For creating a new group of parameters for a matrix using the `WKT1` naming conventions, one can use the following code:

    Map<String,?> properties = Map.of(ParameterValueGroup.NAME_KEY, "Affine");
    ParameterValueGroup p = TensorParameters.WKT1.createValueGroup(properties);

For setting the elements of a few values, then create a matrix from the parameter values:

    p.parameter("elt_0_0").setValue(4);    // "A0" also accepted as a synonymous of "elt_0_0".
    p.parameter("elt_1_1").setValue(6);    // "B1" also accepted as a synonymous of "elt_1_1".
    Matrix m = TensorParameters.WKT1.toMatrix(p);

Since:
  0.4
See Also:
  - `Matrices`
  - Serialized Form

- ## Field Summary

  Fields
  Modifier and Type
  Field
  Description
  `static final TensorParameters<Double>`
  `ALPHANUM`
  Parses and creates matrix parameters with alphanumeric names.
  `protected final String`
  `prefix`
  The prefix of parameter names for tensor elements.
  `protected final String`
  `separator`
  The separator between row and column in parameter names for tensor elements.
  `static final TensorParameters<Double>`
  `WKT1`
  Parses and creates matrix parameters with names matching the Well Known Text version 1 (WKT 1) convention.

- ## Constructor Summary

  Constructors
  Constructor
  Description
  `TensorParameters(Class<E> elementType, String prefix, String separator, ParameterDescriptor<Integer>... dimensions)`
  Constructs a descriptors provider.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `protected ParameterDescriptor<E>`
  `createElementDescriptor(int[] indices)`
  Creates a new parameter descriptor for a matrix or tensor element at the given indices.
  `ParameterValueGroup`
  `createValueGroup(Map<String,?> properties)`
  Creates a new instance of parameter group with default values of 1 on the diagonal, and 0 everywhere else.
  `ParameterValueGroup`
  `createValueGroup(Map<String,?> properties, Matrix matrix)`
  Creates a new instance of parameter group initialized to the given matrix.
  `boolean`
  `equals(Object other)`
  Compares this object with the given object for equality.
  `ParameterDescriptor<?>[]`
  `getAllDescriptors(int... actualSize)`
  Returns all parameters in this group for a tensor of the specified dimensions.
  `protected E`
  `getDefaultValue(int[] indices)`
  Returns the default value for the parameter descriptor at the given indices.
  `final ParameterDescriptor<Integer>`
  `getDimensionDescriptor(int i)`
  Returns the parameter descriptor for the dimension at the given index.
  `final ParameterDescriptor<E>`
  `getElementDescriptor(int... indices)`
  Returns the parameter descriptor for a matrix or tensor element at the given indices.
  `final Class<E>`
  `getElementType()`
  Returns the type of tensor element values.
  `int`
  `hashCode()`
  Returns a hash code value for this object.
  `protected String`
  `indicesToName(int[] indices)`
  Returns the parameter descriptor name of a matrix or tensor element at the given indices.
  `protected int[]`
  `nameToIndices(String name)`
  Returns the indices of matrix element for the given parameter name, or `null` if none.
  `final int`
  `rank()`
  Returns the rank of the tensor objects for which this instance will create parameters.
  `Matrix`
  `toMatrix(ParameterValueGroup parameters)`
  Constructs a matrix from a group of parameters.

  ### Methods inherited from class Object

  `clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait`

- ## Field Details

  - ### ALPHANUM

    public static final TensorParameters<Double> ALPHANUM
    Parses and creates matrix parameters with alphanumeric names. Names are made of a letter indicating the row (first row is `"A"`), followed by a digit indicating the column index (first column is `"0"`). Aliases are the names as they were defined in version 1 of Well Known Text (WKT) format.

    Parameter names for a 3×3 matrix
    Primary name | Alias
    --- | ---
           ┌            ┐
           │ A0  A1  A2 │
           │ B0  B1  B2 │
           │ C0  C1  C2 │
           └            ┘
           ┌                             ┐
           │ elt_0_0   elt_0_1   elt_0_2 │
           │ elt_1_0   elt_1_1   elt_1_2 │
           │ elt_2_0   elt_2_1   elt_2_2 │
           └                             ┘

    #### Relationship with EPSG

    The above-cited group of parameters are close, but not identical, to the definitions provided by the "Affine parametric transformation" (EPSG:9624) operation method. The differences are:
    - EPSG:9624 is for matrices of size 3×3 and does not provide any way to specify the matrix size. This `ALPHANUM` convention extends the definition to matrices of arbitrary size and accepts `"num_row"` and `"num_col"` as optional parameters.
    - EPSG:9624 is restricted to affine matrices and consequently define parameters only for the two first rows. This class accepts also parameters for the last row (namely `"C0"`, `"C1"` and `"C2"` in a 3×3 matrices).
    Because of the above-cited extensions, this `TensorParameters` constant cannot be named `EPSG`.
    Since:
      0.6

  - ### WKT1

    public static final TensorParameters<Double> WKT1
    Parses and creates matrix parameters with names matching the Well Known Text version 1 (WKT 1) convention.
    - First parameter is `"num_row"`.
    - Second parameter is `"num_col"`.
    - All other parameters are of the form `"elt_`row`_`col`"`. Those parameters have alias of the form `"A0"`, `"A1"`, etc. where the letter indicates the row (first row is `"A"`) and the digit is the column index (first column is `"0"`).

    #### Example

    `"elt_1_2"` is the element name for the value at row 1 and column 2. Its alias is `"B2"`, which is the EPSG name for the same parameter.

  - ### prefix

    protected final String prefix
    The prefix of parameter names for tensor elements. This is `"elt_"` in WKT 1.

  - ### separator

    protected final String separator
    The separator between row and column in parameter names for tensor elements. This is `"_"` in WKT 1.

- ## Constructor Details

  - ### TensorParameters

    @SafeVarargs public TensorParameters(Class<E> elementType, String prefix, String separator, ParameterDescriptor<Integer>... dimensions)
    Constructs a descriptors provider.
    Parameters:
      `elementType` - the type of tensor element values.
      `prefix` - the prefix to insert in front of parameter name for each tensor elements.
      `separator` - the separator between dimension (row, column, …) indices in parameter names.
      `dimensions` - the parameter for the size of each dimension, usually in an array of length 2. Length may be different if the caller wants to generalize usage of this class to tensors.

- ## Method Details

  - ### getElementType

    public final Class<E> getElementType()
    Returns the type of tensor element values.
    Returns:
      the type of tensor element values.

  - ### rank

    public final int rank()
    Returns the rank of the tensor objects for which this instance will create parameters. The rank determines the type of objects represented by the parameters:

    Tensor types implied by rank
    Rank | Type | Used with
    --- | --- | ---
    0 | scalar |
    1 | vector |
    2 | matrix | Affine parametric transformation
    k | rank k tensor

    Returns:
      the rank of the tensors for which to create parameters.

  - ### getDimensionDescriptor

    public final ParameterDescriptor<Integer> getDimensionDescriptor(int i)
    Returns the parameter descriptor for the dimension at the given index.
    Parameters:
      `i` - the dimension index, from 0 inclusive to `rank()` exclusive.
    Returns:
      the parameter descriptor for the dimension at the given index.
    See Also:
      - `getElementDescriptor(int...)`
      - `getAllDescriptors(int...)`

  - ### getElementDescriptor

    public final ParameterDescriptor<E> getElementDescriptor(int... indices)
    Returns the parameter descriptor for a matrix or tensor element at the given indices. The length of the given `indices` array shall be equal to the rank. That length is usually 2, where `indices[0]` is the row index and `indices[1]` is the column index.
    Parameters:
      `indices` - the indices of the tensor element for which to get the descriptor.
    Returns:
      the parameter descriptor for the given tensor element.
    Throws:
      `IllegalArgumentException` - if the given array does not have the expected length or have illegal value.
    See Also:
      - `getDimensionDescriptor(int)`
      - `getAllDescriptors(int...)`

  - ### createElementDescriptor

    protected ParameterDescriptor<E> createElementDescriptor(int[] indices) throws IllegalArgumentException
    Creates a new parameter descriptor for a matrix or tensor element at the given indices. This method is invoked by `getElementDescriptor(int[])` when a new descriptor needs to be created.

    #### Default implementation

    The default implementation converts the given indices to a parameter name by invoking the `indicesToName(int[])` method, then creates a descriptor for an optional parameter of that name. The default value is given by `getDefaultValue(int[])`.

    #### Subclassing

    Subclasses can override this method if they want more control on descriptor properties like identification information, aliases or value domain.
    Parameters:
      `indices` - the indices of the tensor element for which to create a parameter.
    Returns:
      the parameter descriptor for the given tensor element.
    Throws:
      `IllegalArgumentException` - if the given array does not have the expected length or have illegal value.
    See Also:
      - `indicesToName(int[])`
      - `getDefaultValue(int[])`

  - ### indicesToName

    protected String indicesToName(int[] indices) throws IllegalArgumentException
    Returns the parameter descriptor name of a matrix or tensor element at the given indices. The returned name shall be parsable by the `nameToIndices(String)` method.

    #### Default implementation

    The default implementation requires an `indices` array having a length equals to the rank. That length is usually 2, where `indices[0]` is the row index and `indices[1]` is the column index. Then this method builds a name with the “`prefix` + row + `separator` + column + …” pattern (e.g. `"elt_0_0"`).

    #### Subclassing

    If a subclass overrides this method for creating different names, then that subclass shall also override `nameToIndices(String)` for parsing those names.
    Parameters:
      `indices` - the indices of the tensor element for which to create a parameter name.
    Returns:
      the parameter descriptor name for the tensor element at the given indices.
    Throws:
      `IllegalArgumentException` - if the given array does not have the expected length or have illegal value.

  - ### nameToIndices

    protected int[] nameToIndices(String name) throws IllegalArgumentException
    Returns the indices of matrix element for the given parameter name, or `null` if none. This method is the converse of `indicesToName(int[])`.

    #### Default implementation

    The default implementation expects a name matching the “`prefix` + row + `separator` + column + …” pattern and returns an array containing the row, column and other indices, in that order.
    Parameters:
      `name` - the parameter name to parse.
    Returns:
      indices of the tensor element of the given name, or `null` if the name is not recognized.
    Throws:
      `IllegalArgumentException` - if the name has been recognized but an error occurred while parsing it (e.g. an `NumberFormatException`, which is an `IllegalArgumentException` subclass).

  - ### getDefaultValue

    protected E getDefaultValue(int[] indices)
    Returns the default value for the parameter descriptor at the given indices. The default implementation returns 1 if all indices are equals, or 0 otherwise.
    Parameters:
      `indices` - the indices of the tensor element for which to get the default value.
    Returns:
      the default value for the tensor element at the given indices, or `null` if none.
    Since:
      0.6
    See Also:
      - `DefaultParameterDescriptor​.getDefaultValue()`

  - ### getAllDescriptors

    public ParameterDescriptor<?>[] getAllDescriptors(int... actualSize)
    Returns all parameters in this group for a tensor of the specified dimensions. The returned array contains all descriptors returned by `getDimensionDescriptor(int)` and `getElementDescriptor(int...)`.
    Parameters:
      `actualSize` - the matrix (or tensor) dimensions for which to get the parameters.
    Returns:
      the tensor parameters, including all elements.
    Since:
      0.6
    See Also:
      - `getDimensionDescriptor(int)`
      - `getElementDescriptor(int...)`

  - ### createValueGroup

    public ParameterValueGroup createValueGroup(Map<String,?> properties)
    Creates a new instance of parameter group with default values of 1 on the diagonal, and 0 everywhere else. The returned parameter group is extensible, i.e. the number of elements will depend upon the value associated to the parameters that define the matrix (or tensor) dimension.

    The properties map is given unchanged to the identified object constructor. The following table is a reminder of main (not all) properties:

    Recognized properties (non exhaustive list)
    Property name | Value type | Returned by
    --- | --- | ---
    "name" | `ReferenceIdentifier` or `String` | `AbstractIdentifiedObject.getName()`
    "alias" | `GenericName` or `CharSequence` (optionally as array) | `AbstractIdentifiedObject.getAlias()`
    "identifiers" | `ReferenceIdentifier` (optionally as array) | `AbstractIdentifiedObject.getIdentifiers()`
    "remarks" | `InternationalString` or `String` | `AbstractIdentifiedObject.getRemarks()`

    Parameters:
      `properties` - the properties to be given to the identified object.
    Returns:
      a new parameter group initialized to the default values.

  - ### createValueGroup

    public ParameterValueGroup createValueGroup(Map<String,?> properties, Matrix matrix)
    Creates a new instance of parameter group initialized to the given matrix. This operation is allowed only for tensors of rank 2.
    Parameters:
      `properties` - the properties to be given to the identified object.
      `matrix` - the matrix to copy in the new parameter group.
    Returns:
      a new parameter group initialized to the given matrix.
    See Also:
      - `toMatrix(ParameterValueGroup)`

  - ### toMatrix

    public Matrix toMatrix(ParameterValueGroup parameters) throws InvalidParameterNameException
    Constructs a matrix from a group of parameters. This operation is allowed only for tensors of rank 2.
    Parameters:
      `parameters` - the group of parameters.
    Returns:
      a matrix constructed from the specified group of parameters.
    Throws:
      `InvalidParameterNameException` - if a parameter name was not recognized.
    See Also:
      - `createValueGroup(Map, Matrix)`

  - ### hashCode

    public int hashCode()
    Returns a hash code value for this object.
    Overrides:
      `hashCode` in class `Object`
    Returns:
      a hash code value.

  - ### equals

    public boolean equals(Object other)
    Compares this object with the given object for equality.
    Overrides:
      `equals` in class `Object`
    Parameters:
      `other` - the other object to compare with this object.
    Returns:
      `true` if both object are equal.