Uses of Interface
dev.nm.algebra.structure.AbelianGroup
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Uses of AbelianGroup in dev.nm.algebra.linear.matrix.doubles
Subinterfaces of AbelianGroup in dev.nm.algebra.linear.matrix.doubles Modifier and Type Interface Description interface
Matrix
interface
MatrixRing
A matrix ring is the set of all n × n matrices over an arbitraryRing
R.Classes in dev.nm.algebra.linear.matrix.doubles that implement AbelianGroup Modifier and Type Class Description class
ImmutableMatrix
This is a read-only view of aMatrix
instance. -
Uses of AbelianGroup in dev.nm.algebra.linear.matrix.doubles.matrixtype
Classes in dev.nm.algebra.linear.matrix.doubles.matrixtype that implement AbelianGroup 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 AbelianGroup in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense
Classes in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense that implement AbelianGroup Modifier and Type Class Description class
DenseMatrix
This class implements the standard, dense,double
based matrix representation. -
Uses of AbelianGroup in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.diagonal
Classes in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.diagonal that implement AbelianGroup 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 AbelianGroup in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.triangle
Classes in dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.triangle that implement AbelianGroup 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 AbelianGroup in dev.nm.algebra.linear.matrix.doubles.matrixtype.sparse
Subinterfaces of AbelianGroup in dev.nm.algebra.linear.matrix.doubles.matrixtype.sparse Modifier and Type Interface Description interface
SparseMatrix
A sparse matrix stores only non-zero values.Classes in dev.nm.algebra.linear.matrix.doubles.matrixtype.sparse that implement AbelianGroup Modifier and Type Class Description 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.class
SparseVector
A sparse vector stores only non-zero values. -
Uses of AbelianGroup in dev.nm.algebra.linear.matrix.doubles.operation
Classes in dev.nm.algebra.linear.matrix.doubles.operation that implement AbelianGroup 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'APclass
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, satisfiesA.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 whereclass
MAT
MAT
is the inverse operator ofSVEC
.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-1APclass
SubMatrixRef
This is a 'reference' to a sub-matrix of a larger matrix without copying it.class
SVEC
SVEC
converts a symmetric matrix K = {Kij} into a vector of dimension n(n+1)/2.class
SymmetricKronecker
Compute the symmetric Kronecker product of two matrices.class
VariancebtX
Computes \(b'Xb\). -
Uses of AbelianGroup in dev.nm.algebra.linear.matrix.doubles.operation.positivedefinite
Classes in dev.nm.algebra.linear.matrix.doubles.operation.positivedefinite that implement AbelianGroup 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 AbelianGroup in dev.nm.algebra.linear.matrix.generic
Subinterfaces of AbelianGroup 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 AbelianGroup in dev.nm.algebra.linear.matrix.generic.matrixtype
Classes in dev.nm.algebra.linear.matrix.generic.matrixtype that implement AbelianGroup Modifier and Type Class Description class
ComplexMatrix
This is aComplex
matrix.class
GenericFieldMatrix<F extends Field<F>>
This is a generic matrix over aField
.class
RealMatrix
This is aReal
matrix. -
Uses of AbelianGroup in dev.nm.algebra.linear.vector.doubles
Subinterfaces of AbelianGroup in dev.nm.algebra.linear.vector.doubles Modifier and Type Interface Description interface
Vector
An Euclidean vector is a geometric object that has both a magnitude/length and a direction.Classes in dev.nm.algebra.linear.vector.doubles that implement AbelianGroup Modifier and Type Class Description class
CombinedVectorByRef
For efficiency, this wrapper concatenates two or more vectors by references (without data copying).class
ImmutableVector
This is a read-only view of aVector
instance.class
SubVectorRef
Represents a sub-vector backed by the referenced vector, without data copying. -
Uses of AbelianGroup in dev.nm.algebra.linear.vector.doubles.dense
Classes in dev.nm.algebra.linear.vector.doubles.dense that implement AbelianGroup Modifier and Type Class Description class
DenseVector
This class implements the standard, dense,double
based vector representation. -
Uses of AbelianGroup in dev.nm.algebra.linear.vector.doubles.operation
Classes in dev.nm.algebra.linear.vector.doubles.operation that implement AbelianGroup Modifier and Type Class Description class
Basis
A basis is a set of linearly independent vectors spanning a vector space. -
Uses of AbelianGroup in dev.nm.algebra.structure
Subinterfaces of AbelianGroup in dev.nm.algebra.structure Modifier and Type Interface Description interface
BanachSpace<B,F extends Field<F> & Comparable<F>>
A Banach space, B, is a complete normed vector space such that every Cauchy sequence (with respect to the metric d(x, y) = |x - y|) in B has a limit in B.interface
Field<F>
As an algebraic structure, every field is a ring, but not every ring is a field.interface
HilbertSpace<H,F extends Field<F> & Comparable<F>>
A Hilbert space is an inner product space, an abstract vector space in which distances and angles can be measured.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.interface
VectorSpace<V,F extends Field<F>>
A vector space is a set V together with two binary operations that combine two entities to yield a third, called vector addition and scalar multiplication. -
Uses of AbelianGroup in dev.nm.analysis.differentiation.multivariate
Classes in dev.nm.analysis.differentiation.multivariate that implement AbelianGroup 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
Gradient
The gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and of which the magnitude is the greatest rate of change.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 AbelianGroup in dev.nm.analysis.differentiation.univariate
Classes in dev.nm.analysis.differentiation.univariate that implement AbelianGroup Modifier and Type Class Description class
DPolynomial
This is the first order derivative function of aPolynomial
, which, again, is a polynomial. -
Uses of AbelianGroup in dev.nm.analysis.function.polynomial
Classes in dev.nm.analysis.function.polynomial that implement AbelianGroup Modifier and Type Class Description class
CauchyPolynomial
The Cauchy's polynomial of a polynomial takes this form:class
Polynomial
A polynomial is aUnivariateRealFunction
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 AbelianGroup in dev.nm.number
Classes in dev.nm.number that implement AbelianGroup Modifier and Type Class Description class
Real
A real number is an arbitrary precision number. -
Uses of AbelianGroup in dev.nm.number.complex
Classes in dev.nm.number.complex that implement AbelianGroup 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 AbelianGroup in dev.nm.stat.descriptive.correlation
Classes in dev.nm.stat.descriptive.correlation that implement AbelianGroup 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 AbelianGroup in dev.nm.stat.descriptive.covariance
Classes in dev.nm.stat.descriptive.covariance that implement AbelianGroup 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 AbelianGroup in tech.nmfin.returns
Classes in tech.nmfin.returns that implement AbelianGroup Modifier and Type Class Description class
ReturnsMatrix
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