Altaxo.Calc.LinearAlgebra Namespace

Contains matrix and vector types, linear algebra algorithms, and related utilities.

Classes

	Class	Description
	BandDoubleMatrix	Represents a band matrix configuration for storing and manipulating a 2D array of double-precision floating-point numbers.
	CreateMatrix	Provides convenience factory methods for creating matrices.
	CreateVector	Provides convenience factory methods for creating vectors.
	DataColumnWrapper	Provides wrappers that expose data columns as vectors and matrices.
	DataTableWrapper	Wraps DataColumnCollections to matrices.
	DoubleBandMatrix	Represents a band matrix in compact storage format (stored as a linear array).
	DoubleMatrixInArray1DColumnMajorRepresentation	Wraps a linear array to a read-write matrix. The linear array is in column-major order, i.e. the first elements of the linear array belong to the first column of the matrix (i.e. the row values change more quickly). The index of the linear array is calculated as index = row + column*NumberOfRows. This representation is used for instance by LAPACK, Fortran, Julia, MATLAB, Octave, Scilab, GLSL and HLSL.
	DoubleMatrixInArray1DRowMajorRepresentation	Wraps a linear array to a read-write matrix. The array is in row-major order, i.e. the first elements of the linear array belong to the first row of the matrix (the column values change more quickly). The index of the linear array is calculated as index = column + row * NumberOfColumns. This representation is used for instance by C, C++, Mathematica, Pascal and Python.
	FastNonnegativeLeastSquares	Implementation of an algorithm that finds a vector x with all elements xi>=0 which minimizes \|X*x-y\|.
	GaussianEliminationSolver	Provides implementation of Gaussian elimination with partial pivoting
	GenericVectorT	Base class of the vector classes. Implements non-arithmetic stuff common to all vectors.
	IntegerVector	Vector of integer elements.
	InvalidContentMatrixException	The exception is thrown when a singular matrix is passed a method not expecting one.
	InvalidDimensionMatrixException	The exception is thrown when a singular matrix is passed a method not expecting one.
	JaggedArrayMath	This provides array math for a special case of matrices, so called jagged arrays.
	JaggedArrayMatrix	JaggedArrayMatrix is a matrix implementation that is relatively easy to extend to the bottom, i.e. to append rows. It is horizontal oriented, i.e. the storage is as a number of horizontal vectors. Furthermore, as a compromise, it provides fully access to its underlying jagged array.
	LinearAlgebraException	Represents errors that occur when using the dnA library.
	LinearAlgebraProviderSettings	Provides access to linear algebra provider settings.
	LinearlySpacedIntervalByEndCountStep	Defines a linearly spaced closed interval defined by end, number of elements, and step size.
	LinearlySpacedIntervalByEndCountStepSerializationSurrogate0	XML serialization surrogate for LinearlySpacedIntervalByEndCountStep.
	LinearlySpacedIntervalByStartCountStep	Defines a linearly spaced closed interval defined by start, number of elements, and step size.
	LinearlySpacedIntervalByStartCountStepSerializationSurrogate0	Serialization surrogate for LinearlySpacedIntervalByStartCountStep.
	LinearlySpacedIntervalByStartEndCount	Defines a linearly spaced closed interval defined by start, end, and number of elements.
	LinearlySpacedIntervalByStartEndCountSerializationSurrogate0	Serialization surrogate for LinearlySpacedIntervalByStartEndCount.
	LinearlySpacedIntervalByStartEndStep	Defines a linearly spaced closed interval defined by start, end and step size.
	LinearlySpacedIntervalByStartEndStepSerializationSurrogate0	Surrogate class for XML serialization of LinearlySpacedIntervalByStartEndStep.
	MapackMatrix	Matrix provides the fundamental operations of numerical linear algebra.
	MatrixT	Defines the base class for Matrix classes.
	MatrixBuilderT	Generic linear algebra type builder, for situations where a matrix or vector must be created in a generic way. Usage of generic builders should not be required in normal user code.
	MatrixException	Represents errors that occur when using the matrix classes.
	MatrixExtensions	Provides extension methods for converting matrices between numeric types.
	MatrixMath	Class MatrixMath provides common static methods for matrix manipulation and arithmetic in tow dimensions.
	MatrixMathLeftSpineJaggedArrayMatrixT	BEMatrix is a matrix implementation that is relatively easy to extend to the botton, i.e. to append rows. It is horizontal oriented, i.e. the storage is as a number of horizontal vectors.
	MatrixMathMatrixColumnROVectorT	Wrapper for a matrix column to a read-only vector.
	MatrixMathMatrixColumnVectorT	Wrapper for a matrix row to a vector.
	MatrixMathMatrixFromColumnMajorLinearArrayT	Wraps a linear array to a read-write matrix. The array is column oriented, i.e. consecutive elements belong mostly to one column. This is the convention used for LAPACK routines.
	MatrixMathMatrixFromRowMajorLinearArrayT	Wraps a linear array to a read-write matrix. The array is row oriented, i.e. consecutive elements belong mostly to one row.
	MatrixMathMatrixRowROVectorT	Wrapper for a row of an existing matrix to a read-only vector.
	MatrixMathMatrixRowVectorT	Wrapper for a matrix row to a vector.
	MatrixMathMatrixWithOneColumnT	Implements a vertical vector, i.e. a matrix which has only one column, but many rows.
	MatrixMathMatrixWithOneRowT	Implements a horizontal vector, i.e. a matrix which has only one row, but many columns.
	MatrixMathROMatrixFrom2DArrayT	Wraps a 2d array to a read-only matrix.
	MatrixMathROMatrixFromColumnMajorLinearArrayT	Wraps a linear array to a read-only matrix. The array is column oriented, i.e. consecutive elements belong mostly to one column. This is the convention used for LAPACK routines.
	MatrixMathROMatrixFromRowMajorLinearArrayT	Wraps a linear array to a read-only matrix. The array is column oriented, i.e. consecutive elements belong mostly to one column. This is the convention used for LAPACK routines.
	MatrixMathRWMatrixFrom2DArrayT	Wraps a 2D array to a read-only matrix.
	MatrixMathScalarAsMatrixT	Implements a scalar as a special case of the matrix which has the dimensions (1,1).
	MatrixMathSingularValueDecomposition	Class to calculate the singular value decomposition.
	MatrixMathTopSpineJaggedArrayMatrixT	REMatrix is a matrix implementation that is relatively easy to extend to the right, i.e. to append columns. It is vertical oriented, i.e. the storage is as a number of vertical vectors.
	NotPositiveDefiniteException	The exception is thrown when a none positive definite matrix is passed a method not expecting one.
	NotSquareMatrixException	The exception is thrown when a none square matrix is passed a method not expecting one.
	Regularization	Helper class to add regularization terms to linear algebra problems. Regularization is used to stabilize the solution of ill-posed problems by adding additional constraints that enforce smoothness or other desired properties on the solution. For this, the parameters of the linear equation system must have the same meaning and order of magnitude. Regularization is typically applied in least squares problems to prevent overfitting and improve the generalization of the solution. Examples are Inverse Laplace transformations, deconvolution problems.
	RODoubleMatrixInArray1DColumnMajorRepresentation	Wraps a linear array to a read-only matrix. The linear array is in column-major order, i.e. the first elements of the linear array belong to the first column of the matrix (i.e. the row values change more quickly). The index of the linear array is calculated as index = row + column*NumberOfRows. This representation is used for instance by LAPACK, Fortran, Julia, MATLAB, Octave, Scilab, GLSL and HLSL.
	RODoubleMatrixInArray1DRowMajorRepresentation	Wraps a linear array to a read-only matrix. The array is in row-major order, i.e. the first elements of the linear array belong to the first row of the matrix (the column values change more quickly). The index of the linear array is calculated as index = column + row*NumberOfColumns. This representation is used for instance by C, C++, Mathematica, Pascal and Python.
	ROVectorBaseT	Base class for read-only vector implementations.
	SingularMatrixException	The exception is thrown when a singular matrix is passed a method not expecting one.
	SparseDoubleVector	Represents a sparse vector of double-precision values.
	TikhonovRegularizedNonnegativeMatrixFactorization	Provides routines for nonnegative matrix factorization with Tikhonov regularization.
	VectorT	Defines the generic class for Vector classes.
	VectorBuilderT	Generic linear algebra type builder, for situations where a matrix or vector must be created in a generic way. Usage of generic builders should not be required in normal user code.
	VectorExtensions	Provides conversion helpers for vectors with common numeric element types.
	VectorMath	VectorMath provides common static functions concerning vectors.
	VectorMathROVectorWrapperOfIROVectorT	Provides a read-only wrapper around an IReadOnlyListT to represent a subvector.
	VectorMathVectorWrapperOfIVectorT	Provides a read-write wrapper around an IVectorT to represent a subvector.
	VectorSpacingEvaluator	Statistics of the spacing between adjacent vector elements. The spaces are defined in the forward direction, i.e. as vec[i+1]-vec[i].

Structures

	Structure	Description
	MatrixWrapperStructForColumnMajorOrderLinearArrayT	Very thin wrapper structure that wraps a column major order linear array, i.e. consecutive elements of the linear array belong most probably to the same column, to provide information on number of rows and columns. Attention: this is not LAPACK convention (!)).
	MatrixWrapperStructForLeftSpineJaggedArrayT	Very thin wrapper structure around a jagged array just to provided number of rows and columns along with the array itself. The spine array is oriented vertically, thus access to the array is down by array[row][column].
	MatrixWrapperStructForRowMajorOrderLinearArrayT	Thin wrapper structure that wraps a row major order linear array, i.e. consecutive elements of the linear array belong most probably to the same row, to provide information on number of rows and columns. Attention: this is not LAPACK convention (!)). If using LAPACK, you need column major order (MatrixWrapperStructForColumnMajorOrderLinearArrayT).
	MatrixWrapperStructForTopSpineJaggedArrayT	Very thin wrapper structure around a jagged array just to provided number of rows and columns along with the array itself. The spine array is oriented vertically, i.e. the rows protruding to the right from the spine array. Access to the underlying array is done by array[row][column].
	VectorMathRODoubleArrayWrapperStructAmendedUnshifted	Serves as thin wrapper struct for an array when additional data at the start and the end of the array are neccessary.
	VectorMathROFloatArrayWrapperStructAmendedUnshifted	Serves as thin wrapper struct for an array when additional data at the start and the end of the array are neccessary.
	VectorMathROIntArrayWrapperStructAmendedUnshifted	Serves as thin wrapper struct for an array when additional data at the start and the end of the array are neccessary.
	VectorMathROSByteArrayWrapperStructAmendedUnshifted	Serves as thin wrapper struct for an array when additional data at the start and the end of the array are neccessary.
	VectorMathROShortArrayWrapperStructAmendedUnshifted	Serves as thin wrapper struct for an array when additional data at the start and the end of the array are neccessary.

Interfaces

	Interface	Description
	IBottomExtensibleComplexDoubleMatrix	Extends IComplexDoubleMatrix in a way that another matrix of appropriate dimensions can be appended to the bottom of the matrix.
	IBottomExtensibleComplexFloatMatrix	Extends IComplexFloatMatrix in a way that another matrix of appropriate dimensions can be appended to the bottom of the matrix.
	IBottomExtensibleMatrixT	IBottomExtensibleMatrix extends IMatrix in a way that another matrix of appropriate dimensions can be appended to the bottom of the matrix.
	ICholeskyDecomposition	Cholesky Decomposition of a symmetric, positive definite matrix.
	IComplexDoubleMatrix	Represents the simplest form of a 2D matrix of Altaxo.Calc.LinearAlgebra.Complex values, which is readable and writeable.
	IComplexDoubleSequence	Represents a read-only indexed sequence of complex double-precision values.
	IComplexDoubleVector	Interface for a readable and writeable vector of Complex values.
	IComplexFloatMatrix	Represents the simplest form of a 2D matrix of Complex32 values, which is readable and writeable.
	IComplexFloatSequence	Interface for a sequence of Complex values.
	IComplexFloatVector	Interface for a readable and writeable vector of Complex values.
	IEigenvalueDecomposition	Determines the eigenvalues and eigenvectors of a real square matrix.
	IExtensibleComplexDoubleMatrix	Extends IComplexDoubleMatrix in a way that another matrix of appropriate dimensions can be appended either to the right or to the bottom of the matrix.
	IExtensibleComplexDoubleVector	Special vector to which another vector can be appended to.
	IExtensibleComplexFloatMatrix	Extends IComplexFloatMatrix in a way that another matrix of appropriate dimensions can be appended either to the right or to the bottom of the matrix.
	IExtensibleComplexFloatVector	Special vector to which another vector can be appended to.
	IExtensibleMatrixT	IExtensibleMatrix extends IMatrix in a way that another matrix of appropriate dimensions can be appended either to the right or to the bottom of the matrix.
	IExtensibleVectorT	Extends IVectorT in a way that another vector can be appended at the end of this vector.
	ILinearEquationSolverT	Interface to a solver for linear equations. The procedure can either be non-destructive (keeping the matrix and the vector b), or destructive (not keeping matrix m and vector b). The destructive solving process may be faster, since saving of the matrix and the vector is not required.
	ILuDecomposition	LU decomposition of a rectangular matrix.
	IMapackMatrix	Matrix provides the fundamental operations of numerical linear algebra.
	IMatrixT	IMatrix represents the simplest form of a 2D matrix, which is readable and writeable.
	IMatrixInArray1DColumnMajorRepresentationTElement	Designates that the matrix is represented as a linear array of TElement values. The linear array is in column-major order, i.e. the first elements of the linear array belong to the first column of the matrix (i.e. the row values change more quickly). The index of the linear array is calculated as index = row + column*NumberOfRows. This representation is used for instance by Fortran, Julia, MATLAB, Octave, Scilab, GLSL and HLSL.
	IMatrixInArray1DRowMajorRepresentationTElement	Designates that the matrix is represented as a linear array of TElement values. The array is in row-major order, i.e. the first elements of the linear array belong to the first row of the matrix (the column values change more quickly). The index of the linear array is calculated as index = column + row*NumberOfColumns. This representation is used for instance by C, C++, Mathematica, Pascal and Python.
	IMatrixLevel1T	IMatrixLevel1 represents the simplest form of a 2D matrix, which is readable and writeable, and provides level-1 matrix operations.
	INumericSequenceT	Interface to a sequence of elements with unknown length.
	IQrDecomposition	QR decomposition for a rectangular matrix.
	IRightExtensibleComplexDoubleMatrix	Extends IComplexDoubleMatrix in a way that another matrix of appropriate dimensions can be appended to the right of the matrix.
	IRightExtensibleComplexFloatMatrix	Extends IComplexFloatMatrix in a way that another matrix of appropriate dimensions can be appended to the right of the matrix.
	IRightExtensibleMatrixT	IRightExtensibleMatrix extends IMatrix in a way that another matrix of appropriate dimensions can be appended to the right of the matrix.
	IROBandMatrixT	IROBandMatrix represents a read-only band matrix of values.
	IROComplexDoubleMatrix	IROMatrix represents a read-only matrix of Altaxo.Calc.LinearAlgebra.Complex values.
	IROComplexDoubleVector	Interface for a read-only vector of Complex values.
	IROComplexFloatMatrix	IROMatrix represents a read-only matrix of Complex32 values.
	IROComplexFloatVector	Interface for a read-only vector of Complex values.
	IROMatrixT	IROMatrix represents a read-only matrix of values.
	IROMatrixLevel1T	Operations on matrices which do not change the matrix instance.
	IROSparseMatrixT	IROSparseMatrix represents a read-only sparse matrix of values.
	ISingularValueDecomposition	Singular Value Decomposition for a rectangular matrix.
	ISpacedInterval	Represents an immutable interval with evenly spaced values.
	IVectorT	Interface for a a readable and writeable vector vector of values.

Enumerations

	Enumeration	Description
	ExistingData	Specifies assumptions about data already present in a target storage area.
	LinearAlgebraProvider	Identifies the linear algebra provider to use.
	Symmetricity	Specifies whether a matrix is known to be symmetric or Hermitian.
	Zeros	Specifies how zero values should be treated during linear algebra operations.