Package jline.util.matrix

Class Matrix

java.lang.Object

jline.util.matrix.Matrix

All Implemented Interfaces:

Serializable

public final class Matrix
extends Object
implements Serializable

A sparse matrix data structure supporting linear algebra functions similar to those available in MATLAB. TABLE OF CONTENTS: 1. CONSTRUCTORS AND INITIALIZATION 2. CORE ELEMENT ACCESS AND MODIFICATION 3. BASIC ARITHMETIC OPERATIONS 4. ELEMENT-WISE OPERATIONS 5. MATRIX TRANSFORMATIONS 6. LINEAR ALGEBRA OPERATIONS 7. MATRIX SLICING AND EXTRACTION 8. MATRIX CONCATENATION AND ASSEMBLY 9. STATISTICAL OPERATIONS 10. MATRIX PROPERTIES AND COMPARISONS 11. FINDING AND FILTERING 12. MATRIX MANIPULATION 13. SPECIAL MATRIX OPERATIONS 14. I/O OPERATIONS 15. FACTORY METHODS 16. UTILITY METHODS

See Also:

• Serialized Form

Constructor Summary

Constructors

Constructor	Description
Matrix(double[] array)	Creates a column vector from a double array.
Matrix(double[][] arrays)	Creates a matrix from a 2D double array.
Matrix(int[] array)	Creates a column vector from an integer array.
Matrix(int numRows, int numCols)	Creates a sparse matrix with the specified dimensions.
Matrix(int numRows, int numCols, int arrayLength)	Creates a sparse matrix with the specified dimensions and capacity.
Matrix(Double[][] arrays)	Creates a matrix from a Kotlin Array type.
Matrix(String matrixString)	Parse matrix from string in MATLAB or Python formats MATLAB format assumes commas between row elements and semicolon between rows
Matrix(ArrayList<List<Double>> arrays)
Matrix(List<Double> array)
Matrix(Matrix matrix)	Creates a copy of the specified matrix.
Matrix(org.ejml.data.DMatrix matrix)	Creates a matrix from an EJML DMatrix (sparse).
Matrix(org.ejml.data.DMatrixRMaj matrix)	Creates a matrix from an EJML DMatrixRMaj (dense).
Matrix(org.ejml.simple.SimpleMatrix matrix)

Method Summary

Modifier and Type	Method	Description
void	absEq()
Matrix	add(double alpha)	Adds a scalar multiple of the all-ones matrix to this matrix: this + alpha * 1.
Matrix	add(double alpha, Matrix matrix)	Adds alpha * matrix to this matrix.
Matrix	add(Matrix matrix)	Adds another matrix to this matrix: this + matrix.
void	addEq(double alpha)	Adds a scalar value to each element of the matrix in-place.
void	addEq(double alpha, Matrix matrix)	Adds alpha * matrix to this matrix in-place: this += alpha * matrix.
void	addEq(Matrix matrix)	Adds another matrix to this matrix in-place: this += matrix.
static Matrix	allbut(Matrix y, int k)	Returns all elements in a matrix except the first ones
boolean	allEqualToOne()	Checks whether all elements in the matrix are equal to 1.
boolean	any()
void	apply(double source, double target, String op)	Applies a conditional element-wise transformation to the matrix.
static Matrix	broadcastColPlusRow(Matrix colVector, Matrix rowVector)	Computes the element-wise sum of a column vector and a row vector, producing a matrix where each entry (i, j) is the sum of colVector[i] and rowVector[j].
static Matrix	cartesian(Matrix matrixA, Matrix matrixB)	Cartesian product of two matrices.
Matrix	ceil()	Returns a new matrix where each element is the ceiling of the corresponding element in this matrix.
Matrix	ceilEq()	Applies the ceiling operation in-place to each element of this matrix.
static Matrix	cell2mat(Map<Integer,Matrix> cellArray)	Concatenates a collection of matrices stored in a map into a single row vector.
static Matrix	cellsum(Map<Integer,Matrix> cellArray)	Computes the element-wise sum of all matrices stored in a map.
void	changeSign()	Negates all values in the matrix, in-place.
void	colIncrease(int col, double a)
Matrix	colon()	Returns the matrix in column-major order.
Matrix	columnMajorOrder()	Equivalent to the colon operator in MATLAB (:).
static double[]	columnMatrixToDoubleArray(Matrix columnMatrix)	Converts a column matrix (of size m x 1) to a dense double array of length m.
static boolean	compare(Matrix A, Matrix B, String op)	Compares two matrices element-wise using a specified comparison operator.
boolean	compareMatrix(Matrix matrix)	Compares this matrix to another matrix for approximate equality.
Matrix	compatibleSizesAdd(Matrix b)	Performs element-wise addition with shape broadcasting where applicable.
Matrix	concatCols(Matrix other)	Concatenates this matrix with another matrix horizontally.
static Matrix	concatColumns(Matrix left, Matrix right, Matrix out)	Concatenates two matrices horizontally (column-wise).
static Matrix	concatRows(Matrix top, Matrix bottom, Matrix out)	Concatenates two matrices vertically (row-wise).
Matrix	copy()	Returns a deep copy of this matrix.
int	count(double val)	Counts how many elements in the matrix are equal to a specified value.
Matrix	countEachRow(double val)	Counts the number of occurrences of a value in each row of the matrix.
Matrix	createBlockDiagonal(Matrix matrix2)	Creates a block diagonal matrix by placing the current matrix in the top-left and another matrix (if provided) in the bottom-right.
static Matrix	createLike(Matrix B)	Creates a new empty matrix with the same shape and internal structure as the given matrix.
Matrix	cumsumViaCol()	Computes the cumulative sum of the matrix down each column.
Matrix	cumsumViaRow()	Computes the cumulative sum of the matrix across each row.
static Matrix	decorate(Matrix inspace1, Matrix inspace2)
double	det()	Computes the determinant of the matrix.
static Matrix	diag(double... values)	Creates a square diagonal matrix from the given values.
static Matrix	diagMatrix(double[] values)	Creates a square diagonal matrix from a given array of values.
static Matrix	diagMatrix(Matrix values)	Creates a square diagonal matrix from the elements of a column or row vector matrix.
static Matrix	diagMatrix(Matrix A, double[] values, int offset, int length)	Creates or fills a square diagonal matrix with the specified values.
Matrix	div(Matrix den)	Performs element-wise division between this matrix and the provided matrix.
void	divEq(Matrix den)	Performs in-place element-wise division between this matrix and the provided matrix.
void	divide(double scalar, Matrix outputB, boolean flag)	Divides this matrix by a scalar and stores the result in the output matrix.
void	divideEq(double scalar)	Performs in-place division of this matrix by a scalar.
void	divideRows(double[] diag, int offset)	Divides each row of this matrix by the corresponding diagonal element (with an offset).
static Matrix	dlyap(Matrix A, Matrix B, Matrix C)	Solves the discrete Sylvester equation A * X * B - X + C = 0.
List<org.apache.commons.math3.complex.Complex>	eig()	Computes the eigenvalues of this square matrix, including complex eigenvalues.
Ret.Eigs	eigval()	Computes the eigenvalues of this square matrix.
Ret.Eigs	eigvec()	Computes the eigenvalues and eigenvectors of this square matrix.
Matrix	elementDiv(Matrix B)	Performs element-wise division of this matrix by another matrix.
Matrix	elementDivide(Matrix b)	Performs element-wise division with another matrix.
Matrix	elementIncrease(double val)	Increases each element of the matrix by a constant value.
double	elementMax()	Returns the maximum value among all elements in the matrix.
double	elementMaxAbs()	Returns the maximum absolute value among all elements in the matrix.
double	elementMin()	Returns the minimum value among all elements in the matrix.
static double	elementMinNonZero(Matrix matrix)	Returns the smallest non-zero positive element in the given matrix.
double	elementMult()	Computes the product of the elements of a row or column vector.
Matrix	elementMult(Matrix B)	Performs in-place element-wise multiplication with another matrix.
Matrix	elementMult(Matrix B, Matrix output)	Performs element-wise multiplication with another matrix, storing the result in the given output matrix.
Matrix	elementMultWithVector(Matrix B)	Performs element-wise multiplication between this matrix and a row vector.
Matrix	elementPow(double a)	Raises each non-zero element of the matrix to the specified power.
Matrix	elementPower(double t)	Raises each element of the matrix to the given power.
double	elementSum()	Computes the sum of all elements in the matrix.
boolean	equals(Object obj)	Checks for matrix equality.
Matrix	exp()	Applies the exponential function to each element of the matrix.
void	expandMatrix(int rows, int cols, int nz_length)	Expands the matrix dimensions to the specified size while preserving data.
void	expandMatrixToSquare()	Expands the matrix to be square, padding with zeros as needed.
Matrix	expm()	Computes the matrix exponential.
Matrix	expm_higham()	Computes the matrix exponential using Higham's scaling and squaring method.
static Matrix	extract(Matrix src, int srcX0, int srcX1, int srcY0, int srcY1)	Extracts a rectangular submatrix from the given source matrix.
static void	extract(Matrix src, int srcX0, int srcX1, int srcY0, int srcY1, Matrix dst, int dstY0, int dstX0)	Extracts a rectangular submatrix from a source matrix and stores it in a destination matrix.
Matrix	extractCols(int col0, int col1)	Extracts a range of columns from this matrix (instance method).
static Matrix	extractColumn(Matrix A, int column, Matrix out)	Extracts a single column from the given matrix.
static Matrix	extractColumns(Matrix A, int col0, int col1)	Extracts a range of columns from the matrix [col0:col1).
static Matrix	extractColumns(Matrix A, int col0, int col1, Matrix out)	Extracts a range of columns from the matrix [col0:col1) into a destination matrix.
static void	extractDiag(Matrix A, Matrix outputB)	Extracts the diagonal elements of a matrix and stores them in a destination matrix.
Matrix	extractRows(int row0, int row1)	Extracts rows from this matrix (instance method).
static Matrix	extractRows(Matrix A, int row0, int row1)	Extracts a range of rows from the matrix [row0:row1).
static Matrix	extractRows(Matrix A, int row0, int row1, Matrix out)	Extracts a range of rows from the matrix [row0:row1) into a destination matrix.
static Matrix	eye(int length)	Creates an identity matrix of given size.
Matrix	fact()	Computes the factorial of each element in the matrix.
Matrix	factln()	Computes the natural logarithm of the factorial for each element.
static Matrix	factln(Matrix n)	Computes the natural logarithm of the factorial (log(x!)) for each element in the input matrix.
Matrix	fill(double val)	Fills all entries in the matrix with the given value.
Matrix	find()	Returns the linear indices of all non-zero elements in the matrix.
static List<Integer>	findIndexWithZeroSum(Matrix matrix, boolean isRow)	Finds the indices of all rows or columns in a matrix that have a sum of zero.
Matrix	findNonNegative()	Returns the linear indices of all elements that are non-negative (≥ 0).
List<Integer>	findNonZeroRowsInColumn(int column)	Finds all row indices in a given column where the value is non-zero.
Matrix	findNumber(double number)	Finds all linear indices where the matrix has a specific value.
static List<Integer>	findRows(Matrix matrix, Matrix row)	Finds the indices of all rows in a matrix that exactly match a given row vector.
Matrix	findZero()	Finds all linear indices where the matrix value is zero.
static double	firstNorm(Matrix a)	Computes the 1-norm (maximum absolute column sum) of the matrix.
Matrix	fromArray2D(double[][] matrix)	Populates the matrix from a 2D double array.
Matrix	fromArray2D(int[][] matrix)	Populates the matrix from a 2D integer array.
static Matrix	fromRows(List<List<Double>> rows)	Constructs a Matrix from a list of rows, where each inner list is a row.
double	get(int idx)	Returns the value at the specified index.
double	get(int i, int j)	Returns the value at the specified row and column.
int[]	getColIndexes()	Returns internal column index array from the sparse matrix structure.
static int	getColIndexSum(Map<Integer,Matrix> cellArray)	Computes the total number of elements across all matrices in a map, summing numRows * numCols for each matrix.
int	getColMax(int col)	Returns the row index of the maximum value in the specified column.
Matrix	getColumn(int j)	Returns a column of the matrix as a new single-column matrix.
ColumnView	getColumnView(int j)	Returns a lightweight view into the specified column without copying data.
org.ejml.data.DMatrix	getData()
int[]	getNonZeroCols()	Returns an array of unique column indices containing non-zero elements.
int	getNonZeroLength()	Returns the number of non-zero values in the matrix.
int[]	getNonZeroRows()	Returns array of row indices of non-zero entries.
int	getNonZeros()	Returns the number of non-zero elements in this matrix.
double[]	getNonZeroValues()	Returns array of non-zero values in the matrix.
int	getNumCols()	Returns the number of columns in this matrix.
int	getNumElements()	Returns total number of elements in the matrix.
int	getNumNonZeros()
int	getNumRows()	Returns the number of rows in this matrix.
Matrix	getRow(int i)	Returns the specified row as a single-row matrix.
int	getRowMax(int row)	Returns column index of maximum element in a specified row.
Matrix	getRowsFrom(int row)	Returns a new matrix consisting of rows from the given start index to the end.
RowView	getRowView(int i)	Returns a lightweight view into the specified row without copying data.
Matrix	getSlice(boolean[] rowFlags, boolean[] colFlags)	Extracts a submatrix from rows/columns marked as true in input flags.
Matrix	getSlice(int r0, int r1, int c0, int c1)	Extracts a submatrix based on row/column bounds.
static Matrix	getSubMatrix(Matrix sourceMatrix, int x0, int x1, int y0, int y1)	Extracts a submatrix from the source matrix using zero-based index ranges.
Matrix	getSubMatrix(Matrix rows, Matrix cols)	Returns a matrix consisting of rows and columns selected by two index matrices.
void	growMaxColumns(int newmax, boolean preserve)	Increases the internal column capacity of the matrix.
void	growMaxLength(int newmax, boolean preserve)	Increases the internal non-zero element capacity of the matrix.
Matrix	hadamard(Matrix B)	Performs the Hadamard (element-wise) product of two matrices.
boolean	hasDuplicates()
boolean	hasFinite()
int	hashCode()	Generates a hash code for the matrix based on its values.
boolean	hasInfinite()
boolean	hasMultipleFinite()
boolean	hasNaN()
double	infinityNorm()	Computes the infinity norm of this matrix.
static double	infNorm(Matrix a)	Computes the infinity norm (maximum absolute row sum) of the matrix.
void	insertSubMatrix(int start_row, int start_col, int end_row, int end_col, Matrix matrix_to_be_inserted)	Inserts a sub-matrix into the current matrix at the specified location.
static List<Double>	intersect(Matrix matrixA, Matrix matrixB)	Computes the intersection of scalar values present in two matrices.
Matrix	inv()	Computes the inverse of the matrix.
static Matrix	inv(Matrix m)	Computes the inverse of the given matrix.
boolean	isAssigned(int row, int col)	Checks whether a specific element is assigned in the sparse matrix.
boolean	isDiag()	Determines whether the matrix is a diagonal matrix.
boolean	isEmpty()	Checks if the matrix is empty (has zero rows or columns).
boolean	isEqualTo(Matrix m)	Checks if two matrices are exactly equal.
boolean	isEqualToTol(Matrix m, double tol)	Checks if two matrices are equal within a specified tolerance.
boolean	isFinite()	Checks whether all matrix elements are finite.
boolean	isInteger()	Checks if all values in the matrix are integers.
void	keepCols(Collection<Integer> cols)	Keeps only the specified columns in the matrix.
void	keepRows(Collection<Integer> rows)	Keeps only the specified rows in the matrix.
Matrix	kron(Matrix b)	Computes the Kronecker product of this matrix and another matrix.
Matrix	krons(Matrix other)	Computes the Kronecker sum of two matrices: A ⊕ B = A \otimes I + I \otimes B, where \otimes is the Kronecker product and I is the identity matrix of matching size.
Matrix	leftMatrixDivide(Matrix b)	Solves the equation AX = B for X, where A is this matrix and B is the right-hand side.
int	length()	Returns the length of the matrix, defined as max(rows, cols).
Matrix	log()	Applies the natural logarithm element-wise.
static double	logSum(Matrix matrix)	Computes the sum of the natural logarithms of all elements in the matrix.
static double	logsumexp(Matrix x)	Computes log(sum_i exp(x_i)) in a numerically stable way (log-sum-exp trick).
static Matrix	lyap(Matrix A, Matrix B, Matrix C, Matrix D)	Computes the solution to the continuous-time Lyapunov equation AX + XAᵀ + Q = 0.
static int	matchrow(Matrix matrix, Matrix row)	Returns the index of the row in the matrix that exactly matches the given row vector.
static Matrix	matrixAddVector(Matrix matrix, Matrix vector)	Adds a vector to each row or column of the matrix, depending on the vector's orientation.
static double	maxAbsDiff(Matrix a, Matrix b)	Computes the maximum relative absolute difference between corresponding elements of two matrices: max(abs((a - b) / b)).
Matrix	meanCol()	Computes the mean of each column.
Matrix	meanRow()	Computes the mean of each row.
void	mulByMinusOne()	Multiplies all elements in the matrix by -1 in-place.
Matrix	mult(Matrix B)	Performs matrix multiplication: this * B
Matrix	mult(Matrix B, Matrix out)	Performs matrix multiplication: this * B
double	multColumnView(ColumnView columnView)	Efficiently multiplies this row vector with a column view.
void	multEq(Matrix B)	Replaces this matrix with the result of this * B.
double	multRowView(RowView rowView)	Efficiently multiplies a row view with this column vector.
Matrix	neg()	Returns the negation of this matrix (all elements multiplied by -1).
static Matrix	negative(Matrix a)	Negates all elements in the matrix and returns the result.
double	norm()	Computes the Euclidean norm of a matrix
double	norm1()	Computes the 1-norm of the matrix (maximum absolute column sum).
double	normFrobenius()	Computes the Frobenius norm of a matrix (alias for norm()).
static Matrix	oneMinusMatrix(Matrix matrix)	Computes the matrix 1 - A, where diagonal entries become 1 - A(i, i) and off-diagonal entries become -A(i, j).
static Matrix	oner(Matrix N, Integer s)	Decreases a single element of an integer vector by one.
static Matrix	oner(Matrix N, List<Integer> r)	Decreases multiple elements of an integer vector by one.
void	ones()	Fills the matrix with ones.
static Matrix	ones(int rows, int cols)	Creates a matrix of the given shape filled with ones.
Matrix	pinv()	Computes the Moore-Penrose pseudo-inverse of the matrix using SVD.
static Matrix	pow(Matrix a, int b)	Computes the matrix power A^b for a non-negative integer exponent b.
double	powerSumCols(int col, double alpha)	Computes the sum of powers of absolute values in a column: ∑ |A_{ji}|^alpha
double	powerSumRows(int row, double alpha)	Computes the sum of powers of absolute values in a row: ∑ |A_{ij}|^alpha
void	prettyPrint()	Pretty prints the matrix with automatic formatting and alignment.
void	prettyPrintInt()	Pretty prints the matrix assuming integer values.
void	print()	Prints the matrix with appropriate formatting, either as floats or integers.
void	printNonZero()	Prints only non-zero values and their positions in the matrix.
Map<String,Matrix>	qr()	Performs QR decomposition on the matrix.
void	randMatrix(int length)	Fills the matrix with random values between 0 and 1.
int	rank()	Computes the rank of the matrix.
static Matrix	readFromFile(String fileName)	Reads a CSV-formatted matrix from a file.
Matrix	reciprocal()	Computes the element-wise reciprocal (1/x) of the matrix.
void	remove(int row, int col)	Removes a specific element from the matrix at the given row and column.
void	removeCols(Collection<Integer> cols)	Removes the specified columns from the matrix.
void	removeInfinite()	Replaces all infinite values (positive or negative) in the matrix with 0.
void	removeInfinity()	Removes all infinite values (positive or negative) from the sparse matrix structure.
void	removeNaN()	Removes all NaN values from the matrix structure.
void	removeNegative()	Removes all negative values from the matrix structure.
static double[][][]	removeRows(double[][][] array, Matrix rowsToRemove)
void	removeRows(Collection<Integer> rows)	Removes the specified rows from the matrix.
static String	removeTrailingNewLine(String str)
void	removeZeros(double val)	Removes values from the matrix that are equal to the specified value.
void	replace(double delete, double replacement)	Replaces all occurrences of a specific value with a new value in the matrix.
Matrix	repmat(int rows, int cols)	Repeats the matrix to match the specified row and column replication.
void	reshape(int numRows, int numCols)	Reshapes the matrix to the specified number of rows and columns.
void	reshape(int numRows, int numCols, int arrayLength)	Reshapes the matrix with new dimensions and internal storage length.
Matrix	reverse()	Reverses the elements of a vector (row or column) matrix.
Matrix	reverseRows()	Reverses the order of rows in the matrix.
Matrix	rightMatrixDivide(Matrix b)	Performs right matrix division A / B = A * inv(B)
static Matrix	robustLeftDivide(Matrix A, Matrix B)	Robust linear solve for A·X = B that handles singular matrices.
void	rowIncrease(int row, double a)	Increases all elements in the specified row by a scalar value.
Matrix	safeMult(Matrix B)
Matrix	scale(double scalar)	Scales the matrix by the given scalar value.
void	scaleEq(double scalar)	Scales this matrix in-place by the given scalar value.
void	scaleEq(double scalar, Matrix output)	Scales this matrix by the given scalar value and stores the result in the provided output matrix.
static Matrix	scaleMult(Matrix a, double n)	Multiplies all elements of a matrix by a scalar.
Map<String,Matrix>	schur()	Computes the Schur decomposition with the default method and iteration count.
Map<String,Matrix>	schur(String method, Integer iter)	Computes the Schur decomposition of the matrix.
Map<String,ComplexMatrix>	schurComplex()	Computes the complex Schur decomposition of this matrix, equivalent to MATLAB's schur(A,'complex').
void	set(int idx, double val)	Sets the element at absolute index position to the given value.
void	set(int row, int col, double val)	Sets the element at specified row and column.
void	set(int row, int col, int val)	Sets the element at specified row and column using an integer value.
Matrix	setColumn(int j, Matrix col)	Sets the specified column to the values in the given vector.
Matrix	setColumns(int j0, int j1, Matrix cols)	Sets multiple columns starting from column index j0 to j1 (exclusive) using values from another matrix.
void	setData(org.ejml.data.DMatrix newData)
void	setNaNTo(double val)	Replaces all NaN entries in the matrix with the specified value.
void	setNaNToZero()	Replaces all NaN entries in the matrix with zero.
Matrix	setRow(int j, Matrix row)	Sets the specified row to the values in the given vector.
Matrix	setRows(int i0, int i1, Matrix rows)	Sets multiple rows starting from row index i0 to i1 (exclusive) using values from another matrix.
Matrix	setSlice(int rowStart, int rowEnd, int colStart, int colEnd, Matrix newSlice)	Returns a new matrix representing the updated slice after assigning values from newSlice.
void	setSliceEq(int rowStart, int rowEnd, int colStart, int colEnd, Matrix newSlice)	Sets the values of a submatrix (in-place) using the specified newSlice matrix.
void	setTo(Matrix m)	Copies the data from another matrix into this matrix.
void	setToNaN()	Sets all elements of the matrix to NaN.
void	shrinkNumCols(int newmax)
void	shrinkNumRows(int newmax)
static Matrix	singleton(double value)	Creates a 1×1 matrix containing a single scalar value.
static boolean	solve(Matrix a, Matrix b, Matrix x)	Solves the sparse linear system Ax = b.
static boolean	solveDirect(Matrix a, Matrix b, Matrix x)	Solves the linear system A*x = b directly using LU decomposition without singularity checks.
static boolean	solveSafe(Matrix a, Matrix b, Matrix x)	Solves the linear system Ax = b for x, handling singular matrices gracefully.
Matrix	sort()	Returns a new matrix with the non-zero values sorted in ascending order.
Matrix	sortEq()	Sorts the current matrix's non-zero values in place.
static Ret.SpectralDecomposition	spectd(Matrix A)	Computes the spectral decomposition of a matrix A using its eigendecomposition.
Matrix	sqrt()	Computes the element-wise square root of the matrix.
Matrix	square()	Computes the matrix multiplied by itself.
Matrix	sub(double x)	Subtract a scalar from all elements.
Matrix	sub(double alpha, Matrix matrix)	Subtracts alpha-scaled version of the provided matrix.
Matrix	sub(Matrix matrix)	Subtracts another matrix.
void	subEq(double x)	Subtracts a scalar from the current matrix in place.
void	subEq(double alpha, Matrix matrix)	Subtracts a scaled matrix from the current matrix in place.
void	subEq(Matrix matrix)	Subtracts a matrix from the current matrix in place.
double	sumAbsCols(int col)	Sums the absolute values of the given column.
double	sumAbsRows(int row)	Sums the absolute values of the given row.
Matrix	sumCols()	Sums the values in each column and returns the results as a row vector.
double	sumCols(int col)	Sums the elements in the specified column.
Matrix	sumCols(int startRow, int endRow)	Computes the sum of a subset of rows for each column.
static double	sumCumprod(Matrix matrix)	Computes the sum of the cumulative product along a row vector.
Matrix	sumRows()	Computes the sum of each row and returns the result as a column vector.
double	sumRows(int row)	Computes the sum of the values in a specific row.
Matrix	sumRows(int startCol, int endCol)	Computes the sum over a subrange of columns for each row.
double	sumSubMatrix(boolean[] rowIndexes, boolean[] colIndexes)	Computes the sum of a submatrix defined by boolean selection flags.
double	sumSubMatrix(int[] rowIndexes, int[] colIndexes)	Computes the sum of a submatrix defined by specific row and column indices.
double	sumSubMatrix(int startRow, int endRow, int startCol, int endCol)	Computes the sum of the values in a rectangular submatrix.
Ret.SVD	svd()	Computes the Singular Value Decomposition (SVD) of this matrix.
static Matrix	sylv(Matrix A, Matrix B, Matrix C)	Solves the Sylvester equation A·X + X·B = -C using a Schur decomposition-based method.
double[]	toArray1D()	Converts the matrix to a flat 1D array in row-major order.
double[][]	toArray2D()	Converts the matrix to a 2D array representation.
org.ejml.data.DMatrixSparseCSC	toDMatrixSparseCSC()	Converts this matrix to a copy of its underlying DMatrixSparseCSC structure.
org.ejml.data.DMatrixSparseCSC	toDMatrixSparseCSC(Matrix matrix)	Converts a specified matrix to a copy of its underlying DMatrixSparseCSC structure.
Double	toDouble()	Converts this matrix to a single Double value.
List<List<Double>>	toDoubleList()	Converts the matrix to a nested list of Double values.
int[]	toIntArray1D()	Converts the matrix to a 1D array of int, flattening in row-major order.
List<Double>	toList1D()	Converts the matrix into a 1D List of Double values in row-major order.
String	toString()	Returns a formatted string representation of the matrix.
Matrix	transpose()	Computes the transpose of the current matrix.
static Matrix	tril(Matrix matrix)	Returns the lower triangular part of a matrix (zeroing elements above the main diagonal).
static Matrix	tril(Matrix matrix, int k)	Returns the elements on and below the kth diagonal of matrix A.
static Matrix	union(Matrix A, Matrix B)	Computes the union of two matrices A and B.
Matrix	uniqueInCol(int colIdx)	Finds unique integer values in the specified column of the matrix.
Matrix	uniqueInRow(int rowIdx)	Finds unique integer values in the specified row of the matrix.
Matrix	uniqueNonNegativeInCol(int colIdx)	Finds unique positive values (strictly greater than 0) in the specified column.
Matrix	uniqueNonNegativeInRow(int rowIdx)	Finds unique positive values (strictly greater than 0) in the specified row.
Matrix	uniqueNonZerosInCol(int colIdx)	Finds unique non-zero values in the specified column.
Matrix	uniqueNonZerosInRow(int rowIdx)	Finds unique non-zero values in the specified row.
static UniqueRowResult	uniqueRowIndexes(Matrix m)	Finds the indices of unique rows in a matrix without returning a matrix of the unique rows themselves.
static UniqueRowResult	uniqueRowIndexesFromColumn(Matrix m, int startCol)	Identifies unique rows in a matrix starting from a specified column index.
static UniqueRowResult	uniqueRows(Matrix m)	Finds all unique rows in a matrix and returns the unique sorted rows, along with mapping indices to/from the original matrix.
void	unsafeSet(int row, int col, double val)	Sets a value in the matrix without bounds checking.
double	value()	Returns the value at position (0, 0).
static Set<Set<Integer>>	weaklyConnect(Matrix param, Set<Integer> colsToIgnore)	Weakly-connected components of a sub-matrix.
void	zero()	Sets all entries in the matrix to zero.
static Matrix	zeros(int rows, int cols)	Creates a matrix of the specified shape filled with zeros.

Methods inherited from class java.lang.Object

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

Constructor Details

Matrix

public Matrix(int numRows,
 int numCols,
 int arrayLength)

Creates a sparse matrix with the specified dimensions and capacity.

Parameters:

numRows - number of rows in the matrix

numCols - number of columns in the matrix

arrayLength - initial capacity for non-zero elements

Matrix

public Matrix(int numRows,
 int numCols)

Creates a sparse matrix with the specified dimensions.

Parameters:

numRows - number of rows in the matrix

numCols - number of columns in the matrix

Matrix

public Matrix(Matrix matrix)

Creates a copy of the specified matrix.

Parameters:

matrix - the matrix to copy

Throws:

UnsupportedOperationException - if the matrix type is not supported

Matrix

public Matrix(org.ejml.data.DMatrix matrix)

Creates a matrix from an EJML DMatrix (sparse).

Parameters:

matrix - the EJML sparse matrix to wrap

Matrix

public Matrix(org.ejml.data.DMatrixRMaj matrix)

Creates a matrix from an EJML DMatrixRMaj (dense).

Parameters:

matrix - the EJML dense matrix to wrap

Matrix

public Matrix(double[][] arrays)

Creates a matrix from a 2D double array. Uses EJML's triplet format for efficient single-pass batch insertion.

Parameters:

arrays - 2D array containing the matrix elements

Matrix

public Matrix(Double[][] arrays)

Creates a matrix from a Kotlin Array type. This constructor enables direct initialization from Kotlin's arrayOf(doubleArrayOf(...)) syntax. Uses EJML's triplet format for efficient single-pass batch insertion.

Parameters:

arrays - Kotlin Array containing DoubleArray rows

Matrix

public Matrix(int[] array)

Creates a column vector from an integer array.

Parameters:

array - integer array to convert to column vector

Matrix

public Matrix(double[] array)

Creates a column vector from a double array.

Parameters:

array - double array to convert to column vector

Matrix

public Matrix(List<Double> array)

Matrix

public Matrix(ArrayList<List<Double>> arrays)

Matrix

public Matrix(org.ejml.simple.SimpleMatrix matrix)

Matrix

public Matrix(String matrixString)

Parse matrix from string in MATLAB or Python formats MATLAB format assumes commas between row elements and semicolon between rows

Parameters:

matrixString - input string, e.g., "[10,4;5,9]" or "[[10,4],[4,9]]"

Method Details

fromRows

public static Matrix fromRows(List<List<Double>> rows)

Constructs a Matrix from a list of rows, where each inner list is a row. Static factory because constructor would clash with Matrix(List<Double>) under erasure.

allbut

public static Matrix allbut(Matrix y,
 int k)

Returns all elements in a matrix except the first ones

Parameters:

y - - a matrix

k - - a position of an element in the matrix

Returns:

- A row vector with all elements of y but ypos

broadcastColPlusRow

public static Matrix broadcastColPlusRow(Matrix colVector,
 Matrix rowVector)

Computes the element-wise sum of a column vector and a row vector, producing a matrix where each entry (i, j) is the sum of colVector[i] and rowVector[j]. This is equivalent to broadcasting the column vector along columns and the row vector along rows.

Parameters:

colVector - A column vector of size (m x 1)

rowVector - A row vector of size (1 x n)

Returns:

A matrix of size (m x n) where each element is colVector[i] + rowVector[j]

cartesian

public static Matrix cartesian(Matrix matrixA,
 Matrix matrixB)

Cartesian product of two matrices. It replicates elements of the first input matrix and pairs them with each row of the second input matrix.

Parameters:

matrixA - first input matrix

matrixB - second input matrix

cell2mat

public static Matrix cell2mat(Map<Integer,Matrix> cellArray)

Concatenates a collection of matrices stored in a map into a single row vector. Each matrix is flattened in column-major order and concatenated sequentially based on the map's value order. Only non-zero values are inserted to preserve sparse structure.

Parameters:

cellArray - A map from integer indices to Matrix objects to be concatenated

Returns:

A single-row Matrix containing all elements from the input matrices in sequence

cellsum

public static Matrix cellsum(Map<Integer,Matrix> cellArray)

Computes the element-wise sum of all matrices stored in a map. Each matrix must have the same dimensions. The matrices are summed in the order of their integer keys (0 to N-1). The result is accumulated in-place for efficiency.

Parameters:

cellArray - A map from integer indices to Matrix objects to be summed

Returns:

A Matrix representing the element-wise sum of all matrices in the map

Throws:

RuntimeException - if the map is empty or if any matrices have incompatible dimensions

columnMatrixToDoubleArray

public static double[] columnMatrixToDoubleArray(Matrix columnMatrix)

Converts a column matrix (of size m x 1) to a dense double array of length m.

Parameters:

columnMatrix - A Matrix with exactly one column

Returns:

A double array containing the values from the column matrix

Throws:

IllegalArgumentException - if the input matrix does not have exactly one column

compare

public static boolean compare(Matrix A,
 Matrix B,
 String op)

Compares two matrices element-wise using a specified comparison operator. The matrices must have the same dimensions. Supported operators are: "eq", "equal", "lt", "lessthan", "lte", "lessthanequal", "gt", "greater", "gte", "greaterthanequal".

Parameters:

A - The first matrix

B - The second matrix

op - The comparison operator as a string

Returns:

true if the comparison holds for all elements, false otherwise

concatColumns

public static Matrix concatColumns(Matrix left,
 Matrix right,
 Matrix out)

Concatenates two matrices horizontally (column-wise). If either matrix is empty, returns the non-empty matrix. If an output matrix is provided, writes the result into it; otherwise, returns a newly allocated matrix.

Parameters:

left - The matrix to appear on the left

right - The matrix to appear on the right

out - (Optional) Output matrix to store the result; can be null

Returns:

A matrix representing [left | right]

concatRows

public static Matrix concatRows(Matrix top,
 Matrix bottom,
 Matrix out)

Concatenates two matrices vertically (row-wise). If either matrix is empty, returns the non-empty matrix. If an output matrix is provided, writes the result into it; otherwise, returns a newly allocated matrix.

Parameters:

top - The matrix to appear on top

bottom - The matrix to appear below

out - (Optional) Output matrix to store the result; can be null

Returns:

A matrix representing [top; bottom]

createLike

public static Matrix createLike(Matrix B)

Creates a new empty matrix with the same shape and internal structure as the given matrix. The contents are uninitialized and all values are implicitly zero (sparse).

Parameters:

B - The matrix to copy the structure from

Returns:

A new matrix with the same dimensions and sparsity structure as B

decorate

public static Matrix decorate(Matrix inspace1,
 Matrix inspace2)

diag

public static Matrix diag(double... values)

Creates a square diagonal matrix from the given values. The input values are placed on the main diagonal; all off-diagonal entries are zero.

Parameters:

values - The values to place on the diagonal

Returns:

A square sparse matrix with values[i] at position (i, i)

diagMatrix

public static Matrix diagMatrix(double[] values)

Creates a square diagonal matrix from a given array of values. This is a low-level wrapper that constructs a diagonal matrix using EJML internals. Equivalent to placing values[i] at position (i, i) for all i.

Parameters:

values - An array of values to place on the main diagonal

Returns:

A square sparse matrix with values[i] at position (i, i)

diagMatrix

public static Matrix diagMatrix(Matrix values)

Creates a square diagonal matrix from the elements of a column or row vector matrix. Each element in the input matrix is placed on the main diagonal of the resulting matrix.

Parameters:

values - A matrix interpreted as a vector (either row or column) containing diagonal values

Returns:

A square sparse matrix with the input values along the main diagonal

diagMatrix

public static Matrix diagMatrix(Matrix A,
 double[] values,
 int offset,
 int length)

Creates or fills a square diagonal matrix with the specified values. If the input matrix A is null, a new diagonal matrix is created. Otherwise, the provided matrix A is filled with the diagonal values.

Parameters:

A - An optional matrix to be filled with the diagonal values; can be null

values - The array of values to place on the main diagonal

offset - The starting index in values to read from

length - The number of values to place on the diagonal

Returns:

A matrix with values[offset + i] placed at position (i, i)

elementMinNonZero

public static double elementMinNonZero(Matrix matrix)

Returns the smallest non-zero positive element in the given matrix. If no such element exists, returns 0.

Parameters:

matrix - The input matrix

Returns:

The minimum strictly positive element, or 0 if all elements are zero or negative

extract

public static void extract(Matrix src,
 int srcX0,
 int srcX1,
 int srcY0,
 int srcY1,
 Matrix dst,
 int dstY0,
 int dstX0)

Extracts a rectangular submatrix from a source matrix and stores it in a destination matrix. Equivalent to slicing rows [srcY0:srcY1) and columns [srcX0:srcX1) from src.

Parameters:

src - The source matrix

srcX0 - Starting column (inclusive)

srcX1 - Ending column (exclusive)

srcY0 - Starting row (inclusive)

srcY1 - Ending row (exclusive)

dst - The destination matrix to store the result

dstY0 - Starting row index in dst

dstX0 - Starting column index in dst

extract

public static Matrix extract(Matrix src,
 int srcX0,
 int srcX1,
 int srcY0,
 int srcY1)

Extracts a rectangular submatrix from the given source matrix. Equivalent to src[srcY0:srcY1, srcX0:srcX1].

Parameters:

src - The source matrix

srcX0 - Starting column (inclusive)

srcX1 - Ending column (exclusive)

srcY0 - Starting row (inclusive)

srcY1 - Ending row (exclusive)

Returns:

A new matrix containing the extracted submatrix

extractColumn

public static Matrix extractColumn(Matrix A,
 int column,
 Matrix out)

Extracts a single column from the given matrix.

Parameters:

A - The input matrix

column - The index of the column to extract

out - (Optional) Matrix to store the output; if null, a new matrix is created

Returns:

A matrix containing the extracted column

extractColumns

public static Matrix extractColumns(Matrix A,
 int col0,
 int col1)

Extracts a range of columns from the matrix [col0:col1).

Parameters:

A - The source matrix

col0 - Starting column index (inclusive)

col1 - Ending column index (exclusive)

Returns:

A new matrix containing the specified columns

extractColumns

public static Matrix extractColumns(Matrix A,
 int col0,
 int col1,
 Matrix out)

Extracts a range of columns from the matrix [col0:col1) into a destination matrix.

Parameters:

A - The source matrix

col0 - Starting column index (inclusive)

col1 - Ending column index (exclusive)

out - Output matrix to hold the result

Returns:

A matrix with the specified columns

extractDiag

public static void extractDiag(Matrix A,
 Matrix outputB)

Extracts the diagonal elements of a matrix and stores them in a destination matrix.

Parameters:

A - The source matrix

outputB - The matrix to store the diagonal values

extractRows

public static Matrix extractRows(Matrix A,
 int row0,
 int row1)

Extracts a range of rows from the matrix [row0:row1).

Parameters:

A - The source matrix

row0 - Starting row index (inclusive)

row1 - Ending row index (exclusive)

Returns:

A matrix containing the specified rows

extractRows

public static Matrix extractRows(Matrix A,
 int row0,
 int row1,
 Matrix out)

Extracts a range of rows from the matrix [row0:row1) into a destination matrix.

Parameters:

A - The source matrix

row0 - Starting row index (inclusive)

row1 - Ending row index (exclusive)

out - (Optional) Output matrix to store the result; can be null

Returns:

A matrix containing the extracted rows

eye

public static Matrix eye(int length)

Creates an identity matrix of given size.

Parameters:

length - The number of rows and columns in the identity matrix

Returns:

A sparse identity matrix of size length x length

factln

public static Matrix factln(Matrix n)

Computes the natural logarithm of the factorial (log(x!)) for each element in the input matrix. The input matrix is assumed to contain non-negative integers or values appropriate for factln().

Parameters:

n - Input matrix

Returns:

A matrix where each element is log(n_i!)

findIndexWithZeroSum

public static List<Integer> findIndexWithZeroSum(Matrix matrix,
 boolean isRow)

Finds the indices of all rows or columns in a matrix that have a sum of zero.

Parameters:

matrix - The matrix to check

isRow - If true, checks rows; if false, checks columns

Returns:

A list of indices corresponding to zero-sum rows or columns

findRows

public static List<Integer> findRows(Matrix matrix,
 Matrix row)

Finds the indices of all rows in a matrix that exactly match a given row vector.

Parameters:

matrix - The matrix to search

row - A 1-row matrix to compare against

Returns:

A list of row indices in matrix that match row

firstNorm

public static double firstNorm(Matrix a)

Computes the 1-norm (maximum absolute column sum) of the matrix.

Parameters:

a - The input matrix

Returns:

The 1-norm of the matrix

getColIndexSum

public static int getColIndexSum(Map<Integer,Matrix> cellArray)

Computes the total number of elements across all matrices in a map, summing numRows * numCols for each matrix.

Parameters:

cellArray - A map of matrices

Returns:

The total number of scalar elements across all matrices

getSubMatrix

public static Matrix getSubMatrix(Matrix sourceMatrix,
 int x0,
 int x1,
 int y0,
 int y1)

Extracts a submatrix from the source matrix using zero-based index ranges. The submatrix spans rows [x0:x1) and columns [y0:y1).

Parameters:

sourceMatrix - The source matrix

x0 - Starting row index (inclusive)

x1 - Ending row index (exclusive)

y0 - Starting column index (inclusive)

y1 - Ending column index (exclusive)

Returns:

A new matrix containing the specified submatrix

infNorm

public static double infNorm(Matrix a)

Computes the infinity norm (maximum absolute row sum) of the matrix.

Parameters:

a - The input matrix

Returns:

The infinity norm of the matrix

infinityNorm

public double infinityNorm()

Computes the infinity norm of this matrix. The infinity norm is the maximum row sum of absolute values.

Returns:

The infinity norm of this matrix

extractCols

public Matrix extractCols(int col0,
 int col1)

Extracts a range of columns from this matrix (instance method).

Parameters:

col0 - The starting column index (inclusive)

col1 - The ending column index (exclusive)

Returns:

A new matrix containing columns [col0, col1)

extractRows

public Matrix extractRows(int row0,
 int row1)

Extracts rows from this matrix (instance method).

Parameters:

row0 - The starting row index (inclusive)

row1 - The ending row index (exclusive)

Returns:

A new matrix containing rows [row0, row1)

intersect

public static List<Double> intersect(Matrix matrixA,
 Matrix matrixB)

Computes the intersection of scalar values present in two matrices. The result is a list of distinct values that appear in both matrices.

Parameters:

matrixA - First input matrix

matrixB - Second input matrix

Returns:

A list of values common to both matrices

inv

public static Matrix inv(Matrix m)

Computes the inverse of the given matrix. Delegates to the matrix's inv() method.

Parameters:

m - The input matrix

Returns:

The inverse of the matrix

logSum

public static double logSum(Matrix matrix)

Computes the sum of the natural logarithms of all elements in the matrix.

Parameters:

matrix - The input matrix

Returns:

The sum of log(x) over all elements x in the matrix

Throws:

ArithmeticException - if any element is ≤ 0

logsumexp

public static double logsumexp(Matrix x)

Computes log(sum_i exp(x_i)) in a numerically stable way (log-sum-exp trick). This is commonly used in probabilistic computations to avoid underflow.

Parameters:

x - Input matrix treated as a vector of values x₁, x₂, ..., xₙ

Returns:

The log-sum-exp of the input values

lyap

public static Matrix lyap(Matrix A,
 Matrix B,
 Matrix C,
 Matrix D)

Computes the solution to the continuous-time Lyapunov equation AX + XAᵀ + Q = 0. Currently redirects to sylv(jline.util.matrix.Matrix, jline.util.matrix.Matrix, jline.util.matrix.Matrix) assuming it implements the solver.

Parameters:

A - The matrix A

B - Ignored

C - The matrix Q

D - Ignored

Returns:

The solution matrix X

dlyap

public static Matrix dlyap(Matrix A,
 Matrix B,
 Matrix C)

Solves the discrete Sylvester equation A * X * B - X + C = 0. Equivalent to MATLAB's dlyap(A, B, C). Uses the Kronecker product formulation: (kron(B', A) - I) * vec(X) = -vec(C)

Parameters:

A - Left coefficient matrix

B - Right coefficient matrix

C - Constant matrix

Returns:

Solution matrix X

matchrow

public static int matchrow(Matrix matrix,
 Matrix row)

Returns the index of the row in the matrix that exactly matches the given row vector.

Parameters:

matrix - The matrix to search

row - A single-row matrix to match

Returns:

The index of the matching row, or -1 if no match is found

matrixAddVector

public static Matrix matrixAddVector(Matrix matrix,
 Matrix vector)

Adds a vector to each row or column of the matrix, depending on the vector's orientation.

Parameters:

matrix - The input matrix

vector - A column vector (adds to each row) or a row vector (adds to each column)

Returns:

A new matrix with the vector added

Throws:

RuntimeException - if the vector shape is incompatible with the matrix

maxAbsDiff

public static double maxAbsDiff(Matrix a,
 Matrix b)

Computes the maximum relative absolute difference between corresponding elements of two matrices: max(abs((a - b) / b)).

Parameters:

a - First matrix

b - Second matrix (denominator for relative difference)

Returns:

The maximum relative absolute difference

negative

public static Matrix negative(Matrix a)

Negates all elements in the matrix and returns the result. Operates directly on the sparse structure for performance.

Parameters:

a - The input matrix

Returns:

A new matrix with all values negated

oneMinusMatrix

public static Matrix oneMinusMatrix(Matrix matrix)

Computes the matrix 1 - A, where diagonal entries become 1 - A(i, i) and off-diagonal entries become -A(i, j).

Parameters:

matrix - The input matrix

Returns:

A matrix where each element is replaced by (1 - A(i, i)) on the diagonal and -A(i, j) elsewhere

oner

public static Matrix oner(Matrix N,
 Integer s)

Decreases a single element of an integer vector by one.

Parameters:

N - The input vector

s - The index to decrement

Returns:

A new vector with element s decreased by one, if in bounds

oner

public static Matrix oner(Matrix N,
 List<Integer> r)

Decreases multiple elements of an integer vector by one.

Parameters:

N - The input vector

r - A list of indices to decrement

Returns:

A new vector with elements at positions in r decreased by one

ones

public static Matrix ones(int rows,
 int cols)

Creates a matrix of the given shape filled with ones.

Parameters:

rows - Number of rows

cols - Number of columns

Returns:

A matrix of shape (rows x cols) filled with ones

pow

public static Matrix pow(Matrix a,
 int b)

Computes the matrix power A^b for a non-negative integer exponent b. This is done by repeated multiplication and assumes b ≥ 0.

Parameters:

a - The base matrix

b - The exponent (must be ≥ 0)

Returns:

The matrix a raised to the power b

readFromFile

public static Matrix readFromFile(String fileName)

Reads a CSV-formatted matrix from a file. Each line is interpreted as a row. Supports numeric values as well as "Inf" and "-Inf".

Parameters:

fileName - Path to the CSV file

Returns:

A new Matrix containing the data read from the file

Throws:

RuntimeException - if the file cannot be read or parsed

removeRows

public static double[][][] removeRows(double[][][] array,
 Matrix rowsToRemove)

removeTrailingNewLine

public static String removeTrailingNewLine(String str)

scaleMult

public static Matrix scaleMult(Matrix a,
 double n)

Multiplies all elements of a matrix by a scalar. (Marked for removal — consider using matrix.scaleEq(n) directly.)

Parameters:

a - The input matrix

n - The scalar multiplier

Returns:

A new matrix equal to a * n

singleton

public static Matrix singleton(double value)

Creates a 1×1 matrix containing a single scalar value.

Parameters:

value - The scalar to store in the matrix

Returns:

A 1×1 matrix with the given value

solve

public static boolean solve(Matrix a,
 Matrix b,
 Matrix x)

Solves the sparse linear system Ax = b.

Parameters:

a - The coefficient matrix A

b - The right-hand side vector or matrix b

x - The solution matrix x (output)

Returns:

true if a solution was found, false otherwise

solveSafe

public static boolean solveSafe(Matrix a,
 Matrix b,
 Matrix x)

Solves the linear system Ax = b for x, handling singular matrices gracefully. This method does not throw exceptions for singular matrices, instead returning false and filling the result matrix with NaN values to match MATLAB behavior.

Parameters:

a - The coefficient matrix A

b - The right-hand side vector/matrix b

x - The solution matrix x (output)

Returns:

true if a solution was found, false if matrix is singular

solveDirect

public static boolean solveDirect(Matrix a,
 Matrix b,
 Matrix x)

Solves the linear system A*x = b directly using LU decomposition without singularity checks. Faster than solveSafe(jline.util.matrix.Matrix, jline.util.matrix.Matrix, jline.util.matrix.Matrix) for cases where the matrix is known to be non-singular or where the caller handles failures.

Parameters:

a - The coefficient matrix A (must be square)

b - The right-hand side matrix b

x - The solution matrix x (output)

Returns:

true if a solution was found, false if the LU solver failed

spectd

public static Ret.SpectralDecomposition spectd(Matrix A)

Computes the spectral decomposition of a matrix A using its eigendecomposition. Returns a diagonal matrix of eigenvalues and a cell array of spectral projectors. For diagonalizable matrices: A = V * D * V⁻¹, where D is the spectrum and each projector is v_k * (v_k⁻¹)^T. For defective matrices, falls back to Jordan decomposition or provides approximation.

Parameters:

A - The input matrix

Returns:

A SpectralDecomposition containing the diagonal spectrum and associated projectors

Throws:

RuntimeException - if the matrix cannot be decomposed

sumCumprod

public static double sumCumprod(Matrix matrix)

Computes the sum of the cumulative product along a row vector. For vector [a, b, c], returns a + ab + abc.

Parameters:

matrix - A 1-row matrix (row vector)

Returns:

The scalar sum of cumulative products

robustLeftDivide

public static Matrix robustLeftDivide(Matrix A,
 Matrix B)

Robust linear solve for A·X = B that handles singular matrices. Tries standard leftMatrixDivide first, falls back to pseudo-inverse on failure.

Parameters:

A - Coefficient matrix (may be singular)

B - Right-hand side matrix

Returns:

Solution matrix X

sylv

public static Matrix sylv(Matrix A,
 Matrix B,
 Matrix C)

Solves the Sylvester equation A·X + X·B = -C using a Schur decomposition-based method. Handles the case where B = Aᵀ with a specialized backward solve, otherwise proceeds forward.

Parameters:

A - Left coefficient matrix

B - Right coefficient matrix

C - Constant matrix

Returns:

Solution matrix X

tril

public static Matrix tril(Matrix matrix)

Returns the lower triangular part of a matrix (zeroing elements above the main diagonal).

Parameters:

matrix - The input matrix

Returns:

A lower triangular matrix with upper entries set to zero

tril

public static Matrix tril(Matrix matrix,
 int k)

Returns the elements on and below the kth diagonal of matrix A. For k = 0, returns the main diagonal and below. For k = -1, returns only below the main diagonal (strict lower triangular). For k = 1, returns the main diagonal, below, and first superdiagonal.

Parameters:

matrix - the input matrix

k - the diagonal offset (0 = main diagonal, -1 = below main, 1 = above main)

Returns:

matrix with elements on and below the kth diagonal, others set to zero

union

public static Matrix union(Matrix A,
 Matrix B)

Computes the union of two matrices A and B. For each non-zero element in B, overwrites the corresponding value in A. The resulting matrix is a clone of A with B's non-zero entries inserted.

Parameters:

A - The base matrix

B - The matrix whose non-zero entries override A

Returns:

A matrix representing the union of A and B

uniqueRowIndexes

public static UniqueRowResult uniqueRowIndexes(Matrix m)

Finds the indices of unique rows in a matrix without returning a matrix of the unique rows themselves. Returns: - vi: indices of the first occurrence of each unique row - vj_map: maps unique row indices to a list of positions where that row occurs

Parameters:

m - The input matrix

Returns:

A UniqueRowResult containing index mappings of unique rows

uniqueRowIndexesFromColumn

public static UniqueRowResult uniqueRowIndexesFromColumn(Matrix m,
 int startCol)

Identifies unique rows in a matrix starting from a specified column index. Does not return the unique row data itself, only index mappings. Uses string-based keys to handle state spaces that exceed integer hash range.

Parameters:

m - The input matrix

startCol - The column index from which uniqueness is considered

Returns:

A UniqueRowResult containing: - vi: indices of first occurrence of each unique row pattern - vj_map: groupings of row indices by unique pattern

uniqueRows

public static UniqueRowResult uniqueRows(Matrix m)

Finds all unique rows in a matrix and returns the unique sorted rows, along with mapping indices to/from the original matrix. Uses efficient array-based hashing instead of Matrix objects as keys.

Parameters:

m - The input matrix

Returns:

A UniqueRowResult containing: - the matrix of sorted unique rows, - vi: indices of first occurrences, - vj_map: row groupings in the original matrix

weaklyConnect

public static Set<Set<Integer>> weaklyConnect(Matrix param,
 Set<Integer> colsToIgnore)

Weakly-connected components of a sub-matrix. Constructs an undirected graph from the input matrix, ignoring specified columns, and returns the set of weakly connected components.

Parameters:

param - Input matrix

colsToIgnore - Indexes to be ignored

Returns:

A set of sets, each representing a weakly connected component

zeros

public static Matrix zeros(int rows,
 int cols)

Creates a matrix of the specified shape filled with zeros.

Parameters:

rows - Number of rows

cols - Number of columns

Returns:

A zero-initialized matrix of size (rows x cols)

absEq

public void absEq()

add

public Matrix add(Matrix matrix)

Adds another matrix to this matrix: this + matrix.

Parameters:

matrix - The matrix to add

Returns:

A new matrix containing the sum

add

public Matrix add(double alpha)

Adds a scalar multiple of the all-ones matrix to this matrix: this + alpha * 1.

Parameters:

alpha - The scalar multiplier

Returns:

A new matrix representing the addition

add

public Matrix add(double alpha,
 Matrix matrix)

Adds alpha * matrix to this matrix.

Parameters:

alpha - The scalar multiplier

matrix - The matrix to add

Returns:

A new matrix containing the result

addEq

public void addEq(double alpha)

Adds a scalar value to each element of the matrix in-place.

Parameters:

alpha - The scalar value to add

addEq

public void addEq(Matrix matrix)

Adds another matrix to this matrix in-place: this += matrix.

Parameters:

matrix - The matrix to add

addEq

public void addEq(double alpha,
 Matrix matrix)

Adds alpha * matrix to this matrix in-place: this += alpha * matrix.

Parameters:

alpha - The scalar multiplier

matrix - The matrix to add

allEqualToOne

public boolean allEqualToOne()

Checks whether all elements in the matrix are equal to 1.

Returns:

true if all elements are exactly 1.0, false otherwise

any

public boolean any()

apply

public void apply(double source,
 double target,
 String op)

Applies a conditional element-wise transformation to the matrix. For each element matching a condition based on source and op, the value is replaced with target.

Supported operations include: "equal", "notequal", "great", "greatequal", "less", "lessequal".

This method safely handles special cases like zero, NaN, and Infinity.

Parameters:

source - The reference value for the comparison

target - The value to assign if the condition holds

op - The comparison operator

ceil

public Matrix ceil()

Returns a new matrix where each element is the ceiling of the corresponding element in this matrix.

Returns:

A new matrix with the ceiling applied element-wise.

ceilEq

public Matrix ceilEq()

Applies the ceiling operation in-place to each element of this matrix.

Returns:

This matrix after applying ceiling element-wise.

changeSign

public void changeSign()

Negates all values in the matrix, in-place.

copy

public Matrix copy()

Returns a deep copy of this matrix.

Returns:

A cloned matrix identical to this one.

colIncrease

public void colIncrease(int col,
 double a)

colon

public Matrix colon()

Returns the matrix in column-major order.

Returns:

The same matrix interpreted in column-major order.

columnMajorOrder

public Matrix columnMajorOrder()

Equivalent to the colon operator in MATLAB (:). Flattens the matrix in column-major order into a single column vector.

Returns:

A column vector representing the matrix in column-major order.

compareMatrix

public boolean compareMatrix(Matrix matrix)

Compares this matrix to another matrix for approximate equality. Tolerance is defined by GlobalConstants.FineTol.

Parameters:

matrix - The matrix to compare against.

Returns:

true if all elements are approximately equal, false otherwise.

compatibleSizesAdd

public Matrix compatibleSizesAdd(Matrix b)

Performs element-wise addition with shape broadcasting where applicable.

Parameters:

b - Matrix to be added.

Returns:

Result of the addition with compatible broadcasting.

concatCols

public Matrix concatCols(Matrix other)

Concatenates this matrix with another matrix horizontally.

Parameters:

other - Matrix to concatenate.

Returns:

A new matrix with columns of both matrices concatenated.

count

public int count(double val)

Counts how many elements in the matrix are equal to a specified value.

Parameters:

val - Value to count.

Returns:

Number of occurrences of the value.

countEachRow

public Matrix countEachRow(double val)

Counts the number of occurrences of a value in each row of the matrix.

Parameters:

val - Value to count.

Returns:

A column vector where each entry is the count for the corresponding row.

createBlockDiagonal

public Matrix createBlockDiagonal(Matrix matrix2)

Creates a block diagonal matrix by placing the current matrix in the top-left and another matrix (if provided) in the bottom-right.

Parameters:

matrix2 - The second matrix to place on the block diagonal. Can be null.

Returns:

A new block diagonal matrix combining this and matrix2.

cumsumViaCol

public Matrix cumsumViaCol()

Computes the cumulative sum of the matrix down each column.

Returns:

A matrix where each element is the cumulative sum along its column.

cumsumViaRow

public Matrix cumsumViaRow()

Computes the cumulative sum of the matrix across each row.

Returns:

A matrix where each element is the cumulative sum along its row.

det

public double det()

Computes the determinant of the matrix.

Returns:

Determinant value.

div

public Matrix div(Matrix den)

Performs element-wise division between this matrix and the provided matrix.

Parameters:

den - The denominator matrix.

Returns:

A new matrix resulting from element-wise division.

divEq

public void divEq(Matrix den)

Performs in-place element-wise division between this matrix and the provided matrix.

Parameters:

den - The denominator matrix.

divide

public void divide(double scalar,
 Matrix outputB,
 boolean flag)

Divides this matrix by a scalar and stores the result in the output matrix.

Parameters:

scalar - The scalar divisor.

outputB - The matrix to store the result.

flag - If true, performs matrix / scalar; if false, scalar / matrix.

divideEq

public void divideEq(double scalar)

Performs in-place division of this matrix by a scalar.

Parameters:

scalar - The scalar divisor.

divideRows

public void divideRows(double[] diag,
 int offset)

Divides each row of this matrix by the corresponding diagonal element (with an offset).

Parameters:

diag - Array of diagonal values.

offset - Starting offset in the diagonal array.

eigval

public Ret.Eigs eigval()

Computes the eigenvalues of this square matrix.

Returns:

A Ret.Eigs object containing the eigenvalues as a column matrix. If the matrix has complex eigenvalues, the result contains NaN values.

eig

public List<org.apache.commons.math3.complex.Complex> eig()

Computes the eigenvalues of this square matrix, including complex eigenvalues.

Returns:

A list of complex eigenvalues (using Apache Commons Math3 Complex class).

eigvec

public Ret.Eigs eigvec()

Computes the eigenvalues and eigenvectors of this square matrix.

Returns:

A Ret.Eigs object containing the eigenvalues and eigenvectors.

svd

public Ret.SVD svd()

Computes the Singular Value Decomposition (SVD) of this matrix. The decomposition is A = U * S * V^T where: - U contains the left singular vectors - S is a diagonal matrix of singular values - V contains the right singular vectors

Returns:

A Ret.SVD object containing U, S (as column vector), and V matrices.

expm

public Matrix expm()

Computes the matrix exponential. This is a convenience method that delegates to expm_higham().

Returns:

The matrix exponential e^A

Throws:

IllegalArgumentException - if the matrix is not square

expm_higham

public Matrix expm_higham()

Computes the matrix exponential using Higham's scaling and squaring method. This is an implementation of the algorithm from: Higham, N.J. (2005). "The scaling and squaring method for the matrix exponential revisited." SIAM Journal on Matrix Analysis and Applications, 26(4), 1179-1193.

Returns:

The matrix exponential e^A

Throws:

IllegalArgumentException - if the matrix is not square

norm1

public double norm1()

Computes the 1-norm of the matrix (maximum absolute column sum).

Returns:

The 1-norm of the matrix

elementDiv

public Matrix elementDiv(Matrix B)

Performs element-wise division of this matrix by another matrix.

Parameters:

B - The divisor matrix (must match dimensions).

Returns:

A new matrix with the result of element-wise division A ./ B.

Throws:

IllegalArgumentException - if matrix dimensions do not match.

elementDivide

public Matrix elementDivide(Matrix b)

Performs element-wise division with another matrix.

Parameters:

b - the matrix to divide by

Returns:

the result of element-wise division

Throws:

RuntimeException - if matrix dimensions do not match

elementIncrease

public Matrix elementIncrease(double val)

Increases each element of the matrix by a constant value.

Parameters:

val - the value to add to each element

Returns:

a new matrix with incremented values

elementMax

public double elementMax()

Returns the maximum value among all elements in the matrix.

Returns:

maximum element value

elementMaxAbs

public double elementMaxAbs()

Returns the maximum absolute value among all elements in the matrix.

Returns:

maximum absolute element value

elementMin

public double elementMin()

Returns the minimum value among all elements in the matrix.

Returns:

minimum element value

elementMult

public Matrix elementMult(Matrix B)

Performs in-place element-wise multiplication with another matrix.

Parameters:

B - the matrix to multiply with

Returns:

the updated matrix (this)

elementMult

public Matrix elementMult(Matrix B,
 Matrix output)

Performs element-wise multiplication with another matrix, storing the result in the given output matrix.

Parameters:

B - the matrix to multiply with

output - the matrix to store the result in (if null, a new matrix is created)

Returns:

the result of the element-wise multiplication

elementMult

public double elementMult()

Computes the product of the elements of a row or column vector.

Returns:

the product of all elements

Throws:

IllegalArgumentException - if the matrix is not a row or column vector

elementMultWithVector

public Matrix elementMultWithVector(Matrix B)

Performs element-wise multiplication between this matrix and a row vector. Each row of the matrix is scaled by the corresponding value in the vector.

Parameters:

B - the row vector to multiply with

Returns:

the result of the element-wise multiplication

elementPow

public Matrix elementPow(double a)

Raises each non-zero element of the matrix to the specified power.

Parameters:

a - the exponent

Returns:

a new matrix with powered elements

elementPower

public Matrix elementPower(double t)

Raises each element of the matrix to the given power.

Parameters:

t - the exponent

Returns:

a new matrix with each element raised to the power of t

elementSum

public double elementSum()

Computes the sum of all elements in the matrix.

Returns:

the sum of all elements

equals

public boolean equals(Object obj)

Checks for matrix equality.

Overrides:

equals in class Object

Parameters:

obj - the object to compare with

Returns:

true if matrices are equal, false otherwise

exp

public Matrix exp()

Applies the exponential function to each element of the matrix.

Returns:

a new matrix with exponentiated elements

expandMatrix

public void expandMatrix(int rows,
 int cols,
 int nz_length)

Expands the matrix dimensions to the specified size while preserving data.

Parameters:

rows - new row count

cols - new column count

nz_length - estimated non-zero count

expandMatrixToSquare

public void expandMatrixToSquare()

Expands the matrix to be square, padding with zeros as needed.

fact

public Matrix fact()

Computes the factorial of each element in the matrix. Equivalent to exp(factln()).

Returns:

a matrix with the factorial of each element

factln

public Matrix factln()

Computes the natural logarithm of the factorial for each element.

Returns:

a matrix where each element is the log-factorial of the original element

fill

public Matrix fill(double val)

Fills all entries in the matrix with the given value.

Parameters:

val - the value to fill with

Returns:

this matrix after filling

find

public Matrix find()

Returns the linear indices of all non-zero elements in the matrix.

Returns:

a column vector containing indices of non-zero entries

findNonNegative

public Matrix findNonNegative()

Returns the linear indices of all elements that are non-negative (≥ 0).

Returns:

a column vector of indices for non-negative elements

findNonZeroRowsInColumn

public List<Integer> findNonZeroRowsInColumn(int column)

Finds all row indices in a given column where the value is non-zero.

Parameters:

column - the column index to check

Returns:

a list of row indices with non-zero values in the given column

findNumber

public Matrix findNumber(double number)

Finds all linear indices where the matrix has a specific value.

Parameters:

number - the value to search for

Returns:

a matrix containing the linear indices where the value matches

findZero

public Matrix findZero()

Finds all linear indices where the matrix value is zero.

Returns:

a matrix containing the linear indices of zero-valued elements

fromArray2D

public Matrix fromArray2D(int[][] matrix)

Populates the matrix from a 2D integer array.

Parameters:

matrix - 2D array of integers

Returns:

this matrix after population

fromArray2D

public Matrix fromArray2D(double[][] matrix)

Populates the matrix from a 2D double array.

Parameters:

matrix - 2D array of doubles

Returns:

this matrix after population

get

public double get(int i,
 int j)

Returns the value at the specified row and column.

Parameters:

i - row index

j - column index

Returns:

value at (i, j)

get

public double get(int idx)

Returns the value at the specified index. For vectors (either row or column), returns the idx-th element. For matrices, returns the value at the flattened index (column-major).

Parameters:

idx - absolute index

Returns:

value at index

getColIndexes

public int[] getColIndexes()

Returns internal column index array from the sparse matrix structure.

Returns:

array of column indexes

getColMax

public int getColMax(int col)

Returns the row index of the maximum value in the specified column.

Parameters:

col - column index

Returns:

row index of maximum value

getColumn

public Matrix getColumn(int j)

Returns a column of the matrix as a new single-column matrix.

Parameters:

j - column index

Returns:

column matrix

getColumnView

public ColumnView getColumnView(int j)

Returns a lightweight view into the specified column without copying data. This is much more efficient than getColumn() for large sparse matrices as it doesn't create a new Matrix object or copy any data.

Use this when you need to iterate through column elements or perform operations that don't require a full Matrix object.

Parameters:

j - column index

Returns:

a ColumnView providing efficient access to the column

getData

public org.ejml.data.DMatrix getData()

setData

public void setData(org.ejml.data.DMatrix newData)

getNonZeroCols

public int[] getNonZeroCols()

Returns an array of unique column indices containing non-zero elements.

Returns:

array of column indices

getNonZeroLength

public int getNonZeroLength()

Returns the number of non-zero values in the matrix.

Returns:

number of non-zero elements

getNonZeroRows

public int[] getNonZeroRows()

Returns array of row indices of non-zero entries.

Returns:

array of row indices

getNonZeroValues

public double[] getNonZeroValues()

Returns array of non-zero values in the matrix.

Returns:

array of non-zero values

getNonZeros

public int getNonZeros()

Returns the number of non-zero elements in this matrix.

Returns:

the number of non-zero elements

getNumCols

public int getNumCols()

Returns the number of columns in this matrix.

Returns:

the number of columns

getNumElements

public int getNumElements()

Returns total number of elements in the matrix.

Returns:

total element count

getNumNonZeros

public int getNumNonZeros()

getNumRows

public int getNumRows()

Returns the number of rows in this matrix.

Returns:

the number of rows

getRow

public Matrix getRow(int i)

Returns the specified row as a single-row matrix.

Parameters:

i - row index

Returns:

row matrix

getRowMax

public int getRowMax(int row)

Returns column index of maximum element in a specified row.

Parameters:

row - the row index

Returns:

column index of max value

getRowView

public RowView getRowView(int i)

Returns a lightweight view into the specified row without copying data. This is much more efficient than getRow() for large sparse matrices as it doesn't create a new Matrix object or copy any data.

Use this when you need to iterate through row elements or perform operations that don't require a full Matrix object.

Parameters:

i - row index

Returns:

a RowView providing efficient access to the row

getRowsFrom

public Matrix getRowsFrom(int row)

Returns a new matrix consisting of rows from the given start index to the end.

Parameters:

row - starting row index

Returns:

matrix slice

getSlice

public Matrix getSlice(int r0,
 int r1,
 int c0,
 int c1)

Extracts a submatrix based on row/column bounds.

Parameters:

r0 - start row

r1 - end row (exclusive)

c0 - start column

c1 - end column (exclusive)

Returns:

submatrix

getSlice

public Matrix getSlice(boolean[] rowFlags,
 boolean[] colFlags)

Extracts a submatrix from rows/columns marked as true in input flags.

Parameters:

rowFlags - boolean array for rows

colFlags - boolean array for columns

Returns:

submatrix

getSubMatrix

public Matrix getSubMatrix(Matrix rows,
 Matrix cols)

Returns a matrix consisting of rows and columns selected by two index matrices.

Parameters:

rows - matrix of row indices

cols - matrix of column indices

Returns:

submatrix

growMaxColumns

public void growMaxColumns(int newmax,
 boolean preserve)

Increases the internal column capacity of the matrix.

Parameters:

newmax - new max columns

preserve - true if data should be preserved

growMaxLength

public void growMaxLength(int newmax,
 boolean preserve)

Increases the internal non-zero element capacity of the matrix.

Parameters:

newmax - new max size

preserve - true if data should be preserved

hadamard

public Matrix hadamard(Matrix B)

Performs the Hadamard (element-wise) product of two matrices.

Parameters:

B - the other matrix

Returns:

matrix resulting from element-wise multiplication

hasDuplicates

public boolean hasDuplicates()

hasFinite

public boolean hasFinite()

hasInfinite

public boolean hasInfinite()

hasMultipleFinite

public boolean hasMultipleFinite()

hasNaN

public boolean hasNaN()

hashCode

public int hashCode()

Generates a hash code for the matrix based on its values.

Overrides:

hashCode in class Object

Returns:

hash code

insertSubMatrix

public void insertSubMatrix(int start_row,
 int start_col,
 int end_row,
 int end_col,
 Matrix matrix_to_be_inserted)

Inserts a sub-matrix into the current matrix at the specified location.

Parameters:

start_row - Starting row index

start_col - Starting column index

end_row - Ending row index

end_col - Ending column index

matrix_to_be_inserted - Matrix to insert

inv

public Matrix inv()

Computes the inverse of the matrix.

Returns:

the inverse matrix

pinv

public Matrix pinv()

Computes the Moore-Penrose pseudo-inverse of the matrix using SVD. Works for singular, rank-deficient, and non-square matrices. For full-rank square matrices, this is equivalent to inv().

Returns:

the pseudo-inverse matrix

isAssigned

public boolean isAssigned(int row,
 int col)

Checks whether a specific element is assigned in the sparse matrix.

Parameters:

row - Row index

col - Column index

Returns:

true if assigned, false otherwise

isDiag

public boolean isDiag()

Determines whether the matrix is a diagonal matrix. Zero matrices are not considered diagonal in this implementation.

Returns:

true if diagonal, false otherwise

isEmpty

public boolean isEmpty()

Checks if the matrix is empty (has zero rows or columns).

Returns:

true if empty, false otherwise

isEqualTo

public boolean isEqualTo(Matrix m)

Checks if two matrices are exactly equal.

Parameters:

m - the matrix to compare

Returns:

true if equal, false otherwise

isEqualToTol

public boolean isEqualToTol(Matrix m,
 double tol)

Checks if two matrices are equal within a specified tolerance.

Parameters:

m - matrix to compare

tol - tolerance value

Returns:

true if equal within tolerance, false otherwise

isFinite

public boolean isFinite()

Checks whether all matrix elements are finite.

Returns:

true if all elements are finite, false otherwise

isInteger

public boolean isInteger()

Checks if all values in the matrix are integers.

Returns:

true if all values are integers, false otherwise

keepCols

public void keepCols(Collection<Integer> cols)

Keeps only the specified columns in the matrix. Any column not listed will be removed. For better performance, prefer passing a HashSet for `cols`.

Parameters:

cols - Collection of column indices to retain

keepRows

public void keepRows(Collection<Integer> rows)

Keeps only the specified rows in the matrix. Any row not listed will be removed. For better performance, prefer passing a HashSet for `rows`.

Parameters:

rows - Collection of row indices to retain

kron

public Matrix kron(Matrix b)

Computes the Kronecker product of this matrix and another matrix.

Parameters:

b - The matrix to compute the Kronecker product with

Returns:

The Kronecker product matrix

krons

public Matrix krons(Matrix other)

Computes the Kronecker sum of two matrices: A ⊕ B = A \otimes I + I \otimes B, where \otimes is the Kronecker product and I is the identity matrix of matching size.

Parameters:

other - The other matrix

Returns:

The Kronecker sum of this matrix and the other matrix

leftMatrixDivide

public Matrix leftMatrixDivide(Matrix b)

Solves the equation AX = B for X, where A is this matrix and B is the right-hand side. For square matrices, this solves the exact system. For rectangular matrices (overdetermined), this computes the least squares solution using the normal equation: X = (A^T * A)^-1 * A^T * B.

Parameters:

b - The right-hand side matrix

Returns:

The solution matrix X

length

public int length()

Returns the length of the matrix, defined as max(rows, cols).

Returns:

The maximum dimension of the matrix

log

public Matrix log()

Applies the natural logarithm element-wise.

Returns:

A new matrix with log applied to each element

meanCol

public Matrix meanCol()

Computes the mean of each column.

Returns:

A 1xN matrix containing the mean of each column

meanRow

public Matrix meanRow()

Computes the mean of each row.

Returns:

An Nx1 matrix containing the mean of each row

mulByMinusOne

public void mulByMinusOne()

Multiplies all elements in the matrix by -1 in-place.

mult

public Matrix mult(Matrix B)

Performs matrix multiplication: this * B

Parameters:

B - The right-hand side matrix

Returns:

Resultant matrix

mult

public Matrix mult(Matrix B,
 Matrix out)

Performs matrix multiplication: this * B

Parameters:

B - The right-hand side matrix

out - Output matrix to write result to (can be null)

Returns:

Resultant matrix

multColumnView

public double multColumnView(ColumnView columnView)

Efficiently multiplies this row vector with a column view. This is optimized for the common pattern: rowVector.mult(matrix.getColumn(j)) by avoiding the creation of intermediate Matrix objects.

Parameters:

columnView - the column view to multiply with

Returns:

the scalar result of the multiplication

Throws:

IllegalArgumentException - if this matrix is not a row vector or dimensions don't match

multEq

public void multEq(Matrix B)

Replaces this matrix with the result of this * B.

Parameters:

B - The right-hand side matrix

multRowView

public double multRowView(RowView rowView)

Efficiently multiplies a row view with this column vector. This is optimized for the common pattern: matrix.getRow(i).mult(columnVector) by avoiding the creation of intermediate Matrix objects.

Parameters:

rowView - the row view to multiply with

Returns:

the scalar result of the multiplication

Throws:

IllegalArgumentException - if this matrix is not a column vector or dimensions don't match

norm

public double norm()

Computes the Euclidean norm of a matrix

Returns:

- the Euclidean norm of the given matrix

normFrobenius

public double normFrobenius()

Computes the Frobenius norm of a matrix (alias for norm()).

Returns:

- the Frobenius norm of the given matrix

ones

public void ones()

Fills the matrix with ones. Matrix must already be initialized with correct size. Throws an exception if matrix cannot be fully filled.

powerSumCols

public double powerSumCols(int col,
 double alpha)

Computes the sum of powers of absolute values in a column: ∑ |A_{ji}|^alpha

Parameters:

col - The column index

alpha - The exponent to raise each absolute value

Returns:

The computed sum

powerSumRows

public double powerSumRows(int row,
 double alpha)

Computes the sum of powers of absolute values in a row: ∑ |A_{ij}|^alpha

Parameters:

row - The row index

alpha - The exponent to raise each absolute value

Returns:

The computed sum

prettyPrint

public void prettyPrint()

Pretty prints the matrix with automatic formatting and alignment. Supports real, NaN, Inf, and -Inf values.

prettyPrintInt

public void prettyPrintInt()

Pretty prints the matrix assuming integer values.

print

public void print()

Prints the matrix with appropriate formatting, either as floats or integers.

printNonZero

public void printNonZero()

Prints only non-zero values and their positions in the matrix.

qr

public Map<String,Matrix> qr()

Performs QR decomposition on the matrix. Only square matrices are currently supported.

Returns:

A map containing "Q" and "R" matrices from the decomposition.

randMatrix

public void randMatrix(int length)

Fills the matrix with random values between 0 and 1.

Parameters:

length - The number of rows and columns in the square matrix.

rank

public int rank()

Computes the rank of the matrix.

Returns:

The rank of the matrix.

reciprocal

public Matrix reciprocal()

Computes the element-wise reciprocal (1/x) of the matrix.

Returns:

A new matrix with reciprocal values.

remove

public void remove(int row,
 int col)

Removes a specific element from the matrix at the given row and column.

Parameters:

row - The row index

col - The column index

removeCols

public void removeCols(Collection<Integer> cols)

Removes the specified columns from the matrix. It is recommended to use a HashSet for efficiency when checking column indices.

Parameters:

cols - The indices of columns to be removed.

removeInfinite

public void removeInfinite()

Replaces all infinite values (positive or negative) in the matrix with 0. Also adjusts internal bookkeeping fields to maintain structural integrity.

removeInfinity

public void removeInfinity()

Removes all infinite values (positive or negative) from the sparse matrix structure. This shifts remaining values to preserve compactness.

removeNaN

public void removeNaN()

Removes all NaN values from the matrix structure. Internal arrays are compacted and updated accordingly.

removeNegative

public void removeNegative()

Removes all negative values from the matrix structure. Shifts non-negative values to preserve compactness.

removeRows

public void removeRows(Collection<Integer> rows)

Removes the specified rows from the matrix. If possible, use a HashSet for better performance.

Parameters:

rows - the indices of the rows to be removed

removeZeros

public void removeZeros(double val)

Removes values from the matrix that are equal to the specified value.

Parameters:

val - the value to be removed (typically 0)

replace

public void replace(double delete,
 double replacement)

Replaces all occurrences of a specific value with a new value in the matrix. Uses optimized sparse iteration when replacing non-zero values.

Parameters:

delete - the value to be replaced

replacement - the value to insert in place of the deleted value

repmat

public Matrix repmat(int rows,
 int cols)

Repeats the matrix to match the specified row and column replication.

Parameters:

rows - number of times to repeat along the row dimension

cols - number of times to repeat along the column dimension

Returns:

a new matrix formed by repeating this matrix

reshape

public void reshape(int numRows,
 int numCols)

Reshapes the matrix to the specified number of rows and columns.

Parameters:

numRows - number of rows

numCols - number of columns

reshape

public void reshape(int numRows,
 int numCols,
 int arrayLength)

Reshapes the matrix with new dimensions and internal storage length.

Parameters:

numRows - number of rows

numCols - number of columns

arrayLength - number of non-zero entries the matrix can store

reverse

public Matrix reverse()

Reverses the elements of a vector (row or column) matrix. Equivalent to MATLAB's v(end:-1:1).

Returns:

a matrix with reversed elements

reverseRows

public Matrix reverseRows()

Reverses the order of rows in the matrix.

Returns:

a new matrix with rows in reverse order

rightMatrixDivide

public Matrix rightMatrixDivide(Matrix b)

Performs right matrix division A / B = A * inv(B)

Parameters:

b - the matrix to divide by (on the right)

Returns:

result of A / B

rowIncrease

public void rowIncrease(int row,
 double a)

Increases all elements in the specified row by a scalar value.

Parameters:

row - the row to modify

a - the scalar to add to each element in the row

safeMult

public Matrix safeMult(Matrix B)

scale

public Matrix scale(double scalar)

Scales the matrix by the given scalar value.

Parameters:

scalar - the value to scale each element by

Returns:

a new matrix scaled by the scalar

neg

public Matrix neg()

Returns the negation of this matrix (all elements multiplied by -1).

Returns:

a new matrix with all elements negated

scaleEq

public void scaleEq(double scalar)

Scales this matrix in-place by the given scalar value.

Parameters:

scalar - the value to scale each element by

scaleEq

public void scaleEq(double scalar,
 Matrix output)

Scales this matrix by the given scalar value and stores the result in the provided output matrix.

Parameters:

scalar - the scalar multiplier

output - the matrix to store the result

schur

public Map<String,Matrix> schur(String method,
 Integer iter)

Computes the Schur decomposition of the matrix.

Parameters:

method - method name, currently only "default" is supported

iter - number of iterations for the default method (null for default=1)

Returns:

a map containing the keys "T" (upper triangular matrix) and "U" (unitary matrix)

schur

public Map<String,Matrix> schur()

Computes the Schur decomposition with the default method and iteration count.

Returns:

a map with matrices "T" and "U" from the Schur decomposition

schurComplex

public Map<String,ComplexMatrix> schurComplex()

Computes the complex Schur decomposition of this matrix, equivalent to MATLAB's schur(A,'complex'). The result has a truly upper-triangular T matrix with complex eigenvalues on the diagonal.

The method first computes the real Schur decomposition (which may have 2x2 blocks on the diagonal for complex eigenvalue pairs), then converts each 2x2 block to upper-triangular form using unitary Givens rotations.

Returns:

a map with keys "U" (ComplexMatrix, unitary) and "T" (ComplexMatrix, upper triangular)

set

public void set(int idx,
 double val)

Sets the element at absolute index position to the given value.

Parameters:

idx - index in flattened format (row + col * numRows)

val - value to set

set

public void set(int row,
 int col,
 double val)

Sets the element at specified row and column. Removes the entry if the value is zero to maintain sparse representation.

Parameters:

row - row index

col - column index

val - value to set

set

public void set(int row,
 int col,
 int val)

Sets the element at specified row and column using an integer value. Interprets Integer.MAX_VALUE as +Inf, MIN_VALUE as -Inf.

Parameters:

row - row index

col - column index

val - value to set

setColumn

public Matrix setColumn(int j,
 Matrix col)

Sets the specified column to the values in the given vector.

Parameters:

j - the index of the column to set

col - the column vector to copy from

Returns:

this matrix after the operation

setColumns

public Matrix setColumns(int j0,
 int j1,
 Matrix cols)

Sets multiple columns starting from column index j0 to j1 (exclusive) using values from another matrix.

Parameters:

j0 - starting column index (inclusive)

j1 - ending column index (exclusive)

cols - the matrix containing new column values

Returns:

this matrix after the operation

setNaNTo

public void setNaNTo(double val)

Replaces all NaN entries in the matrix with the specified value.

Parameters:

val - value to replace NaNs with

setNaNToZero

public void setNaNToZero()

Replaces all NaN entries in the matrix with zero.

setRow

public Matrix setRow(int j,
 Matrix row)

Sets the specified row to the values in the given vector.

Parameters:

j - the index of the row to set

row - the row vector to copy from

Returns:

this matrix after the operation

setRows

public Matrix setRows(int i0,
 int i1,
 Matrix rows)

Sets multiple rows starting from row index i0 to i1 (exclusive) using values from another matrix.

Parameters:

i0 - starting row index (inclusive)

i1 - ending row index (exclusive)

rows - the matrix containing new row values

Returns:

this matrix after the operation

setSlice

public Matrix setSlice(int rowStart,
 int rowEnd,
 int colStart,
 int colEnd,
 Matrix newSlice)

Returns a new matrix representing the updated slice after assigning values from newSlice.

Parameters:

rowStart - starting row index (inclusive)

rowEnd - ending row index (exclusive)

colStart - starting column index (inclusive)

colEnd - ending column index (exclusive)

newSlice - the matrix containing the new values

Returns:

the updated submatrix

setSliceEq

public void setSliceEq(int rowStart,
 int rowEnd,
 int colStart,
 int colEnd,
 Matrix newSlice)

Sets the values of a submatrix (in-place) using the specified newSlice matrix.

Parameters:

rowStart - starting row index (inclusive)

rowEnd - ending row index (exclusive)

colStart - starting column index (inclusive)

colEnd - ending column index (exclusive)

newSlice - the matrix to copy values from

setTo

public void setTo(Matrix m)

Copies the data from another matrix into this matrix.

Parameters:

m - the matrix to copy from

setToNaN

public void setToNaN()

Sets all elements of the matrix to NaN.

shrinkNumCols

public void shrinkNumCols(int newmax)

shrinkNumRows

public void shrinkNumRows(int newmax)

sort

public Matrix sort()

Returns a new matrix with the non-zero values sorted in ascending order.

Returns:

a new matrix with sorted values

sortEq

public Matrix sortEq()

Sorts the current matrix's non-zero values in place.

Returns:

this matrix after sorting

sqrt

public Matrix sqrt()

Computes the element-wise square root of the matrix.

Returns:

the resulting matrix

square

public Matrix square()

Computes the matrix multiplied by itself.

Returns:

the squared matrix

sub

public Matrix sub(double x)

Subtract a scalar from all elements.

Parameters:

x - the scalar value to subtract

Returns:

the resulting matrix

sub

public Matrix sub(Matrix matrix)

Subtracts another matrix.

Parameters:

matrix - the matrix to subtract

Returns:

the resulting matrix

sub

public Matrix sub(double alpha,
 Matrix matrix)

Subtracts alpha-scaled version of the provided matrix.

Parameters:

alpha - the scalar multiplier

matrix - the matrix to subtract

Returns:

the resulting matrix

subEq

public void subEq(double x)

Subtracts a scalar from the current matrix in place.

Parameters:

x - the scalar to subtract

subEq

public void subEq(Matrix matrix)

Subtracts a matrix from the current matrix in place.

Parameters:

matrix - the matrix to subtract

subEq

public void subEq(double alpha,
 Matrix matrix)

Subtracts a scaled matrix from the current matrix in place.

Parameters:

alpha - the scale factor

matrix - the matrix to subtract

sumAbsCols

public double sumAbsCols(int col)

Sums the absolute values of the given column.

Parameters:

col - the column index

Returns:

the sum of absolute values in the column

sumAbsRows

public double sumAbsRows(int row)

Sums the absolute values of the given row.

Parameters:

row - the row index

Returns:

the sum of absolute values in the row

sumCols

public double sumCols(int col)

Sums the elements in the specified column.

Parameters:

col - the column index

Returns:

the sum of the column values

sumCols

public Matrix sumCols()

Sums the values in each column and returns the results as a row vector.

Returns:

a row vector with column sums

sumCols

public Matrix sumCols(int startRow,
 int endRow)

Computes the sum of a subset of rows for each column.

Parameters:

startRow - the starting row index (inclusive)

endRow - the ending row index (exclusive)

Returns:

a row vector with the sums of each column over the specified row range

sumRows

public double sumRows(int row)

Computes the sum of the values in a specific row.

Parameters:

row - the row index

Returns:

the sum of the row values

sumRows

public Matrix sumRows()

Computes the sum of each row and returns the result as a column vector.

Returns:

a column vector containing the sum of each row

sumRows

public Matrix sumRows(int startCol,
 int endCol)

Computes the sum over a subrange of columns for each row.

Parameters:

startCol - the starting column (inclusive)

endCol - the ending column (exclusive)

Returns:

a column vector with the row sums over the specified columns

sumSubMatrix

public double sumSubMatrix(int startRow,
 int endRow,
 int startCol,
 int endCol)

Computes the sum of the values in a rectangular submatrix.

Parameters:

startRow - the starting row (inclusive)

endRow - the ending row (exclusive)

startCol - the starting column (inclusive)

endCol - the ending column (exclusive)

Returns:

the sum of the submatrix values

sumSubMatrix

public double sumSubMatrix(int[] rowIndexes,
 int[] colIndexes)

Computes the sum of a submatrix defined by specific row and column indices.

Parameters:

rowIndexes - the array of row indices

colIndexes - the array of column indices

Returns:

the sum of the selected submatrix

sumSubMatrix

public double sumSubMatrix(boolean[] rowIndexes,
 boolean[] colIndexes)

Computes the sum of a submatrix defined by boolean selection flags.

Parameters:

rowIndexes - boolean array indicating selected rows

colIndexes - boolean array indicating selected columns

Returns:

the sum of the selected submatrix

toArray1D

public double[] toArray1D()

Converts the matrix to a flat 1D array in row-major order.

Returns:

the 1D array representation of the matrix

toArray2D

public double[][] toArray2D()

Converts the matrix to a 2D array representation.

Returns:

the 2D array representation of the matrix

toDMatrixSparseCSC

public org.ejml.data.DMatrixSparseCSC toDMatrixSparseCSC()

Converts this matrix to a copy of its underlying DMatrixSparseCSC structure.

Returns:

a deep copy of the internal sparse matrix representation

toDMatrixSparseCSC

public org.ejml.data.DMatrixSparseCSC toDMatrixSparseCSC(Matrix matrix)

Converts a specified matrix to a copy of its underlying DMatrixSparseCSC structure.

Parameters:

matrix - the matrix to convert

Returns:

a deep copy of the sparse matrix representation of the given matrix

toDouble

public Double toDouble()

Converts this matrix to a single Double value. Assumes the matrix is scalar (1x1), otherwise behavior is undefined.

Returns:

the single value contained in the matrix

toDoubleList

public List<List<Double>> toDoubleList()

Converts the matrix to a nested list of Double values.

Returns:

a list of lists representing rows and columns of the matrix

toIntArray1D

public int[] toIntArray1D()

Converts the matrix to a 1D array of int, flattening in row-major order.

Returns:

a 1D int array representing the matrix values cast to integers

toList1D

public List<Double> toList1D()

Converts the matrix into a 1D List of Double values in row-major order.

Returns:

a list containing all matrix elements in row-major order

toString

public String toString()

Returns a formatted string representation of the matrix. Each row is separated by a semicolon and new line.

Overrides:

toString in class Object

Returns:

the string representation of the matrix

transpose

public Matrix transpose()

Computes the transpose of the current matrix.

Returns:

a new matrix representing the transpose of this matrix

uniqueInCol

public Matrix uniqueInCol(int colIdx)

Finds unique integer values in the specified column of the matrix.

Parameters:

colIdx - the index of the column to search

Returns:

a column matrix of unique integer values found in the specified column

uniqueInRow

public Matrix uniqueInRow(int rowIdx)

Finds unique integer values in the specified row of the matrix.

Parameters:

rowIdx - the index of the row to search

Returns:

a column matrix of unique integer values found in the specified row

uniqueNonNegativeInCol

public Matrix uniqueNonNegativeInCol(int colIdx)

Finds unique positive values (strictly greater than 0) in the specified column.

Parameters:

colIdx - the index of the column to search

Returns:

a column matrix of unique positive values

uniqueNonNegativeInRow

public Matrix uniqueNonNegativeInRow(int rowIdx)

Finds unique positive values (strictly greater than 0) in the specified row.

Parameters:

rowIdx - the index of the row to search

Returns:

a column matrix of unique positive values

uniqueNonZerosInCol

public Matrix uniqueNonZerosInCol(int colIdx)

Finds unique non-zero values in the specified column.

Parameters:

colIdx - the index of the column to search

Returns:

a column matrix of unique non-zero values

uniqueNonZerosInRow

public Matrix uniqueNonZerosInRow(int rowIdx)

Finds unique non-zero values in the specified row.

Parameters:

rowIdx - the index of the row to search

Returns:

a column matrix of unique non-zero values

unsafeSet

public void unsafeSet(int row,
 int col,
 double val)

Sets a value in the matrix without bounds checking. Use this only if you're certain the row and column are valid.

Parameters:

row - the row index

col - the column index

val - the value to set

value

public double value()

Returns the value at position (0, 0). Useful for singleton matrices (1x1).

Returns:

the scalar value at the top-left of the matrix

zero

public void zero()

Sets all entries in the matrix to zero.