Modifier and Type | Interface and Description |
---|---|
interface |
Matrix
|
interface |
MatrixRing
A matrix ring is the set of all n × n matrices over an arbitrary
Ring R. |
Modifier and Type | Class and Description |
---|---|
class |
ImmutableMatrix
This is a read-only view of a
Matrix instance. |
Modifier and Type | Class and 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.
|
Modifier and Type | Class and Description |
---|---|
class |
DenseMatrix
This class implements the standard, dense,
double based matrix
representation. |
Modifier and Type | Class and 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.
|
Modifier and Type | Class and 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.
|
Modifier and Type | Interface and Description |
---|---|
interface |
SparseMatrix
A sparse matrix stores only non-zero values.
|
Modifier and Type | Class and 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.
|
Modifier and Type | Class and 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 \(b'Xb\).
|
Modifier and Type | Class and 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.
|
Modifier and Type | Interface and Description |
---|---|
interface |
GenericMatrix<T extends GenericMatrix<T,F>,F extends Field<F>>
This class defines a matrix over a field.
|
Modifier and Type | Class and 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. |
Modifier and Type | Interface and Description |
---|---|
interface |
Field<F>
As an algebraic structure, every field is a ring, but not every ring is a field.
|
Modifier and Type | Class and 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.
|
Modifier and Type | Class and Description |
---|---|
class |
DPolynomial
This is the first order derivative function of a
Polynomial , which, again, is a polynomial. |
Modifier and Type | Class and 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.
|
Modifier and Type | Class and Description |
---|---|
class |
Real
A real number is an arbitrary precision number.
|
Modifier and Type | Class and Description |
---|---|
class |
Complex
A complex number is a number consisting of a real number part and an imaginary number part.
|
Modifier and Type | Class and 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.
|
Modifier and Type | Class and 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.
|
Modifier and Type | Class and Description |
---|---|
class |
ReturnsMatrix |
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