Module org.apache.sis.referencing
Package org.apache.sis.referencing.operation.matrix

Class MatrixSIS

Object
MatrixSIS
All Implemented Interfaces:
Serializable, Cloneable, Lenient­Comparable, Matrix
Direct Known Subclasses:
Matrix1, Matrix2, Matrix3, Matrix4
public abstract class MatrixSIS extends Object implements Matrix, LenientComparable, Cloneable, Serializable
A Matrix able to perform some operations of interest to Spatial Information Systems (SIS). This class completes the GeoAPI Matrix interface with some operations used by org​.apache​.sis​.referencing. It is not a Matrix­SIS goal to provide all possible Matrix operations, as there is too many of them. This class focuses on:
Since:
0.4
See Also:

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    protected
    Matrix­SIS()
    For sub-class constructors.

  • Method Summary

    Modifier and Type
    Method
    Description
    static Matrix­SIS
    cast­Or­Copy(Matrix matrix)
    Casts or copies the given matrix to a SIS implementation.
    Matrix­SIS
    clone()
    Returns a clone of this matrix.
    void
    convert­After(int tgt­Dim, Number scale, Number offset)
    Assuming that this matrix represents an affine transform, pre-concatenates a scale and a translation on the given dimension.
    void
    convert­Before(int src­Dim, Number scale, Number offset)
    Assuming that this matrix represents an affine transform, concatenates a scale and a translation on the given dimension.
    boolean
    equals(Object object)
    Returns true if the specified object is of the same class than this matrix and all of the data members are equal to the corresponding data members in this matrix.
    boolean
    equals(Object object, Comparison­Mode mode)
    Compares this matrix with the given object for equality.
    boolean
    equals(Matrix matrix, double tolerance)
    Compares the given matrices for equality, using the given absolute tolerance threshold.
    double[]
    get­Elements()
    Returns a copy of all matrix elements in a flat, row-major (column indices vary fastest) array.
    long
    get­Integer(int row, int column)
    Deprecated, for removal: This API element is subject to removal in a future version.
    Replaced by Numbers​.round(get­Number(row, column)).
    Number
    get­Number(int row, int column)
    Retrieves the value at the specified row and column of this matrix, wrapped in a Number.
    int
    hash­Code()
    Returns a hash code value based on the data values in this matrix.
    Matrix­SIS
    inverse()
    Returns the inverse of this matrix.
    boolean
    is­Affine()
    Returns true if this matrix represents an affine transform.
    abstract boolean
    is­Identity()
    Returns true if this matrix is an identity matrix.
    double[]
    multiply(double[] vector)
    Returns a new vector which is the result of multiplying this matrix with the specified vector.
    Matrix­SIS
    multiply(Matrix matrix)
    Returns a new matrix which is the result of multiplying this matrix with the specified one.
    Matrix­SIS
    normalize­Columns()
    Normalizes all columns in-place and returns their magnitudes as a row vector.
    Matrix­SIS
    remove­Columns(int lower, int upper)
    Returns a new matrix with the same elements than this matrix except for the specified columns.
    Matrix­SIS
    remove­Rows(int lower, int upper)
    Returns a new matrix with the same elements than this matrix except for the specified rows.
    void
    set­Elements(double[] elements)
    Sets all matrix elements from a flat, row-major (column indices vary fastest) array.
    void
    set­Matrix(Matrix matrix)
    Sets this matrix to the values of another matrix.
    void
    set­Number(int row, int column, Number value)
    Modifies the value at the specified row and column of this matrix.
    Matrix­SIS
    solve(Matrix matrix)
    Returns the value of U which solves this × U = matrix.
    String
    to­String()
    Returns a unlocalized string representation of this matrix.
    void
    translate(double[] vector)
    Multiplies this matrix by a translation matrix.
    abstract void
    transpose()
    Sets the value of this matrix to its transpose.

    Methods inherited from class Object

    finalize, get­Class, notify, notify­All, wait, wait, wait

    Methods inherited from interface Matrix

    get­Element, get­Num­Col, get­Num­Row, set­Element

  • Constructor Details

    • MatrixSIS

      protected MatrixSIS()
      For sub-class constructors.

  • Method Details

    • castOrCopy

      public static MatrixSIS castOrCopy(Matrix matrix)
      Casts or copies the given matrix to a SIS implementation. If matrix is already an instance of Matrix­SIS, then it is returned unchanged. Otherwise all elements are copied in a new Matrix­SIS object.
      Parameters:
      matrix - the matrix to cast or copy, or null.
      Returns:
      the matrix argument if it can be safely casted (including null argument), or a copy of the given matrix otherwise.
      See Also:

    • getInteger

      @Deprecated(since="1.4", forRemoval=true) public long getInteger(int row, int column)
      Deprecated, for removal: This API element is subject to removal in a future version.
      Replaced by Numbers​.round(get­Number(row, column)).
      Retrieves the value at the specified row and column of this matrix, rounded to nearest integer. This method may be more accurate than Matrix​.get­Element(int, int) in some implementations when the value is expected to be an integer (for example in conversions of pixel coordinates).
      Parameters:
      row - the row index, from 0 inclusive to Matrix​.get­Num­Row() exclusive.
      column - the column index, from 0 inclusive to Matrix​.get­Num­Col() exclusive.
      Returns:
      the current value at the given row and column, rounded to nearest integer.
      Throws:
      Index­Out­Of­Bounds­Exception - if the specified row or column is out of bounds.
      Arithmetic­Exception - if the value is NaN or overflows integer capacity.
      Since:
      1.3
      See Also:

    • getNumber

      public Number getNumber(int row, int column)
      Retrieves the value at the specified row and column of this matrix, wrapped in a Number. The Number type depends on the matrix accuracy.

      Use case

      This method may be more accurate than Matrix​.get­Element(int, int) in some implementations when the value is expected to be an integer, for example in conversions of pixel coordinates. Number​.long­Value() can be more accurate than Number​.double­Value() because a long may have more significant digits than what a double can contain. For safety against rounding errors and overflows, Numbers​.round(Number) should be used instead of Number​.long­Value().
      Parameters:
      row - the row index, from 0 inclusive to Matrix​.get­Num­Row() exclusive.
      column - the column index, from 0 inclusive to Matrix​.get­Num­Col() exclusive.
      Returns:
      the current value at the given row and column.
      Throws:
      Index­Out­Of­Bounds­Exception - if the specified row or column is out of bounds.
      See Also:

    • setNumber

      public void setNumber(int row, int column, Number value)
      Modifies the value at the specified row and column of this matrix. This method is the converses of get­Number(int, int).
      Parameters:
      row - the row index, from 0 inclusive to Matrix​.get­Num­Row() exclusive.
      column - the column index, from 0 inclusive to Matrix​.get­Num­Col() exclusive.
      value - the new matrix element value. A null value is interpreted as zero.
      Throws:
      Index­Out­Of­Bounds­Exception - if the specified row or column is out of bounds.
      Unsupported­Operation­Exception - if this matrix is unmodifiable.
      Since:
      0.8
      See Also:

    • getElements

      public double[] getElements()
      Returns a copy of all matrix elements in a flat, row-major (column indices vary fastest) array. The array length is Matrix​.get­Num­Row() * Matrix​.get­Num­Col().
      Returns:
      a copy of all current matrix elements in a row-major array.

    • setElements

      public void setElements(double[] elements)
      Sets all matrix elements from a flat, row-major (column indices vary fastest) array. The array length shall be Matrix​.get­Num­Row() * Matrix​.get­Num­Col().
      Parameters:
      elements - The new matrix elements in a row-major array.
      Throws:
      Illegal­Argument­Exception - if the given array does not have the expected length.
      Unsupported­Operation­Exception - if this matrix is unmodifiable.
      See Also:

    • setMatrix

      public void setMatrix(Matrix matrix) throws MismatchedMatrixSizeException
      Sets this matrix to the values of another matrix. The given matrix must have the same size.
      Parameters:
      matrix - the matrix to copy.
      Throws:
      Mismatched­Matrix­Size­Exception - if the given matrix has a different size than this matrix.
      Since:
      0.7

    • isAffine

      public boolean isAffine()
      Returns true if this matrix represents an affine transform. A transform is affine if the matrix is square and its last row contains only zeros, except in the last column which contains 1.
      Returns:
      true if this matrix represents an affine transform.
      See Also:

    • isIdentity

      public abstract boolean isIdentity()
      Returns true if this matrix is an identity matrix. This method is equivalent to the following code, except that it is potentially more efficient: 
      return Matrices.isIdentity(this, 0.0);
      Specified by:
      is­Identity in interface Matrix
      Returns:
      true if this matrix is an identity matrix.
      See Also:

    • transpose

      public abstract void transpose()
      Sets the value of this matrix to its transpose.
      Throws:
      Unsupported­Operation­Exception - if this matrix is unmodifiable.

    • normalizeColumns

      public MatrixSIS normalizeColumns()
      Normalizes all columns in-place and returns their magnitudes as a row vector. Each columns in this matrix is considered as a vector. For each column (vector), this method computes the magnitude (vector length) as the square root of the sum of all squared values. Then, all values in the column are divided by that magnitude.

      This method is useful when the matrix is a transform derivative. In such matrix, each column is a vector representing the displacement in target space when an coordinate in the source space is increased by one. Invoking this method turns those vectors into unitary vectors, which is useful for forming the basis of a new coordinate system.

      Returns:
      the magnitude for each column in a matrix having only one row.
      Throws:
      Unsupported­Operation­Exception - if this matrix is unmodifiable.

    • convertBefore

      public void convertBefore(int srcDim, Number scale, Number offset)
      Assuming that this matrix represents an affine transform, concatenates a scale and a translation on the given dimension. Converting a point with the resulting matrix is equivalent to first convert the point with coordinates[src­Dim] = coordinates[src­Dim] * scale + offset, then apply the original matrix.

      Equivalence between this method and Java2D Affine­Transform methods

      If this matrix was an instance of Java2D Affine­Transform, then invoking this method would be equivalent to invoking the following Affine­Transform methods in the order shown below:
      Equivalence between this method and AffineTransform methods
      MatrixSIS method AffineTransform methods
      convertBefore(0, scale, offset) at.translate(offset, 0); at.scale(scale, 1);
      convertBefore(1, scale, offset) at.translate(0, offset); at.scale(1, scale);
      Parameters:
      src­Dim - the dimension of the coordinate to rescale in the source coordinates.
      scale - the amount by which to multiply the source coordinate value before to apply the transform, or null if none.
      offset - the amount by which to translate the source coordinate value before to apply the transform, or null if none.
      Throws:
      Unsupported­Operation­Exception - if this matrix is unmodifiable.
      Since:
      0.6
      See Also:

    • convertAfter

      public void convertAfter(int tgtDim, Number scale, Number offset)
      Assuming that this matrix represents an affine transform, pre-concatenates a scale and a translation on the given dimension. Converting a point with the resulting matrix is equivalent to first convert the point with the original matrix, then convert the result with coordinates[tgt­Dim] = coordinates[tgt­Dim] * scale + offset.
      Parameters:
      tgt­Dim - the dimension of the coordinate to rescale in the target coordinates.
      scale - the amount by which to multiply the target coordinate value after this transform, or null if none.
      offset - the amount by which to translate the target coordinate value after this transform, or null if none.
      Throws:
      Unsupported­Operation­Exception - if this matrix is unmodifiable.
      Since:
      0.6
      See Also:

    • multiply

      public MatrixSIS multiply(Matrix matrix) throws MismatchedMatrixSizeException
      Returns a new matrix which is the result of multiplying this matrix with the specified one. In other words, returns this × matrix.

      Relationship with coordinate operations

      In the context of coordinate operations, Matrix​.multiply(other) is equivalent to Affine­Transform​.concatenate(other): first transforms by the other transform and then transform the result by this transform.
      Parameters:
      matrix - the matrix to multiply to this matrix.
      Returns:
      the result of this × matrix.
      Throws:
      Mismatched­Matrix­Size­Exception - if the number of rows in the given matrix is not equals to the number of columns in this matrix.

    • multiply

      public double[] multiply(double[] vector)
      Returns a new vector which is the result of multiplying this matrix with the specified vector. In other words, returns this × vector. The length of the given vector must be equal to the number of columns in this matrix, and the length of the returned vector will be equal to the number of rows in this matrix.

      Relationship with coordinate operations

      In the context of coordinate operations, Matrix​.multiply(vector) is related to Affine­Transform​.transform(…) except that the last vector number is implicitly 1 in Affine­Transform operations. While this multiply(double[]) method could be used for coordinate transformation, it is not its purpose. This method is designed for occasional uses when accuracy is more important than performance.
      Parameters:
      vector - the vector to multiply to this matrix.
      Returns:
      the result of this × vector.
      Throws:
      Mismatched­Matrix­Size­Exception - if the length of the given vector is not equals to the number of columns in this matrix.
      Since:
      0.8

    • translate

      public void translate(double[] vector)
      Multiplies this matrix by a translation matrix. Invoking this method is equivalent to invoking multiply(T) where T is a matrix like below (size varies): 
              ┌                    ┐
        │ 1  0  0  vector[0] │
    T = │ 0  1  0  vector[1] │
        │ 0  0  1  vector[2] │
        │ 0  0  0  vector[3] │
        └                    ┘
      The length of the given vector must be equal to the number of columns in this matrix. The last vector element is 1 for an affine transform, but other values are allowed. This matrix will be modified in-place.

      If this matrix is used for coordinate conversions, then converting a position with the resulting matrix is equivalent to first translating the point by the given vector, then applying the conversion represented by the original matrix.

      Parameters:
      vector - a vector representing a translation to be applied before this matrix.
      Since:
      1.0
      See Also:

    • solve

      public MatrixSIS solve(Matrix matrix) throws MismatchedMatrixSizeException, NoninvertibleMatrixException
      Returns the value of U which solves this × U = matrix. This is equivalent to first computing the inverse of this, then multiplying the result by the given matrix.
      Parameters:
      matrix - the matrix to solve.
      Returns:
      the U matrix that satisfies this × U = matrix.
      Throws:
      Mismatched­Matrix­Size­Exception - if the number of rows in the given matrix is not equals to the number of columns in this matrix.
      Noninvertible­Matrix­Exception - if this matrix is not invertible.

    • inverse

      public MatrixSIS inverse() throws NoninvertibleMatrixException
      Returns the inverse of this matrix.
      Returns:
      the inverse of this matrix.
      Throws:
      Noninvertible­Matrix­Exception - if this matrix is not invertible.
      See Also:

    • removeRows

      public MatrixSIS removeRows(int lower, int upper)
      Returns a new matrix with the same elements than this matrix except for the specified rows. This method is useful for removing a range of target dimensions in an affine transform.
      Parameters:
      lower - index of the first row to remove (inclusive).
      upper - index after the last row to remove (exclusive).
      Returns:
      a copy of this matrix with the specified rows removed.
      Since:
      0.7

    • removeColumns

      public MatrixSIS removeColumns(int lower, int upper)
      Returns a new matrix with the same elements than this matrix except for the specified columns. This method is useful for removing a range of source dimensions in an affine transform. Coordinates will be converted as if the values in the removed dimensions were zeros.
      Parameters:
      lower - index of the first column to remove (inclusive).
      upper - index after the last column to remove (exclusive).
      Returns:
      a copy of this matrix with the specified columns removed.
      Since:
      0.7

    • hashCode

      public int hashCode()
      Returns a hash code value based on the data values in this matrix.
      Overrides:
      hash­Code in class Object
      Returns:
      a hash code value for this matrix.

    • equals

      public boolean equals(Object object)
      Returns true if the specified object is of the same class than this matrix and all of the data members are equal to the corresponding data members in this matrix.
      Specified by:
      equals in interface Lenient­Comparable
      Overrides:
      equals in class Object
      Parameters:
      object - the object to compare with this matrix for equality.
      Returns:
      true if the given object is equal to this matrix.
      See Also:

    • equals

      public boolean equals(Matrix matrix, double tolerance)
      Compares the given matrices for equality, using the given absolute tolerance threshold. The given matrix does not need to be the same implementation class than this matrix.

      The matrix elements are compared as below:

      • Double​.Na­N values are considered equals to all other NaN values.
      • Infinite values are considered equal to other infinite values of the same sign.
      • All other values are considered equal if the absolute value of their difference is smaller than or equals to the given threshold.
      Parameters:
      matrix - the matrix to compare.
      tolerance - the tolerance value.
      Returns:
      true if this matrix is close enough to the given matrix given the tolerance value.
      See Also:

    • equals

      public boolean equals(Object object, ComparisonMode mode)
      Compares this matrix with the given object for equality. To be considered equal, the two objects must met the following conditions, which depend on the mode argument:
      • STRICT: the two matrices must be of the same class, have the same size and the same element values.
      • BY_CONTRACT: the two matrices must have the same size and the same element values, but are not required to be the same implementation class (any Matrix is okay).
      • IGNORE_METADATA: same as BY_CONTRACT.
      • APPROXIMATE: the two matrices must have the same size, but the element values can differ up to some threshold. The threshold value is determined empirically and may change in any future SIS versions.
      Specified by:
      equals in interface Lenient­Comparable
      Parameters:
      object - the object to compare to this.
      mode - the strictness level of the comparison.
      Returns:
      true if both objects are equal.
      See Also:

    • clone

      public MatrixSIS clone()
      Returns a clone of this matrix.
      Specified by:
      clone in interface Matrix
      Overrides:
      clone in class Object
      Returns:
      a new matrix of the same class and with the same values than this matrix.
      See Also:

    • toString

      public String toString()
      Returns a unlocalized string representation of this matrix. For each column, the numbers are aligned on the decimal separator.
      Overrides:
      to­String in class Object
      See Also: