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SuanShu, a Java numerical and statistical library | |||||||
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T matrix, such that
T = Q %*% A %*% Q
T is triangular.
T matrix as in the real Schur canonical form
Q'MQ = T
T is quasi upper triangular.
T, such that
T %*% A == U
T, such that
T %*% A == U
T, such that
T %*% A == U
To find a particular solution for a non-homogeneous system of linear equations with the same A,
i.e.,
Ax = b
we do
x = T %*% b
where x is a particular solution.
t(this)
Compute the transpose of this matrix.
t(A)
t(A) = A.
t(A)
T.
R matrix.
(a + bi).
(a + bi).
tau ensures that the result is not too close to the boundary
t, where
x̄ - μ
t = ------------
s / sqrt(N)
x̄ is the sample mean;
μ is the population mean;
s is the square root of the sample variance;
N is the sample size;
The importance of the Student's distribution is
when (as in nearly all practical statistical work) the population standard deviation is unknown and has to be estimated from the data.x satisfies the if part of the statement.
threshold, the summing process stops.
A1.nrow !
- throwIfIncompatible4Multiplication(MatrixDimension, MatrixDimension) -
Static method in class com.numericalmethod.suanshu.matrix.DimensionCheck
- Throws if
A1.ncol !
- throwIfIncompatible4Multiplication(MatrixDimension, Vector) -
Static method in class com.numericalmethod.suanshu.matrix.DimensionCheck
- Throws if
A.ncol !
- throwIfInvalidColumn(MatrixDimension, int) -
Static method in class com.numericalmethod.suanshu.matrix.DimensionCheck
- Throws if accessing an out of range column.
- throwIfInvalidRow(MatrixDimension, int) -
Static method in class com.numericalmethod.suanshu.matrix.DimensionCheck
- Throws if accessing an out of range row.
- time(int) -
Method in class com.numericalmethod.suanshu.stats.timeseries.multivariate.GenericTimeTimeSeries
- Get the time at position
index.
- time -
Variable in class com.numericalmethod.suanshu.stats.timeseries.TimeSeries.Entry
- the time index, timestamp
- time(int) -
Method in class com.numericalmethod.suanshu.stats.timeseries.univariate.GenericTimeTimeSeries
- Get the time at position
index.
- TimeGrid - Interface in com.numericalmethod.suanshu.stats.stochasticprocess.timepoints
- This interface represents the discrete time points in [t1, tn = T] for a stochastic process.
- TimeInterval - Class in com.numericalmethod.suanshu.time
- This class represents a time interval.
- TimeInterval(ComparableDateTime, ComparableDateTime) -
Constructor for class com.numericalmethod.suanshu.time.TimeInterval
- Construct a time interval from two time points.
- TimeInterval(DateTime, DateTime) -
Constructor for class com.numericalmethod.suanshu.time.TimeInterval
- Construct a time interval from two time points.
- TimeIntervals - Class in com.numericalmethod.suanshu.time
-
- TimeIntervals() -
Constructor for class com.numericalmethod.suanshu.time.TimeIntervals
-
- TimeIntervals(ComparableDateTime, ComparableDateTime) -
Constructor for class com.numericalmethod.suanshu.time.TimeIntervals
-
- TimeIntervals(DateTime, DateTime) -
Constructor for class com.numericalmethod.suanshu.time.TimeIntervals
-
- TimeIntervals(Interval<ComparableDateTime>) -
Constructor for class com.numericalmethod.suanshu.time.TimeIntervals
-
- TimeIntervals(Interval<ComparableDateTime>...) -
Constructor for class com.numericalmethod.suanshu.time.TimeIntervals
-
- TimeIntervals(Intervals<ComparableDateTime>) -
Constructor for class com.numericalmethod.suanshu.time.TimeIntervals
-
- timePoints -
Variable in class com.numericalmethod.suanshu.stats.stochasticprocess.univariate.integration.sde.PathByIdImpl
- the set of discretized time points
- TimeSeries<T,V> - Interface in com.numericalmethod.suanshu.stats.timeseries
- A time series is an serially indexed collection of items.
- TimeSeries - Interface in com.numericalmethod.suanshu.stats.timeseries.univariate.realtime
- This represents a univariate time series indexed by integers.
- TimeSeries<T> - Interface in com.numericalmethod.suanshu.stats.timeseries.univariate
- This represents a univariate time series indexed by some notion of time.
- TimeSeries.Entry<T,V> - Class in com.numericalmethod.suanshu.stats.timeseries
- A time series is composed of a sequence of Entrys.
- TimeSeries.Entry(T, V) -
Constructor for class com.numericalmethod.suanshu.stats.timeseries.TimeSeries.Entry
- Construct an entry from a time-value pair.
- TimeSeries.Entry - Class in com.numericalmethod.suanshu.stats.timeseries.univariate.realtime
- the TimeSeries.Entry for an integer-indexed univariate time series
- TimeSeries.Entry(int, double) -
Constructor for class com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.TimeSeries.Entry
-
- TimeSeries.Entry<T> - Class in com.numericalmethod.suanshu.stats.timeseries.univariate
- the TimeSeries.Entry for a univariate time series
- TimeSeries.Entry(T, double) -
Constructor for class com.numericalmethod.suanshu.stats.timeseries.univariate.TimeSeries.Entry
-
- TimeSeries.Iterator<E extends TimeSeries.Entry<?,?>> - Class in com.numericalmethod.suanshu.stats.timeseries
- the Iterator to read a time series
This class provides a default implementation of an Iterator for subclasses to override.
- TimeSeries.Iterator(TimeSeries<?, ?>) -
Constructor for class com.numericalmethod.suanshu.stats.timeseries.TimeSeries.Iterator
- Construct an iterator to read a time series.
- TimeSeries.Iterator - Class in com.numericalmethod.suanshu.stats.timeseries.univariate.realtime
- the Iterator to read an integer-indexed univariate time series
- TimeSeries.Iterator(TimeSeries) -
Constructor for class com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.TimeSeries.Iterator
-
- TimeSeries.Iterator<E extends TimeSeries.Entry<?>> - Class in com.numericalmethod.suanshu.stats.timeseries.univariate
- the Iterator to read a univariate time series
- TimeSeries.Iterator(TimeSeries<?>) -
Constructor for class com.numericalmethod.suanshu.stats.timeseries.univariate.TimeSeries.Iterator
-
- timestamps() -
Method in class com.numericalmethod.suanshu.stats.timeseries.multivariate.GenericTimeTimeSeries
- Get all the timestamps.
- timestamps() -
Method in class com.numericalmethod.suanshu.stats.timeseries.univariate.GenericTimeTimeSeries
- Get all the timestamps.
- to1DArray(DenseMatrix) -
Static method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrixUtils
- Get all matrix entries in the form of a 1D double[] array.
- to1DArray(Matrix) -
Static method in class com.numericalmethod.suanshu.matrix.doubles.operation.MatrixUtils
- Get all matrix entries in the form of a 1D double[] array.
- to2DArray(DenseMatrix) -
Static method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrixUtils
- Get all matrix entries in the form of a 2D double[][] array.
- to2DArray(Matrix) -
Static method in class com.numericalmethod.suanshu.matrix.doubles.operation.MatrixUtils
- Get all matrix entries in the form of a 2D double[][] array.
- toArray() -
Method in class com.numericalmethod.suanshu.datastructure.list.VectorList
- Get an array of all the elements in this list.
- toArray() -
Method in class com.numericalmethod.suanshu.datastructure.MathTable.Row
- Convert the row to a double array, double[], excluding the index.
- toArray() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.SparseVector
-
- toArray(int) -
Method in class com.numericalmethod.suanshu.signalprocessing.Innovations
- Get a copy of the (truncated) innovations.
- toArray() -
Method in class com.numericalmethod.suanshu.signalprocessing.Innovations
- Get a copy of the innovations.
- toArray() -
Method in class com.numericalmethod.suanshu.stats.stochasticprocess.univariate.integration.sde.RandomWalk.Realization
-
- toArray() -
Method in class com.numericalmethod.suanshu.stats.timeseries.multivariate.GenericTimeTimeSeries
-
- toArray() -
Method in class com.numericalmethod.suanshu.stats.timeseries.univariate.GenericTimeTimeSeries
-
- toArray() -
Method in class com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.OneDimensionTimeSeries
-
- toArray() -
Method in class com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.SimpleTimeSeries
-
- toArray() -
Method in interface com.numericalmethod.suanshu.stats.timeseries.univariate.TimeSeries
- Convert this time series into an array.
- toArray() -
Method in class com.numericalmethod.suanshu.vector.doubles.dense.DenseVector
-
- toArray() -
Method in class com.numericalmethod.suanshu.vector.doubles.ImmutableVector
-
- toArray() -
Method in interface com.numericalmethod.suanshu.vector.doubles.Vector
- Get a copy of all vector entries in the form of a 1D
double[] array.
- toDense() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix
-
- toDense() -
Method in interface com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.Densifiable
- Densify a matrix, i.e., convert a matrix implementation to a standard
dense matrix,
DenseMatrix.
- toDense() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.LowerTriangularMatrix
-
- toDense() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix
-
- toDense() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.UpperTriangularMatrix
-
- toDense() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.CsrSparseMatrix
-
- toDense() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.DokSparseMatrix
-
- toDense() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.LilSparseMatrix
-
- toDouble() -
Method in class com.numericalmethod.suanshu.number.complex.Complex
- Cast the complex number to a
Double if it is a real number.
- toElementList() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.CsrSparseMatrix
-
- toElementList() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.DokSparseMatrix
-
- toElementList() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.LilSparseMatrix
-
- toElementList() -
Method in interface com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.SparseMatrix
- Export the non-zero values in the matrix as a list of
SparseElements.
- TOKYO -
Static variable in class com.numericalmethod.suanshu.time.JodaTimeUtils
- Tokyo
- tol -
Variable in class com.numericalmethod.suanshu.analysis.uniroot.Uniroot
- the convergence criterion such that the search succeeds when
|f(x)| < tol
- tol -
Variable in class com.numericalmethod.suanshu.optimization.unconstrained.linesearch.Fletcher
- the convergence tolerance
- tol -
Variable in class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent
- the convergence tolerance
- tol -
Variable in class com.numericalmethod.suanshu.optimization.univariate.BracketSearch
- the convergence tolerance
It should be no less than the square root of the machine precision.
- tolerance(Tolerance) -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.IterativeSolver.Problem
- Override the tolerance instance.
- tolerance() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.IterativeSolver.Problem
- Get the specified
Tolerance instance.
- Tolerance - Interface in com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative
- The tolerance criteria for the iterative algorithm to stop.
- toMatrix() -
Method in class com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.integration.sde.RandomWalk.MultiVariateRealization
-
- toMatrix() -
Method in class com.numericalmethod.suanshu.stats.timeseries.multivariate.GenericTimeTimeSeries
-
- toMatrix() -
Method in interface com.numericalmethod.suanshu.stats.timeseries.multivariate.MultiVariateTimeSeries
- Convert this multivariate time series into an m x n matrix, where
m is the dimension, and n the length.
- toMatrix() -
Method in class com.numericalmethod.suanshu.stats.timeseries.multivariate.realtime.SimpleMultiVariateTimeSeries
-
- toMatrix(TimeSeries<?>) -
Static method in class com.numericalmethod.suanshu.stats.timeseries.univariate.Util
- Cast a time series into a column matrix, discarding the timestamps.
- toString() -
Method in class com.numericalmethod.suanshu.analysis.function.polynomial.Polynomial
-
- toString() -
Method in class com.numericalmethod.suanshu.analysis.function.rn2r1.RealScalarFunctionFixedVariables.Value
-
- toString() -
Method in class com.numericalmethod.suanshu.interval.Interval
-
- toString() -
Method in class com.numericalmethod.suanshu.interval.Intervals
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.CharacteristicPolynomial
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.ImmutableMatrix
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.GivensMatrix
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.SparseVector.Entry
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.SparseVector
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.operation.ElementaryOperation
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.operation.Householder.Context
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.doubles.operation.SubMatrixRef
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.generic.matrixtype.ComplexMatrix
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.generic.matrixtype.GenericMatrix
-
- toString() -
Method in class com.numericalmethod.suanshu.matrix.generic.matrixtype.RealMatrix
-
- toString() -
Method in class com.numericalmethod.suanshu.number.complex.Complex
-
- toString(double[][]) -
Static method in class com.numericalmethod.suanshu.number.DoubleUtils
- Convert a double[][] array to the format that we can copy and paste to re-create the array in Java code.
- toString() -
Method in class com.numericalmethod.suanshu.number.Real
-
- toString() -
Method in class com.numericalmethod.suanshu.optimization.constrained.linearprogramming.simplex.Tableau.Label
-
- toString() -
Method in class com.numericalmethod.suanshu.optimization.constrained.linearprogramming.simplex.Tableau
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.descriptive.Covariance
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.descriptive.moment.Kurtosis
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.descriptive.moment.Mean
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.descriptive.moment.Moments
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.descriptive.moment.Skewness
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.descriptive.moment.Variance
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.descriptive.rank.Max
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.descriptive.rank.Min
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.timeseries.multivariate.GenericTimeTimeSeries
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.timeseries.multivariate.realtime.SimpleMultiVariateTimeSeries
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.timeseries.univariate.GenericTimeTimeSeries
-
- toString() -
Method in class com.numericalmethod.suanshu.stats.timeseries.univariate.realtime.SimpleTimeSeries
-
- toString() -
Method in class com.numericalmethod.suanshu.time.ComparableDateTime
-
- toString() -
Method in class com.numericalmethod.suanshu.vector.doubles.dense.DenseVector
-
- toString() -
Method in class com.numericalmethod.suanshu.vector.doubles.ImmutableVector
-
- toVector(TimeSeries<?>) -
Static method in class com.numericalmethod.suanshu.stats.timeseries.univariate.Util
- Cast a time series into a vector, discarding the timestamps.
- tr(Matrix) -
Static method in class com.numericalmethod.suanshu.matrix.doubles.operation.Measure
- Compute the sum of the diagonal elements, i.e., the trace of a matrix.
- train(HiddenMarkovModel, int[]) -
Method in class com.numericalmethod.suanshu.stats.hmm.HmmTrainByEM
- Construct a trained (discrete) hidden Markov model using the train algorithm.
- transpose(Matrix) -
Method in interface com.numericalmethod.suanshu.matrix.doubles.matrixtype.mathoperation.MatrixMathOperation
t(A)
- transpose(Matrix) -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.mathoperation.SimpleMatrixMathOperation
-
- transposeSolve(Vector) -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.preconditioner.IdentityPreconditioner
- Returns the input
Vector x.
- transposeSolve(Vector) -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.preconditioner.JacobiPreconditioner
- P-t = P-1 for this preconditioner.
- transposeSolve(Vector) -
Method in interface com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.preconditioner.Preconditioner
- Solve Mtv = x, where M is the preconditioner matrix.
- transposeSolve(Vector) -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.sparse.solver.iterative.preconditioner.SsorPreconditioner
- M-tx = M-1x because M is symmetric.
- Trapezoidal - Class in com.numericalmethod.suanshu.analysis.integration.univariate.riemann
- The Trapezoidal rule is a closed type Newton–Cotes formula,
where the integral interval is evenly divided into
N sub-intervals. - Trapezoidal(double, int) -
Constructor for class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.Trapezoidal
- Construct an integrator that uses the Trapezoidal rule.
- trend -
Variable in class com.numericalmethod.suanshu.stats.test.timeseries.adf.AdfAsymptoticDistribution
- the type of augmented Dickey-Fuller (ADF) test
- trend -
Variable in class com.numericalmethod.suanshu.stats.test.timeseries.adf.AdfFiniteSampleDistribution
- the type of augmented Dickey-Fuller (ADF) test
- trend -
Variable in class com.numericalmethod.suanshu.stats.timeseries.linear.univariate.stationaryprocess.MADecomposition
- the estimated trend of the time series
- TriangularMatrix<T extends TriangularMatrix> - Class in com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle
- A triangular matrix is a square matrix
where all entries below (or above) the main diagonal are zero.
- tridiagonal(Matrix, double) -
Static method in class com.numericalmethod.suanshu.matrix.doubles.IsMatrix
- Check if a matrix is tridiagonal.
- Tridiagonalization - Class in com.numericalmethod.suanshu.matrix.doubles.factorization.diagonalization
- A tridiagonal matrix A is a matrix such that
it has non-zero elements only in the main diagonal, the first diagonal below this,
and the first diagonal above the main diagonal.
- Tridiagonalization(Matrix) -
Constructor for class com.numericalmethod.suanshu.matrix.doubles.factorization.diagonalization.Tridiagonalization
- Construct an instance of the Tridiagonalization process.
- TridiagonalMatrix - Class in com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal
- This class represents a matrix with non-zero entries only on the super, main and sub diagonals.
- TridiagonalMatrix(int) -
Constructor for class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.TridiagonalMatrix
- Construct a tridiagonal matrix of dimension
dim * dim.
- TridiagonalMatrix(double[][]) -
Constructor for class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.TridiagonalMatrix
- Construct a tridiagonal matrix from a 2D double[][] array.
- TridiagonalMatrix(TridiagonalMatrix) -
Constructor for class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.TridiagonalMatrix
- Copy constructor performing a deep copy.
- truncation -
Variable in class com.numericalmethod.suanshu.stats.test.timeseries.adf.AdfFiniteSampleDistribution
- the number of truncated values
- ts -
Variable in class com.numericalmethod.suanshu.stats.timeseries.TimeSeries.Iterator
- the time series to be iterated
- TSS -
Variable in class com.numericalmethod.suanshu.stats.regression.linear.ols.Residuals
- diagnostic measure: the total sum of squares, Σ((y-y_mean)^2)
- type -
Variable in class com.numericalmethod.suanshu.analysis.differentiation.univariate.FiniteDifference
- the type of finite difference chosen
- type() -
Method in class com.numericalmethod.suanshu.analysis.function.polynomial.root.Cubic
-
- type() -
Method in class com.numericalmethod.suanshu.analysis.function.polynomial.root.jenkinstraub.JenkinsTraubReal
-
- type() -
Method in class com.numericalmethod.suanshu.analysis.function.polynomial.root.Linear
-
- type() -
Method in class com.numericalmethod.suanshu.analysis.function.polynomial.root.Polyroot
-
- type() -
Method in class com.numericalmethod.suanshu.analysis.function.polynomial.root.Quadratic
-
- type() -
Method in class com.numericalmethod.suanshu.analysis.function.polynomial.root.Quartic
-
- type() -
Method in interface com.numericalmethod.suanshu.analysis.function.polynomial.root.Solver
- Get the type of the solver.
- type -
Variable in class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.EulerMaclaurin
- indicate whether the two end points are included for computation
- type -
Variable in class com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.PowerLawSingularity
-
- type() -
Method in class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.diagonal.BidiagonalMatrix
- Get the type of the bidiagonal matrix.
- type -
Variable in class com.numericalmethod.suanshu.optimization.constrained.linearprogramming.simplex.Tableau.Label
-
- type -
Variable in class com.numericalmethod.suanshu.stats.descriptive.rank.Quantile
- the quantile definition
- type -
Variable in class com.numericalmethod.suanshu.stats.test.distribution.kolmogorov.KolmogorovSmirnov
- the type of Kolmogorov-Smirnov test to be performed
- type -
Variable in class com.numericalmethod.suanshu.stats.test.timeseries.adf.AugmentedDickeyFuller
- the trend type
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SuanShu, a Java numerical and statistical library | |||||||
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