| Package | Description |
|---|---|
| dev.nm.algebra.linear.matrix.doubles |
Real-valued matrices with one-based row and column indices.
|
| dev.nm.algebra.linear.matrix.doubles.matrixtype | |
| dev.nm.algebra.linear.matrix.doubles.matrixtype.dense | |
| dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.diagonal | |
| dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.triangle | |
| dev.nm.algebra.linear.matrix.doubles.matrixtype.sparse | |
| dev.nm.algebra.linear.matrix.doubles.operation | |
| dev.nm.algebra.linear.matrix.doubles.operation.positivedefinite | |
| dev.nm.algebra.linear.matrix.generic | |
| dev.nm.algebra.linear.matrix.generic.matrixtype | |
| dev.nm.analysis.differentiation.multivariate | |
| dev.nm.misc.datastructure | |
| dev.nm.solver.multivariate.constrained.convex.sdp.socp.qp.lp.simplex | |
| dev.nm.stat.descriptive.correlation | |
| dev.nm.stat.descriptive.covariance | |
| tech.nmfin.returns |
Converting price changes to absolute, simple, or logarithmic returns.
|
| Modifier and Type | Interface and Description |
|---|---|
interface |
Matrix
|
interface |
MatrixAccess
This interface defines the methods for accessing entries in a matrix.
|
interface |
MatrixTable
A matrix is represented by a rectangular table structure with accessors.
|
| 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 |
DefaultMatrixStorage
There are multiple ways to implement the storage data structure depending on the matrix type for
optimization purpose.
|
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 |
DenseData
This implementation of the storage of a dense matrix stores the data of a 2D matrix as an 1D
array.
|
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.,
\[
B = P^{\mathsf T}AP
\]
|
class |
DiagonalSum
Add diagonal elements to a matrix, an efficient implementation.
|
class |
ElementaryOperation
There are three elementary row operations which are equivalent to left multiplying an elementary
matrix.
|
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
\[
c_{st} = a_{ij} b_{kl}
\]
where
\[
\begin{gathered}
s = p(i - 1) + k \\
t = q(j - 1) + l
\end{gathered}
\]
|
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, \(A^{n}\).
|
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.,
\[
B = P^{-1}AP
\]
|
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.
|
| 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 | 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 |
FlexibleTable
This is a 2D table that can shrink or grow by row or by column.
|
| Modifier and Type | Method and Description |
|---|---|
static boolean |
DimensionCheck.isArray(Table A)
Check if a table is a row or a column.
|
static boolean |
DimensionCheck.isColumn(Table A)
Check if a table is a column.
|
static boolean |
DimensionCheck.isFat(Table A)
Check if a table is fat.
|
static boolean |
DimensionCheck.isRow(Table A)
Check if a table is a row.
|
static boolean |
DimensionCheck.isSameDimension(Table A1,
Table A2)
Check if two tables have the same dimension.
|
static boolean |
DimensionCheck.isSquare(Table A)
Check if a table is square.
|
static boolean |
DimensionCheck.isTall(Table A)
Check if a table is tall.
|
static void |
DimensionCheck.throwIfDifferentDimension(Table A1,
Table A2)
Throws if
A1.nRows() ! |
static void |
DimensionCheck.throwIfIncompatible4Multiplication(Table A1,
Table A2)
Throws if
A1.nCols() ! |
static void |
DimensionCheck.throwIfIncompatible4Multiplication(Table A,
Vector v)
Throws if
A.nCols() ! |
static void |
DimensionCheck.throwIfInvalidColumn(Table A,
int j)
Throws if accessing an out of range column.
|
static void |
DimensionCheck.throwIfInvalidRow(Table A,
int i)
Throws if accessing an out of range row.
|
| Modifier and Type | Class and Description |
|---|---|
class |
SimplexTable
This is a simplex table used to solve a linear programming problem using a simplex method.
|
| 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
\(corr(X_{i}, X_{j}\)), the correlation between
\(X_{1}\) and \(X_{n}\).
|
| 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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