org.jeometry.math.Matrix Maven / Gradle / Ivy
package org.jeometry.math;
import java.awt.Dimension;
import org.jeometry.Geometry;
import org.jeometry.math.decomposition.EigenDecomposition;
import org.jeometry.math.decomposition.LUDecomposition;
import org.jeometry.math.decomposition.SVDDecomposition;
/**
* This interface describe a general two dimensional matrix. A matrix A is a two-dimensional array of double values that is defined such as:
* $$
* A = \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* where:
*
* - n is the number of rows.
*
- m is the number of columns.
*
- aij is the value located at row i and column j
*
* @author Julien Seinturier - COMEX S.A. - [email protected] - https://github.com/jorigin/jeometry
* @version {@value Geometry#version} b{@value Geometry#BUILD}
* @since 1.0.0
*/
public interface Matrix {
/**
* Indicates that the export of a matrix data to a linear array is row-major (made row by row from the first to the last).
* @see #COLUMN_MAJOR
*/
public static final int ROW_MAJOR = 1;
/**
* Indicates that the the export of a matrix data to a linear array is column-major (made column by column from the first to the last).
* @see #ROW_MAJOR
*/
public static final int COLUMN_MAJOR = 2;
/**
* Get the matrix values as a linear array according to the given ordering.
* If the ordering is {@link #ROW_MAJOR}, the output array contains the sequence of all rows from the first to the last.
* On the other hand, if the ordering is {@link #COLUMN_MAJOR}, the output array contains the sequence of all columns from the first to the last.
* @param ordering the ordering to use ({@link #ROW_MAJOR} or {@link #COLUMN_MAJOR}).
* @return the matrix values as a linear array.
* @see #setDataArray(int, double[])
*/
public double[] getDataArray(int ordering);
/**
* Get the matrix values as a linear array according to the given ordering.
* If the ordering is {@link #ROW_MAJOR}, the output array contains the sequence of all rows from the first to the last.
* On the other hand, if the ordering is {@link #COLUMN_MAJOR}, the output array contains the sequence of all columns from the first to the last.
* @param ordering the ordering to use ({@link #ROW_MAJOR} or {@link #COLUMN_MAJOR}).
* @param output the array where the value are stored.
* @return the matrix values as a linear array.
* @see #setDataArray(int, double[])
* @throws IllegalArgumentException if the output array does not fit the matrix capabilities.
*/
public double[] getDataArray(int ordering, double[] output) throws IllegalArgumentException;
/**
* Set the matrix values from a linear array according to the given ordering.
* If the ordering is {@link #ROW_MAJOR}, the output array contains the sequence of all rows from the first to the last.
* On the other hand, if the ordering is {@link #COLUMN_MAJOR}, the output array contains the sequence of all columns from the first to the last.
* @param ordering the ordering of the linear array ({@link #ROW_MAJOR} or {@link #COLUMN_MAJOR}).
* @param data the matrix values.
* @throws IllegalArgumentException if the given data does not fit the matrix capabilities.
*/
public void setDataArray(int ordering, double[] data) throws IllegalArgumentException;
/**
* Get the matrix values as a two-dimensionnal array.
* The output array has the same number of rows and columns as the matrix.
* @return the matrix values as a two-dimensionnal array.
* @see #setDataArray2D(double[][])
*/
public double[][] getDataArray2D();
/**
* Get the matrix values as a two-dimensionnal array.
* The output array has the same number of rows and columns as the matrix.
* @param output the two-dimensional array where the value are stored.
* @return the matrix values as a two-dimensionnal array.
* @see #setDataArray2D(double[][])
*/
public double[][] getDataArray2D(double[][] output);
/**
* Set the matrix values from a two-dimensionnal array.
* The input array has to have the same number of rows and columns as the matrix.
* @param data the matrix values
* @throws IllegalArgumentException if the given data does not fir the matrix capabilities.
*/
public void setDataArray2D(double[][] data) throws IllegalArgumentException;
/**
* Get the value that is stored at the given (row, column).
* @param row the row that holds the value.
* @param col the column that holds the value.
* @return the value that is stored at the given (row, column).
* @throws IllegalArgumentException if the row or col does not fit the matrix size.
* @see #setValue(int, int, double)
*/
public double getValue(int row, int col) throws IllegalArgumentException;
/**
* Set the value that is stored at the given (row, column).
* @param row the row that holds the value.
* @param col the column that holds the value.
* @param value value to store at the given (row, column).
* @throws IllegalArgumentException if the row or col does not fit the matrix size.
* @see #getValue(int, int)
*/
public void setValue(int row, int col, double value) throws IllegalArgumentException;
/**
* Get the number of rows that this matrix contains.
* @return the number of rows that this matrix contains.
* @see #getColumnsCount()
* @see #getDimension()
*/
public int getRowsCount();
/**
* Get the number of columns that this matrix contains.
* @return the number of columns that this matrix contains.
* @see #getRowsCount()
* @see #getDimension()
*/
public int getColumnsCount();
/**
* Get the dimension (the number of rows and columns) of this matrix.
* @return the dimension (the number of rows and columns) of this matrix.
* @see #getRowsCount()
* @see #getColumnsCount()
*/
public Dimension getDimension();
/**
* Compute the matrix determinant. Let A be a general n×m sized matrix such that:
* $$
* A = \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* where:
*
* - n is the number of rows.
*
- m is the number of columns.
*
- aij is the value located at row i and column j
*
* Its determinant, denoted |A| is such that:
* $$
* |A|\ =\ \sum_{k=1}^{k}a_{ij}C_{ij}
* $$
* where Cij is the cofactor of aij defined by:
* $$
* C_{ij}\ =\ (-1)^{i+j}M_{ij}
* $$
* with Mij the minor of matrix A formed by eliminating row i and column j from A.
* Many implementation of the determinant can be provided, this description is purely formal.
* @return the matrix determinant.
*/
public double determinant();
/**
* Compute the transpose of the current matrix and return it.
* Let A be a matrix, the transpose of A, denoted AT
* is the matrix that is obtained by exchanging A rows and columns. A matrix and its transpose satisfy:
* (AT)-1 = (A-1)T
*
* Note that the transpose of an A, B matrices product is such as:
* (A×B)T = AT×BT
* @return the transpose of the current matrix.
*/
public Matrix transpose();
/**
* Compute the transpose of the current matrix and store it within the given result.
* Let A be a matrix, the transpose of A, denoted AT
* is the matrix that is obtained by exchanging A rows and columns. A matrix and its transpose satisfy:
* (AT)-1 = (A-1)T
*
* Note that the transpose of an A, B matrices product is such as:
* (A×B)T = AT×BT
* @param result the matrix that has to store the result of the transpose.
* @return the same reference as result
* @throws IllegalArgumentException is the given result does not fit the transpose matrix.
*/
public Matrix transpose(Matrix result) throws IllegalArgumentException;
/**
* Modify this matrix by its transpose.
* Let A be a matrix, the transpose of A, denoted AT
* is the matrix that is obtained by exchanging A rows and columns. A matrix and its transpose satisfy:
* (AT)-1 = (A-1)T
*
* Note that the transpose of an A, B matrices product is such as:
* (A×B)T = AT×BT
* @return a reference on this matrix.
*/
public Matrix transposeAffect();
/**
* Multiply the current matrix by the given one (regarding to matrix product). Formally, this methods compute:
* M = A×B
* where:
*
* - M is the returned result.
*
- A is this matrix.
*
- B is the matrix given by
b.
*
* @param b the matrix to multiply.
* @return the product of this matrix by the given one.
* @throws IllegalArgumentException if the matrix are incompatible for multiplication.
*/
public Matrix multiply(Matrix b) throws IllegalArgumentException;
/**
* Multiply the current matrix by the given one (regarding to matrix product). Formally, this methods compute:
* M = A×B
* where:
*
* - M is the returned result.
*
- A is this matrix.
*
- B is the matrix given by
b.
*
* @param b the matrix to multiply.
* @param result the matrix that has to store the result of the multiplication.
* @return the same reference as result.
* @throws IllegalArgumentException if the matrix are incompatible for multiplication.
*/
public Matrix multiply(Matrix b, Matrix result) throws IllegalArgumentException;
/**
* Modify this matrix to be the result of the multiplication of this matrix with the given one (regarding to matrix product).
* Formally, this methods compute:
* M = A×B
* where:
*
* - M is the returned result.
*
- A is this matrix.
*
- B is the matrix given by
b.
*
* @param b the matrix to multiply.
* @return a reference on this matrix.
* @throws IllegalArgumentException if the matrix are incompatible for multiplication.
*/
public Matrix multiplyAffect(Matrix b) throws IllegalArgumentException;
/**
* Return the {@link Vector vector} resulting of the multiplication of this matrix with the given one.
* (regarding to matrix product).
* Formally, this methods compute:
* u = A×v
* where:
*
* - u is the returned result.
*
- A is this matrix.
*
- v is the input vector.
*
* @param v the vector to multiply.
* @return the {@link Vector vector} resulting of the multiplication of this matrix with the given one.
*/
public Vector multiply(Vector v);
/**
* Affect the result {@link Vector vector} with the result of the multiplication of this matrix with the given vector v.
* (regarding to matrix product)
* Formally, this methods compute:
* u = A×v
* where:
*
* - u is the returned result.
*
- A is this matrix.
*
- v is the input vector.
*
* @param v the vector to multiply.
* @param result the vector that store the result.
* @return the same reference as result.
*/
public Vector multiply(Vector v, Vector result);
/**
* Return the matrix resulting of the multiplication of this matrix with a scalar.
* Formally, let A a matrix such that:
* $$
* A = \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The result of the multiplcation of A by a scalar s is the matrix As that verifies:
* $$
* A_{s} = \begin{bmatrix}
* sa_{00} & \dots & sa_{0i} & \dots & sa_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* sa_{i0} & \dots & sa_{ij} & \dots & sa_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* sa_{n0} & \dots & sa_{nj} & \dots & sa_{nm}
* \end{bmatrix}
* $$
* @param scalar the scalar to multiply.
* @return the matrix resulting of the multiplication of this matrix with a scalar.
*/
public Matrix multiply(double scalar);
/**
* Store the result of the multiplication of this matrix with a scalar within the given result.
* Formally, let M a matrix such that:
* $$
* A = \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The result of the multiplcation of A by a scalar s is the matrix As that verifies:
* $$
* A_{s} = \begin{bmatrix}
* sa_{00} & \dots & sa_{0i} & \dots & sa_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* sa_{i0} & \dots & sa_{ij} & \dots & sa_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* sa_{n0} & \dots & sa_{nj} & \dots & sa_{nm}
* \end{bmatrix}
* $$
* @param scalar the scalar to multiply.
* @param result the matrix that have to store the result of the multiplication of this matrix with the scalar.
* @return the same reference as result
* @throws IllegalArgumentException if the result matrix does not fit the multiplication.
*/
public Matrix multiply(double scalar, Matrix result) throws IllegalArgumentException;
/**
* Modify this matrix with the result of the multiplication of this matrix with a scalar.
* Formally, let A a matrix such that:
* $$
* A = \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The result of the multiplcation of A by a scalar s is the matrix As that verifies:
* $$
* A_{s} = \begin{bmatrix}
* sa_{00} & \dots & sa_{0i} & \dots & sa_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* sa_{i0} & \dots & sa_{ij} & \dots & sa_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* sa_{n0} & \dots & sa_{nj} & \dots & sa_{nm}
* \end{bmatrix}
* $$
* @param scalar the scalar to multiply.
* @return a reference on this matrix.
*/
public Matrix multiplyAffect(double scalar);
/**
* Compute and return the addition of this matrix with the given one.
* Formally, let A and B two matrices such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* and\ B\ =\ \begin{bmatrix}
* b_{00} & \dots & b_{0i} & \dots & b_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0} & \dots & b_{ij} & \dots & b_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0} & \dots & b_{nj} & \dots & b_{nm}
* \end{bmatrix}
* $$
* The addition of A and B, denoted A + B is such that:
* $$
* A+B\ =\ \begin{bmatrix}
* b_{00}+a_{00} & \dots & b_{0i}+a_{0i} & \dots & b_{0m}+a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0}+a_{i0} & \dots & b_{ij}+a_{ij} & \dots & b_{im}+a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0}+a_{n0} & \dots & b_{nj}+a_{nj} & \dots & b_{nm}+a_{nm}
* \end{bmatrix}
* $$
* @param b the matrix to add. This matrix has to be same sized as this matrix.
* @return the addition of this matrix with the given one. If the input matrix is null then null is returned.
* @throws IllegalArgumentException if the input matrix size differs from this one.
*/
public Matrix add(Matrix b) throws IllegalArgumentException;
/**
* Compute the addition of this matrix with the given one and store it within the result matrix.
* Formally, let A and B two matrices such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* and\ B\ =\ \begin{bmatrix}
* b_{00} & \dots & b_{0i} & \dots & b_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0} & \dots & b_{ij} & \dots & b_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0} & \dots & b_{nj} & \dots & b_{nm}
* \end{bmatrix}
* $$
* The addition of A and B, denoted A + B is such that:
* $$
* A+B\ =\ \begin{bmatrix}
* b_{00}+a_{00} & \dots & b_{0i}+a_{0i} & \dots & b_{0m}+a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0}+a_{i0} & \dots & b_{ij}+a_{ij} & \dots & b_{im}+a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0}+a_{n0} & \dots & b_{nj}+a_{nj} & \dots & b_{nm}+a_{nm}
* \end{bmatrix}
* $$
* @param b the matrix to add. This matrix has to be same sized as this matrix.
* @param result the matrix that store the result. This matrix has to be same sized as this matrix.
* @return the same reference as result.
* @throws IllegalArgumentException if the input or result matrices size differs from this one.
*/
public Matrix add(Matrix b, Matrix result) throws IllegalArgumentException;
/**
* Affect this matrix with the result of its addition with the given one.
* Formally, let A and B two matrices such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* and\ B\ =\ \begin{bmatrix}
* b_{00} & \dots & b_{0i} & \dots & b_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0} & \dots & b_{ij} & \dots & b_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0} & \dots & b_{nj} & \dots & b_{nm}
* \end{bmatrix}
* $$
* The addition of A and B, denoted A + B is such that:
* $$
* A+B\ =\ \begin{bmatrix}
* b_{00}+a_{00} & \dots & b_{0i}+a_{0i} & \dots & b_{0m}+a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0}+a_{i0} & \dots & b_{ij}+a_{ij} & \dots & b_{im}+a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0}+a_{n0} & \dots & b_{nj}+a_{nj} & \dots & b_{nm}+a_{nm}
* \end{bmatrix}
* $$
* @param b the matrix to add. This matrix has to be same sized as this matrix.
* @return a reference on this matrix.
* @throws IllegalArgumentException if the input matrix size differs from this one.
*/
public Matrix addAffect(Matrix b) throws IllegalArgumentException;
/**
* Compute and return the addition of this matrix with the given scalar.
* Formally, let s be a scalar and A a matrix such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The addition of A and s, denoted As is such that:
* $$
* A_{s}\ =\ \begin{bmatrix}
* s+a_{00} & \dots & s+a_{0i} & \dots & s+a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* s+a_{i0} & \dots & s+a_{ij} & \dots & s+a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* s+a_{n0} & \dots & s+a_{nj} & \dots & s+a_{nm}
* \end{bmatrix}
* $$
* @param s the scalar to add.
* @return the addition of this matrix with the given scalar.
*/
public Matrix add(double s);
/**
* Compute the addition of this matrix with the given scalar and store it within the given result matrix.
* Formally, let s be a scalar and A a matrix such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The addition of A and s, denoted As is such that:
* $$
* A_{s}\ =\ \begin{bmatrix}
* s+a_{00} & \dots & s+a_{0i} & \dots & s+a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* s+a_{i0} & \dots & s+a_{ij} & \dots & s+a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* s+a_{n0} & \dots & s+a_{nj} & \dots & s+a_{nm}
* \end{bmatrix}
* $$
* @param s the scalar to add.
* @param result the matrix that store the result. This matrix has to be same sized as this matrix.
* @return the addition of this matrix with the given scalar. If the result matrix is null then null is returned.
* @throws IllegalArgumentException if the result matrix size differs from this one.
*/
public Matrix add(double s, Matrix result) throws IllegalArgumentException;
/**
* Affect this matrix with the result of the addition of this matrix with the given scalar.
* Formally, let s be a scalar and A a matrix such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The addition of A and s, denoted As is such that:
* $$
* A_{s}\ =\ \begin{bmatrix}
* s+a_{00} & \dots & s+a_{0i} & \dots & s+a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* s+a_{i0} & \dots & s+a_{ij} & \dots & s+a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* s+a_{n0} & \dots & s+a_{nj} & \dots & s+a_{nm}
* \end{bmatrix}
* $$
* @param s the scalar to add.
* @return a reference on this matrix.
*/
public Matrix addAffect(double s);
/**
* Compute and return the subtraction of this matrix with the given one.
* Formally, let A and B two matrices such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* and\ B\ =\ \begin{bmatrix}
* b_{00} & \dots & b_{0i} & \dots & b_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0} & \dots & b_{ij} & \dots & b_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0} & \dots & b_{nj} & \dots & b_{nm}
* \end{bmatrix}
* $$
* The subtraction of A and B, denoted A - B is such that:
* $$
* A+B\ =\ \begin{bmatrix}
* b_{00}-a_{00} & \dots & b_{0i}-a_{0i} & \dots & b_{0m}-a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0}-a_{i0} & \dots & b_{ij}-a_{ij} & \dots & b_{im}-a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0}-a_{n0} & \dots & b_{nj}-a_{nj} & \dots & b_{nm}-a_{nm}
* \end{bmatrix}
* $$
* @param b the matrix to subtract. This matrix has to be same sized as this matrix.
* @return the subtraction of this matrix with the given one. If the input matrix is null then null is returned.
* @throws IllegalArgumentException if the input matrix size differs from this one.
*/
public Matrix subtract(Matrix b) throws IllegalArgumentException;
/**
* Compute the subtraction of this matrix with the given one and store it within the result matrix.
* Formally, let A and B two matrices such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* and\ B\ =\ \begin{bmatrix}
* b_{00} & \dots & b_{0i} & \dots & b_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0} & \dots & b_{ij} & \dots & b_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0} & \dots & b_{nj} & \dots & b_{nm}
* \end{bmatrix}
* $$
* The subtraction of A and B, denoted A - B is such that:
* $$
* A+B\ =\ \begin{bmatrix}
* b_{00}-a_{00} & \dots & b_{0i}-a_{0i} & \dots & b_{0m}-a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0}-a_{i0} & \dots & b_{ij}-a_{ij} & \dots & b_{im}-a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0}-a_{n0} & \dots & b_{nj}-a_{nj} & \dots & b_{nm}-a_{nm}
* \end{bmatrix}
* $$
* @param b the matrix to subtract. This matrix has to be same sized as this matrix.
* @param result the matrix that store the result. This matrix has to be same sized as this matrix.
* @return the same reference as result.
* @throws IllegalArgumentException if the input or result matrices size differs from this one.
*/
public Matrix subtract(Matrix b, Matrix result) throws IllegalArgumentException;
/**
* Affect this matrix with the result of its subtraction with the given one.
* Formally, let A and B two matrices such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* and\ B\ =\ \begin{bmatrix}
* b_{00} & \dots & b_{0i} & \dots & b_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0} & \dots & b_{ij} & \dots & b_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0} & \dots & b_{nj} & \dots & b_{nm}
* \end{bmatrix}
* $$
* The subtraction of A and B, denoted A - B is such that:
* $$
* A+B\ =\ \begin{bmatrix}
* b_{00}-a_{00} & \dots & b_{0i}-a_{0i} & \dots & b_{0m}-a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{i0}-a_{i0} & \dots & b_{ij}-a_{ij} & \dots & b_{im}-a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* b_{n0}-a_{n0} & \dots & b_{nj}-a_{nj} & \dots & b_{nm}-a_{nm}
* \end{bmatrix}
* $$
* @param b the matrix to subtract. This matrix has to be same sized as this matrix.
* @return a reference on this matrix.
* @throws IllegalArgumentException if the input matrix size differs from this one.
*/
public Matrix subtractAffect(Matrix b) throws IllegalArgumentException;
/**
* Compute and return the subtraction of this matrix with the given scalar.
* Formally, let s be a scalar and A a matrix such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The subtraction of A and s, denoted As is such that:
* $$
* A_{s}\ =\ \begin{bmatrix}
* a_{00}-s & \dots & a_{0i}-s & \dots & a_{0m}-s \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0}-s & \dots & a_{ij}-s & \dots & a_{im}-s \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0}-s & \dots & a_{nj}-s & \dots & a_{nm}-s
* \end{bmatrix}
* $$
* @param s the scalar to subtract.
* @return the subtraction of this matrix with the given scalar.
*/
public Matrix subtract(double s);
/**
* Compute the subtraction of this matrix with the given scalar and store it within the given result matrix.
* Formally, let s be a scalar and A a matrix such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The subtraction of A and s, denoted As is such that:
* $$
* A_{s}\ =\ \begin{bmatrix}
* a_{00}-s & \dots & a_{0i}-s & \dots & a_{0m}-s \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0}-s & \dots & a_{ij}-s & \dots & a_{im}-s \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0}-s & \dots & a_{nj}-s & \dots & a_{nm}-s
* \end{bmatrix}
* $$
* @param s the scalar to subtract.
* @param result the matrix that store the result. This matrix has to be same sized as this matrix.
* @return the subtraction of this matrix with the given scalar. If the result matrix is null then null is returned.
* @throws IllegalArgumentException if the result matrix size differs from this one.
*/
public Matrix subtract(double s, Matrix result) throws IllegalArgumentException;
/**
* Affect this matrix with the result of the subtraction of this matrix with the given scalar.
* Formally, let s be a scalar and A a matrix such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0m} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{im} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nm}
* \end{bmatrix}
* $$
* The subtraction of A and s, denoted As is such that:
* $$
* A_{s}\ =\ \begin{bmatrix}
* a_{00}-s & \dots & a_{0i}-s & \dots & a_{0m}-s \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0}-s & \dots & a_{ij}-s & \dots & a_{im}-s \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0}-s & \dots & a_{nj}-s & \dots & a_{nm}-s
* \end{bmatrix}
* $$
* @param s the scalar to subtract.
* @return a reference on this matrix.
*/
public Matrix subtractAffect(double s);
/**
* Return the inverse of the current matrix. Let A be a square matrix, its inverse, denoted A-1 is such that:
* A×A-1 = I
* where I is the identity matrix and × is the standard matrix product.
* @return the inverse of the current matrix.
* @throws IllegalStateException if the matrix is not invertible.
*/
public Matrix invert() throws IllegalStateException;
/**
* Compute the inverse of the current matrix and store it within the result matrix.
* Let A be a square matrix, its inverse, denoted A-1 is such that:
* A×A-1 = I
* where I is the identity matrix and × is the standard matrix product.
* @param result the matrix that has to store the inverse of the current matrix.
* @return the same reference as result
* @throws IllegalStateException if the result is not same sized as this matrix.
* @throws IllegalArgumentException if the matrix is not invertible.
*/
public Matrix invert(Matrix result) throws IllegalStateException, IllegalArgumentException;
/**
* Compute the cofactor matrix. Formally, let A a square matrix defined such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0n} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{in} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nn}
* \end{bmatrix}
* $$
* The cofactor matrix of A, denoted C, is such that:
* $$
* C\ =\ \begin{bmatrix}
* c_{00} & \dots & c_{0i} & \dots & c_{0n} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* c_{i0} & \dots & c_{ij} & \dots & c_{in} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* c_{n0} & \dots & c_{nj} & \dots & c_{nn}
* \end{bmatrix}
* $$
*
where cij = (-1)(i+j)|M(ij)|
* with Mij is the minor matrix from A obtained by ignoring row i and column j from A
*
* @return the cofactor matrix.
* @throws IllegalStateException if the matrix is not square.
*/
public Matrix cofactor() throws IllegalStateException;
/**
* Compute the cofactor matrix and store it within the given result. Formally, let A a square matrix defined such that:
* $$
* A\ =\ \begin{bmatrix}
* a_{00} & \dots & a_{0i} & \dots & a_{0n} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{i0} & \dots & a_{ij} & \dots & a_{in} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* a_{n0} & \dots & a_{nj} & \dots & a_{nn}
* \end{bmatrix}
* $$
* The cofactor matrix of A, denoted C, is such that:
* $$
* C\ =\ \begin{bmatrix}
* c_{00} & \dots & c_{0i} & \dots & c_{0n} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* c_{i0} & \dots & c_{ij} & \dots & c_{in} \\
* \vdots & \ddots & \vdots & \ddots & \vdots \\
* c_{n0} & \dots & c_{nj} & \dots & c_{nn}
* \end{bmatrix}
* $$
*
where cij = (-1)(i+j)|M(ij)|
* with Mij is the minor matrix from A obtained by ignoring row i and column j from A
*
* @param result the matrix that have to store the result.
* @return the same reference as result
* @throws IllegalStateException if the matrix is not square.
* @throws IllegalArgumentException if the result has not the same size as this matrix.
*/
public Matrix cofactor(Matrix result) throws IllegalStateException, IllegalArgumentException;
/**
* Compute the SVD decomposition of the matrix.
*
* Let A be a real matrix that has a matrix of {@link EigenDecomposition Eigen vectors} P that is not invertible
* (no {@link EigenDecomposition Eigen decomposition} can be computed).
*
* If A is an m × n real matrix with m > n, then A can be written using a so-called singular value decomposition of the form
* A = UDVT
*
* where:
*
* - U is a m × m matrix with orthogonal columns (UTU = I)
*
- D is a m × n diagonal matrix
*
- V is a n × n matrix with orthogonal columns (VTV = I)
*
*
*
* source: Wolfram math
* @return the {@link SVDDecomposition SVD decomposition} of the matrix
* @throws UnsupportedOperationException if the matrix cannot be decomposed
*/
public SVDDecomposition decomposeSVD();
/**
* Compute the LU decomposition of the matrix.
*
* Let A be a square matrix, the LU decomposition compute a lower triangular matrix L and an upper triangular matrix U such that:
*
* L×U = A
*
* where × is the standard matrix product.
* @return the {@link LUDecomposition LU decomposition} of the matrix.
* @throws UnsupportedOperationException if the matrix cannot be decomposed
*/
public LUDecomposition decomposeLU();
}
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