Package org.ejml.dense.fixed

Class CommonOps_DDF3

java.lang.Object

org.ejml.dense.fixed.CommonOps_DDF3

@Generated("org.ejml.dense.fixed.GenerateCommonOps_DDF")
public class CommonOps_DDF3
extends Object

Common matrix operations for fixed sized matrices which are 3 x 3 or 3 element vectors.

DO NOT MODIFY. Automatically generated code created by GenerateCommonOps_DDF

Constructor Summary

Constructors

Constructor	Description
CommonOps_DDF3()

Method Summary

Modifier and Type	Method	Description
static void	add(DMatrix3 a, DMatrix3 b, DMatrix3 c)	Performs the following operation: c = a + b ci = ai + bi
static void	add(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = a + b cij = aij + bij
static void	addEquals(DMatrix3 a, DMatrix3 b)	Performs the following operation: a = a + b ai = ai + bi
static void	addEquals(DMatrix3x3 a, DMatrix3x3 b)	Performs the following operation: a = a + b aij = aij + bij
static void	changeSign(DMatrix3 a)	Changes the sign of every element in the vector. ai = -ai
static void	changeSign(DMatrix3x3 a)	Changes the sign of every element in the matrix. aij = -aij
static boolean	cholL(DMatrix3x3 A)	Performs a lower Cholesky decomposition of matrix 'A' and stores result in A.
static boolean	cholU(DMatrix3x3 A)	Performs an upper Cholesky decomposition of matrix 'A' and stores result in A.
static double	det(DMatrix3x3 mat)	Computes the determinant using minor matrices. WARNING: Potentially less stable than using LU decomposition.
static void	diag(DMatrix3x3 input, DMatrix3 out)	Extracts all diagonal elements from 'input' and places them inside the 'out' vector.
static void	divide(DMatrix3 a, double alpha)	Performs an in-place element by element scalar division.
static void	divide(DMatrix3 a, double alpha, DMatrix3 b)	Performs an element by element scalar division.
static void	divide(DMatrix3x3 a, double alpha)	Performs an in-place element by element scalar division.
static void	divide(DMatrix3x3 a, double alpha, DMatrix3x3 b)	Performs an element by element scalar division.
static double	dot(DMatrix3 a, DMatrix3 b)	Performs the vector dot product: c = a * b c ≥ ∑k=1:n { bk * ak }
static void	elementDiv(DMatrix3 a, DMatrix3 b)	Performs an element by element division operation: ai = ai / bi
static void	elementDiv(DMatrix3 a, DMatrix3 b, DMatrix3 c)	Performs an element by element division operation: ci = ai / bi
static void	elementDiv(DMatrix3x3 a, DMatrix3x3 b)	Performs an element by element division operation: aij = aij / bij
static void	elementDiv(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs an element by element division operation: cij = aij / bij
static double	elementMax(DMatrix3 a)	Returns the value of the element in the vector that has the largest value. Max{ ai } for all i
static double	elementMax(DMatrix3x3 a)	Returns the value of the element in the matrix that has the largest value. Max{ aij } for all i and j
static double	elementMaxAbs(DMatrix3 a)	Returns the absolute value of the element in the vector that has the largest absolute value. Max{ |ai| } for all i
static double	elementMaxAbs(DMatrix3x3 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	elementMin(DMatrix3 a)	Returns the value of the element in the vector that has the minimum value. Min{ ai } for all
static double	elementMin(DMatrix3x3 a)	Returns the value of the element in the matrix that has the minimum value. Min{ aij } for all i and j
static double	elementMinAbs(DMatrix3 a)	Returns the absolute value of the element in the vector that has the smallest absolute value. Min{ |ai| } for all i
static double	elementMinAbs(DMatrix3x3 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 void	elementMult(DMatrix3 a, DMatrix3 b)	Performs an element by element multiplication operation: ai = ai * bi
static void	elementMult(DMatrix3 a, DMatrix3 b, DMatrix3 c)	Performs an element by element multiplication operation: ci = ai * bj
static void	elementMult(DMatrix3x3 a, DMatrix3x3 b)	Performs an element by element multiplication operation: aij = aij * bij
static void	elementMult(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs an element by element multiplication operation: cij = aij * bij
static DMatrix3	extractColumn(DMatrix3x3 a, int column, DMatrix3 out)	Extracts the column from the matrix a.
static DMatrix3	extractRow(DMatrix3x3 a, int row, DMatrix3 out)	Extracts the row from the matrix a.
static void	fill(DMatrix3 a, double v)	Sets every element in the vector to the specified value. ai = value
static void	fill(DMatrix3x3 a, double v)	Sets every element in the matrix to the specified value. aij = value
static boolean	invert(DMatrix3x3 a, DMatrix3x3 inv)	Inverts matrix 'a' using minor matrices and stores the results in 'inv'.
static void	mult(double alpha, DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = α * a * b cij = α ∑k=1:n { aik * bkj}
static void	mult(DMatrix3 a, DMatrix3x3 b, DMatrix3 c)	Performs vector to matrix multiplication: c = a * b cj = ∑k=1:n { bk * akj }
static void	mult(DMatrix3x3 a, DMatrix3 b, DMatrix3 c)	Performs matrix to vector multiplication: c = a * b ci = ∑k=1:n { aik * bk}
static void	mult(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = a * b cij = ∑k=1:n { aik * bkj}
static void	multAdd(double alpha, DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c += α * a * b cij += α ∑k=1:n { aik * bkj}
static void	multAdd(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c += a * b cij += ∑k=1:n { aik * bkj}
static void	multAddOuter(double alpha, DMatrix3x3 A, double beta, DMatrix3 u, DMatrix3 v, DMatrix3x3 C)	C = αA + βu*vT
static void	multAddTransA(double alpha, DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c += α * aT * b cij += α * ∑k=1:n { aki * bkj}
static void	multAddTransA(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c += aT * b cij += ∑k=1:n { aki * bkj}
static void	multAddTransAB(double alpha, DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c += α*aT * bT cij += α*∑k=1:n { aki * bjk}
static void	multAddTransAB(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c += aT * bT cij += ∑k=1:n { aki * bjk}
static void	multAddTransB(double alpha, DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c += α * a * bT cij += α*∑k=1:n { aik * bjk}
static void	multAddTransB(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c += a * bT cij += ∑k=1:n { aik * bjk}
static void	multTransA(double alpha, DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = α * aT * b cij = α * ∑k=1:n { aki * bkj}
static void	multTransA(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = aT * b cij = ∑k=1:n { aki * bkj}
static void	multTransAB(double alpha, DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = α*aT * bT cij = α*∑k=1:n { aki * bjk}
static void	multTransAB(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = aT * bT cij = ∑k=1:n { aki * bjk}
static void	multTransB(double alpha, DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = α * a * bT cij = α*∑k=1:n { aik * bjk}
static void	multTransB(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = a * bT cij = ∑k=1:n { aik * bjk}
static void	scale(double alpha, DMatrix3 a)	Performs an in-place element by element scalar multiplication. aij = α*aij
static void	scale(double alpha, DMatrix3 a, DMatrix3 b)	Performs an element by element scalar multiplication. bi = α*ai
static void	scale(double alpha, DMatrix3x3 a)	Performs an in-place element by element scalar multiplication. aij = α*aij
static void	scale(double alpha, DMatrix3x3 a, DMatrix3x3 b)	Performs an element by element scalar multiplication. bij = α*aij
static void	setIdentity(DMatrix3x3 a)	Sets all the diagonal elements equal to one and everything else equal to zero.
static void	subtract(DMatrix3 a, DMatrix3 b, DMatrix3 c)	Performs the following operation: c = a - b ci = ai - bi
static void	subtract(DMatrix3x3 a, DMatrix3x3 b, DMatrix3x3 c)	Performs the following operation: c = a - b cij = aij - bij
static void	subtractEquals(DMatrix3 a, DMatrix3 b)	Performs the following operation: a = a - b ai = ai - bi
static void	subtractEquals(DMatrix3x3 a, DMatrix3x3 b)	Performs the following operation: a = a - b aij = aij - bij
static double	trace(DMatrix3x3 a)	This computes the trace of the matrix: trace = ∑i=1:n { aii }
static void	transpose(DMatrix3x3 m)	Performs an in-place transpose.
static DMatrix3x3	transpose(DMatrix3x3 input, DMatrix3x3 output)	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

Constructor Details

CommonOps_DDF3

public CommonOps_DDF3()

Method Details

add

public static void add(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

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.

c - A Matrix where the results are stored. Modified.

add

public static void add(DMatrix3 a,
 DMatrix3 b,
 DMatrix3 c)

Performs the following operation:

c = a + b
c_i = a_i + b_i

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

Parameters:

a - A Vector. Not modified.

b - A Vector. Not modified.

c - A Vector where the results are stored. Modified.

addEquals

public static void addEquals(DMatrix3x3 a,
 DMatrix3x3 b)

Performs the following operation:

a = a + b
a_ij = a_ij + b_ij

Parameters:

a - A Matrix. Modified.

b - A Matrix. Not modified.

addEquals

public static void addEquals(DMatrix3 a,
 DMatrix3 b)

Performs the following operation:

a = a + b
a_i = a_i + b_i

Parameters:

a - A Vector. Modified.

b - A Vector. Not modified.

subtract

public static void subtract(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

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.

c - A Matrix where the results are stored. Modified.

subtract

public static void subtract(DMatrix3 a,
 DMatrix3 b,
 DMatrix3 c)

Performs the following operation:

c = a - b
c_i = a_i - b_i

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

Parameters:

a - A Vector. Not modified.

b - A Vector. Not modified.

c - A Vector where the results are stored. Modified.

subtractEquals

public static void subtractEquals(DMatrix3x3 a,
 DMatrix3x3 b)

Performs the following operation:

a = a - b
a_ij = a_ij - b_ij

Parameters:

a - A Matrix. Modified.

b - A Matrix. Not modified.

subtractEquals

public static void subtractEquals(DMatrix3 a,
 DMatrix3 b)

Performs the following operation:

a = a - b
a_i = a_i - b_i

Parameters:

a - A Vector. Modified.

b - A Vector. Not modified.

transpose

public static void transpose(DMatrix3x3 m)

Performs an in-place transpose. This algorithm is only efficient for square matrices.

Parameters:

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

transpose

public static DMatrix3x3 transpose(DMatrix3x3 input,
 DMatrix3x3 output)

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

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

Parameters:

input - The original matrix. Not modified.

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

Returns:

The transposed matrix.

mult

public static void mult(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

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.

c - (Output) Where the results of the operation are stored. Modified.

mult

public static void mult(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

c = α * a * b

c_ij = α ∑_k=1:n { a_ik * b_kj}

Parameters:

alpha - Scaling factor.

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

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

c - (Output) Where the results of the operation are stored. Modified.

multTransA

public static void multTransA(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

c = a^T * b

c_ij = ∑_k=1:n { a_ki * b_kj}

Parameters:

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

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

c - (Output) Where the results of the operation are stored. Modified.

multTransA

public static void multTransA(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

c = α * a^T * b

c_ij = α * ∑_k=1:n { a_ki * b_kj}

Parameters:

alpha - Scaling factor.

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

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

c - (Output) Where the results of the operation are stored. Modified.

multTransAB

public static void multTransAB(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

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

Parameters:

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

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

c - (Output) Where the results of the operation are stored. Modified.

multTransAB

public static void multTransAB(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

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 - (Input) The left matrix in the multiplication operation. Not modified.

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

c - (Output) Where the results of the operation are stored. Modified.

multTransB

public static void multTransB(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

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

Parameters:

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

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

c - (Output) Where the results of the operation are stored. Modified.

multTransB

public static void multTransB(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

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

Parameters:

alpha - Scaling factor.

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

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

c - (Output) Where the results of the operation are stored. Modified.

multAdd

public static void multAdd(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

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.

c - (Output) Where the results of the operation are stored. Modified.

multAdd

public static void multAdd(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

c += α * a * b

c_ij += α ∑_k=1:n { a_ik * b_kj}

Parameters:

alpha - Scaling factor.

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

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

c - (Output) Where the results of the operation are stored. Modified.

multAddTransA

public static void multAddTransA(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

c += a^T * b

c_ij += ∑_k=1:n { a_ki * b_kj}

Parameters:

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

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

c - (Output) Where the results of the operation are stored. Modified.

multAddTransA

public static void multAddTransA(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

c += α * a^T * b

c_ij += α * ∑_k=1:n { a_ki * b_kj}

Parameters:

alpha - Scaling factor.

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

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

c - (Output) Where the results of the operation are stored. Modified.

multAddTransAB

public static void multAddTransAB(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

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

Parameters:

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

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

c - (Output) Where the results of the operation are stored. Modified.

multAddTransAB

public static void multAddTransAB(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

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 - (Input) The left matrix in the multiplication operation. Not modified.

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

c - (Output) Where the results of the operation are stored. Modified.

multAddTransB

public static void multAddTransB(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

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

Parameters:

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

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

c - (Output) Where the results of the operation are stored. Modified.

multAddTransB

public static void multAddTransB(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs the following operation:

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

Parameters:

alpha - Scaling factor.

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

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

c - (Output) Where the results of the operation are stored. Modified.

multAddOuter

public static void multAddOuter(double alpha,
 DMatrix3x3 A,
 double beta,
 DMatrix3 u,
 DMatrix3 v,
 DMatrix3x3 C)

C = αA + βu*v^T

Parameters:

alpha - scale factor applied to A

A - matrix

beta - scale factor applies to outer product

u - vector

v - vector

C - Storage for solution. Can be same instance as A.

mult

public static void mult(DMatrix3x3 a,
 DMatrix3 b,
 DMatrix3 c)

Performs matrix to vector multiplication:

c = a * b

c_i = ∑_k=1:n { a_ik * b_k}

Parameters:

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

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

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

mult

public static void mult(DMatrix3 a,
 DMatrix3x3 b,
 DMatrix3 c)

Performs vector to matrix multiplication:

c = a * b

c_j = ∑_k=1:n { b_k * a_kj }

Parameters:

a - The left vector 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.

dot

public static double dot(DMatrix3 a,
 DMatrix3 b)

Performs the vector dot product:

c = a * b

c ≥ ∑_k=1:n { b_k * a_k }

Parameters:

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

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

Returns:

The dot product

setIdentity

public static void setIdentity(DMatrix3x3 a)

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:

a - A matrix.

invert

public static boolean invert(DMatrix3x3 a,
 DMatrix3x3 inv)

Inverts matrix 'a' using minor matrices and stores the results in 'inv'. Scaling is applied to improve stability against overflow and underflow. WARNING: Potentially less stable than using LU decomposition.

Parameters:

a - (Input) Matrix.

inv - (Output) Inverted matrix. Can be the same as 'a'.

Returns:

true if it was successful or false if it failed. Not reliable.

det

public static double det(DMatrix3x3 mat)

Computes the determinant using minor matrices.
WARNING: Potentially less stable than using LU decomposition.

Parameters:

mat - Input matrix. Not modified.

Returns:

The determinant.

cholL

public static boolean cholL(DMatrix3x3 A)

Performs a lower Cholesky decomposition of matrix 'A' and stores result in A.

Parameters:

A - (Input) SPD Matrix. (Output) lower cholesky.

Returns:

true if it was successful or false if it failed. Not always reliable.

cholU

public static boolean cholU(DMatrix3x3 A)

Performs an upper Cholesky decomposition of matrix 'A' and stores result in A.

Parameters:

A - (Input) SPD Matrix. (Output) upper cholesky.

Returns:

true if it was successful or false if it failed. Not always reliable.

trace

public static double trace(DMatrix3x3 a)

This computes the trace of the matrix:

trace = ∑_i=1:n { a_ii }

The trace is only defined for square matrices.

Parameters:

a - A square matrix. Not modified.

diag

public static void diag(DMatrix3x3 input,
 DMatrix3 out)

Extracts all diagonal elements from 'input' and places them inside the 'out' vector. Elements are in sequential order.

Parameters:

input - Matrix. Not modified.

out - Vector containing diagonal elements. Modified.

elementMax

public static double elementMax(DMatrix3x3 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(DMatrix3 a)

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

Max{ a_i } for all i

Parameters:

a - A vector. Not modified.

Returns:

The max element value of the matrix.

elementMaxAbs

public static double elementMaxAbs(DMatrix3x3 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(DMatrix3 a)

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

Max{ |a_i| } for all i

Parameters:

a - A matrix. Not modified.

Returns:

The max abs element value of the vector.

elementMin

public static double elementMin(DMatrix3x3 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(DMatrix3 a)

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

Min{ a_i } for all

Parameters:

a - A matrix. Not modified.

Returns:

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

elementMinAbs

public static double elementMinAbs(DMatrix3x3 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(DMatrix3 a)

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

Min{ |a_i| } for all i

Parameters:

a - A matrix. Not modified.

Returns:

The max element value of the vector.

elementMult

public static void elementMult(DMatrix3x3 a,
 DMatrix3x3 b)

Performs 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 void elementMult(DMatrix3 a,
 DMatrix3 b)

Performs an element by element multiplication operation:

a_i = a_i * b_i

Parameters:

a - The left vector in the multiplication operation. Modified.

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

elementMult

public static void elementMult(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs 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.

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

elementMult

public static void elementMult(DMatrix3 a,
 DMatrix3 b,
 DMatrix3 c)

Performs an element by element multiplication operation:

c_i = a_i * b_j

Parameters:

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

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

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

elementDiv

public static void elementDiv(DMatrix3x3 a,
 DMatrix3x3 b)

Performs 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 void elementDiv(DMatrix3 a,
 DMatrix3 b)

Performs an element by element division operation:

a_i = a_i / b_i

Parameters:

a - The left vector in the division operation. Modified.

b - The right vector in the division operation. Not modified.

elementDiv

public static void elementDiv(DMatrix3x3 a,
 DMatrix3x3 b,
 DMatrix3x3 c)

Performs 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.

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

elementDiv

public static void elementDiv(DMatrix3 a,
 DMatrix3 b,
 DMatrix3 c)

Performs an element by element division operation:

c_i = a_i / b_i

Parameters:

a - The left vector in the division operation. Not modified.

b - The right vector in the division operation. Not modified.

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

scale

public static void scale(double alpha,
 DMatrix3x3 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,
 DMatrix3 a)

Performs an in-place element by element scalar multiplication.

a_ij = α*a_ij

Parameters:

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

alpha - the amount each element is multiplied by.

scale

public static void scale(double alpha,
 DMatrix3x3 a,
 DMatrix3x3 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.

scale

public static void scale(double alpha,
 DMatrix3 a,
 DMatrix3 b)

Performs an element by element scalar multiplication.

b_i = α*a_i

Parameters:

alpha - the amount each element is multiplied by.

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

b - Where the scaled matrix is stored. Modified.

divide

public static void divide(DMatrix3x3 a,
 double alpha)

Performs an in-place element by element scalar division. Scalar denominator.

a_ij = a_ij/α

Parameters:

a - The matrix whose elements are to be divided. Modified.

alpha - the amount each element is divided by.

divide

public static void divide(DMatrix3 a,
 double alpha)

Performs an in-place element by element scalar division. Scalar denominator.

a_i = a_i/α

Parameters:

a - The vector whose elements are to be divided. Modified.

alpha - the amount each element is divided by.

divide

public static void divide(DMatrix3x3 a,
 double alpha,
 DMatrix3x3 b)

Performs an element by element scalar division. Scalar denominator.

b_ij = a_ij /α

Parameters:

alpha - the amount each element is divided by.

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

b - Where the results are stored. Modified.

divide

public static void divide(DMatrix3 a,
 double alpha,
 DMatrix3 b)

Performs an element by element scalar division. Scalar denominator.

b_i = a_i /α

Parameters:

alpha - the amount each element is divided by.

a - The vector whose elements are to be divided. Not modified.

b - Where the results are stored. Modified.

changeSign

public static void changeSign(DMatrix3x3 a)

Changes the sign of every element in the matrix.

a_ij = -a_ij

Parameters:

a - A matrix. Modified.

changeSign

public static void changeSign(DMatrix3 a)

Changes the sign of every element in the vector.

a_i = -a_i

Parameters:

a - A vector. Modified.

fill

public static void fill(DMatrix3x3 a,
 double v)

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.

v - The value each element will have.

fill

public static void fill(DMatrix3 a,
 double v)

Sets every element in the vector to the specified value.

a_i = value

Parameters:

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

v - The value each element will have.

extractRow

public static DMatrix3 extractRow(DMatrix3x3 a,
 int row,
 DMatrix3 out)

Extracts the row from the matrix a.

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 DMatrix3 extractColumn(DMatrix3x3 a,
 int column,
 DMatrix3 out)

Extracts the column from the matrix a.

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.