# Uses of Interfacedev.nm.algebra.structure.Monoid

Packages that use Monoid
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.doubles

Modifier and Type
Interface
Description
interface
Matrix
This interface defines a Matrix as a Ring, a Table, and a few more methods not already defined in its mathematical definition.
interface
MatrixRing
A matrix ring is the set of all n × n matrices over an arbitrary Ring R.
Modifier and Type
Class
Description
class
ImmutableMatrix
This is a read-only view of a Matrix instance.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.doubles.matrixtype

Modifier and Type
Class
Description
class
GivensMatrix
Givens rotation is a rotation in the plane spanned by two coordinates axes.
class
HilbertMatrix
A Hilbert matrix, H, is a symmetric matrix with entries being the unit fractions H[i][j] = 1 / (i + j -1)
class
PermutationMatrix
A permutation matrix is a square matrix that has exactly one entry '1' in each row and each column and 0's elsewhere.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense

Modifier and Type
Class
Description
class
DenseMatrix
This class implements the standard, dense, double based matrix representation.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.diagonal

Modifier and Type
Class
Description
class
BidiagonalMatrix
A bi-diagonal matrix is either upper or lower diagonal.
class
DiagonalMatrix
A diagonal matrix has non-zero entries only on the main diagonal.
class
TridiagonalMatrix
A tri-diagonal matrix has non-zero entries only on the super, main and sub diagonals.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.triangle

Modifier and Type
Class
Description
class
LowerTriangularMatrix
A lower triangular matrix has 0 entries where column index > row index.
class
SymmetricMatrix
A symmetric matrix is a square matrix such that its transpose equals to itself, i.e., A[i][j] = A[j][i]
class
UpperTriangularMatrix
An upper triangular matrix has 0 entries where row index is greater than column index.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.doubles.matrixtype.sparse

Modifier and Type
Interface
Description
interface
SparseMatrix
A sparse matrix stores only non-zero values.
Modifier and Type
Class
Description
class
CSCSparseMatrix
The Compressed Sparse Row (CSC) format for sparse matrix has this representation: (value, row_ind, col_ptr).
class
CSRSparseMatrix
The Compressed Sparse Row (CSR) format for sparse matrix has this representation: (value, col_ind, row_ptr).
class
DOKSparseMatrix
The Dictionary Of Key (DOK) format for sparse matrix uses the coordinates of non-zero entries in the matrix as keys.
class
LILSparseMatrix
The list of lists (LIL) format for sparse matrix stores one list per row, where each entry stores a column index and value.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.doubles.operation

Modifier and Type
Class
Description
class
ColumnBindMatrix
A fast "cbind" matrix from vectors.
class
CongruentMatrix
Given a matrix A and an invertible matrix P, we create the congruent matrix B s.t., B = P'AP
class
DiagonalSum
Add diagonal elements to a matrix, an efficient implementation.
class
FastKroneckerProduct
This is a fast and memory-saving implementation of computing the Kronecker product.
class
Inverse
For a square matrix A, the inverse, A-1, if exists, satisfies A.multiply(A.inverse()) == A.ONE() There are multiple ways to compute the inverse of a matrix.
class
KroneckerProduct
Given an m-by-n matrix A and a p-by-q matrix B, their Kronecker product C, also called their matrix direct product, is an (mp)-by-(nq) matrix with entries defined by cst = aij bkl where
class
MAT
MAT is the inverse operator of SVEC.
class
MatrixRootByDiagonalization
The square root of a matrix extends the notion of square root from numbers to matrices.
class
OuterProduct
The outer product of two vectors a and b, is a row vector multiplied on the left by a column vector.
class
Pow
This is a square matrix A to the power of an integer n, An.
class
PseudoInverse
The Moore-Penrose pseudo-inverse of an m x n matrix A is A+.
class
SimilarMatrix
Given a matrix A and an invertible matrix P, we construct the similar matrix B s.t., B = P-1AP
class
SubMatrixRef
This is a 'reference' to a sub-matrix of a larger matrix without copying it.
class
SymmetricKronecker
Compute the symmetric Kronecker product of two matrices.
class
VariancebtX
Computes $$b'Xb$$.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.doubles.operation.positivedefinite

Modifier and Type
Class
Description
class
GoldfeldQuandtTrotter
Goldfeld, Quandt and Trotter propose the following way to coerce a non-positive definite Hessian matrix to become symmetric, positive definite.
class
MatthewsDavies
Matthews and Davies propose the following way to coerce a non-positive definite Hessian matrix to become symmetric, positive definite.
class
PositiveDefiniteMatrixByPositiveDiagonal
This class "converts" a matrix into a symmetric, positive definite matrix, if it is not already so, by forcing the diagonal entries in the eigen decomposition to a small non-negative number, e.g., 0.
class
PositiveSemiDefiniteMatrixNonNegativeDiagonal
This class "converts" a matrix into a symmetric, positive semi-definite matrix, if it is not already so, by forcing the negative diagonal entries in the eigen decomposition to 0.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.generic

Modifier and Type
Interface
Description
interface
GenericMatrix<T extends GenericMatrix<T,F>,F extends Field<F>>
This class defines a matrix over a field.
• ## Uses of Monoid in dev.nm.algebra.linear.matrix.generic.matrixtype

Modifier and Type
Class
Description
class
ComplexMatrix
This is a Complex matrix.
class
GenericFieldMatrix<F extends Field<F>>
This is a generic matrix over a Field.
class
RealMatrix
This is a Real matrix.
• ## Uses of Monoid in dev.nm.algebra.structure

Subinterfaces of Monoid in dev.nm.algebra.structure
Modifier and Type
Interface
Description
interface
Field<F>
As an algebraic structure, every field is a ring, but not every ring is a field.
interface
Ring<R>
A ring is a set R equipped with two binary operations called addition and multiplication: + : R × R → R and ⋅ : R × R → R To qualify as a ring, the set and two operations, (R, +, ⋅), must satisfy the requirements known as the ring axioms.
• ## Uses of Monoid in dev.nm.analysis.differentiation.multivariate

Modifier and Type
Class
Description
class
BorderedHessian
A bordered Hessian matrix consists of the Hessian of a multivariate function f, and the gradient of a multivariate function g.
class
Hessian
The Hessian matrix is the square matrix of the second-order partial derivatives of a multivariate function.
class
Jacobian
The Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
• ## Uses of Monoid in dev.nm.analysis.differentiation.univariate

Modifier and Type
Class
Description
class
DPolynomial
This is the first order derivative function of a Polynomial, which, again, is a polynomial.
• ## Uses of Monoid in dev.nm.analysis.function.polynomial

Modifier and Type
Class
Description
class
CauchyPolynomial
The Cauchy's polynomial of a polynomial takes this form:
class
Polynomial
A polynomial is a UnivariateRealFunction that represents a finite length expression constructed from variables and constants, using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents.
class
QuadraticMonomial
A quadratic monomial has this form: x2 + ux + v.
class
ScaledPolynomial
This constructs a scaled polynomial that has neither too big or too small coefficients, hence avoiding overflow or underflow.
• ## Uses of Monoid in dev.nm.number

Classes in dev.nm.number that implement Monoid
Modifier and Type
Class
Description
class
Real
A real number is an arbitrary precision number.
• ## Uses of Monoid in dev.nm.number.complex

Classes in dev.nm.number.complex that implement Monoid
Modifier and Type
Class
Description
class
Complex
A complex number is a number consisting of a real number part and an imaginary number part.
• ## Uses of Monoid in dev.nm.stat.descriptive.correlation

Modifier and Type
Class
Description
class
CorrelationMatrix
The correlation matrix of n random variables X1, ..., Xn is the n × n matrix whose i,j entry is corr(Xi, Xj), the correlation between X1 and Xn.
• ## Uses of Monoid in dev.nm.stat.descriptive.covariance

Classes in dev.nm.stat.descriptive.covariance that implement Monoid
Modifier and Type
Class
Description
class
SampleCovariance
This class computes the Covariance matrix of a matrix, where the (i, j) entry is the covariance of the i-th column and j-th column of the matrix.
• ## Uses of Monoid in tech.nmfin.returns

Classes in tech.nmfin.returns that implement Monoid
Modifier and Type
Class
Description
class
ReturnsMatrix