Package org.ejml.dense.row

Class CommonOps_DDRM

java.lang.Object

org.ejml.dense.row.CommonOps_DDRM

public class CommonOps_DDRM
extends Object

Common matrix operations are contained here. Which specific underlying algorithm is used is not specified just the out come of the operation. Nor should calls to these functions reply on the underlying implementation. Which algorithm is used can depend on the matrix being passed in.

For more exotic and specialized generic operations see SpecializedOps_DDRM.

See Also:

• MatrixMatrixMult_DDRM
• MatrixVectorMult_DDRM
• SpecializedOps_DDRM
• MatrixFeatures_DDRM

Method Summary

Modifier and Type	Method	Description
static void	abs(DMatrixD1 a)	Performs absolute value of a matrix: a = abs(a) aij = abs(aij)
static void	abs(DMatrixD1 a, DMatrixD1 c)	Performs absolute value of a matrix: c = abs(a) cij = abs(aij)
static <T extends DMatrixD1> T	add(double alpha, T a, double beta, T b, T output)	Performs the following operation: c = α * a + β * b cij = α * aij + β * bij
static <T extends DMatrixD1> T	add(double alpha, T a, T b, T output)	Performs the following operation: c = α * a + b cij = α * aij + bij
static void	add(DMatrixD1 a, double val)	Performs an in-place scalar addition: a = a + val aij = aij + val
static <T extends DMatrixD1> T	add(T a, double val, T output)	Performs scalar addition: c = a + val cij = aij + val
static <T extends DMatrixD1> T	add(T a, double beta, T b, T output)	Performs the following operation: c = a + β * b cij = aij + β * bij
static <T extends DMatrixD1> T	add(T a, T b, T output)	Performs the following operation: c = a + b cij = aij + bij
static void	addEquals(DMatrixD1 a, double beta, DMatrixD1 b)	Performs the following operation: a = a + β * b aij = aij + β * bij
static void	addEquals(DMatrixD1 a, DMatrixD1 b)	Performs the following operation: a = a + b aij = aij + bij
static DMatrixRMaj	apply(DMatrixRMaj input, DOperatorUnary func)
static DMatrixRMaj	apply(DMatrixRMaj input, DOperatorUnary func, @Nullable DMatrixRMaj output)	This applies a given unary function on every value stored in the matrix
static void	changeSign(DMatrixD1 a)	Changes the sign of every element in the matrix. aij = -aij
static <T extends DMatrixD1> T	changeSign(T input, T output)	Changes the sign of every element in the matrix. outputij = -inputij
static DMatrixRMaj[]	columnsToVector(DMatrixRMaj A, @Nullable DMatrixRMaj[] v)	Converts the columns in a matrix into a set of vectors.
static DMatrixRMaj	concatColumns(DMatrixRMaj a, DMatrixRMaj b, @Nullable DMatrixRMaj output)	output = [a , b]
static DMatrixRMaj	concatColumnsMulti(DMatrixRMaj... m)	Concatenates all the matrices together along their columns.
static void	concatRows(DMatrixRMaj a, DMatrixRMaj b, DMatrixRMaj output)	output = [a ; b]
static DMatrixRMaj	concatRowsMulti(DMatrixRMaj... m)	Concatenates all the matrices together along their columns.
static int	countTrue(BMatrixRMaj A)	Counts the number of elements in A which are true
static double	det(DMatrixRMaj mat)	Returns the determinant of the matrix.
static DMatrixRMaj	diag(double... diagEl)	Creates a new square matrix whose diagonal elements are specified by diagEl and all the other elements are zero. aij = 0 if i ≤ j aij = diag[i] if i = j
static DMatrixRMaj	diag(@Nullable DMatrixRMaj ret, int width, double... diagEl)
static DMatrixRMaj	diagR(int numRows, int numCols, double... diagEl)	Creates a new rectangular matrix whose diagonal elements are specified by diagEl and all the other elements are zero. aij = 0 if i ≤ j aij = diag[i] if i = j
static void	divide(double alpha, DMatrixD1 a)	Performs an in-place element by element scalar division with the scalar on top. aij = α/aij
static <T extends DMatrixD1> T	divide(double alpha, T input, T output)	Performs an element by element scalar division with the scalar on top. bij = α/aij
static void	divide(DMatrixD1 a, double alpha)	Performs an in-place element by element scalar division with the scalar on bottom. aij = aij/α
static <T extends DMatrixD1> T	divide(T input, double alpha, T output)	Performs an element by element scalar division with the scalar on botton. bij = aij /α
static void	divideCols(DMatrixRMaj A, double[] values)	Divides every element in column i by value[i].
static void	divideRows(double[] values, DMatrixRMaj A)	Divides every element in row i by value[i].
static void	divideRowsCols(double[] diagA, int offsetA, DMatrixRMaj B, double[] diagC, int offsetC)	Equivalent to multiplying a matrix B by the inverse of two diagonal matrices.
static double	dot(DMatrixD1 a, DMatrixD1 b)	Computes the dot product or inner product between two vectors.
static BMatrixRMaj	elementBoolean(DMatrixRMaj input, DElementCoorBoolean func, @Nullable BMatrixRMaj output)	Applies a binary operator to even element in the input matrix.
static void	elementDiv(DMatrixD1 A, DMatrixD1 B)	Performs the an element by element division operation: aij = aij / bij
static <T extends DMatrixD1> T	elementDiv(T A, T B, T output)	Performs the an element by element division operation: cij = aij / bij
static <T extends DMatrixD1> T	elementExp(T A, T output)	Element-wise exp operation cij = Math.exp(aij)
static BMatrixRMaj	elementLessThan(DMatrixRMaj A, double value, @Nullable BMatrixRMaj output)	Applies the > operator to each element in A.
static BMatrixRMaj	elementLessThan(DMatrixRMaj A, DMatrixRMaj B, @Nullable BMatrixRMaj output)	Applies the < operator to each element in A.
static BMatrixRMaj	elementLessThanOrEqual(DMatrixRMaj A, double value, @Nullable BMatrixRMaj output)	Applies the ≥ operator to each element in A.
static BMatrixRMaj	elementLessThanOrEqual(DMatrixRMaj A, DMatrixRMaj B, @Nullable BMatrixRMaj output)	Applies the A ≤ B operator to each element.
static <T extends DMatrixD1> T	elementLog(T A, T output)	Element-wise log operation cij = Math.log(aij)
static double	elementMax(DMatrixD1 a)	Returns the value of the element in the matrix that has the largest value. Max{ aij } for all i and j
static double	elementMax(DMatrixD1 a, ElementLocation loc)	Returns the value of the element in the matrix that has the largest value. Max{ aij } for all i and j
static double	elementMaxAbs(DMatrixD1 a)	Returns the absolute value of the element in the matrix that has the largest absolute value. Max{ |aij| } for all i and j
static double	elementMaxAbs(DMatrixD1 a, ElementLocation loc)	Returns the absolute value of the element in the matrix that has the largest absolute value. Max{ |aij| } for all i and j
static double	elementMin(DMatrixD1 a)	Returns the value of the element in the matrix that has the minimum value. Min{ aij } for all i and j
static double	elementMin(DMatrixD1 a, ElementLocation loc)	Returns the value of the element in the matrix that has the minimum value. Min{ aij } for all i and j
static double	elementMinAbs(DMatrixD1 a)	Returns the absolute value of the element in the matrix that has the smallest absolute value. Min{ |aij| } for all i and j
static double	elementMinAbs(DMatrixD1 a, ElementLocation loc)	Returns the absolute value of the element in the matrix that has the smallest absolute value. Min{ |aij| } for all i and j
static BMatrixRMaj	elementMoreThan(DMatrixRMaj A, double value, @Nullable BMatrixRMaj output)	Applies the > operator to each element in A.
static BMatrixRMaj	elementMoreThanOrEqual(DMatrixRMaj A, double value, @Nullable BMatrixRMaj output)	Applies the ≥ operator to each element in A.
static void	elementMult(DMatrixD1 A, DMatrixD1 B)	Performs the an element by element multiplication operation: aij = aij * bij
static <T extends DMatrixD1> T	elementMult(T A, T B, T output)	Performs the an element by element multiplication operation: cij = aij * bij
static <T extends DMatrixD1> T	elementPower(double a, T B, T output)	Element-wise power operation cij = a ^ bij
static <T extends DMatrixD1> T	elementPower(T A, double b, T output)	Element-wise power operation cij = aij ^ b
static <T extends DMatrixD1> T	elementPower(T A, T B, T output)	Element-wise power operation cij = aij ^ bij
static DMatrixRMaj	elements(DMatrixRMaj A, BMatrixRMaj marked, @Nullable DMatrixRMaj output)	Returns a row matrix which contains all the elements in A which are flagged as true in 'marked'
static double	elementSum(DMatrixD1 mat)	Computes the sum of all the elements in the matrix: sum(i=1:m , j=1:n ; aij)
static double	elementSumAbs(DMatrixD1 mat)	Computes the sum of the absolute value all the elements in the matrix: sum(i=1:m , j=1:n ; |aij|)
static void	extract(DMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, DMatrix dst)	Extract where the destination is reshaped to match the extracted region
static void	extract(DMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, DMatrix dst, int dstY0, int dstX0)	Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
static void	extract(DMatrix src, int srcY0, int srcX0, DMatrix dst)	Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
static DMatrixRMaj	extract(DMatrixRMaj src, int[] rows, int rowsSize, int[] cols, int colsSize, @Nullable DMatrixRMaj dst)	Extracts out a matrix from source given a sub matrix with arbitrary rows and columns specified in two array lists
static DMatrixRMaj	extract(DMatrixRMaj src, int[] indexes, int length, @Nullable DMatrixRMaj dst)	Extracts the elements from the source matrix by their 1D index.
static DMatrixRMaj	extract(DMatrixRMaj src, int srcY0, int srcY1, int srcX0, int srcX1)	Creates a new matrix which is the specified submatrix of 'src'
static DMatrixRMaj	extractColumn(DMatrixRMaj a, int column, @Nullable DMatrixRMaj out)	Extracts the column from a matrix.
static DMatrixRMaj	extractDiag(DMatrixRMaj src, @Nullable DMatrixRMaj dst)	Extracts the diagonal elements 'src' write it to the 'dst' vector.
static DMatrixRMaj	extractRow(DMatrixRMaj a, int row, @Nullable DMatrixRMaj out)	Extracts the row from a matrix.
static void	fill(DMatrixD1 a, double value)	Sets every element in the matrix to the specified value. aij = value
static DMatrixRMaj	identity(int width)	Creates an identity matrix of the specified size. aij = 0 if i ≠ j aij = 1 if i = j
static DMatrixRMaj	identity(int numRows, int numCols)	Creates a rectangular matrix which is zero except along the diagonals.
static void	insert(DMatrixRMaj src, DMatrixRMaj dst, int[] rows, int rowsSize, int[] cols, int colsSize)	Inserts into the specified elements of dst the source matrix.
static void	insert(DMatrix src, DMatrix dest, int destY0, int destX0)	Inserts matrix 'src' into matrix 'dest' with the (0,0) of src at (row,col) in dest.
static boolean	invert(DMatrixRMaj mat)	Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix. a = a-1
static boolean	invert(DMatrixRMaj mat, DMatrixRMaj result)	Performs a matrix inversion operation that does not modify the original and stores the results in another matrix.
static boolean	invertSPD(DMatrixRMaj mat, DMatrixRMaj result)	Matrix inverse for symmetric positive definite matrices.
static DMatrixRMaj	kron(DMatrixRMaj A, DMatrixRMaj B, @Nullable DMatrixRMaj C)	The Kronecker product of two matrices is defined as: Cij = aijB where Cij is a sub matrix inside of C ∈ ℜ m*k × n*l, A ∈ ℜ m × n, and B ∈ ℜ k × l.
static DMatrixRMaj	maxCols(DMatrixRMaj input, @Nullable DMatrixRMaj output)	Finds the element with the minimum value along column in the input matrix and returns the results in a vector: bj = min(i=1:m ; aij)
static DMatrixRMaj	maxRows(DMatrixRMaj input, @Nullable DMatrixRMaj output)	Finds the element with the maximum value along each row in the input matrix and returns the results in a vector: bj = max(i=1:n ; aji)
static DMatrixRMaj	minCols(DMatrixRMaj input, @Nullable DMatrixRMaj output)	Finds the element with the minimum value along column in the input matrix and returns the results in a vector: bj = min(i=1:m ; aij)
static DMatrixRMaj	minRows(DMatrixRMaj input, @Nullable DMatrixRMaj output)	Finds the element with the minimum value along each row in the input matrix and returns the results in a vector: bj = min(i=1:n ; aji)
static <T extends DMatrix1Row> T	mult(double alpha, T a, T b, T output)	Performs the following operation: c = α * a * b cij = α ∑k=1:n { * aik * bkj}
static <T extends DMatrix1Row> T	mult(T a, T b, T output)	Performs the following operation: c = a * b cij = ∑k=1:n { aik * bkj}
static void	multAdd(double alpha, DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)	Performs the following operation: c = c + α * a * b cij = cij + α * ∑k=1:n { aik * bkj}
static void	multAdd(DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)	Performs the following operation: c = c + a * b cij = cij + ∑k=1:n { aik * bkj}
static void	multAddTransA(double alpha, DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)	Performs the following operation: c = c + α * aT * b cij =cij + α * ∑k=1:n { aki * bkj}
static void	multAddTransA(DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)	Performs the following operation: c = c + aT * b cij = cij + ∑k=1:n { aki * bkj}
static void	multAddTransAB(double alpha, DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)	Performs the following operation: c = c + α * aT * bT cij = cij + α * ∑k=1:n { aki * bjk}
static void	multAddTransAB(DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)	Performs the following operation: c = c + aT * bT cij = cij + ∑k=1:n { aki * bjk}
static void	multAddTransB(double alpha, DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)	Performs the following operation: c = c + α * a * bT cij = cij + α * ∑k=1:n { aik * bjk}
static void	multAddTransB(DMatrix1Row a, DMatrix1Row b, DMatrix1Row c)	Performs the following operation: c = c + a * bT cij = cij + ∑k=1:n { aik * bjk}
static void	multCols(DMatrixRMaj A, double[] values)	Multiplies every element in column i by value[i].
static <T extends DMatrix1Row> T	multInner(T a, T output)	Computes the matrix multiplication inner product: c = aT * a cij = ∑k=1:n { aki * akj}
static <T extends DMatrix1Row> T	multOuter(T a, T output)	Computes the matrix multiplication outer product: c = a * aT cij = ∑k=1:m { aik * ajk}
static void	multRows(double[] values, DMatrixRMaj A)	Multiplies every element in row i by value[i].
static <T extends DMatrix1Row> T	multTransA(double alpha, T a, T b, T output)	Performs the following operation: c = α * aT * b cij = α ∑k=1:n { aki * bkj}
static <T extends DMatrix1Row> T	multTransA(T a, T b, T output)	Performs the following operation: c = aT * b cij = ∑k=1:n { aki * bkj}
static <T extends DMatrix1Row> T	multTransAB(double alpha, T a, T b, T output)	Performs the following operation: c = α * aT * bT cij = α ∑k=1:n { aki * bjk}
static <T extends DMatrix1Row> T	multTransAB(T a, T b, T output)	Performs the following operation: c = aT * bT cij = ∑k=1:n { aki * bjk}
static <T extends DMatrix1Row> T	multTransB(double alpha, T a, T b, T output)	Performs the following operation: c = α * a * bT cij = α ∑k=1:n { aik * bjk}
static <T extends DMatrix1Row> T	multTransB(T a, T b, T output)	Performs the following operation: c = a * bT cij = ∑k=1:n { aik * bjk}
static DMatrixRMaj	permuteRowInv(int[] pinv, DMatrixRMaj input, DMatrixRMaj output)	Applies the row permutation specified by the vector to the input matrix and save the results in the output matrix.
static void	pinv(DMatrixRMaj A, DMatrixRMaj invA)	Computes the Moore-Penrose pseudo-inverse: pinv(A) = (ATA)-1 AT or pinv(A) = AT(AAT)-1
static void	removeColumns(DMatrixRMaj A, int col0, int col1)	Removes columns from the matrix.
static DMatrixRMaj[]	rowsToVector(DMatrixRMaj A, @Nullable DMatrixRMaj[] v)	Converts the rows in a matrix into a set of vectors.
static DMatrixRMaj	rref(DMatrixRMaj A, int numUnknowns, @Nullable DMatrixRMaj reduced)	Puts the augmented system matrix into reduced row echelon form (RREF) using Gauss-Jordan elimination with row (partial) pivots.
static void	scale(double alpha, DMatrixD1 a)	Performs an in-place element by element scalar multiplication. aij = α*aij
static void	scale(double alpha, DMatrixD1 a, DMatrixD1 b)	Performs an element by element scalar multiplication. bij = α*aij
static void	scaleCol(double alpha, DMatrixRMaj A, int col)	In-place scaling of a column in A
static void	scaleRow(double alpha, DMatrixRMaj A, int row)	In-place scaling of a row in A
static void	setIdentity(DMatrix1Row mat)	Sets all the diagonal elements equal to one and everything else equal to zero.
static boolean	solve(DMatrixRMaj a, DMatrixRMaj b, DMatrixRMaj x)	Solves for x in the following equation: A*x = b
static boolean	solveSPD(DMatrixRMaj A, DMatrixRMaj b, DMatrixRMaj x)	Linear solver for systems which are symmetric positive definite. A*x = b
static <T extends DMatrixD1> T	subtract(double val, T a, T output)	Performs matrix scalar subtraction: c = val - a cij = val - aij
static <T extends DMatrixD1> T	subtract(T a, double val, T output)	Performs matrix scalar subtraction: c = a - val cij = aij - val
static <T extends DMatrixD1> T	subtract(T a, T b, T output)	Performs the following subtraction operation: c = a - b cij = aij - bij
static void	subtractEquals(DMatrixD1 a, DMatrixD1 b)	Performs the following subtraction operation: a = a - b aij = aij - bij
static DMatrixRMaj	sumCols(DMatrixRMaj input, @Nullable DMatrixRMaj output)	Computes the sum of each column in the input matrix and returns the results in a vector: bj = sum(i=1:m ; aij)
static DMatrixRMaj	sumRows(DMatrixRMaj input, @Nullable DMatrixRMaj output)	Computes the sum of each row in the input matrix and returns the results in a vector: bj = sum(i=1:n ; aji)
static void	symmLowerToFull(DMatrixRMaj A)	Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.
static void	symmUpperToFull(DMatrixRMaj A)	Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.
static double	trace(DMatrix1Row a)	Computes the matrix trace: trace = ∑i=1:n { aii } where n = min(numRows,numCols)
static void	transpose(DMatrixRMaj mat)	Performs an "in-place" transpose.
static DMatrixRMaj	transpose(DMatrixRMaj A, @Nullable DMatrixRMaj A_tran)	Transposes matrix 'a' and stores the results in 'b': bij = aji where 'b' is the transpose of 'a'.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

mult

public static <T extends DMatrix1Row> T mult(T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = a * b

c_ij = ∑_k=1:n { a_ik * b_kj}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

mult

public static <T extends DMatrix1Row> T mult(double alpha,
 T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = α * a * b

c_ij = α ∑_k=1:n { * a_ik * b_kj}

Parameters:

alpha - Scaling factor.

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

multTransA

public static <T extends DMatrix1Row> T multTransA(T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = a^T * b

c_ij = ∑_k=1:n { a_ki * b_kj}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

multTransA

public static <T extends DMatrix1Row> T multTransA(double alpha,
 T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = α * a^T * b

c_ij = α ∑_k=1:n { a_ki * b_kj}

Parameters:

alpha - Scaling factor.

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

multTransB

public static <T extends DMatrix1Row> T multTransB(T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = a * b^T
c_ij = ∑_k=1:n { a_ik * b_jk}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

multTransB

public static <T extends DMatrix1Row> T multTransB(double alpha,
 T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = α * a * b^T
c_ij = α ∑_k=1:n { a_ik * b_jk}

Parameters:

alpha - Scaling factor.

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

multTransAB

public static <T extends DMatrix1Row> T multTransAB(T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = a^T * b^T
c_ij = ∑_k=1:n { a_ki * b_jk}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

multTransAB

public static <T extends DMatrix1Row> T multTransAB(double alpha,
 T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = α * a^T * b^T
c_ij = α ∑_k=1:n { a_ki * b_jk}

Parameters:

alpha - Scaling factor.

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

dot

public static double dot(DMatrixD1 a,
 DMatrixD1 b)

Computes the dot product or inner product between two vectors. If the two vectors are columns vectors then it is defined as:
dot(a,b) = a<sup>T</sup> * b
If the vectors are column or row or both is ignored by this function.

Parameters:

a - Vector

b - Vector

Returns:

Dot product of the two vectors

multInner

public static <T extends DMatrix1Row> T multInner(T a,
 @Nullable
 T output)

Computes the matrix multiplication inner product:

c = a^T * a

c_ij = ∑_k=1:n { a_ki * a_kj}

Is faster than using a generic matrix multiplication by taking advantage of symmetry. For vectors there is an even faster option, see VectorVectorMult_DDRM.innerProd(DMatrixD1, DMatrixD1)

Parameters:

a - The matrix being multiplied. Not modified.

output - Where the results of the operation are stored. Modified.

multOuter

public static <T extends DMatrix1Row> T multOuter(T a,
 @Nullable
 T output)

Computes the matrix multiplication outer product:

c = a * a^T

c_ij = ∑_k=1:m { a_ik * a_jk}

Is faster than using a generic matrix multiplication by taking advantage of symmetry.

Parameters:

a - The matrix being multiplied. Not modified.

output - Where the results of the operation are stored. Modified.

multAdd

public static void multAdd(DMatrix1Row a,
 DMatrix1Row b,
 DMatrix1Row c)

Performs the following operation:

c = c + a * b
c_ij = c_ij + ∑_k=1:n { a_ik * b_kj}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

multAdd

public static void multAdd(double alpha,
 DMatrix1Row a,
 DMatrix1Row b,
 DMatrix1Row c)

Performs the following operation:

c = c + α * a * b
c_ij = c_ij + α * ∑_k=1:n { a_ik * b_kj}

Parameters:

alpha - scaling factor.

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

multAddTransA

public static void multAddTransA(DMatrix1Row a,
 DMatrix1Row b,
 DMatrix1Row c)

Performs the following operation:

c = c + a^T * b
c_ij = c_ij + ∑_k=1:n { a_ki * b_kj}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

multAddTransA

public static void multAddTransA(double alpha,
 DMatrix1Row a,
 DMatrix1Row b,
 DMatrix1Row c)

Performs the following operation:

c = c + α * a^T * b
c_ij =c_ij + α * ∑_k=1:n { a_ki * b_kj}

Parameters:

alpha - scaling factor

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

multAddTransB

public static void multAddTransB(DMatrix1Row a,
 DMatrix1Row b,
 DMatrix1Row c)

Performs the following operation:

c = c + a * b^T
c_ij = c_ij + ∑_k=1:n { a_ik * b_jk}

Parameters:

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

multAddTransB

public static void multAddTransB(double alpha,
 DMatrix1Row a,
 DMatrix1Row b,
 DMatrix1Row c)

Performs the following operation:

c = c + α * a * b^T
c_ij = c_ij + α * ∑_k=1:n { a_ik * b_jk}

Parameters:

alpha - Scaling factor.

a - The left matrix in the multiplication operation. Not modified.

b - The right matrix in the multiplication operation. Not modified.

c - Where the results of the operation are stored. Modified.

multAddTransAB

public static void multAddTransAB(DMatrix1Row a,
 DMatrix1Row b,
 DMatrix1Row c)

Performs the following operation:

c = c + a^T * b^T
c_ij = c_ij + ∑_k=1:n { a_ki * b_jk}

Parameters:

a - The left matrix in the multiplication operation. Not Modified.

b - The right matrix in the multiplication operation. Not Modified.

c - Where the results of the operation are stored. Modified.

multAddTransAB

public static void multAddTransAB(double alpha,
 DMatrix1Row a,
 DMatrix1Row b,
 DMatrix1Row c)

Performs the following operation:

c = c + α * a^T * b^T
c_ij = c_ij + α * ∑_k=1:n { a_ki * b_jk}

Parameters:

alpha - Scaling factor.

a - The left matrix in the multiplication operation. Not Modified.

b - The right matrix in the multiplication operation. Not Modified.

c - Where the results of the operation are stored. Modified.

solve

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

Solves for x in the following equation:

A*x = b

If the system could not be solved then false is returned. If it returns true that just means the algorithm finished operating, but the results could still be bad because 'A' is singular or nearly singular.

If repeat calls to solve are being made then one should consider using LinearSolverFactory_DDRM instead.

It is ok for 'b' and 'x' to be the same matrix.

Parameters:

a - A matrix that is m by n. Not modified.

b - A matrix that is n by k. Not modified.

x - A matrix that is m by k. Modified.

Returns:

true if it could invert the matrix false if it could not.

solveSPD

public static boolean solveSPD(DMatrixRMaj A,
 DMatrixRMaj b,
 DMatrixRMaj x)

Linear solver for systems which are symmetric positive definite.
A*x = b

Parameters:

A - A matrix that is n by n and SPD. Not modified.

b - A matrix that is n by k. Not modified.

x - A matrix that is n by k. Modified.

Returns:

true if it could invert the matrix false if it could not.

See Also:

• UnrolledCholesky_DDRM
• LinearSolverFactory_DDRM

transpose

public static void transpose(DMatrixRMaj mat)

Performs an "in-place" transpose.

For square matrices the transpose is truly in-place and does not require additional memory. For non-square matrices, internally a temporary matrix is declared and transpose(DMatrixRMaj, DMatrixRMaj) is invoked.

Parameters:

mat - The matrix that is to be transposed. Modified.

transpose

public static DMatrixRMaj transpose(DMatrixRMaj A,
 @Nullable
 @Nullable DMatrixRMaj A_tran)

Transposes matrix 'a' and stores the results in 'b':

b_ij = a_ji
where 'b' is the transpose of 'a'.

Parameters:

A - The original matrix. Not modified.

A_tran - Where the transpose is stored. If null a new matrix is created. Modified.

Returns:

The transposed matrix.

trace

public static double trace(DMatrix1Row a)

Computes the matrix trace:

trace = ∑_i=1:n { a_ii }
where n = min(numRows,numCols)

Parameters:

a - (Input) A matrix

det

public static double det(DMatrixRMaj mat)

Returns the determinant of the matrix. If the inverse of the matrix is also needed, then using LUDecomposition_F64 directly (or any similar algorithm) can be more efficient.

Parameters:

mat - The matrix whose determinant is to be computed. Not modified.

Returns:

The determinant.

invert

public static boolean invert(DMatrixRMaj mat)

Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix.

a = a^-1

If the algorithm could not invert the matrix then false is returned. If it returns true that just means the algorithm finished. The results could still be bad because the matrix is singular or nearly singular.

Parameters:

mat - The matrix that is to be inverted. Results are stored here. Modified.

Returns:

true if it could invert the matrix false if it could not.

invert

public static boolean invert(DMatrixRMaj mat,
 DMatrixRMaj result)

Performs a matrix inversion operation that does not modify the original and stores the results in another matrix. The two matrices must have the same dimension.

b = a^-1

If the algorithm could not invert the matrix then false is returned. If it returns true that just means the algorithm finished. The results could still be bad because the matrix is singular or nearly singular.

For medium to large matrices there might be a slight performance boost to using LinearSolverFactory_DDRM instead.

Parameters:

mat - The matrix that is to be inverted. Not modified.

result - Where the inverse matrix is stored. Modified.

Returns:

true if it could invert the matrix false if it could not.

invertSPD

public static boolean invertSPD(DMatrixRMaj mat,
 DMatrixRMaj result)

Matrix inverse for symmetric positive definite matrices. For small matrices an unrolled cholesky is used. Otherwise a standard decomposition.

Parameters:

mat - (Input) SPD matrix

result - (Output) Inverted matrix.

Returns:

true if it could invert the matrix false if it could not.

See Also:

• UnrolledCholesky_DDRM
• LinearSolverFactory_DDRM.chol(int)

pinv

public static void pinv(DMatrixRMaj A,
 DMatrixRMaj invA)

Computes the Moore-Penrose pseudo-inverse:

pinv(A) = (A^TA)^-1 A^T
or
pinv(A) = A^T(AA^T)^-1

Internally it uses SolvePseudoInverseSvd_DDRM to compute the inverse. For performance reasons, this should only be used when a matrix is singular or nearly singular.

Parameters:

A - A m by n Matrix. Not modified.

invA - Where the computed pseudo inverse is stored. n by m. Modified.

columnsToVector

public static DMatrixRMaj[] columnsToVector(DMatrixRMaj A,
 @Nullable
 @Nullable DMatrixRMaj[] v)

Converts the columns in a matrix into a set of vectors.

Parameters:

A - Matrix. Not modified.

Returns:

An array of vectors.

rowsToVector

public static DMatrixRMaj[] rowsToVector(DMatrixRMaj A,
 @Nullable
 @Nullable DMatrixRMaj[] v)

Converts the rows in a matrix into a set of vectors.

Parameters:

A - Matrix. Not modified.

Returns:

An array of vectors.

setIdentity

public static void setIdentity(DMatrix1Row mat)

Sets all the diagonal elements equal to one and everything else equal to zero. If this is a square matrix then it will be an identity matrix.

Parameters:

mat - A square matrix.

See Also:

• identity(int)

identity

public static DMatrixRMaj identity(int width)

Creates an identity matrix of the specified size.

a_ij = 0 if i ≠ j
a_ij = 1 if i = j

Parameters:

width - The width and height of the identity matrix.

Returns:

A new instance of an identity matrix.

identity

public static DMatrixRMaj identity(int numRows,
 int numCols)

Creates a rectangular matrix which is zero except along the diagonals.

Parameters:

numRows - Number of rows in the matrix.

numCols - NUmber of columns in the matrix.

Returns:

A matrix with diagonal elements equal to one.

diag

public static DMatrixRMaj diag(double... diagEl)

Creates a new square matrix whose diagonal elements are specified by diagEl and all the other elements are zero.

a_ij = 0 if i ≤ j
a_ij = diag[i] if i = j

Parameters:

diagEl - Contains the values of the diagonal elements of the resulting matrix.

Returns:

A new matrix.

See Also:

• diagR(int, int, double...)

diag

public static DMatrixRMaj diag(@Nullable
 @Nullable DMatrixRMaj ret,
 int width,
 double... diagEl)

See Also:

• diag(double...)

diagR

public static DMatrixRMaj diagR(int numRows,
 int numCols,
 double... diagEl)

Creates a new rectangular matrix whose diagonal elements are specified by diagEl and all the other elements are zero.

a_ij = 0 if i ≤ j
a_ij = diag[i] if i = j

Parameters:

numRows - Number of rows in the matrix.

numCols - Number of columns in the matrix.

diagEl - Contains the values of the diagonal elements of the resulting matrix.

Returns:

A new matrix.

See Also:

• diag(double...)

kron

public static DMatrixRMaj kron(DMatrixRMaj A,
 DMatrixRMaj B,
 @Nullable
 @Nullable DMatrixRMaj C)

The Kronecker product of two matrices is defined as:
C_ij = a_ijB
where C_ij is a sub matrix inside of C ∈ ℜ ^{m*k × n*l}, A ∈ ℜ ^{m × n}, and B ∈ ℜ ^{k × l}.

Parameters:

A - The left matrix in the operation. Not modified.

B - The right matrix in the operation. Not modified.

C - Where the results of the operation are stored. Nullable. Modified.

extract

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

Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.

s_{i-y0 , j-x0} = o_ij for all y0 ≤ i < y1 and x0 ≤ j < x1

where 's_ij' is an element in the submatrix and 'o_ij' is an element in the original matrix.

Parameters:

src - The original matrix which is to be copied. Not modified.

srcX0 - Start column.

srcX1 - Stop column+1.

srcY0 - Start row.

srcY1 - Stop row+1.

dst - Where the submatrix are stored. Modified.

dstY0 - Start row in dst.

dstX0 - start column in dst.

extract

public static void extract(DMatrix src,
 int srcY0,
 int srcY1,
 int srcX0,
 int srcX1,
 DMatrix dst)

Extract where the destination is reshaped to match the extracted region

Parameters:

src - The original matrix which is to be copied. Not modified.

srcX0 - Start column.

srcX1 - Stop column+1.

srcY0 - Start row.

srcY1 - Stop row+1.

dst - Where the submatrix are stored. Modified.

extract

public static void extract(DMatrix src,
 int srcY0,
 int srcX0,
 DMatrix dst)

Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'. Uses the shape of dst to determine the size of the matrix extracted.

Parameters:

src - The original matrix which is to be copied. Not modified.

srcY0 - Start row in src.

srcX0 - Start column in src.

dst - Where the matrix is extracted into.

extract

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

Creates a new matrix which is the specified submatrix of 'src'

s_{i-y0 , j-x0} = o_ij for all y0 ≤ i < y1 and x0 ≤ j < x1

where 's_ij' is an element in the submatrix and 'o_ij' is an element in the original matrix.

Parameters:

src - The original matrix which is to be copied. Not modified.

srcX0 - Start column.

srcX1 - Stop column+1.

srcY0 - Start row.

srcY1 - Stop row+1.

Returns:

Extracted submatrix.

extract

public static DMatrixRMaj extract(DMatrixRMaj src,
 int[] rows,
 int rowsSize,
 int[] cols,
 int colsSize,
 @Nullable
 @Nullable DMatrixRMaj dst)

Extracts out a matrix from source given a sub matrix with arbitrary rows and columns specified in two array lists

Parameters:

src - Source matrix. Not modified.

rows - array of row indexes

rowsSize - maximum element in row array

cols - array of column indexes

colsSize - maximum element in column array

dst - output matrix. Must be correct shape.

extract

public static DMatrixRMaj extract(DMatrixRMaj src,
 int[] indexes,
 int length,
 @Nullable
 @Nullable DMatrixRMaj dst)

Extracts the elements from the source matrix by their 1D index.

Parameters:

src - Source matrix. Not modified.

indexes - array of row indexes

length - maximum element in row array

dst - output matrix. Must be a vector of the correct length.

insert

public static void insert(DMatrixRMaj src,
 DMatrixRMaj dst,
 int[] rows,
 int rowsSize,
 int[] cols,
 int colsSize)

Inserts into the specified elements of dst the source matrix.

 for i in len(rows):
   for j in len(cols):
      dst(rows[i],cols[j]) = src(i,j)
 

Parameters:

src - Source matrix. Not modified.

dst - output matrix. Must be correct shape.

rows - array of row indexes.

rowsSize - maximum element in row array

cols - array of column indexes

colsSize - maximum element in column array

extractDiag

public static DMatrixRMaj extractDiag(DMatrixRMaj src,
 @Nullable
 @Nullable DMatrixRMaj dst)

Extracts the diagonal elements 'src' write it to the 'dst' vector. 'dst' can either be a row or column vector.

Parameters:

src - Matrix whose diagonal elements are being extracted. Not modified.

dst - A vector the results will be written into. Modified.

extractRow

public static DMatrixRMaj extractRow(DMatrixRMaj a,
 int row,
 @Nullable
 @Nullable DMatrixRMaj out)

Extracts the row from a matrix.

Parameters:

a - Input matrix

row - Which row is to be extracted

out - output. Storage for the extracted row. If null then a new vector will be returned.

Returns:

The extracted row.

extractColumn

public static DMatrixRMaj extractColumn(DMatrixRMaj a,
 int column,
 @Nullable
 @Nullable DMatrixRMaj out)

Extracts the column from a matrix.

Parameters:

a - Input matrix

column - Which column is to be extracted

out - output. Storage for the extracted column. If null then a new vector will be returned.

Returns:

The extracted column.

removeColumns

public static void removeColumns(DMatrixRMaj A,
 int col0,
 int col1)

Removes columns from the matrix.

Parameters:

A - Matrix. Modified

col0 - First column

col1 - Last column, inclusive.

insert

public static void insert(DMatrix src,
 DMatrix dest,
 int destY0,
 int destX0)

Inserts matrix 'src' into matrix 'dest' with the (0,0) of src at (row,col) in dest. This is equivalent to calling extract(src,0,src.numRows,0,src.numCols,dest,destY0,destX0).

Parameters:

src - matrix that is being copied into dest. Not modified.

dest - Where src is being copied into. Modified.

destY0 - Start row for the copy into dest.

destX0 - Start column for the copy into dest.

elementMax

public static double elementMax(DMatrixD1 a)

Returns the value of the element in the matrix that has the largest value.

Max{ a_ij } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The max element value of the matrix.

elementMax

public static double elementMax(DMatrixD1 a,
 ElementLocation loc)

Returns the value of the element in the matrix that has the largest value.

Max{ a_ij } for all i and j

Parameters:

a - A matrix. Not modified.

loc - (Output) Location of selected element.

Returns:

The max element value of the matrix.

elementMaxAbs

public static double elementMaxAbs(DMatrixD1 a)

Returns the absolute value of the element in the matrix that has the largest absolute value.

Max{ |a_ij| } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The max abs element value of the matrix.

elementMaxAbs

public static double elementMaxAbs(DMatrixD1 a,
 ElementLocation loc)

Returns the absolute value of the element in the matrix that has the largest absolute value.

Max{ |a_ij| } for all i and j

Parameters:

a - A matrix. Not modified.

loc - (Output) Location of element element.

Returns:

The max abs element value of the matrix.

elementMin

public static double elementMin(DMatrixD1 a)

Returns the value of the element in the matrix that has the minimum value.

Min{ a_ij } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The value of element in the matrix with the minimum value.

elementMin

public static double elementMin(DMatrixD1 a,
 ElementLocation loc)

Returns the value of the element in the matrix that has the minimum value.

Min{ a_ij } for all i and j

Parameters:

a - A matrix. Not modified.

loc - (Output) Location of selected element.

Returns:

The value of element in the matrix with the minimum value.

elementMinAbs

public static double elementMinAbs(DMatrixD1 a)

Returns the absolute value of the element in the matrix that has the smallest absolute value.

Min{ |a_ij| } for all i and j

Parameters:

a - A matrix. Not modified.

Returns:

The max element value of the matrix.

elementMinAbs

public static double elementMinAbs(DMatrixD1 a,
 ElementLocation loc)

Returns the absolute value of the element in the matrix that has the smallest absolute value.

Min{ |a_ij| } for all i and j

Parameters:

a - (Input) A matrix. Not modified.

loc - (Output) Location of selected element.

Returns:

The max element value of the matrix.

elementMult

public static void elementMult(DMatrixD1 A,
 DMatrixD1 B)

Performs the an element by element multiplication operation:

a_ij = a_ij * b_ij

Parameters:

A - The left matrix in the multiplication operation. Modified.

B - The right matrix in the multiplication operation. Not modified.

elementMult

public static <T extends DMatrixD1> T elementMult(T A,
 T B,
 @Nullable
 T output)

Performs the an element by element multiplication operation:

c_ij = a_ij * b_ij

Parameters:

A - The left matrix in the multiplication operation. Not modified.

B - The right matrix in the multiplication operation. Not modified.

output - Where the results of the operation are stored. Modified.

elementDiv

public static void elementDiv(DMatrixD1 A,
 DMatrixD1 B)

Performs the an element by element division operation:

a_ij = a_ij / b_ij

Parameters:

A - The left matrix in the division operation. Modified.

B - The right matrix in the division operation. Not modified.

elementDiv

public static <T extends DMatrixD1> T elementDiv(T A,
 T B,
 @Nullable
 T output)

Performs the an element by element division operation:

c_ij = a_ij / b_ij

Parameters:

A - The left matrix in the division operation. Not modified.

B - The right matrix in the division operation. Not modified.

output - Where the results of the operation are stored. Modified.

elementSum

public static double elementSum(DMatrixD1 mat)

Computes the sum of all the elements in the matrix:

sum(i=1:m , j=1:n ; a_ij)

Parameters:

mat - An m by n matrix. Not modified.

Returns:

The sum of the elements.

elementSumAbs

public static double elementSumAbs(DMatrixD1 mat)

Computes the sum of the absolute value all the elements in the matrix:

sum(i=1:m , j=1:n ; |a_ij|)

Parameters:

mat - An m by n matrix. Not modified.

Returns:

The sum of the absolute value of each element.

elementPower

public static <T extends DMatrixD1> T elementPower(T A,
 T B,
 @Nullable
 T output)

Element-wise power operation
c_ij = a_ij ^ b_ij

Parameters:

A - left side

B - right side

output - output (modified)

elementPower

public static <T extends DMatrixD1> T elementPower(double a,
 T B,
 @Nullable
 T output)

Element-wise power operation
c_ij = a ^ b_ij

Parameters:

a - left scalar

B - right side

output - output (modified)

elementPower

public static <T extends DMatrixD1> T elementPower(T A,
 double b,
 @Nullable
 T output)

Element-wise power operation
c_ij = a_ij ^ b

Parameters:

A - left side

b - right scalar

output - output (modified)

elementLog

public static <T extends DMatrixD1> T elementLog(T A,
 @Nullable
 T output)

Element-wise log operation
c_ij = Math.log(a_ij)

Parameters:

A - (input) A matrix

output - (input/output) Storage for results. can be null. (modified)

Returns:

The results

elementExp

public static <T extends DMatrixD1> T elementExp(T A,
 @Nullable
 T output)

Element-wise exp operation
c_ij = Math.exp(a_ij)

Parameters:

A - (input) A matrix

output - (input/output) Storage for results. can be null. (modified)

Returns:

The results

multRows

public static void multRows(double[] values,
 DMatrixRMaj A)

Multiplies every element in row i by value[i].

Parameters:

values - array. Not modified.

A - Matrix. Modified.

divideRows

public static void divideRows(double[] values,
 DMatrixRMaj A)

Divides every element in row i by value[i].

Parameters:

values - array. Not modified.

A - Matrix. Modified.

multCols

public static void multCols(DMatrixRMaj A,
 double[] values)

Multiplies every element in column i by value[i].

Parameters:

A - Matrix. Modified.

values - array. Not modified.

divideCols

public static void divideCols(DMatrixRMaj A,
 double[] values)

Divides every element in column i by value[i].

Parameters:

A - Matrix. Modified.

values - array. Not modified.

divideRowsCols

public static void divideRowsCols(double[] diagA,
 int offsetA,
 DMatrixRMaj B,
 double[] diagC,
 int offsetC)

Equivalent to multiplying a matrix B by the inverse of two diagonal matrices. B = inv(A)*B*inv(C), where A=diag(a) and C=diag(c).

Parameters:

diagA - Array of length offsteA + B.numRows

offsetA - First index in A

B - Rectangular matrix

diagC - Array of length indexC + B.numCols

offsetC - First index in C

sumRows

public static DMatrixRMaj sumRows(DMatrixRMaj input,
 @Nullable
 @Nullable DMatrixRMaj output)

Computes the sum of each row in the input matrix and returns the results in a vector:

b_j = sum(i=1:n ; a_ji)

Parameters:

input - INput matrix whose rows are summed.

output - Optional storage for output. Reshaped into a column. Modified.

Returns:

Vector containing the sum of each row in the input.

minRows

public static DMatrixRMaj minRows(DMatrixRMaj input,
 @Nullable
 @Nullable DMatrixRMaj output)

Finds the element with the minimum value along each row in the input matrix and returns the results in a vector:

b_j = min(i=1:n ; a_ji)

Parameters:

input - Input matrix

output - Optional storage for output. Reshaped into a column. Modified.

Returns:

Vector containing the sum of each row in the input.

maxRows

public static DMatrixRMaj maxRows(DMatrixRMaj input,
 @Nullable
 @Nullable DMatrixRMaj output)

Finds the element with the maximum value along each row in the input matrix and returns the results in a vector:

b_j = max(i=1:n ; a_ji)

Parameters:

input - Input matrix

output - Optional storage for output. Reshaped into a column. Modified.

Returns:

Vector containing the sum of each row in the input.

sumCols

public static DMatrixRMaj sumCols(DMatrixRMaj input,
 @Nullable
 @Nullable DMatrixRMaj output)

Computes the sum of each column in the input matrix and returns the results in a vector:

b_j = sum(i=1:m ; a_ij)

Parameters:

input - Input matrix

output - Optional storage for output. Reshaped into a row vector. Modified.

Returns:

Vector containing the sum of each column

minCols

public static DMatrixRMaj minCols(DMatrixRMaj input,
 @Nullable
 @Nullable DMatrixRMaj output)

Finds the element with the minimum value along column in the input matrix and returns the results in a vector:

b_j = min(i=1:m ; a_ij)

Parameters:

input - Input matrix

output - Optional storage for output. Reshaped into a row vector. Modified.

Returns:

Vector containing the minimum of each column

maxCols

public static DMatrixRMaj maxCols(DMatrixRMaj input,
 @Nullable
 @Nullable DMatrixRMaj output)

Finds the element with the minimum value along column in the input matrix and returns the results in a vector:

b_j = min(i=1:m ; a_ij)

Parameters:

input - Input matrix

output - Optional storage for output. Reshaped into a row vector. Modified.

Returns:

Vector containing the maximum of each column

addEquals

public static void addEquals(DMatrixD1 a,
 DMatrixD1 b)

Performs the following operation:

a = a + b
a_ij = a_ij + b_ij

Parameters:

a - (input/output) A Matrix. Modified.

b - (input) A Matrix. Not modified.

addEquals

public static void addEquals(DMatrixD1 a,
 double beta,
 DMatrixD1 b)

Performs the following operation:

a = a + β * b
a_ij = a_ij + β * b_ij

Parameters:

beta - The number that matrix 'b' is multiplied by.

a - (input/output) A Matrix. Modified.

b - (input) A Matrix. Not modified.

add

public static <T extends DMatrixD1> T add(T a,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = a + b
c_ij = a_ij + b_ij

Matrix C can be the same instance as Matrix A and/or B.

Parameters:

a - A Matrix. Not modified.

b - A Matrix. Not modified.

output - (output) A Matrix where the results are stored. Can be null. Modified.

Returns:

The results.

add

public static <T extends DMatrixD1> T add(T a,
 double beta,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = a + β * b
c_ij = a_ij + β * b_ij

Matrix C can be the same instance as Matrix A and/or B.

Parameters:

a - A Matrix. Not modified.

beta - Scaling factor for matrix b.

b - A Matrix. Not modified.

output - (output) A Matrix where the results are stored. Can be null. Modified.

Returns:

The results.

add

public static <T extends DMatrixD1> T add(double alpha,
 T a,
 double beta,
 T b,
 @Nullable
 T output)

Performs the following operation:

c = α * a + β * b
c_ij = α * a_ij + β * b_ij

Matrix C can be the same instance as Matrix A and/or B.

Parameters:

alpha - A scaling factor for matrix a.

a - A Matrix. Not modified.

beta - A scaling factor for matrix b.

b - A Matrix. Not modified.

output - (output) A Matrix where the results are stored. Can be null. Modified.

Returns:

The results.

add

public static <T extends DMatrixD1> T add(double alpha,
 T a,
 T b,
 T output)

Performs the following operation:

c = α * a + b
c_ij = α * a_ij + b_ij

Matrix C can be the same instance as Matrix A and/or B.

Parameters:

alpha - A scaling factor for matrix a.

a - A Matrix. Not modified.

b - A Matrix. Not modified.

output - (output) A Matrix where the results are stored. Can be null. Modified.

Returns:

The results.

add

public static void add(DMatrixD1 a,
 double val)

Performs an in-place scalar addition:

a = a + val
a_ij = a_ij + val

Parameters:

a - A matrix. Modified.

val - The value that's added to each element.

add

public static <T extends DMatrixD1> T add(T a,
 double val,
 T output)

Performs scalar addition:

c = a + val
c_ij = a_ij + val

Parameters:

a - A matrix. Not modified.

val - The value that's added to each element.

output - (output) Storage for results. Can be null. Modified.

Returns:

The resulting matrix

subtract

public static <T extends DMatrixD1> T subtract(T a,
 double val,
 @Nullable
 T output)

Performs matrix scalar subtraction:

c = a - val
c_ij = a_ij - val

Parameters:

a - (input) A matrix. Not modified.

val - (input) The value that's subtracted to each element.

output - (output) Storage for results. Can be null. Modified.

Returns:

The resulting matrix

subtract

public static <T extends DMatrixD1> T subtract(double val,
 T a,
 @Nullable
 T output)

Performs matrix scalar subtraction:

c = val - a
c_ij = val - a_ij

Parameters:

val - (input) The value that's subtracted to each element.

a - (input) A matrix. Not modified.

output - (output) Storage for results. Can be null. Modified.

Returns:

The resulting matrix

subtractEquals

public static void subtractEquals(DMatrixD1 a,
 DMatrixD1 b)

Performs the following subtraction operation:

a = a - b
a_ij = a_ij - b_ij

Parameters:

a - (input) A Matrix. Modified.

b - (input) A Matrix. Not modified.

subtract

public static <T extends DMatrixD1> T subtract(T a,
 T b,
 @Nullable
 T output)

Performs the following subtraction operation:

c = a - b
c_ij = a_ij - b_ij

Matrix C can be the same instance as Matrix A and/or B.

Parameters:

a - (input) A Matrix. Not modified.

b - (input) A Matrix. Not modified.

output - (output) A Matrix. Can be null. Modified.

Returns:

The resulting matrix

scale

public static void scale(double alpha,
 DMatrixD1 a)

Performs an in-place element by element scalar multiplication.

a_ij = α*a_ij

Parameters:

a - The matrix that is to be scaled. Modified.

alpha - the amount each element is multiplied by.

scale

public static void scale(double alpha,
 DMatrixD1 a,
 DMatrixD1 b)

Performs an element by element scalar multiplication.

b_ij = α*a_ij

Parameters:

alpha - the amount each element is multiplied by.

a - The matrix that is to be scaled. Not modified.

b - Where the scaled matrix is stored. Modified.

scaleRow

public static void scaleRow(double alpha,
 DMatrixRMaj A,
 int row)

In-place scaling of a row in A

Parameters:

alpha - scale factor

A - matrix

row - which row in A

scaleCol

public static void scaleCol(double alpha,
 DMatrixRMaj A,
 int col)

In-place scaling of a column in A

Parameters:

alpha - scale factor

A - matrix

col - which row in A

divide

public static void divide(double alpha,
 DMatrixD1 a)

Performs an in-place element by element scalar division with the scalar on top.

a_ij = α/a_ij

Parameters:

a - (input/output) The matrix whose elements are divide the scalar. Modified.

alpha - top value in division

divide

public static void divide(DMatrixD1 a,
 double alpha)

Performs an in-place element by element scalar division with the scalar on bottom.

a_ij = a_ij/α

Parameters:

a - (input/output) The matrix whose elements are to be divided. Modified.

alpha - the amount each element is divided by.

divide

public static <T extends DMatrixD1> T divide(double alpha,
 T input,
 T output)

Performs an element by element scalar division with the scalar on top.

b_ij = α/a_ij

Parameters:

alpha - The numerator.

input - The matrix whose elements are the divisor. Not modified.

output - Where the results are stored. Modified. Can be null.

Returns:

The resulting matrix

divide

public static <T extends DMatrixD1> T divide(T input,
 double alpha,
 @Nullable
 T output)

Performs an element by element scalar division with the scalar on botton.

b_ij = a_ij /α

Parameters:

input - The matrix whose elements are to be divided. Not modified.

alpha - the amount each element is divided by.

output - Where the results are stored. Modified. Can be null.

Returns:

The resulting matrix

changeSign

public static void changeSign(DMatrixD1 a)

Changes the sign of every element in the matrix.

a_ij = -a_ij

Parameters:

a - A matrix. Modified.

changeSign

public static <T extends DMatrixD1> T changeSign(T input,
 @Nullable
 T output)

Changes the sign of every element in the matrix.

output_ij = -input_ij

Parameters:

input - A matrix. Modified.

fill

public static void fill(DMatrixD1 a,
 double value)

Sets every element in the matrix to the specified value.

a_ij = value

Parameters:

a - A matrix whose elements are about to be set. Modified.

value - The value each element will have.

rref

public static DMatrixRMaj rref(DMatrixRMaj A,
 int numUnknowns,
 @Nullable
 @Nullable DMatrixRMaj reduced)

Puts the augmented system matrix into reduced row echelon form (RREF) using Gauss-Jordan elimination with row (partial) pivots. A matrix is said to be in RREF is the following conditions are true:

1. If a row has non-zero entries, then the first non-zero entry is 1. This is known as the leading one.
2. If a column contains a leading one then all other entries in that column are zero.
3. If a row contains a leading 1, then each row above contains a leading 1 further to the left.

[1] Page 19 in, Otter Bretscherm "Linear Algebra with Applications" Prentice-Hall Inc, 1997

Parameters:

A - Input matrix. Unmodified.

numUnknowns - Number of unknowns/columns that are reduced. Set to -1 to default to A.numCols, which works for most applications.

reduced - Storage for reduced echelon matrix. If null then a new matrix is returned. Modified.

Returns:

Reduced echelon form of A

See Also:

• RrefGaussJordanRowPivot_DDRM

elementLessThan

public static BMatrixRMaj elementLessThan(DMatrixRMaj A,
 double value,
 @Nullable
 @Nullable BMatrixRMaj output)

Applies the > operator to each element in A. Results are stored in a boolean matrix.

Parameters:

A - Input matrx

value - value each element is compared against

output - (Optional) Storage for results. Can be null. Is reshaped.

Returns:

Boolean matrix with results

See Also:

• for a more generalized element wise binary operator

elementLessThanOrEqual

public static BMatrixRMaj elementLessThanOrEqual(DMatrixRMaj A,
 double value,
 @Nullable
 @Nullable BMatrixRMaj output)

Applies the ≥ operator to each element in A. Results are stored in a boolean matrix.

Parameters:

A - Input matrix

value - value each element is compared against

output - (Optional) Storage for results. Can be null. Is reshaped.

Returns:

Boolean matrix with results

See Also:

• for a more generalized element wise binary operator

elementMoreThan

public static BMatrixRMaj elementMoreThan(DMatrixRMaj A,
 double value,
 @Nullable
 @Nullable BMatrixRMaj output)

Applies the > operator to each element in A. Results are stored in a boolean matrix.

Parameters:

A - Input matrix

value - value each element is compared against

output - (Optional) Storage for results. Can be null. Is reshaped.

Returns:

Boolean matrix with results

See Also:

• for a more generalized element wise binary operator

elementMoreThanOrEqual

public static BMatrixRMaj elementMoreThanOrEqual(DMatrixRMaj A,
 double value,
 @Nullable
 @Nullable BMatrixRMaj output)

Applies the ≥ operator to each element in A. Results are stored in a boolean matrix.

Parameters:

A - Input matrix

value - value each element is compared against

output - (Optional) Storage for results. Can be null. Is reshaped.

Returns:

Boolean matrix with results

See Also:

• for a more generalized element wise binary operator

elementLessThan

public static BMatrixRMaj elementLessThan(DMatrixRMaj A,
 DMatrixRMaj B,
 @Nullable
 @Nullable BMatrixRMaj output)

Applies the < operator to each element in A. Results are stored in a boolean matrix.

Parameters:

A - Input matrix

B - Input matrix

output - (Optional) Storage for results. Can be null. Is reshaped.

Returns:

Boolean matrix with results

See Also:

• for a more generalized element wise binary operator

elementLessThanOrEqual

public static BMatrixRMaj elementLessThanOrEqual(DMatrixRMaj A,
 DMatrixRMaj B,
 @Nullable
 @Nullable BMatrixRMaj output)

Applies the A ≤ B operator to each element. Results are stored in a boolean matrix.

Parameters:

A - Input matrix

B - Input matrix

output - (Optional) Storage for results. Can be null. Is reshaped.

Returns:

Boolean matrix with results

See Also:

• for a more generalized element wise binary operator

elements

public static DMatrixRMaj elements(DMatrixRMaj A,
 BMatrixRMaj marked,
 @Nullable
 @Nullable DMatrixRMaj output)

Returns a row matrix which contains all the elements in A which are flagged as true in 'marked'

Parameters:

A - Input matrix

marked - Input matrix marking elements in A

output - Storage for output row vector. Can be null. Will be reshaped.

Returns:

Row vector with marked elements

countTrue

public static int countTrue(BMatrixRMaj A)

Counts the number of elements in A which are true

Parameters:

A - input matrix

Returns:

number of true elements

concatColumns

public static DMatrixRMaj concatColumns(DMatrixRMaj a,
 DMatrixRMaj b,
 @Nullable
 @Nullable DMatrixRMaj output)

output = [a , b]

concatColumnsMulti

public static DMatrixRMaj concatColumnsMulti(DMatrixRMaj... m)

Concatenates all the matrices together along their columns. If the rows do not match the upper elements are set to zero.

A = [ m[0] , ... , m[n-1] ]

Parameters:

m - Set of matrices

Returns:

Resulting matrix

concatRows

public static void concatRows(DMatrixRMaj a,
 DMatrixRMaj b,
 DMatrixRMaj output)

output = [a ; b]

concatRowsMulti

public static DMatrixRMaj concatRowsMulti(DMatrixRMaj... m)

Concatenates all the matrices together along their columns. If the rows do not match the upper elements are set to zero.

A = [ m[0] ; ... ; m[n-1] ]

Parameters:

m - Set of matrices

Returns:

Resulting matrix

permuteRowInv

public static DMatrixRMaj permuteRowInv(int[] pinv,
 DMatrixRMaj input,
 DMatrixRMaj output)

Applies the row permutation specified by the vector to the input matrix and save the results in the output matrix. output[perm[j],:] = input[j,:]

Parameters:

pinv - (Input) Inverse permutation vector. Specifies new order of the rows.

input - (Input) Matrix which is to be permuted

output - (Output) Matrix which has the permutation stored in it. Is reshaped.

abs

public static void abs(DMatrixD1 a,
 DMatrixD1 c)

Performs absolute value of a matrix:

c = abs(a)
c_ij = abs(a_ij)

Parameters:

a - A matrix. Not modified.

c - A matrix. Modified.

abs

public static void abs(DMatrixD1 a)

Performs absolute value of a matrix:

a = abs(a)
a_ij = abs(a_ij)

Parameters:

a - A matrix. Modified.

symmLowerToFull

public static void symmLowerToFull(DMatrixRMaj A)

Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.

Parameters:

A - (Input) Lower triangular matrix (Output) symmetric matrix

symmUpperToFull

public static void symmUpperToFull(DMatrixRMaj A)

Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.

Parameters:

A - (Input) Lower triangular matrix (Output) symmetric matrix

apply

public static DMatrixRMaj apply(DMatrixRMaj input,
 DOperatorUnary func,
 @Nullable
 @Nullable DMatrixRMaj output)

This applies a given unary function on every value stored in the matrix

 output[i,j] = func(input[i,j])
 

A and B can be the same instance.

Parameters:

input - (Input) input matrix. Not modified

func - Unary function accepting a double

output - (Output) Matrix. Can be same instance as A. Modified.

Returns:

The output matrix

apply

public static DMatrixRMaj apply(DMatrixRMaj input,
 DOperatorUnary func)

elementBoolean

public static BMatrixRMaj elementBoolean(DMatrixRMaj input,
 DElementCoorBoolean func,
 @Nullable
 @Nullable BMatrixRMaj output)

Applies a binary operator to even element in the input matrix. In the lambda, the coordinate (row, col), and the value at that element is provided. This is designed to enable arbitrary operations.

For example, to apply an arbitrary boolean operatorto elements between two matrices, you can do the following:

BMatrixRMaj found = CommonOps_DDRM.elementBoolean(A, ( row, col, value ) -> B.get(row, col) < value, null);

Parameters:

input - Input matrix

func - Element wise function that outputs a boolean value

output - (Optional) Output matrix.

Returns:

Resulting binary matrix