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Imsl.Math Namespace
Imsl.Math namespace contains a wide range of mathematical classes, beginning with basic data types such as complex numbers and matrices and progressing to advanced numerical analysis.
Classes
  ClassDescription
Public classAllConstraintsNotSatisfiedException
All constraints are not satisfied.
Public classBadInitialGuessException
Penalty function point infeasible for original problem. Try new initial guess.
Public classBessel
Collection of Bessel functions.
Public classBoundaryInconsistentException
The boundary conditions are inconsistent.
Public classBoundedLeastSquares
Solves a nonlinear least-squares problem subject to bounds on the variables using a modified Levenberg-Marquardt algorithm.
Public classBoundedVariableLeastSquares
Solve a linear least-squares problem with bounds on the variables.
Public classBoundsInconsistentException
The bounds given are inconsistent.
Public classBsInterpolate
Extension of the BSpline class to interpolate data points.
Public classBsLeastSquares
Extension of the BSpline class to compute a least squares spline approximation to data points.
Public classBSpline
Spline represents and evaluates univariate B-splines.
Public classCholesky
Cholesky factorization of a matrix of type double.
Public classComplexFFT
Complex FFT.
Public classComplexLU
LU factorization of a matrix of type Complex.
Public classComplexMatrix
Complex matrix manipulation functions.
Public classComplexSparseCholesky
Sparse Cholesky factorization of a matrix of type ComplexSparseMatrix.
Public classComplexSparseCholeskyNumericFactor
Data structures and functions for the numeric Cholesky factor.
Public classComplexSparseCholeskySymbolicFactor
Data structures and functions for the symbolic Cholesky factor.
Public classComplexSparseMatrix
A general complex sparse matrix which is intended to be efficiently and easily updated.
Public classComplexSparseMatrixSparseArray
The SparseArray class uses public fields to hold the data for a sparse matrix in the Sparse Array format.
Public classComplexSuperLU
Computes the LU factorization of a general sparse matrix of type ComplexSparseMatrix by a column method and solves a sparse linear system of equations Ax=b.
Public classConjugateGradient
Solves a real symmetric definite linear system using the conjugate gradient method with optional preconditioning.
Public classConstraintEvaluationException
Constraint evaluation returns an error with current point.
Public classConstraintsInconsistentException
The equality constraints are inconsistent.
Public classConstraintsNotSatisfiedException
No vector x satisfies all of the constraints.
Public classCorrectorConvergenceException
Corrector failed to converge.
Public classCsAkima
Extension of the Spline class to handle the Akima cubic spline.
Public classCsInterpolate
Extension of the Spline class to interpolate data points.
Public classCsPeriodic
Extension of the Spline class to interpolate data points with periodic boundary conditions.
Public classCsShape
Extension of the Spline class to interpolate data points consistent with the concavity of the data.
Public classCsSmooth
Extension of the Spline class to construct a smooth cubic spline from noisy data points.
Public classCsSmoothC2
Extension of the Spline class used to construct a spline for noisy data points using an alternate method.
Public classCsTCB
Extension of the Spline class to handle a tension-continuity-bias (TCB) cubic spline, also known as a Kochanek-Bartels spline and is a generalization of the Catmull-Rom spline.
Public classCyclingOccurringException
The algorithm appears to be cycling. Using refinement may help.
Public classDenseLP
Solves a linear programming problem using an active set strategy.
Public classDidNotConvergeException
Maximum number of iterations exceeded.
Public classEigen
Collection of Eigen System functions.
Public classEpsilonAlgorithm
The class is used to determine the limit of a sequence of approximations, by means of the Epsilon algorithm of P. Wynn.
Public classEqualityConstraintsException
The variables are determined by the equality constraints.
Public classErrorTestException
Error test failure detected.
Public classFalseConvergenceException
False convergence, the iterates appear to be converging to a noncritical point.
Public classFeynmanKac
Solves the generalized Feynman-Kac PDE.
Public classFFT
FFT functions.
Public classGenMinRes
Linear system solver using the restarted Generalized Minimum Residual (GMRES) method.
Public classHyperRectangleQuadrature
HyperRectangleQuadrature integrates a function over a hypercube.
Public classIllConditionedException
Problem is singular or ill-conditioned.
Public classInconsistentSystemException
Inconsistent system.
Public classInitialConstraintsException
The constraints at the initial point are inconsistent.
Public classInvalidMPSFileException
Invalid MPS file.
Public classIterationMatrixSingularException
Iteration matrix is singular.
Public classLimitingAccuracyException
Limiting accuracy reached for a singular problem.
Public classLinearlyDependentGradientsException
Working set gradients are linearly dependent.
Public classLU
LU factorization of a matrix of type double.
Public classMatrix
Matrix manipulation functions.
Public classMaxFcnEvalsExceededException
Maximum function evaluations exceeded.
Public classMaxIterationsException
Maximum number of iterations exceeded.
Public classMaxNumberStepsAllowedException
Maximum number of steps allowed exceeded.
Public classMinConGenLin
Minimizes a general objective function subject to linear equality/inequality constraints.
Public classMinConNLP
General nonlinear programming solver.
Public classMinUncon
Finds the minimum point for a smooth univariate function using function and optionally first derivative evaluations.
Public classMinUnconMultiVar
Minimizes a multivariate function using a quasi-Newton method.
Public classMPSReader
Reads a linear programming problem from an MPS file.
Public classMPSReaderElement
An element in the sparse contraint matrix.
Public classMPSReaderRow
A row either in the constraint matrix or a free row.
Public classMultipleSolutionsException
The problem has multiple solutions producing essentially the same minimum.
Public classNoAcceptablePivotException
An acceptable pivot could not be found.
Public classNoAcceptableStepsizeException
No acceptable stepsize in [SIGMA,SIGLA].
Public classNoConvergenceException
The conjugate gradient method did not converge within the allowed maximum number of iterations.
Public classNoLPSolutionException
No solution for the LP problem with h = 0 was found by DenseLP.
Public classNonlinLeastSquares
Solves a nonlinear least squares problem using a modified Levenberg-Marquardt algorithm.
Public classNonNegativeLeastSquares
Solves a linear least squares problem with nonnegativity constraints.
Public classNoProgressException
The algorithm is not making any progress. Try a new initial guess.
Public classNotDefiniteAMatrixException
The input matrix A is indefinite, that is the matrix is not positive or negative definite.
Public classNotDefiniteJacobiPreconditionerException
The Jacobi preconditioner is not strictly positive or negative definite.
Public classNotDefinitePreconditionMatrixException
The Precondition matrix is indefinite.
Public classNotSPDException
The matrix is not symmetric, positive definite.
Public classNumericalDerivatives
Compute the Jacobian matrix for a function f(y) with m components in n independent variables.
Public classNumericDifficultyException
Numerical difficulty occurred.
Public classObjectiveEvaluationException
Objective evaluation returns an error with current point.
Public classODE
ODE represents and solves an initial-value problem for ordinary differential equations.
Public classOdeAdamsGear
Extension of the ODE class to solve a stiff initial-value problem for ordinary differential equations using the Adams-Gear methods.
Public classOdeRungeKutta
Solves an initial-value problem for ordinary differential equations using the Runge-Kutta-Verner fifth-order and sixth-order method.
Public classPenaltyFunctionPointInfeasibleException
Penalty function point infeasible.
Public classPrintMatrix
Matrix printing utilities.
Public classPrintMatrixFormat
This class can be used to customize the actions of PrintMatrix.
Public classPrintMatrixFormatParsePosition
Tracks the current position during parsing.
Public classPrintMatrixString
This is an internal class to conveniently use PrintMatrix in logging operations. The requirement is to get the output from PrintMatrix.print() into a String that can be passed to the logging framework. This class uses a StringBuffer object to collect all print() calls made internally in PrintMatrix. Once the call completes, use the method getOutput() to return what would have been printed as a String that includes proper spacing and line breaks. Working this into the PrintMatrix class would have involved extra overhead in all the cases where a string wouldn't be required, so it's best to include this as a separate undocumented class. Public access is required to use from the packages outside of Imsl.Math.
Public classProblemInfeasibleException
The problem is not feasible. The constraints are inconsistent.
Public classProblemUnboundedException
The problem is unbounded.
Public classProblemVacuousException
The problem is vacuous.
Public classQPInfeasibleException
QP problem seemingly infeasible.
Public classQPProblemUnboundedException
The object value for the problem is unbounded.
Public classQR
QR Decomposition of a matrix.
Public classQuadraticProgramming
Solves the convex quadratic programming problem subject to equality or inequality constraints.
Public classQuadrature
Quadrature is a general-purpose integrator that uses a globally adaptive scheme in order to reduce the absolute error.
Public classRadialBasis
RadialBasis computes a least-squares fit to scattered data in {\bf R}^d, where d is the dimension.
Public classRadialBasisGaussian
The Gaussian basis function, e^{-ax^2}.
Public classRadialBasisHardyMultiquadric
The Hardy multiquadric basis function, \sqrt{r^2+\delta^2}.
Public classSfun
Collection of special functions.
Public classSingularException
Problem is singular.
Public classSingularMatrixException
The matrix is singular.
Public classSingularPreconditionMatrixException
The Precondition matrix is singular.
Public classSolutionNotFoundException
A solution was not found. Try using DenseLP.
Public classSomeConstraintsDiscardedException
Some constraints were discarded because they were too linearly dependent on other active constraints.
Public classSparseCholesky
Sparse Cholesky factorization of a matrix of type SparseMatrix.
Public classSparseCholeskyNumericFactor
The numeric Cholesky factorization of a matrix.
Public classSparseCholeskySymbolicFactor
The symbolic Cholesky factorization of a matrix.
Public classSparseMatrix
A general real sparse matrix intended to be efficiently and easily updated.
Public classSparseMatrixSparseArray
The SparseArray class uses public fields to hold the data for a sparse matrix in the Sparse Array format.
Public classSpline
Spline represents and evaluates univariate piecewise polynomial splines.
Public classSpline2D
Represents and evaluates tensor-product splines.
Public classSpline2DInterpolate
Computes a two-dimensional, tensor-product spline interpolant from two-dimensional, tensor-product data.
Public classSpline2DLeastSquares
Computes a two-dimensional, tensor-product spline approximant using least squares.
Public classSuperLU
Computes the LU factorization of a general sparse matrix of type SparseMatrix by a column method and solves the real sparse linear system of equations Ax=b.
Public classSVD
Singular Value Decomposition (SVD) of a rectangular matrix of type double.
Public classSymEigen
Computes the eigenvalues and eigenvectors of a real symmetric matrix.
Public classTcurrentTstopInconsistentException
The end value for the integration in time, tout, is not consistent with the current time value, t.
Public classTEqualsToutException
The current integration point in time and the end point are equal.
Public classTerminationCriteriaNotSatisfiedException
Termination criteria are not satisfied.
Public classTimeIntervalTooSmallException
Distance between starting time point and end point for the integration is too small.
Public classToleranceTooSmallException
Tolerance is too small.
Public classTooManyIterationsException
Maximum number of iterations exceeded.
Public classTooManyStepsException
Too many steps were taken between two consecutive time steps.
Public classTooMuchTimeException
Maximum time allowed for solve is exceeded.
Public classUnboundedBelowException
Five consecutive steps of the maximum allowable stepsize have been taken, either the function is unbounded below, or has a finite asymptote in some directionor the maximum allowable step size is too small.
Public classVarBoundsInconsistentException
The equality constraints and the bounds on the variables are found to be inconsistent.
Public classWorkingSetSingularException
Working set is singular in dual extended QP.
Public classZeroPolynomial
The ZeroPolynomial class computes the zeros of a polynomial with complex coefficients, Aberth's method.
Public classZerosFunction
Finds the real zeros of a real, continuous, univariate function, f(x).
Public classZeroSystem
Solves a system of n nonlinear equations f(x) = 0 using a modified Powell hybrid algorithm.
Structures
  StructureDescription
Public structureComplex
Set of mathematical functions for complex numbers. It provides the basic operations (addition, subtraction, multiplication, division) as well as a set of complex functions.
Public structurePhysical
Return the value of various mathematical and physical constants.
Interfaces
  InterfaceDescription
Public interfaceBoundedLeastSquaresIFunction
Public interface for the user-supplied function to evaluate the function that defines the least-squares problem.
Public interfaceBoundedLeastSquaresIJacobian
Public interface for the user-supplied function to compute the Jacobian.
Public interfaceConjugateGradientIFunction
Public interface for the user supplied function to ConjugateGradient.
Public interfaceConjugateGradientIPreconditioner
Public interface for the user supplied function to ConjugateGradient used for preconditioning.
Public interfaceFeynmanKacIBoundaries
Public interface for user supplied boundary coefficients and terminal condition the PDE must satisfy.
Public interfaceFeynmanKacIForcingTerm
Public interface for non-zero forcing term in the Feynman-Kac equation.
Public interfaceFeynmanKacIInitialData
Public interface for adjustment of initial data or as an opportunity for output during the integration steps.
Public interfaceFeynmanKacIPdeCoefficients
Interface for computation of coefficients of the Feynman-Kac PDE.
Public interfaceGenMinResIFunction
Public interface for the user supplied function to GenMinRes.
Public interfaceGenMinResINorm
Public interface for the user supplied function to the GenMinRes object used for the norm  \Vert X \Vert when the Gram-Schmidt implementation is used.
Public interfaceGenMinResIPreconditioner
Public interface for the user supplied function to GenMinRes used for preconditioning.
Public interfaceGenMinResIVectorProducts
Public interface for the user supplied function to the GenMinRes object used for the inner product when the Gram-Schmidt implementation is used.
Public interfaceHyperRectangleQuadratureIFunction
Interface for the HyperRectangleQuadrature function.
Public interfaceMinConGenLinIFunction
Public interface for the user-supplied function to evaluate the function to be minimized.
Public interfaceMinConGenLinIGradient
Public interface for the user-supplied function to compute the gradient.
Public interfaceMinConNLPIFunction
Public interface for the user supplied function to the MinConNLP object.
Public interfaceMinConNLPIGradient
Public interface for the user supplied function to compute the gradient for MinConNLP object.
Public interfaceMinUnconIDerivative
Interface for the smooth function of a single variable to be minimized and its derivative.
Public interfaceMinUnconIFunction
Interface for the user supplied function for the smooth function of a single variable to be minimized.
Public interfaceMinUnconMultiVarIFunction
Interface for the user supplied multivariate function to be minimized.
Public interfaceMinUnconMultiVarIGradient
Interface for the user supplied multivariate function to be minimized and its gradient.
Public interfaceNonlinLeastSquaresIFunction
Interface for the user supplied nonlinear least-squares function.
Public interfaceNonlinLeastSquaresIJacobian
Interface for the user supplied nonlinear least squares function and its Jacobian.
Public interfaceNumericalDerivativesIFunction
Public interface function.
Public interfaceNumericalDerivativesIJacobian
Public interface for the user-supplied function to compute the Jacobian.
Public interfaceOdeAdamsGearIFunction
Public interface for user supplied function to OdeAdamsGear object.
Public interfaceOdeAdamsGearIJacobian
Public interface for the user supplied function to evaluate the Jacobian matrix.
Public interfaceOdeRungeKuttaIFunction
Public interface for user supplied function to OdeRungeKutta object.
Public interfaceQuadratureIFunction
Interface defining function for the Quadrature class.
Public interfaceRadialBasisIFunction
Public interface for the user supplied function to the RadialBasis object.
Public interfaceZerosFunctionIFunction
Public interface for the user supplied function to ZerosFunction.
Public interfaceZeroSystemIFunction
Public interface for user supplied function to ZeroSystem object.
Public interfaceZeroSystemIJacobian
Public interface for user supplied function to ZeroSystem object.
Enumerations
  EnumerationDescription
Public enumerationComplexSparseCholeskyNumericFactorization
Numeric Factorization methods.
Public enumerationComplexSuperLUColumnOrdering
The column permutation method to be used.
Public enumerationComplexSuperLUPerformanceParameters
Performance tuning parameters which can be adjusted via method SetPerformanceTuningParameters.
Public enumerationComplexSuperLUScaling
Equilibration method before factorization, this setting is returned from GetEquilibrationMethod.
Public enumerationCsInterpolateCondition
Denotes the type of condition at an endpoint.
Public enumerationFeynmanKacPDEStepControlMethod
Indicates which step control method is used in the integration of the Feynman-Kac PDE.
Public enumerationGenMinResImplementationMethod
Implementation methods.
Public enumerationGenMinResResidualMethod
Residual updating methods.
Public enumerationNumericalDerivativesDifferencingMethod
Specifies the differencing method.
Public enumerationODEErrorNormOptions
ErrorNorm options
Public enumerationODEExamineStepOptions
ExamineStep options
Public enumerationOdeAdamsGearIntegrationType
Integration type.
Public enumerationOdeAdamsGearSolveOption
Solve option.
Public enumerationPrintMatrixMatrixType
MatrixType indicates what part of the matrix is to be printed.
Public enumerationPrintMatrixFormatColumnLabelType
Type for column labels.
Public enumerationPrintMatrixFormatFormatType
FormatType specifies the argument to format.
Public enumerationPrintMatrixFormatRowLabelType
Type for row labels.
Public enumerationSparseCholeskyNumericFactorization
Numeric factorization methods.
Public enumerationSuperLUColumnOrdering
The column permutation method to be used.
Public enumerationSuperLUPerformanceParameters
Performance tuning parameters which can be adjusted via method SetPerformanceTuningParameters.
Public enumerationSuperLUScaling
One of several possible equilibration option return values for property EquilibrationMethod.